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IN-PLANE, FLEXURAL, TWISTING AND THICKNESS-SHEAR COEFFICIENTS
FOR STIFFNESS AND DAMPING OF A MONOLAYER FILAMENTARY COMPOSITE
Final Report (Part I )NASA Research Grant NGR-37-003-055
by
C.W. Bert & S. ChangSchool of Aerospace, Mechanical & Nuclear Engineering
The University of OklahomaNorman, Oklahoma 73069
Prepared for
National Aeronautics and Space AdministrationWashington, D.C.
March 1972
1. Report No. 2. Government Accession No.
NASA CR-H2I4I4. Title and Subtitle
IN-PLANE, FLEXURAL, TWISTING AND THIOCOEFFICIENTS FOR STIFFNESS AND DAMPIMONOLAYER FILAMFNTARY COMPOSITE
CNESS -SHEARNG OF A
7. Author(s)
C. W. Bert and S. Chang
9. Performing Organization Name and Address
School of Aerospace, Mechanical, and Nuclear EngineeringThe University of OklahomaNorman, Oklahoma 73069
12. Sponsoring Agency Name and Address
National Aeronautics and Space AdministrationWashington, D. C. 20546
3. Recipient's Catalog No.
5. Report Date
6. Performing Organization Code
8. Performing Organization Report No.
10. Work Unit No.
50! -22-03-0311. Contract or Grant No.
NGR-37-003-05513. Type of Report and Period Covered
Contractor Report14. Sponsoring Agency Code
15. Supplementary Notes
16. Abstract
Results are presented for elastic and damping analyses resulting in determinationsof all of the various stiffnesses and associated loss tangents for the completecharacterization of the elastic and damping behavior of a monofilament composite layer.For the determination of the various stiffnesses, either an elementary mechanics -of -materials formulation or a more rigorous mixed -boundary-value elasticity formulationis used. For determining the loss tangents associated with the various stiffnesses,either the viscoelastic correspondence principle or an energy analysis based on theappropriate elastic stress distribution is used.
The numerical results obtained from this analysis compare favorably with someexisting analytical and experimental results for various practical combinations ofconstituent materials, specifically boron-epoxy, boron-aluminum, and E glass-epoxycomposites. Finally a complete set of property curves for a boron-epoxy monofilamentcomposite for a frequency range of 50 to 2,000 Hz are presented to facilitate elasticand damping analyses of a structure consisting of multiple layers of such a composite.Design data for other composites, namely, boron-aluminum and E glass-epoxy, whichare valid for a similar frequency range, are summarized in tabulated form. Completecomputer program documentation and listing are given to facilitate calculations of monolayerprop" fly ya|i|pc. fnr nrppr rnmpnsitps
1 7. *J<eyTWord^ (Suggested by, Author(s) )Composite materialsVibration dampingStiffnessVibrationMicromprhanirs
18. Distribution Statement
Unclassified - Unlimited
19. Security dassif . (of this report) 20. Security Classif. (of this page)
Unclassified Unclassified21. No. of Pages 22. Price*
338
For sale by the National Technical I nformation Service, Springfield, Virginia 22151
IN-PLANE, FLEXURAL, TWISTING AND THICKNESS-SHEAR COEFFICIENTS FOR
STIFFNESS AND DAMPING OF A MONOLAYER FILAMENTARY COMPOSITE
CONTENTS
Page
ABSTRACT tii
SYMBOLS v
I. INTRODUCTION 1
1.1 Introductory Remarks 1
1.2 A Brief Survey of Micromechanics Analysis ofFilamentary Composite Materials . 5
II. ELASTIC ANALYSIS 11
2.1 Introduction and Hypotheses 11
2.2 Longitudinal In-plane Stiffnesses 16
2.3 Transverse In-plane Stiffnesses 20
2.4 Longitudinal Flexural Stiffnesses 26
2.5 Transverse Flexural Stiffnesses 30
2.6 Twisting Stiffness 33
2.7 Longitudinal Thickness-Shear Stiffness . . . . . . 39
2.8 Transverse Thickness-Shear Stiffness 50
III. DAMPING ANALYSES : 55
3.1 Introduction . 56
3.2 Longitudinal In-plane Loss Tangents . . . . . . . . 59
3.3 Transverse In-plane Loss Tangents 63
3.4 Longitudinal Flexural Loss Tangents 64
3.5 Transverse Flexural Loss Tangents . 67
3.6 Twisting Loss Tangent 67
3.7 Longitudinal Thickness-shear Loss Tangent .... 68
3.8 Transverse Thickness-shear Loss Tangent .69
IV. NUMERICAL RESULTS AND COMPARISON WITH EXPERIMENTALRESULTS 71
4.1 Comparison with Conventional MicromechanicsResults 71
4.2 Storage Moduli and Associated Loss Tangents ... 79
4.3 Design Curves arid Tables - Storage Moduli andAssociated Loss Tangents Versus Frequency forVarious Fiber Volume Fractions 81
V. CONCLUSIONS 83
APPENDIXES 85
A. BOUNDARY-POINT-LEAST-SQUARE METHOD ... 85
B. MODELS AND MEASURES OF MATERIAL DAMPING 88
C. DETAILS OF FORMULAS DERIVED IN SECTION II .... 114
D. EXPERIMENTAL DETERMINATION OF COMPLEX STIFF-NESS AND DAMPING OF A BORON FIBER . 125
E. COMPUTER PROGRAM DOCUMENATION 127
REFERENCES 129
TABLES . . . 145
FIGURES 214
COMPUTER PROGRAM LISTING 253
ii
ABSTRACT
To make a static or dynamic structural engineering analysis of a
structure laminated of fiber-reinforced composite material, one must
know beforehand the macroscopic equivalent orthotropic plate properties
of a single layer. In the case of a monofilament composite layer,
which consists of only a single row of parallel, equally spaced rein-
forced filaments embedded in the matrix material, flexural and twist-
ing stiffness analyses must be carried out in addition to the in-plane
and thickness-shear stiffness analyses owing to the inhomogeneous pro-
perty distribution along the thickness direction of the layer.
In this work are carried out elastic and damping analyses result-
ing in determinations of all of the various stiffnesses and associated
loss tangents for the complete characterization of the elastic and damp-
ing behavior of a monofilament composite layer.
For the determination of the various stiffnesses, either an
elementary mechanics-of-materials formulation or a more rigorous
mixed-boundary-value elasticity formulation is used. The solution for
the latter formulation is obtained by means of the boundary-point least-
square error technique. .
Kimball-Lovell type damping is assumed for each of the con-
stituent materials. For determining the loss tangents associated with
the various stiffnesses, either the viscoelastic correspondence principle
or an energy analysis based on the appropriate elastic stress distribution
is used.
iii
The numerical results obtained from this analysis compare favorably
with some existing analytical and experimental results for various
practical combinations of constituent .materials, specifically boron-
epoxy, boron-aluminum, and E glass-epoxy composites. Finally a
complete set of property curves for a boron-epoxy monofilament com-
posite for a frequency range of 50 to 2,000 Hz are presented to
facilitate elastic and damping analyses of a structure consisting of
multiple layers of such a composite. Design data for other composites,
namely, boron-aluminum and E glass-epoxy, which are valid for a
similar frequency range, are summarized in tabulated form. Complete
computer program documentation and listing are given to facilitate
calculations of monolayer property values for other composites.
IV
SYMBOLS
A cross-sectional area of a typical rectangular mono-filament element
A a general m x n coefficient matrix
A transpose of A
A ann x nsymmetric matrix defined in eq. (A-5)
A,,A cross-sectional areas of the respective fiber andmatrix regions in a typical rectangular element
A heredity constants, eq. (B-21)
a(x,),a(x») wave amplitudes at positions x.. and x.
a ,a -,a free-vibration amplitudes corresponding to the i-th,1 i-t-i i-i-n ,,.,x_h> and (i+n)th cycles
a, coefficients of the fiber-region series solution to thePrandtl torsion problem
a initial amplitude
a ,a' coefficients of the biharmonic series solution to eq. (20)n n valid in the respective fiber and matrix regions (i=f,m)
B constant defined in eq. (118)
B n-dimensional column vector of prescribed boundary values
K an n-dimensional column vector defined in eq. (A-6)
b material damping coefficient defined in eq. (B-10)
b critical material damping coefficient
b, ,b , coefficients of the matrix-region series solution tothe Prandtl torsion problem
b ,b' coefficients of the biharmonic series valid in the re-n n spective fiber and matrix regions (i=f,m)
C damping coefficient defined in eq. (B-22)
C' damping coefficient defined in eq. (B-8)d
Cw, empirical constant factor
C. .C.. fiber-matrix interface, inter-element, and externalboundaries, respectively
c viscous damping coefficient
c Kelvin-Voigt complex damping coefficient defined ineq. (B-4)
DI 1 longitudinal flexural stiffness
D.2 Poisson flexural stiffness
D»7 transverse flexural stiffness
D,, twisting stiffnessDO
d distance between the origin and the center of the n-thelement fiber; see fig. 7
E Young's modulus
E,.,E Young's moduli of the fiber and matrix materials, re-I m ,spectively
E. equivalent Young's moduli (i=x,y,z)
E 1 , , £ _ » , £ _ « Young's moduli of a specially orthotropic material inII x^directions (i=l,2,3)
E^j equivalent Young's modulus for flexural loading
2E mean-square error
Ei(u) exponential integral defined in eq. (B-18)
e base of the natural logarithms, e ~ 2.7183
F(T]) function defined in eq. (51)
F exciting force amplitude
F, damping forced
F (p).F'(p) functions of the normalized radial coordinate pdefining the series representation of the matrix-region Airy stress function, eq. (55)
F spring forceS
F F2'F3'F4 integrals defined in eqs. (136,137,182, and 183)
G shear modulus
VI
G f , G m shear moduli of the respective fiber and matr ix 'materials
44' 55' 66 composite shear moduli: transverse thickness-shear,longitudinal thickness-shear, in-plane
g loss tangent
g, parameter of the Biot model
gE-.,etc. subscripted loss tangents where the subscripts (i.e.refer to the associated moduli or stiffnesses; for example,8Eii signifies the loss tangent associated with the major
Young's modulus EJJ
HPMF half-power magnification factor
h total thickness of a single layer
I centroidal rectangular moment of inertia per unit lengthof a longitudinal cross section
I ,1 principal rectangular moments of inertia of a typicalrepeating cross section
I_ weighted moment of inertia defined in eq. (119)
i unit imaginary number ^ /"-T
K shear coefficient
k,k spring constant, complex spring constant
k* stiffness associated with the total in-plane force
k'1 complex spring stiffness defined in eq. (B-12)
k Kelvin-Voigt complex stiffness defined in eq. (B-3)
k' Kimball-Lovell complex stiffness defined in eq. (B-ll)
L effective length of spring
•Ln natural logarithm
log logarithm with base 10
N bending moment per unit width
MF, MF1 magnification factors defined in eqs. (B-38) and (B-16)
m mass
n normal coordinate; degree of heredity, eq. (B-21)
vii
P axial tensile force
P1 expression defined in the first of eqs. (C-30)
Q total shear force (Section 2.7)
Q quality factor (Appendix B)
Qf,Q shear forces in the respective fiber and matrix regions
Q.. elastic coefficients for the plane-stress state (i,j=l,2,6)
R1»R2»R3'R4 integrals defined in eqs. (C-24)
RMF resonant magnification factor
r radius of the fiber
S1'S2'S3'S4 integrals defined in eqs. (C-25)
S,, transverse thickness-shear stiffness
S,.,- longitudinal thickness-shear stiffness
t time
t,,t7 two different specific values of time
U mean displacement defined in eq. (86)
U strain energy per cycle defined in eq. (148)
U, flexural strain energy in an elemental volume
U, damping energy per cycle
U, specific dissipative energy defined in eq. (B-22)
U ,Um strain energies per cycle respectively of the fiberand matrix materials
U shear energy per unit lengths
U strain energy per unit length
U,,UT damping energy per cycle respectively of the fiberand matrix materials
u,v,w rectangular components of a displacement vector
u displacement
u displacement amplitude of vibration
viii
i i iu ,v ,w
Ur'U9
Ust'Ust
u.v.w
u ,w
V,,Vf' m
W
I'
X1'X2
a
QT.P.V
"'
V
Vaverage
effective
r0
rectangular components of a displacement vector in thefiber (i=f) and matrix regions (i=m)
plane polar components of a displacement vector
static displacements; see Appendix B
mean rectangular components of a displacement vector
residual displacements defined in eqs. (87)
volume
fiber and matrix volume fractions, respectively
spatial attenuation constant defined in eq. (B-33)
temporal decay constant defined in eq. (B-30)
mean z-component of displacement defined in eq. (86)
rectangular coordinates; see figs. 3-9
rectangular coordinates associated with the fiber (x.),transverse (x£) , and thickness (x-j) directions
two different specific values of position (Appendix B only)
the arrow symbols signify that the expression is alsovalid with the roles of x and y interchanged
angle of twist per unit length
constants defined in eqs. (31)
heredity constants in eq. (B-21)
transverse flexural curvature
longitudinal flexural curvature
loss angle
average thickness-shear strain
effective thickness-shear strain
plane polar component of the shear strain
spatial attenuation rate defined in eq. (B-34)
Yfc decay rate defined in eq. (B-31)
v ,Y »Y rectangular components of shear strainyz zx *^y
6 ratio of height to width of the typical composite crosssection
5 logarithmic decrement defined in eq. (B-28)
8 logarithmic attenuation defined in eq. (B-32)s
e Biot parameter in eq. (B-17)
e ,eQ plane polar components of the normal strainr W
e >e >e rectangular components of the normal strainx y z
e. average normal strains (i=x,y,z)
el'e2'e6 generalized plane-stress-state strain components
.£ damping ratio
|,T1 normalized rectangular coordinates; see eq. (74)
p,9 normalized polar coordinates; see fig. 4(b)
, functions defined in eqs . (174)
X X = l-v12v21
X ratio of constituent-material shear moduli, X = G,/Gt m
X I ratio of constituent-material Young's moduli, X1 = E /Ei m
\l \l = (X-D/CX41)
^ ratio of width to fiber diameter of a typical mono-filament cross section
-..f m
Poisson's ratio
Poisson's ratios of the fiber and matrix materials
v. . Poisson's ratios of an orthotropic material (i,j = 1,2,3)
v. . equivalent mean Poisson's ratios
TT pi » 3.1415962
) summation symbol
°£»°m axial stress components in the respective fiberand matrix regions
o. plane-stress-state stress components in rectangularcoordinates (i=l,2,6)
a. equivalent mean plane-stress components (i=l,2,6)
a tensile stress; cf., figs. 4 and 6
cr stress amplitude
T dummy time variable in eq. (B-19)
T ,T longitudinal and transverse thickness-shear stresses,respectively
* (t) hereditary kernel defined in eq. (B-21)
$ ,§ Airy stress functions for the respective fiber andmatrix regions
CP phase angle
* i icp ,cp Neumann torsion functions (i=f,m)
cp mean angle of rotation of the cross section
"i i\ >\ Saint-Venant flexure function (i=f,m)
" i iY ,Y Dirichlet torsion function ( i=f,m)
aj angular frequency, rad/sec
u/ resonant angular frequency
J/, ,iju_ angular frequencies def ining the half-powerpoints of the frequency spectrum
2 2 2 2 2 2V Laplace operator; V s(d /ox )+(3 /3y )
2 2dimensionless Laplace operator; 7 =+
Superscripts:
f,m signifies the respective fiber and matrix materials
I,R signifies the respective imaginary and real parts ofthe quantity represented by the main symbol
denotes differentiation with respect to time
X I
SECTION I
INTRODUCTION
1.1 Introductory Remarks
Engineering structural design requirements for aerospace vehicle
structures demand a maximum of strength and stiffness at minimum weight.
In order to fulfill these requirements, engineers have been searching
for new and better materials. This led to the development of glass-
fiber-reinforced plastics in the case of pressure vessels, and to the
use of carbon or boron filamentary composites in the case of stiffness-
critical structures such as fuselage panels. In addition to being highly
efficient structurally (strength/weight and stiffness/weight) , the
modern composite structures present modern structural designers with a
unique advantage over the conventional homogeneous materials in that they
can be designed to give different properties in different directions as
required by the particular application. This is commonly achieved by
*laminating several layers of the monofilament composites with the fila-
ments of each layer oriented in some prescribed direction. Before
macroscopic properties of such laminates can be predicted, it is necessary
to determine the macroscopic behavior of a single monofilament layer.
*In contrast with those filamentary composites with many small reinforcing
filaments randomly distributed throughout the entire cross section, there
is only a single row of regularly-spaced filaments embedded in the midplane
of the layer for the monofilament composites (reference 1).
Owing to their oriented nonhomogeneous nature, one-layer filamentary
composite materials behave as an orthotropic material on a macroscopic
Ibasis. Thus, to use these advantages fully, orthotropic properties of
;the composites must be characterized from the knowledge of constituent
material properties and their respective geometrical configurations.
In the case of a one-layer filamentary composite with many small parallel
:filaments more or less randomly distributed throughout the cross section,
'the complete characterization of the in-plane macroscopic composite
(properties requires four independent elastic coefficients. These coef-
ficients are: two moduli or elasticity E .. , E22' one mo^u^us °* rigidity
G ; and one independent Poisson's ratio v. _ (reference 2) . The flexural66 •!•*
and twisting stiffnesses are then related to the in-plane moduli by the
formula (reference 3) ,
h/2
Ell/X> V12E22/X* E22/X> G66> z* dz
where
However, for a monofilament composite such as boron-epoxy,
consisting of only one row of filaments whose diameter is relatively
large in comparison with the thickness dimension, there is a large amount
*In usual notations, "1" is the filament direction, "G.." (i,j=l,2,3)
denoted the shear modulus in the ij-plane, and v. . (i,j=l,2,3) denotes
the j-direction normal strain-due to unit i-direction normal stress.
of relatively flexible matrix material located at an appreciable distance
from the filament axis. (See figure 1). Thus, the conventional practice
(references 3 and A) of assuming homogeneous property distribution in
the thickness direction will not be expected to be valid in predicting
the macroscopic flexural and twisting stiffnesses of a monofilament com-
posite. In view of this, flexural and torsional analyses must be car-
ried out in addition to the in-plane analyses in order to describe the
behavior of such a composite completely. Furthermore, owing to the
*presence of a relatively flexible matrix material, the thickness-shear
flexibility is expected to be significant (references 5 and 6) for the
filamentary composites.
In the dynamic analysis of a structure consisting of multiple
layers of filamentary composites, the damping characteristics are just
as important as the stiffness characteristics. The damping properties
of a composite may be characterized in a number of ways (reference 7;
also, see Appendix B) .
There have been a few experimental investigations on damping character-
istics of sandwich materials and filamentary composites (references
8-19).
Pottinger (ref. 8) measured the temporal decay of axial vibrations
of bars of glass fiber-epoxy and boron fiber-aluminum composites in the
frequency range of 1 kHz to 100 kHz.
Often referred to as transverse-shear, here the term thickness-shear
is used, so that the term transverse can be reserved to refer to the
direction normal to the longitudinal (filament) direction and con-
tained in the plane of the layer.
Schultz and Tsai (refs. 9 and 10) used the free vibration decay and
resonant response of cantilever beams made of unidirectional and angle-
plied glass fiber-epoxy composites in the 10 to 10,000 Hz range.
James (ref. 11) and Bert et al. (ref. 12 and 13) used the temporal
decay of free-free sandwich beams. The facings of the ref. 12-13 beams
were of glass fiber-epoxy.
Clary (ref. 14) conducted resonant response experiments of free-
edge plates made of unidirectional boron fiber-epoxy composite material
to study the effect of fiber orientation.
Bert et al. (refs. 15-17) carried out resonant response measurements
on a free-edge, circular, truncated conical shell with an aluminum
honeycomb core and glass fiber-epoxy facings.
Richter (ref. 18) used the rotating beam deflection technique to
determine the damping characteristics of glass fiber-epoxy at low fre-
quency (0.01 to 1.07 Hz.).
Kerr and Lazan (ref. 19) made hysteresis measurements on a sand-
wich beam with both core and facings of glass fiber-epoxy.
Analytically, Hashin (references 20 and 21) determined complex moduli
of viscoelastic composites (particulate and filamentary) by develop-
ing a correspondence principle which relates the effective elastic
moduli and creep compliances of^the viscoelastic composites. However,
his analyses are not applicable to those cases where the effective
elastic moduli are not explicitly obtained. Since the steady-state re-
sponse of the filamentary composite structure is of our main concern in
this investigation, the wavelengths of the modal profiles are in general
much greater than the filament diameter or the thickness dimensions; thus,
the Kimball-Lovell type material damping (reference 22) is assumed to
hold. The analysis similar to reference 13 is carried out by using the
numerically obtained stress distributions for the effective elastic
coefficients, and the results are presented in terms of complex moduli
for each assumed loading mode: in-plane, flexural, twisting, and so forth.
In the following subsection 1..2, the current literature on micro-
mechanics analyses of filamentary composites are briefly surveyed.
In Section II, detailed elasticity and mechanics-of-materials analyses
are made to obtain various macroscopic elastic properties pertinent for
the characterization of one-layer composites. In Section III, the elastic-
analysis results are used to calculate the damping properties of the
composites; and in Section IV, the damping properties in terms of complex
moduli are summarized, and some typical numerical results are compared/
with existing analytical and experimental results.
1.2. A Brief Survey of Micromechanics Analysis of Filamentary Composite
Materials
Since the development of practical methods for manufacturing parallel-
filament-reinforced layers of composite materials in the 1950's (references
23, 24), the field of micromechanics analysis mushroomed rapidly starting
with the pioneering analyses of Outwater (reference 25) in the United
States and of Beer (reference 26) in Germany. By micromechanics analysis
is meant an analysis which leads to the prediction of the macroscopic
properties--elastic moduli-- of the composites based only on reinforce-
ment configurations, and the properties and volume fractions of the
constituent materials.
Chamis and Sendeckyj, in their recent survey of the field (ref. 4),
listed 109 references concerned with the prediction of thermoelastic
properties of the fibrous composites. Since a unidirectional filamentary
composite will behave macroscopically as an orthotropic materials, a
complete description of the elastic properties of the composite requires
nine independent elastic coefficients: three Young's moduli (E.... .E .E-.,) ,
three shear moduli (G,, ,G_,-,G,,) , and three Poisson's ratios (v, 2>V23>V31^ '
where the subscript (or subscripts) refers to the orthotropic axes of
the composite along which the properties are measured (see figure 1.)
The analytical methods which have been used in previous micromechanics
analyses may be categorized as:
(1) Netting analysis method
(2) Mechanics-of-materials method
(3) Self-consistent model method
(4) Variational method
(5) Exact classical elasticity method
(6) Statistical method
(7) Discrete element (finite element) method
(8) Semiempirical method
(9) Microstructural method
In netting analysis, fibers are assumed to provide all of the
longitudinal stiffness and the matrix material is assumed to provide the
transverse and shear stiffnesses and the Poisson's effect. This is
equivalent to assuming the disjointed fiber-matrix model, and thus pre-
dicts relatively low values for E_2 and Gj_ (references 25 and 27).
The mechanics-of-materials methods were pioneered by Ekvall (reference
28). In his analysis, the macro-composite properties are expressed in
terms of the averaged stress-strain states, which, in turn, are expressed
in terms of the constituent properties using displacement continuity
and force equilibrium conditions at the matrix-fiber interface. In
general, the predicted transverse and shear stiffnesses are lower than
the experimental values. Thus, the method was later improved upon by
using the concept of restrained matrix model in which the strain in the
matrix parallel to the fiber is assumed to be zero (ref. 1). This method
was later extended to account for the effect of voids in the composite
by Greszczuk (reference 29), and the effects of misalignment by Nosarev
(reference 30).
The self-consistent model method is based on the assumption that
the strain field of a single fiber embedded in an infinite (reference
31) or a finite (reference 32) matrix is indistinguishable from that of
the composite. The results of such analyses are generally accurate
for the case of low-fiber-volume fractions only.
The variational method is based on the energy theorems of classical
elasticity (reference 33) in which lower and upper bounds of the layer
properties are obtained from the theorems of complementary and potential
energy, respectively (references 34 and 35). The upper and lower bounds
are very far apart for composites with high fiber-matrix-stiffness ratio
such as boron-epoxy composites. Thus, correction factors such as contiguity
and misalignment factor, etc. need to be brought in to obtain closer
agreement between the theoretical predictions and the experimental re-
sults (references 34 and 36).
The exact classical elasticity method has many variations depending
on the methods of solution (references 37-39). With the exception of the
relatively simple case of a circular fiber embedded in a circular matrix
material, the solution cannot be obtained in a closed form and thus
various numerical methods must be used. These are practical now with the
aid of modern high-speed digital computers. In all cases, the problem is
formulated with an assumption that the fibers form a regular array
(rectangular or hexagonal); a solution is sought for the resulting
mixed boundary-value problem, subjected to the usual assumption of per-
fect bonds between the fiber-matrix interface and a set of imposed
boundary conditions (uniform tension, shear, etc.). The elastic field
thus obtained is then averaged over the cross section and the boundary
to yield the desired equivalent macroscopic elastic properties of the
composite.
In the statistical methods, the composite is modelled by the random
distribution of the fibers in the matrix materials. Very little success
has been achieved by this method (ref. 20)owing to the statistical averag-
ing process that leads to insurmountable computational difficulties.
The discrete element method was pioneered by Foye (references 40 and
41) for the prediction of E22'G12'V12' 3nd V23° HiS resu^ts ^or circular
filaments in square arrays are in good agreement with those of Ekvall
(ref. 28) and Greszczuk (ref. 29). The method may also be applied to
cases with nonlinear matrix behavior as well as random array arrangements
(ref. 41); however, so far its use has been relatively limited.
The semiempirical method which is most commonly used to date is
due to Tsai (ref. 34). He assumed that the properties of a filamentary
composite with non-contacting fibers may be predicted by a linear inter-
polation between the lower and upper bounds obtained from the variational
method. This linear interpolation was improved upon by Tsai and Halpin with
a more refined nonlinear interpolation (ref. 3). There are other semi-
empirical models (ref. 4) based on the equivalent section concept, parallel
and series connected elements, and the incorporation of certain empirical
factors.
The microstructural method was proposed by Bolotin (reference 42).
Postulating that the fiber behaves as a small rod and that the distances between
the fibers are small in comparison with the characteristic distance of the
body and using a variational principle, he derived the displacement equilib-
rium equation similar to those for a Cosserat medium, that is, a medium
possessing an unsymmetric stress tensor containing couple stresses. Later,
this microstructural model was applied by Herrmann et al.to investigate the
transverse wave propoagation in filamentary composites (reference 43).
Most of the micromechanics analyses described above are based on the
*hypotheses that: (1) The fibers are regularly spaced and aligned. (2)
The fiber and matrix materials are homogeneous and linearly elastic. (3)
There is a complete bond at the fiber-matrix interface. (4) The com-
posite is free of voids. (5) The composite is initially at a stress
*As a rule, these hypotheses are adhered to in the above discussed
analyses. However, there are exceptions in which one or more hypothesis
is relaxed, for example, perfect interface bond is not assumed for the
netting analyses.
free state. (6) The composite behaves as a homogeneous general ortho-
tropic material macroscopically.
There have been a few experimental investigations on the damping
characteristics of composites (refs. 8-19). In general, it was agreed
upon that for small oscillations, the filamentary composites exhibit
anisotropic, linear viscoelastie behavior. Damping properties of some
non-metallic materials are summarized and tabulated in reference 44.
Analytically, Hashin developed a correspondence principle which re-
lates the effective macroscopic .elastic moduli to the effective
viscoelastie moduli (reference 45). This correspondence principle was
then applied to particulate and fibrous composites for the determination
of macroscopic complex moduli of such composites (refs. 20 and 21).
Unfortunately, this correspondence principle cannot be applied to cases
where the effective elastic moduli are not explicitly obtained in a closed
form. Bert etal., in their investigation of the damping in a shear-
flexible sandwich beam (ref. 13), observed that the damping character-
istics of composites may be related to the ratio of the dissipated energy
per cycle to the total potential energy stored per cycle. The analysis
is based on the assumption that the wave length of the normal modes is
large in comparison with the thickness dimension of the beam.
10
SECTION II
ELASTIC ANALYSES
This section is concerned with the detailed elastic analyses lead-
ing toward predictions of macroscopically equivalent orthotropic pro-
perties of a monofilament composite layer. The composite layer is
modelled by a typical repeating cross section consisting of a rec-
tangular matrix with a centrally oriented circular-cross-section fiber. Var-
ious in-plane, flexural, twisting, and thickness-shear properties are
obtained from the solutions of a series of mixed boundary value problems
with approximately prescribed boundary conditions.
2.1 Introduction and Hypotheses
Macroscopically, a single layer of filamentary composite material
behaves as a specially orthotropic material with respect to three mutually
orthogonal planes: the plane normal to the fibers, the plane of the
layer, and the plane normal to the first two planes. The intersection of
these three planes forms three mutually orthogonal axes: the longitudinal
(or fiber) direction, the transverse direction (normal to the fibers
and contained in the plane of the layer), and the thickness direction
(normal to the plane of the layer). Therefore, a complete character-
ization of the elastic properties in three dimensions requires nine
independent elastic coefficients (ref. 2). However, in many structural
engineering applications of filamentary composite materials or the
laminates of such, they are used in the form of thin panels or plates
11
due to the weight considerations in such applications. In view of this,
the thickness dimension of the composites is usually much smaller than the
other dimensions and the radius of curvature of the structure. The three
stress components Oo.d,, and O- therefore may be regarded negligibly
small in comparison with the remaining three stress components, namely,
*a.,,0-, and a, . This is referred to as the generalized plane stress state.1 i o
The constitutive equation for the generalized plane stress state is given
by
(1)
f \1 1°2
i>. >
> -
Qll Q12 °
Q21 Q22 0
. ° ° 2Q66,
1
el
e2
[*6,
where the elastic coefficients Q.. are symmetric, i.e.,
Q i j = Q j i
Hence, there are only four independent elastic coefficients. Equation (1)
may also be written in terms of the engineering moduli E.... , E??, G _, and
Poisson's ratios V2i
as
In terms of double-subscript stress notation (ref. 3. p. 16) ,
where the x_-direction is normal to the plane of the layer.
12
EU/X 0
0
G12.
1
' « !
£2
heI 6 )
(2)
where
= 1 - V12v21
Again, there are only four independent coefficients since the symmetry
in the coefficient matrix, which is a consequence of the existence of the
elastic potential (ref. 2), demands that
V12/E11 = V21/E22
It follows readily from equations (1) and (2) that,
Eii/X
Q12 = V12Q22
Q66 = G66
(3)
Hence, for a single layer of filamentary composite with many small
filaments more or less randomly distributed throughout the entire cross
section, in-plane macroscopic behavior is characterized by specifying
the four elastic coefficients Q.j, Q22> Qj~, and Q^ or equivalently, by
the in-plane engineering moduli E , £„„, G,-, and one of the Poisson's
ratios v,, or voi •
13
Owing to the presence of the relatively flexible matrix material,
the thickness-shear flexibility, is expected to be significant (refs.
5 and 6) for the filamentary composites. Therefore, for complete macro-
scopic property characterization, one will need to specify flexural,
twisting, thickness shear stiffnesses, and flexural Poisson's ratios,
in addition to the in-plane properties. The above-mentioned type of com-
posite has a more or less homogeneous distribution of properties through the
thickness. Thus, only two additional stiffnesses, namely the thickness-
shear moduli G and G,,, need to be calculated, since the flexural and
twisting stiffnesses may be obtained by the previously stated formula,
rh/2(Dn,D12,D22,D66) = J (HU /X,V 1 2E 2 2 /X,E 2 2 /X,G 6 6) z dz (4)
-h/Z
where D ,D ,D , and D denote the longitudinal, Poisson, transverse, and11 12 a DO
twisting stiffnesses, respectively, and h = the thickness of the layer. How-
ever, for a monofilament composite, equation (4) is not expected to hold
because of a more predominant inhomogenelty in the property distribution
through the thickness. In view of this, for the complete characterization
of macroscopic elastic behavior, flexural, as well as torsional, analyses
must be carried out.
Given constitutive properties of the constituent materials and the
fiber-matrix geometrical configurations, determinations of these macroscopic
equivalent orthotropic properties may be carried out in a number of ways
as summarized in reference 4. In the subsequent analyses, approaches
based on mechanics-of-material and classical elasticity theories are used
14
to obtain solutions which are manipulated to yield the required equivalent
orthotropic properties. The elastic solutions obtained in this way are
used in Section III to analyze the damping characteristics of the filament-
ary composite materials where Kimball-Lovell type material damping (see
Appendix B) is assumed to prevail.
The longitudinal in-plane and flexural stiffnesses and the trans-
verse thickness-shear stiffness are handled easily for mechanics-of-
materials analyses. For the remainder of the elastic properties, classical
elasticity analyses are used to formulate a series of appropriate mixed
boundary value problems. Then these problems are solved numerically by
means of the boundary-point-least-square method, as described in Appendix
A, to yield the desired equivalent macroscopic properties.
The monofilament composite material is exemplified by a repeated
rectangular cross section consisting of a circular-cross-section fiber
centrally located, and surrounded by matrix material as depicted in
figure 2.
The basic hypotheses used consistently in the subsequent analyses are
summarized as follows:
HI. Fibers and matrix respectively are homogeneous, linearly elastic,
and isotropic.
H2. Both fibers and matrix are free of voids.
H3. The fiber-matrix interface bonds are perfect without transitional
region between them.
HA. Initially, the composite is in a stress-free state and all
thermal effects are neglected.
15
*H5. Inertial and damping effects are neglected.
2.2 Longitudinal In-Plane Stiffnesses
In this subsection, two in-plane engineering moduli of elasticity,
namely, major Young's modulus E . and in-plane longitudinal shear modulus
G,, , will be discussed. The major Young's modulus E,, is estimated fromDO 11
the law of mechanical mixtures; whereas, the in-plane longitudinal shear
modulus G is obtained from the result of classical theory of elasticitybo
analysis by Adams and Doner (reference 46).
Major Young's Modulus EI1. - A typical repeating element of a mono-
filament composite element is subjected to a uniform longitudinal strain
e, as shown in figure 2. The longitudinal stresses induced in the fiber
and matrix, respectively, are:
' am = Em el
where E and E are the longitudinal Young's moduli of elasticity of the
filament and matrix, respective.'ly.
The total equivalent longitudinal force P in the composite is
P = 0fAf + amAm (6)
where A., and A are the cross-sectional areas of the filament and matrix,r m
respectively.
The equivalent major Young's modulus EI. of the composite is readily
Damping is treated separately in Section III.
16
obtained from equations (5 and 6) as
P/(Ael)=(EfVEmAm)/A
where
A = Af + Am (8)
The volume fractions of fiber and matrix are defined as
V. = A /A , V = A /A (9)t t m m
In terms of the volume fractions Vf and V , the major Young's modulus
EI, is written as
EfVf + EmVm
or
Em
since
- Vf (12)
Since Ef > E in general, equation (11) shows that E varies linearly with
respect to V from the matrix modulus (at V = 0) to the fiber modulus
(at V, = I). For a monofilament composite with a square typical element,
17
the fiber volume fraction ranges between 0 and 0.785. Therefore, the values
of E.../E can vary between 1 and 94.4 for E /E = 120 (borori-epoxy).11 >n f m
Equation (11) is usually known as the simple law of mechanical
9
mixtures or "law of mixtures" for brevity. This relationship is also
valid for the cases where the filament material is transversely isotropic
with the plane of isotropy coinciding with the cross section of the filament,
The Young's modulus E in eq. (11) is then interpreted as the longitudinal
Young's modulus of the fiber.
Since the interaction between the constituent materials, owing to the
difference in their Poisson's ratios, is neglected completely in this
simplied analysis, the major in-plane Young's modulus E . calculated from
eq. (11) is the lower bound as demonstrated by Hill (reference 47). How-
ever, the effects of the difference in the Poisson's ratios of the con-
stituent materials have been shown theoretically to be minute (references
39, 47 and 48) and confirmed experimentally. Therefore, for all practical
purposes eq. (11) may be deemed satisfactory for the prediction of E .
In-plane Longitudinal Shear Modulus G ,,. - Consider one quarter of
a typical repeating element of a monofilament composite as depicted in
figure 3. The displacement field corresponding to the applied longitudinal
shear loading is then assumed to be of the form
u = v = 0, w = w(x,y) (13)
with the corresponding stress components:
»• i — n r.i /Av i- i — r i.
18
Substitution of equation (14) into the equations of equilibrium yields the
governing partial differential equations that must be satisfied in the
fiber and matrix regions
=0 (i=f,m) (15)
The boundary conditions depicted in figure 3 are
mG ow /9y = 0 along y = 0 and y
mw = 0 along x = 0
m -w = w along x
(16)
In solving the problem posed by equations (15) and (16) , the interfacial
continuity conditions on the displacement and the shearing stress need
to be considered. This leads to:
w f = w m on C 1 (17)
and ,
G, ^w /bn= G 6w An on C,E m 1 (18)
where n signifies the outward normal to the boundary C1. The boundary-
value problem defined by eqs. (15-18) are then solved by the f in i t e
difference method (ref. 46), and the effective macroscopic shear modulus
19
of the composite is determined from
Comparisons of the shear modulus predicted by eq. (19) to those obtained
from other analyses (refs. 35 and 38) showed that equation (19) is in
closer agreement with the experimental values (ref. 46).
2.3 Transverse In-plane Stiffnesses
Consider a typical repeating element subjected to a uniform tensile
stress of magnitude a in the y direction as depicted in figure 4(a).
Because of symmetry about both coordinate axes, only one quarter of the
repeating-element cross section needs to be considered, as shown in figure
4(b).
Assuming that a state of plane strain exists in the xy (or £f])
plane and further that each constituent material is isotropic in this
same plane (that is, the fibers can be transversely isotropic), one can
formulate the problem in terms of the Airy stress function $ (reference
49). This requires satisfaction of the following governing partial
differential equation in the absence of body forces which vary nonlinearly
with the spatial coordinates:
tfS1 =0, in A. (i=f,m) (20)
4where v" is the bihartnonic operator, f denotes fiber, and m denotes
matrix.
The general solutions of equation (20) in polar coordinates (p,9)
20
are of the form (ref. 49) :
$f(p,9) = b fp2 + bfp3 cos 9 + Y (a*pn+bo i ^i n nn=2,3,...
cos n 0 (21)
Ap,9) = a™ log p + bomp2 + cos 9 + cos 9
+1n=2 ,3,...
, m n m n+2 , 'm -n,. 'm -n+2. . ov(a p -fb o + a p +b o ) cos n 9 (22)n n n r n
Owing to the symmetry about the x-axls, only those series terms
which are even functions with respect to 9 are retained in equations
(21 and 22). In the usual notations, stress, strain, and displacement
*components are related to the Airy stress function « by :
Og =
2 2
(p-I
I (23)
cr = (1-l-v) E"1 [(1-v) af-v
ee = (l+v) E"1 - \> or] > (24)
The superscripts f and m which signify fiber and matrix regions, re-
spectively are omitted from equations (23-27) for brevity.
21
,-lre = E~ [o -v (C5 + 0Q)1 = 0z z r w
Vrg - 2 (1 + v) E- Trfl
u /R = (1 + v) E"1 f [(1 - ,v) O -v OQ] dpr J t o
uQ/R = (1 + v) E'1 J p[(l-v) aQ-v orl dO - J ur dO
(25)
where v is the Poisson's ratio.
The rectangular components of stress and displacement components are
then related to polar components of stresses and displacements by:
2 20=0 cos 9 + OQ sin 9 - T - sin 2 9x r y rw
2 2a = a sin 9 + a_ cos 9 + T n sin 2 9y r 9 r9
T =(1/2) (o -aQ) sin 2 9 + T Q cos 2 9x y r H rw
(26)
u = u cos 9 - u_ sin 9
v = u sin 9 -J- UQ cos 9r v
(27)
The unknown coefficients of the series solutions, namely, a , b ,1 i ' ia , b (i = f,m), are then determined from the symmetry conditions and
the boundary conditions depicted in figuru A(b), and those on C. , the
fiber-matrix interface.
From the symmetry of geometry and loading, it is apparent that the
22
coefficients of the odd terms in the series must vanish.
u - K -b, = b, =1
a = bn n
'm
m ,m ma = b =an n n = b = 0 (n=odd)
> (28)
Also, in view of the interfacial continuity conditions, the following
relationships must be satisfied.
f m f m f m f mur = Ur • U0 = V Tr9= Tr9
/or>\(29)
Thus, coefficients b , a ,b ,a ,a may be expressed in terms of
b"1 and b'm .n n
f m= (Y b
n n
a"1 = m[-(n+l)b™ + V bn"' ]/n
r. \,ni / i[(l-a)bn - (n-
f (30)
where
2 Gf/Gm
a B X(3-4vm+D/(3-4vf+X)
s 4xU-vm)/(X-l)
(31)
f23
Y = U(3-4v )m
Finally, the remaining coefficients a , b , b , and b1 are so chosen
that the boundary conditions on the external boundary are satisfied at
a discrete set of points. (See Appendix A; also, references 50-52).
The macroscopic equivalent transverse in-plane properties may now
be determined from the average of the displacements on the boundary.
The plane-strain stress-strain relations of an equivalent homogeneous
rectangular element that undergoes the same average deformation as the
monofilament composite element are of the form (ref. 2),
e = <5 /E - v O /E -v a /E xx xx yx y y zx z z -
(32)a = E (v a /E + v o /E )z z xz x x yz y y
where xy indicates that the same equation holds with the roles of x and
y interchanged, and a superscript bar indicates the average stress, strain,
and property values of the equivalent homogeneous orthotropic material.
Also, because of symmetry of the stiffness coefficient matrix,
XL.E. = v.iEi (i,j = x.y.z, i!*j) (33)
For the case considered,
°y T °o ' °x = ez = ° (34)
Substitution of equations (34) into the second and the third of equations
24
(32) yields two simultaneous equations for the determination of E and
V
e = a /E - v a /Ey o y zy z z
o = v a /Ez yz o y
(35)
From equation (35), the minor Young's modulus £„_ and the major Polsson's
ratio V, o are determined as
? = E = E a2 / (E e o+o2)22 y zo z y o z
^. 0 = v =0/012 zy z o
(36)
where,
E = E,. = E + (E, - E ) V,z 1 1 m v f m ' f
I 0 d? dTl/ (u26)2
= f Cv] d_5 (H25r)
> (37)
Although the major Poisson's ratio v,- may be obtained from the second
of equations (36), many experimental and analytical results (references
28,41,48, and 53) show that the rule of mixtures may be used to pre-
dict v,o with sufficient accuracy. In view of this, the following
simplified formula for Vj~ instead of the latter of eqs. (36) will be
used in Section 3.3 for the determination of the loss tangent associated
with v.'12'
(38)
On the other hand, elementary model prediction (Reuss estimate)
of the minor Young's modulus E__ results in the following expression
E22 = [<Vf/Ef> + (W'"1 (39)
which gives much lower values than those obtained experimentally. In fact,
Hill (reference 54) and Paul (reference 55) showed that equation (39)
gives the lower bound on the elastic modulus for a macroscopically
isotropic composite. There are some mechanics-of-materiaIs analyses
(ref. 1) which predict greater values for E~. at low fiber volume
fractions and smaller values for £„„ at high fiber volume fractions.
In contrast, the classical theory of elasticity approach (ref. 56)
predicts a value of E~2 which is consistently higher than the experi-
mental values.
2.4 Longitudinal and Poisson Flexural Stiffnesses
As stated previously, for a monofilament composite layer, the
longitudinal and Poisson flexural stiffness D and D,2 cannot be cal-
culated from the in-plane properties E .,£„»,v,~ and v?. due to the
fact that the assumption of macroscopic homogeneity of the material in
the thickness direction is no longer valid. Therefore, in this subsection
a relatively simple mechanics-of-materials analysis is used to obtain the ef-
fective flexural stiffnesses.
Longitudinal flexural stiffness Dj '. - An element of a monofilament com-
posite layer subjected to a pure bending moment is shown in figure 5.Owing to
symmetry of the loading and geometry, only one quarter of the cross
section needs to be considered for the analysis. As a first approximation,
assume that the Bernoulli-Euler hypothesis holds throughout the cross
section; then the strain distribution is given as
e = a, y (40)z
where ot, = longitudinal bending curvature, and z = distance from mid-z
plane.
Then, the longitudinal stress in the fiber and matrix are given by:
The flexural strain energy in an elemental volume one unit long
and having cross-sectional area (a,.+a ) is:f m
Ub = (1/2)J ^f'V daf + (1/2)J (am /Em)da
af
or
2Ub2 Pr 2 2 2 i, l^6r 2
/OS = (E,-E ) y^ (r -yVdy + Em nry dyz t in J m j
27
which integrates to give
,/<* * = (E -E )(nr4/32) + E (ur)V/6 (42)D z cm m
For an equivalent homogeneous orthotropic one-quarter section:
<43>
where E.. is the equivalent longitudinal Young's modulus for flexural
loading.
Equating the right-hand sides of equations (42 and 43), and solving
for E,. /E , one obtainsl l m
E =1 + U'-l)(3TT/16uV) (44)m
where
X1 s Ef/Em (45)
Finally, the layer flexural stiffness is given by the equation
-u&r
or/L\ -3
(46)
Recalling that the in-plane Young's modulus E.^ is estimated from the
law of mechanical mixtures (see Section 2.2):
28
(X'-l) Vf = l+(X'-l)TT/(4u26) (47)
the ratio E..- /E . is expressed as
(X'-l)(3TT/l$A3)]/[l+U'-l)TT/4a26] (48)
In general, X',u, and 6 are greater than 1; thus, the ratio in
equation (49) gives a value less than 1. This shows that for a monofil-
ament composite, the longitudinal flexural stiffness D as estimated,
eq. (4), by using the in-plane Young's modulus will be unconservative.
Poisson flexural stiffness. - Due to the nonuniform distribution
through the thickness, the transverse Young's modulus £^2 and the Poisson's
ratios v,9 and v51 are dependent locally on the thickness coordinate of the
composite. To carry out the integration indicated in eq. (4), £-„, v,2> and
v?1 must be expressed explicitly in terms of the thickness coordinate. In
the following analysis, a typical monofilament composite element is
considered to be made from the thin dy strip depicted in figure 5(b).
S22*
Thus, on assuming eqs. (38 and 39) to hold for the estimates of E?_ and
, ~ of the elemental strip, one obtains the following expressions:
For O^y^r, (or
*The Reuss estimate, eq. (39), gives excellent results for com-
puting the effective transverse Young's modulus for a thin strip, fig.
5(b), consisting of discrete rectangular aggregates of constituent materials,
29
(49)
J
where X1 is the moduli ratio as defined in eq. (46) and "H is the normalized
thickness coordinate (T|=y/r) .
In view of eqs. (49), the Poisson flexural stiffness for the monofil-
ament composite element is calculated by the following equation:
D12/D12 ={ I F(7° (50)
where D is the Poisson flexural stiffness of a homogeneous element of
the same size and consisting entirely of matrix material, and the function
F(T13 is defined as follows:
D?2(51)
/£„(!»]
2.5 Transverse Flexural Stiffness
The transverse flexural stiffness is obtained in a way similar to that
discussed for transverse tension (Section 2.3). Here, two edges of a typical
element are subjected to linearly varying stress distributions that are
equivalent to pure bending moments. (See figures 6(a) and (b) .)
In view of the antisymmetry condition, the Airy stress functions in
polar coordinates are of the form
00
$f(o,9) = bfp3 cos 9 + Y (afpn+bfpn+2) cos n 9 (52)1 /_j n nn=3,5,...
$m(p>9) = b^o cos 9 + a,"1 p" cos 9 (Cont'd. on next page)1 L 30
- In=l ,3 , . . .
. m m n+2 'm -n 'm -n+2. n - ._ v( a + b p + a p + b p )cos n 9 (53)
Equations (52 and 53) sat isfy the biharmonic equations, equations (20)
(Section 2.3). In view of equations (29) (Section 2 .3) , that specify
continuity of displacements and stresses at the fiber-matrix interface,
those coefficients defining the series solutions may be readily inter-
related as:
a - [-(n+l)« b m+ P b ]/nn n n
b r= Q- b
'm-a m= [-(n+1) bm+ Y b "']/n
n n n
(54)
where #, 3, and > are as defined previously in equations (31).
In view of equations (54) , the matrix-region Airy stress function
may be written as
(p,9) = b p cos 9 + a o cos 9
[Fn(p) b™ + Fn(p)bnm] cos n 9 (55)
n=l,3,...
where
31
F (p) s [-(n+1) p" + + (1-a) p"°+2]/n
(p) s [Yp-n - (n-l)p~n + np"n+2]/n
The coefficients b, , a, , b , and b (n=3,5....) are then deter-1 l n n
mined from the boundary conditions depicted in figure 6(b):
xy
T =0xy
v = 0
v = 0
0 S/U, T =0
on
on
on
on
? = u
1 = 0
T) = 0
"H = U6
(56)
Since the second and third of equations (56) are identically satisfied by
equation (55), these coefficients are determined from the first and fourth
of eqs. (56) in the sense of least square error at a discrete set of
points on the outer boundary § = u and T< = u& (see Appendix A).
The macroscopic equivalent flexural stiffness D-« of a typical element
may now be calculated from the applied bending moment M, and average weighted
curvature aiji/dy °n the f\ = U6 edge.
22 y=u6r (57)
where
M = 2 (ar) o /3o 1r32
2 ^ I(2r /I) J 5 [v] d5 / (58)
o
I = 2UV/3
Finally, substitution of equation (58) into equation (57) yields the
desired result:
D22 = (2 °0"r/9) s ESV/3T1] dl' (59)
2.6 Twisting St i ffness
To determine the macroscopic equivalent twisting s t i f fness D,, of aDO
one-layer monofilament composite, a rectangular cross section consisting of
N repeating typical elements is considered. (See figure 7.) Because of the
symmetry condition, only the quarter of the cross section, which lies in the
first quadrant of the xy plane, needs to be considered.
In the usual notation, u,v, and w are the displacements; and a is the
angle of twist per unit P.- length. Then, for a small angle of twist a-, we
have (reference 57) :
i-ayz, v = oxz, w = orcp (x,y) in R. (i=f,m)
iwhere cp (x,y) are the z-component displacement functions to be determined
from the equilibrium and boundary conditions. The strain and stress
components are readily found to be:
33
and
ex = ey
exz=
ez = exy
a = o = o = T = 0x y z xy
xzT =yz
, (i=f,m)
(i-f
(60")
On application of the equations of equilibrium, one finds that the
first and the second of these equations are identically satisfied and the
third equation gives
V2 ¥ in f,m) (61)
where
' 2 2 2 2 2V = (8 /dx ) + <* /dy ) (62)
The stress equilibrium condition across the fiber-matrix interface GI
requires the satifaction of
\ (dcpf/dn) - (dcpVdn) +(\-l)[y (dx/dn)- x(dy/dn) ] on (^ (63)
where n is the outward normal to the boundary C.. .
Displacement continuity requires that:
34
Cpf = cpm on C (64)
\or, equivalently,
dcpf/ds = dcpm/ds on C (65)
where s is the arc length along the boundary C . Similarly, on
the vertical inter-element boundary C_ (see figure 7),
. j+1 , and [dcpm/d7l].
(66)
where j and j-H refer to the jth and (j+l)-th repeating elements.
Finally, the stress-free condition on the outer boundary C- (see figure 7)
leads to
dcp /dn = [y (dx/dn) - x (dy/dn) J on C3 (67)
The aforementioned torsion problem, equations (61-67) , may also be formulated
*ialternatively in terms of the complex conjugate ¥ that satisfies the
Riemann-Cauchy equations
dcpVdx = oi'Vdy , depVdy =-oYi/Sx (68)
It is readily shown, in view of equation (68), that the alternative
formulation leads to:35
* o •
V Y1 = 0 , in R. (i=f,m) (69)
XYf = Y1" + ^ (X-l) (x2 + y2) + constant on C
A - A
dY /dn = dYm/dn
[dYm/dTl,
(1/2) (x2+y2) + constant
on
on
on C
(70)
(71)
(72)
(73)
For later convenience in numerical analysis, these equations are
normalized by introducing the following notations:
= x/r, -n = y/r, cp = cp/r , , V2 = (d2/d|2)+(d2/dTl2)
(74)
Then, the governing differential equations and the boundary conditions
become:
V2f1=0 , V2cpL=0 in A (i = f .m)
(§2+-n2)
fX (dcpr/dn) = (dcpm/dn)
d f f / dn=dY m / dn , dcp f/ds
(d?/dn) -| (dTj/dn)
(75)
on C (76)
[Ym,cpm]j+1 (7?)
36
? 4 T])
dcpm/dn = U (d£/dn) - | (dT]/dn) ]
. on (78)
and the stress components are:
xz1 - a G^ r [(dcpVdQ-TVJ = o GI r [(dfVdTD-T]]
Z
(i=f,m) (79)
The solution to the problem is obtained by assuming series solutions
for each of the fiber and matrix regions in all N elements that satisfy the
governing partial differential equation exactly in their respective
regions. For example, in terms of polar coordinates with the origin at
the center of the N-th fiber, the solution for the fiber and matrix
regions takes the form:
(n)
..tn'(n)
(n)'(n) cos k 9(n)
>
> (80)
It is interesting to note the fiber-region solution coefficients a,K
may be readily expressed in terms of matrix-region solution coefficients
b. by the use of boundary conditions on C , equation (76).
37
ao = [bo
= 2b1/(X+D +
= xi(brd)
(81)
where
(82)
In view of equations (81), only the coefficients b. nead to be determined
from the boundary conditions on C. and C~, namely, equations (77 and 78),
since a, and b , may be readily calculated from b by the use of (81). OnK. •• K K
writing b , in terms of b, , one has
cos 9 bk(pk+XlP"
k) cos k 0 (83)
k=l 2IV. !.}«-)•••
The problem is now reduced to the determination of the coefficients b, by
the satisfaction of equations (77 and 78) at a discrete set of points on
C_ and C_ in the sense of least square error (see Appendix A).
After determining b, , one can calculate readily the stress components
from equation (79). Finally the torsional stiffness D,, is obtained from—_^
Superscripts are omitted here for brevity.
38
the following equation in a closed form. (See Appendix C for details.)
D,, = (-y T ' + x T ) dx dy/a66 J J xz yzA..+Af m
2 r4 Gm {A JJ [Y f- k (?2+-n2)] d| dT] + JJ [^ - % (?W) ] d? dT] }
A f Am(84)
2.7 Longitudinal Thickness-Shear Stiffness
Owing to the presence of relatively flexible matrix material, the
effect of thickness-shear deformation needs to be considered in the struc-
tural application of monofilament composite materials. As the thickness-
shear stresses are not distributed uniformly across the cross, section, the
effective thickness-shear strain needs to be known for the calculation
of effective thickness-shear stiffnesses. It is a commonly accepted practice
to relate the effective shear strain to the average shear strain by means
of a correction factor K which is usually referred to as the shear coef-
ficient (reference 58).
K= V - /Y ff „. "(85)average effective
Since the thickness-shear strain distribution is dependent on the shape of
the cross section on which the thickness-shear stress acts, it is also re-
ferred to as shear shape factor.
In 1921, Timoshenko derived a theory of flexural beam vibration in
which the effects of rotatory inertia as well as that of thickness shear
were taken into account (reference 59). The shear coefficient K was
defined as the ratio between the average shear strain and that at the
midplane. This yielded a value of 2/3 for a homogeneous, rectangular-
section beam. However, this value of the shear coefficient gave poor
agreement with experimental results. In view of this, numerous
attempts were made to obtain a better value for K which would be in
closer agreement with experimental results. Based on the high-fre-
quency mode of beam vibration, Mindlin and Deresiewicz (reference 60)
obtained a value of 0.822 for a rectangular cross section; whereas,
based on the static mode, Roark (reference 61) gave a value of K of
5/6. Recently, Cowper (reference 62) used a different static approach
to derive a formula for K which is in good agreement with those obtained
by other investigators. This latter approach is deemed to be satisfactory
for long-wavelength, low-frequency deformations such as those encountered
in the vibration of monofilament composites.
Therefore, in this subsection, Cowper's analysis (ref. 62) is
extended to the nonhomogeneous case consisting of a typical repeating
element of a monofilament composite to obtain the effective thickness-
shear strain. The thickness-shear stiffness, which is defined as the re-
sultant shear force divided by the effective shear strain, can then be ob-
tained as a direct consequence of the analysis.
First, the thickness-shear distribution is obtained from the analysis
of a tip-loaded monofilament cantilever beam shown in figure 8(a).
Denoting the displacement components as u,v, and w, one defines the
mean displacements of the cross section and mean angle of rotation of the
cross section cp by the following equations:
ITU = (I/A) Jj u dx dy
A
W = (I/A) JJ w dx dy
A
Cf> = (I/I ) JJ xw dx dy
(86)
where A denotes the entire cross-sectional area, and I is the moment
of inertia of the cross-sectional area with respect to the y axis. Then
the actual displacements of a point on the cross section are written as
x c p + w (87)
where u and w are the residual displacements which are equal to the de-
viations of the actual displacements from the weighted mean displacements.
In view of the definitions, equations (86),
u dx dy = w dx dy = xw dx dy = 0 (88)
The stress-strain relation
T /G = u, + w,xz 'z x
(89)
where a comma represents partial differentiation with retipect to the
spatial variable that follows it, may now be written as
W, + CO = (T /G)-w, -u,'z xz x z
(90)
41
where the shear modulus G is to be interpreted as that of the fiber
or matrix material depending on whether the material point is located
in the fiber or the matrix region of the cross section. Finally, the
integration of equation (90) yields the desired kinematic relations among
the mean values of the midplane slope W, ; flexural slope cp; and thez
ef fec t ive shear strain Y f f:
W,z + cp = (I/A) JJ [(Txz/G) - w, x ] dx dy = Yef£ (91)
A
For a tip loading, the shear force Q is uniform along the entire length
of the beam, hence, the first part of the integral in equation (91) is
evaluated as
JJ <Txz/G) dx dy = (Qf/Gf) + (Qm/Gm) (92)A
where 0,. and 0 represent the respective shear forces that act on thef m
fiber and matrix regions and are related to the total shear force Q by
Q = Q f + Q m (93)
In view of eq. (87), the remaining term in the integral of eq. (91) is
JJ w,x dx dy = Jj(w,x - cp) dx dy (94)
A A
where cp is defined in the third of eqs. (86). Combining eqs. (91-94),
one obtains the effective thickness-shear strain expression,
42
Yeff = W'z + * = (1/A) W+'W "IJ
where Cf and hence w, the displacement field, needs to be known in terras
of the parameters defining the geometrical configuration and the con-
stituent properties before the integration can be carried out. Assuming
that the deformation of the cross section can be approximated by that of
a tip-loaded cantilever, and allowing the constituent materials to be
transversely isotropic with the plane of isotropy normal to the fiber
axis, one can readily formulate the problem using the Saint-Venant semi-
inverse method (refs. 57 and 63).
First, displacement components are assumed to be:
u1 = B [% Vj_ (-6-z) (x2-y2) + V<- z2 - (1/6) z3]
v1 = B v. C-z) xy (i=f,m)
w1 =-B{ x (Iz - fc z2) + X* + [(E./Gp-Zv.K^xy2)}
> (96)
where B is a constant to be determined from the boundary conditions;
E. is the Young's modulus in the fiber direction; G. is the shear
modulus in the vertical plane parallel to the fiber axis; v. is to be
interpreted as the Poisson's ratios v-,=v__; and \ = \. (x,y) (i=f,m)
are functions to be so chosen as to satisfy equilibrium conditions
in their respective regions.
The stress components are readily calculated from equation (96)
to be:
43
o1 = o1 - T1 = 0x y xy
Txz = - BGi
= - BE. (l-z) x
(i=f,m)
-*!3 Xy}
(97)
If the constituent materials are isotropic, E., G., and v. respectively
of the constituent materials are related by
(i=f,m) (98)
Substitution of the stress components in equations (97) into the equili-
brium equation yields the following governing partial differential
equations (Laplace's equations in two dimensions):
= o (i=f,m) (99)
which must be satisfied in the respective regions A,, and A .r m
Consideration of displacement cont inui ty at the fiber-matrix inter-
face C requires tha t :
f m f m f mu = u , v = v , w = w o n C
1(100)
Apparently, the first and the second of equations (100) cannot be satisfied
unless the two Poisson's ratios are equal. However, the interaction
44
between the constituent materials due to the differences in the Poisson's
ratios has only weak effects as evidenced by many theoretical analyses
) (refs. 39, 47, and 48). Hence, it will be assumed for the subsequent
analysis that
V, = v = v (101)I tn
With this assumption, equation (101), the first two of equations (100) are
identically satisfied and the third leads to
Xf =xm on Cl (102)
Continuity of surface traction at the interface C requires that
T (dx/dn) + T (dy/dn) = T (dx/dn) + T (dy/dn) (103)xz y xz y
where n denotes the outward normal coordinate to C. , hence, (dx/dn)
and (dy/dn) are the direction cosines of the unit normal vector to the
interface C .
In terms of the stress components defined in equations (97) , the
condition of equilibrium at the interface, equation (103), is cast readily
in the following form:
f ~mGf (dx/dn) - Gm(d X /an)
=-(Gf-Gm) [[% Ox2 + (L-i? v)y2](dx/dn)+(2+v)xy(dy/dn)]
on Cl (104)
The condition that the lateral surface is free from surface traction
45
leads to
(d xm/dn) = - j[% v x +(l-^v)y ](dx/dn) + (2+v)xy(dy/dn) 1
on C2 (105)
The solutions to the problems posed by the governing differential
equations (99) and the boundary conditions, eqs. (102,104,105) are now ob-
tained by assuming a pair of series solutions which are harmonic in the
respective fiber and matrix regions. The coefficients of these series
solutions are determined so as to satisfy the boundary conditions in the
least-square-error sense (see Appendix A, also Section 2.6.)
Since the solution procedure is very similar to that of Section
2.6, it will be high-lighted by listing these equations which are pertinent
to the solution.
With the introduction of the following transformation,
/ ™-\ / ^" ^ 1 / J s • e* \— v / v Tl = \7/t" v =V / y i i = i mIA / i. ) M y / L j J^ J^ / L \ 1. L 9 lllj
9 9 9 9A + ((106)
eqs. (99), 102, 104, and 105) are rewritten in the following form, which
is convenient for numerical analysis:
= 0 in A. (i = f,m) (107)
X™ on c
HdXf/dn) -(dx
m/dn) = -(X-l) [l%v§2 + (l
+ (2 + v) f 71 (dtl/dn) on q (109)
46
(dxm/dn) 2V 5 -Kl-Vv) Tl] (d|/dn)
+ (2 + 0) ? -n (dT1/dn)j on C, (110)
The series solutions, which are harmonic in the respective regions,
are assumed to be:
X - a akP
cos
k=l
(111)
\m = b + ) (b p + b p ) cos k 9O £_j K ~K
k=l
In view of eqs . (108 and 109), which warrant displacement con-
tinuity and stress equilibrium conditions, the coefficients a , a, ,
and b , (k = 1,2,...) may be expressed in terms of b as:™* K K.
a = bo o
= 2
a3 =
ak =
2 b3/U+l)+
(k = 3,4,...)
-(1/4)]
b = - X, b- k I k(k = 3,4,...)
where
= (X-D/(X+D
(112)
47
Because of the anti-symmetry of the displacement component w with
respect to the £ axis, it may be shown readily that those coefficients
with even subscripts are zero. The condition that the lateral surface
is free from surface traction, eq. (110) , takes the form:
1 cos (k-1) 9 + X1p"k"1 cos (k+1) 9]
[(3+2v)p~2 cos 2 9 - 3p~4 cos 4 9]
U-D [ \ v S2 + U-iv)7\2]
k bR
k-1, 3, 5
sin (k-1) 9 + sin (k+1) 9]
[(3+2v) p"2 sin 2 9 - 3p~4 sin 4 9]
(113)
(2 + v) 5
-1(tan 6<;9<TT/2, OS^, T1=U5)
Next the coefficients b (k • 1,3,...) are obtained according toK
the boundary-point least-square method as described in Appendix A.
With the coefficients b, thus obtained, the constant B which
appears in eqs. (96 and 97) is calculated from the condition that the
resultant shear force is equal to the externally applied tip load Q:
il Zdy = Q (114)
48
Since the stress components in eqs. (97) satisfy equations of equili-
brium in the absence of body forces, the following relation must hold:
or
T1 = BE. x = - T1 - T1 (i=f,m) (115)zz,z i zx,x zy,y
T1 + T1 + BE. x = 0 (i = f,m) (116)zx,x zy.y i
In view of eq. (116), eq. (114) may be written as
• ci=f,m
= Y [I [(x T1 ), + (y T1 ), ] dx dyL JJ zx 'x zy yi=f,m A.
B Ei x dx
i=f,m A.
B Ei x dx
i=f,m A.
IE (117)
where A,, and A are the cross-sectional areas of the respective fiberf m - - -
and matrix regions and I is the weighted moment of inertia of the
cross section. From eq. (117), the constant B is readily obtained as
B = Q/IE (118)
where
49
* dx
i=f,m A.
Finally, the longitudinal thickness-shear flexibility S is obtained
from eq. (95) as
S55 = [Q/(2 6r)]/Yeff
rr i 2 -i= A TT, [%V (I -I ) - (A/I ) x ft +xy )dx dyl (120)
'•E x y y JJA
For an equivalent homogeneous beam with a rectangular cross
section, the longitudinal thickness-shear stiffness is given by
S55 = KA G55/(2^6r) (121)
where the shear coefficient K is obtained as (ref. 60)
K -'10 (l+v)/(12+llv) (122)
Thus, on equating eqs. (120) and (121), one obtains the equivalent
shear modulus G,-c as
x y
- (A/T ) f[ x (Xl+xy2) dx dy]"1 (123)y JJ
2.8 Transverse Thickness-Shear Stiffness
A typical repeating one-quarter cross section shown in figure 9 .
is considered. As a first approximation assuming that the Bernoulli-
50
Euler hypothesis holds, we make an elementary Jourawski-type mechanics-
of-materials analysis to obtain the shear stress and strain distri-
butions in the cross section due to the application of shear force Q
along the vertical boundary of the cross section. (See figure 9(a).)
Then the strain energy is calculated and Castigliano's principle is
applied to obtain the macroscopic shearing strain v . The transverseX
thickness-shear stiffness S.. is then obtained in terms of definite44
Integrals arising from the strain energy calculations.
Assuming that the cross section remains plane, one obtains the
flexural strain distribution as
€x - - a,x y (124)
where e denotes the flexural strain of an element located at a distanceX
y from the midplane, and ry, denotes the bending curvature of the mid-X
plane. The corresponding stress distribution is
Ovi = - ,<v y E (i=f,m) (125)X X !•
Summing the moment due to the stress distribution, one finds that
the flexural moment acting on the cross section is
o -(2/3) Em(u6r)
J[l+(X1-D(u6)HI '
M = \ (126)x
(2/3) Em (U6r)3 a,in
N
where
51
X1 = Ef/Em , 5 = x/r (127)
From equation (126) , the flexural stiffness of a strip Ax in
width is found to be
f (2/3) Em(u6r)3 [l+(X' -1) il6) ~3(1-|2) 3/2]
<*&l (128)
(2/3) E
In view of equations (125-128) , the flexural stress distribution
is now given by the expression:
- (Mx/D22) y E. (i-f,m) (129)
The thickness-shear distribution T is then obtained readilyxy
from the equilibrium of the forces acting on the strip. (See figure
U6r u&r
-f Co X] dy + f [a x] _.. dy = T Ax (130)J x j x y J u x Jx+Ax x yy y ,
Solving for T in equation (130) and using equation (126), one obtains
-1 P6*Txv = (A Mx/Ax) °22 J Ei y dyy
where
AM = [M ] - [M 1 (132)X X X+AX XX
Since the shear force Q = A M /Ax and the integral on the right-X A
hand side of equation (131) can be evaluated, the thickness-shear52
distribution is given by:
For
T = G vxy f xy
(Q /2D )EX X Ul
(Q /2D ) E r2 [<U6)2 - T12)]; (r2-y2)X X ul
(133)
and, for r<x<ur
Txy = GmYxy=(Qx/2Dx)(134)
In view of equations (133 and 134), that part of the strain
energy per unit z-length due to shearing stresses is readily cal-
culated.
U = (l/2)f I T v dx dys J J.• ^ xy xy
ff m
(135)
where
S/21 1 9 1/2 -?} • [(U6)J+U'-l)(l--n ) ' J dTl (136)
J {(8/15)(u6)5-(l-T12) [(u6)4-(2/3)(u6)2(l-Tl2)+(l/5)(l-T12)2]}-
53
•3 9 7/9 9T<W6) + U'-DU-TI) ' ] dT| (137)
Using Castigliano's theorem, one can compute the mean macroscopic
shearing strain y from equation (135) as
Yxy
= (3Qx/2ur) [2/(5 0^6) ](u-l)+(3/4) G ~ F 1 + ( 3 / 4 ) G ~ F (138)
The average transverse thickness-shear stiffness S// is given
by
B.. = Q /Y = KAG..44 xx xy 44
= (2ur Gm/3)[(2/5)(u-l)/(u6) +(3/4) (F 'Vp ]-1 (139)
where
X = G£/Gt m
For a homogeneous rectangular corss section, Cowper's shear
factor K is given by eq. (122). Thus, the equivalent transverse
thickness-shear modulus G,, is given by
G44 = S44/(2u6r K)
54
SECTION III
DAMPING ANALYSES
This section is concerned with the analyses leading toward the char-
acterization of dynamic properties of a single layer of roonof ilament
composites. Many solids, whether they are metallic or otherwise, exhibit
a damping ef fec t ; this phenomenon is essentially due to the dissipation
of energy associated with the deformation. It is convenient, especially
in the case of steady-state vibrational analysis, to represent the dy-
namic properties of the solid by the use of complex dynamic moduli .
For example, the major Young's modulus EI . may be considered to be of
the form
R Iwhere i = /^T , E^ is the storage modulus and Ej is the loss modulus,
since the latter is associated with that component of the strain 90
out of phase from the stress component which gives rise to the energy
dissipation (reference 64). Alternatively, equation (142) may also be
written as
E = E* (1+ig ) (143)il ii b
where g is referred to as the loss tangent which is related to theEll
storage and loss moduli by the equation,
55
g = (E.J/E *) = tan Y (144)&
Here the term, y , is the phase angle by which the sinusoidally varying
strain component lags behind the accompanying stress component on the
phase plane, and is referred to as the loss angle. (See Figure 10.)
In the following subsections, detailed analyses based on the results
of Section II are made to obtain the loss tangents associated with all
the stiffnesses necessary for the characterizing of the damping properties
of a single layer of monof ilament composite.
3.1 Introduction
As previously discussed in Section 1.1, one of the main advantages
that composite materials have over conventional homogeneous materials
is their macroscopic anisotropic nature which gives the modern structural
designer the ability to design stiffness and damping properties and strengths
to fit the requirements of the application by means of lamination. In the
dynamic analysis of a structure consisting of multiple layers of composites,
as in the case of elastic characteristics, damping characteristics of a
single. layer must be known beforehand in order to predict the dynamic
behavior of the laminated structure.
There have been numerous experimental investigations on damping
characteristics of sandwich and filamentary composite materials (ref. 8-19).
Analytically, Hashin (ref. 20-21) derived a correspondence principle for
the determination of complex moduli of viscoelastic composites (particulate
and filamentary). This correspondence principle is particularly suitable
when the elastic moduli are of a form explicit in terms of the moduli of
the constituent materials. However, Hashin's approach cannot be applied
to cases where the moduli are. given in terms of numerical elastic results.
56
Kimball and Lovell (ref. 22) observed that many engineering materials
undergoing sinusoidal motion exhibited energy losses which were proportional
to the square of the amplitude and independent of the frequency. Bert
et al- (ref. 13), in their investigation of damping in sandwich beams,
assumed Kimball -Love 11 type damping for the facing and core materials
and obtained good agreements between the theoretically-calculated and
experimentally-obtained values of the logarithmic decrement for free vibra-
tion.
It is noted that the ratio of the total damping energy dissipated per
cycle Uj to the total potential energy stored per cycle U can be related
to the logarithmic decrement 6 as follows (reference 65):
6 = (1/2) ln[l-(Ud/U)] (145)
For most structural materials, where the logarithmic decrement is small,
it may be approximated by
6 = (l/2)(Ud/U) (146)
In turn, the loss tangent g may be related to 6 by (See Appendix B for
details.)
g = (l/2n)(Ud/U) (147)
The total potential and dissipative energy per cycle of a solid under-
going sinusoidal motion are given by *
(148)
(149)
*Repeated subscripts denote summation where i,j = 1,2,3.
57
where fK. and e.. denote respective stress and strain amplitudes,
C, the damping coefficient, and V the total volume (fiber and matrix)d
occupied by the composite.
In performing the integration indicated in equations (148 and
149), the stress distributions are approximated by those obtained from
the elastic analyses of Section II. Inherently, the stress distributions
are dependent on the excitation frequency; however, for the frequency
range of interest here (well below any micro-scale resonance), the
stress distributions obtained from the elastic analyses of Section II
are expected to be valid.
For the monofilament composite element under consideration
here, with the exceptions of in-plane longitudinal shear modulus G,,ob
and the Poisson's ratio v,~» the following general procedure is adopted
for the calculation of loss tangent of the composite element:
1. First, with the composite element subjected to an appropriate
*loading , the strain energy is calculated for the respective fiber and
matrix regions (U and U ).
2. In view of equation (147), the damping energies for the re-
spective fiber and matrix regions are obtained as follows:
U* = 2n gi U1 (i=f,m) (150)
*By an appropriate loading, we mean the type of loading which
is appropriate for the property under consideration, i.e., longitudinal
tension for £,,> etc.
58
3. Then, the composite loss tangent associated with the pro-
perty under consideration is computed as
g = (l/2n) U/ U (i=f,m) (151)
i i
The determinations of the real parts of the complex moduli;
namely, the storage moduli; are carried out in an analogous manner to
that of Section II by simply replacing the elastic property parameters
with their respective counterparts in the complex moduli.
As for the determinations of the loss tangents for the in-plane
longitudinal shear modulus G,, and the Poisson's ratio VT -, , Hashin'sDO Lf.
correspondence principle is used. The equivalence of the correspondence
principle and the general procedure described above is substantiated
analytically for the case of the longitudinal Young's modulus E and
numerically for the case of the transverse Young's modulus E_2-
In the subsections that follow, detailed analyses are carried
out for the loss tangents corresponding to all of the stiffnesses
characterizing the composite properties.
3.2 Longitudinal In-plane Loss Tangents
Two loss tangents, namely gg and gG/i£> wiH De obtained in
this subsection. As previously discussed in Section 2.2, the major
Young's modulus E is obtained explicitly from the law of mixtures,
whereas the longitudinal in-plane shear modulus G,, is based on the
results of the elasticity analysis of Adams and Doner (ref . 46) .
59
Loss tangent §Eii associated with the Major Youns's modulus E.,,
In terms of the notations used in Section 2.2, the total strain energy
per cycle in the respective fiber and matrix regions are calculated as
follows:
Uf = (1/2) JJ af6l dx dy = (1/2) Afof6lAf
(152)
Um = (1/2) JJ Vl dx dy = (1/2) A^Am
In view of equations (152 and 150) , the total strain energy per cycle
in the composite and the damping energy per cycle are readily cal-
culated as follows:
(Afaf + AmOm)€l (153)
Ud = " (fifAf°f + SmVn)el (154)
where gr and g are the loss tangents associated with the longitudinalr m
Young's moduli of the fiber and matrix materials. The composite loss
tangent ggi-i associated with the major Young's modulus E ^ is now
readily calculated on substituting equations (153 and 154) into equation
(151).
= (8fVf
In view of equations (5 and 9), equation (155) may be written
in terms of volume fractions V, and V and X" as follows:f m
60
' Vf + Vm)/a' VV (I56>
where
as
X' = E R/E R (157)r m
D
The composite storage modulus EI1 is obtained from eq. (10)
E R = V,ER + V ER (158)11 f f m m
It is interesting to note that identical results for the
storage modulus and the loss tangent can also be obtained on utilizing
the elastic-viscoelast ic correspondence principle of ref. 21. Re-
placing the elastic moduli in the right-hand side of eq. (10) with the
corresponding complex moduli, and separating the real and the imagin-
ary parts, one obtains
E.. = (VCER+V ER)Cl + i (gcV,E
R+g V E*) /(VtER+V ER)
11 f f m nr Bf f f 6m m m' f f m m'
(159)
from which equations (156 and 158) readily follow. This substantiates
the equivalence of the correspondence principle and the formula (151).
Loss tangent gc^c associated with the in-plane longitudinal
Pshear modulus G,,. - As mentioned previously, the storage modulus G,,
DO DO
is approximated by the elastic analysis of Adams and Doner (ref. 46) .
To calculate the loss tangent &Gf.f. according to eq. (151) would require
61
lengthy numerical analyses for the determinations of the stress and
strain distributions. To avoid this, it is surmised here that the
results of ref. 47 may be empirically approximated by a much simpler
formula due to Hashin and Rosen (ref. 35), which is given here in
modified form as follows:
G66/Gtn = CV
(160)
where Cy,. is an empirical factor brought in here so that the shear
modulus as calculated by equation (160) coincides with that given
in ref. 46, X is the fiber and matrix shear-moduli ratio defined in
eq. (31), and Vf is the fiber volume fraction.
In view of the explicit expression of eq. (160), the loss
tangent %>&(.(* ^s readily obtained on replacing A. by its complex counter-
part.
\ = XR (1 + ig ) (161)
where
*/G*) (i+g g )/(i+8 2)r m (j.. (j O
f m m
?, = (gr - gr ) / (l+gr gr )Gf Gm Gf Gm
Substitution of equations (161 and 162) into eq. (160) yields:
(162)
62
2
CVf
{[XR( l -V f)4(l+V f)]2 + [\R(l-V f)gx]2} -1 (163)
66 m{gr [U-V,2)UR (1-g 2)+l] + 2\R(1+VL G f X
+ Vf } '
m
(164)
3.3 Transverse In-plane Loss Tangents
Based on the result of elastic analysis and the observation made
in section 2.3, two loss tangents ggoo and gvi2 associated with the in-
plane transverse Young's modulus £„„ and the major Poisson's ratio v,~
will be obtained as follows.
Loss tangent Sg associated with the transverse in-plane Young's
modu1us. - Owing to symmetry in the loading depicted in fig. 4, shear
stresses ^ and T vanish. Hence, the total strain energies per cyclej\z y
for the fiber and the matrix regions, respectively, are:
2.' i ' v~v 1^V'"2viax°v+2Txv ^dX dy
J- A y i *• y J
(i = f ,m) (165)63
where the stress components o ,O ,T are given by the equations (C-4 ,x y xy
5, and 6). In view of equations (150 and 165), the damping energies per
cycle are:
y]dx dy (i=f,m) (166)
A.
The loss tangent §£00 is tnen readily calculated from eq. (151).
n
The storage modulus £«„ is calculated from the first of equations (36)
by means of appropriate storage moduli of the constituent materials
corresponding to the particular frequency of excitation.
Loss tangent gvi „ associated with the in-plane major Poisson's
ratio. - Since the in-plane major Poisson's ratio v, ~ is related to the
constituent Poisson's ratios v and vf by a simple law-of-mechanical-
mixture formula, eq. (38), the complex Poisson's ratio v, is readily
obtained in a manner similar to that used for E •, , eq . (159), by the use
of Hashin's correspondence principle as follows:
(167)y til in J. J- ill It Im
where
R „ R . .. RV12 = Vf + Vm
g = (g V.v,R + g V v R)/(V,v,R+V v R)V , o V . - f f & v m m f f m m '12 f m
(168)
3.4 Longitudinal Flexural Loss Tangents
In this subsection are treated damping analyses for determining
64
the loss tangents §DII and ^Di? associated with the longitudinal and
Poisson flexural stiffnesses. The former is obtained according to eq
(151), whereas the latter is obtained by the application of Hashin's
correspondence principle.
Loss tangent goi-i associated with the longitudinal flexural
stiffness . - In view of eq. (42) derived previously in Section 2.4,
the strain energies per cycle in the fiber and matrix regions are
readily obtained as follows:
nf 2 P RU = a, E.. TTTz r
Um = {[63<ur)4/6] - (rrr4/32)j
(169)
Using eqs. (150 and 151), one can readily obtain the following
expression for the longitudinal flexural stiffness:
gD
{("UI-l)(n/32)+(&3U4/6)}- (170)
D
The storage stiffness D is readily calculated from eq . (46) with
the help of eq. (44) by replacing the static moduli and the Poisson's
ratios with their respective real parts of the corresponding complex
moduli and ratios.
Loss tangent gpi? associated with the Poisson flexural stiffness. -
According to Hashin ' s correspondence pr inciple , the complex Poisson
f lexura l s t i f fness D._ may be calculated from equation (50) by replacing
65
the elastic moduli and Poisson's ratios appearing on the right-hand
side of the equation with their respective complex moduli and Poisson's
ratios as follows:
2 r3 { J [FR
(171)
R Iwhere F (TJ) and F (T\) are the real and imaginary parts of the function
F(T|) defined in equation (51) . Separating the real and imaginary parts
on the right-hand side of equation (171), one readily obtains:
DR2= 2 Em r3[J [FR(TO-gE F^DJdTI + (1/3) [ (u&)
3-l]vR A Rj- (172)o m
= 2 ER Jo m
where
A = (I+im m
A = Real ( A)
m m m m
A = Imaginary ( A )
(U6) 3-l]vR A
m
2 2
m
2 2
'v ' J • Am m : m
(173)
> (174)
66
*» • [ l-\ ( 1-*v » + t2 \ *v Itn . tn
The loss tangent gDi o can now be calculated from eqs. (172-173)
to yield:
~ /^D12/D12
1§D12 l ^o \ F (71) + F <T° df | f<1 3 ^^ "L Vm
• {J (175)in jm
3.5 Transverse Flexural Loss Tangent
Owing to antisymmetry in loading with respect to the J\ axis
as depicted in fig. 6, shear stresses T again vanish as for the case
of the transverse in-plane Young's modulus £„„, Section 3.3. There-
fore, the total strain energy and damping energies per cycle are given
by the eqs. (165 and 166). The loss tangent gDoo and tne storage
Rstiffness D-« are obtained by a procedure similar to that described
in the first subsection of Section 3.3.
3.6 Twisting Loss Tangent
For a composite layer subjected to a pure twisting torque, all
the stress components except T and T vanish. Thus, the strainr xz yz
energy and the damping energy per cycle in the fiber and matrix re-
gions, respectively,are calculated from the following formulas:
67
[[ (T2 + T2 ) dx dy / (2 G.) (l=f,m) (176)J J x z yz ixz yzAL
2n gG u\ (i=f,m) (177)i
where the shear stress components T and T are as given by eqs.
(C-19 through C-22) for each typical composite element depicted in
fig. 7. With the strain energies and damping energies calculated
from eqs. (176 and 177), the loss tangent goA associated with the
twisting stiffness D,, is obtained readily from eq . (151).bo
3.7 Longitudinal Thickness-Shear Loss Tangent
In view of eqs. (97) , the strain energies per cycle for the fiber
and matrix regions are:
1)1 = IJ (Txz+Tyz)dX d^/(2 Gi)+ IJ az dX dy/<2 VA. A.1 (i=f,m) (178)
where the strain components are as given by eqs. (97). According to
eq. (147), the damping energies per cycle in the respective fiber and
matrix regions are therefore equal to:
"a ' 2" SG. II (TxZ+V>dlt d>'/(2 V
+ 2n gE JJ a2 dx dy 1(2 E.) (i=f ,m) (179)
68
The loss tangent ggss assoc*-ate<l with the longitudinal thickness-
shear stiffness is then calculated according to the general procedure
described in Section 3.1 with the help of eq. (151).
3.8 Transverse Thickness-Shear Loss Tangent
The strain energies per cycle for the fiber and matrix regions
may be readily calculated from the results of elastic analysis in
Section 2.8, eqs. (128, 129, and 135-137), as follows:
uf = ufs
(180)
um = ums
(181)
where the subscripts s and b refer to shear and bending, respectively;
F. and F_ are as defined in equations (136 and 137); and F_ and F, are
given by the following expressions:
F3 = J {(u-5)/[l + (X'-l)(u6)"3(l-?2)3/2]}2(l-F32)3/2 d£ (182)
69
= J
(183)
In view of equations (181 and 182) , the damping energies per
cycle in the respective fiber and matrix regions are equal to:
(184)
m
(185)"m
Finally, the loss tangent associated with the transverse thick-
ness-shear stiffness is calculated on substitution of equations (180,
2181, 184, and 185) into eq. (151). It is noted that Q , the square
of the shear force per unit z-length, cancels and thus the loss tangent
is expressed in terms of the loss tangents, moduli ratios, and Poisson's
ratios.
This completes the damping analyses for the determinations of
the loss tangents associated with all the stiffnesses pertinent to
the characterization of the damping behaviors of a single layer of a
monofilament composite. The results obtained herein are used in the
next section, Section IV, for the construction of the design curves and
comparisons of the numerical results with available analytical and
experimental data.70
SECTION IV
NUMERICAL RESULTS
In this section, numerical results as obtained from the foregoing
elastic and damping analyses, Sections II and III, are presented. First,
in Section 4.1, the results of the present elastic analyses are compared
with some available analytical and experimental results obtained else-
where as a verification of the present analyses. Secondly, in Section 4.2,
property data deduction procedures for some of the constituent materials
are briefly described. Then comparisons of the dynamic stiffnesses and
their associated loss tangents are made with the limited experimental
results which are available. Finally, in Section 4.3, the results of the
present analyses are summarized in the form of a set of design curves for
boron-epoxy composites, and in a tabulated form for boron-aluminum and
glass-epoxy composites. This set of design curves is particularly useful
in predicting the elastic and damping behavior of structural elements
consisting of one or more layers of monofilament composites (reference 63).
4.1 Comparison with Conventional Micromechanics Results
This section is concerned with the numerical comparisons of the
stiffnesses calculated from the present analyses with those obtained else-
where in order to assess the accuracy of the present analyses. Two aspects
of the comparisons to be considered here are:
71
1. Comparisons of the in-plane and thickness-shear stiffnesses
with those obtained from conventional micromechanics analysis
where the composite layer consists of many small fibers randomly
or regularly distributed throughout the entire cross section;
see fig. l(b) .
2. Comparisons of the flexural and twisting stiffnesses with those
deduced from the in-plane stiffnesses by the use of eq. (4).
Major Young's modulus E. - There have been many analytical in-
vestigations to determine the major Young's modulus E (refs. 1,39,47, and
48) ranging from a simple mechanics-of -materials analysis to a more sophis-
ticated elastic analysis. In all cases, however, it was demonstrated that
the effect of difference in the Poisson's ratios of the constituent materials
is negligibly small. In fact, Hill (ref. 47) showed by a variational method
that the rule of mixtures, eq. (11), is the lower bound. Therefore, for all
practical design purposes, eq. (11) is deemed sufficiently accurate. Further-
more, experimentally, the published data for Narmco 5505 boron-epoxy com-
posite (reference 64) gave values of E . to be 30.6 x 10 psi in tension and
34.0 x 10 psi in compression; whereas, the value of 30.3 x 10 psi was
obtained from eq. (11) by using nominal Young's modulus values of 60 x 10 psi
for boron and 0.5 x 10 psi for epoxy.
Major in-plane Poisson's. ratio V, ? . - Many analytical investigations
have shown that the major Poisson's ratio may be predicted by the rule of
mixtures, eq. (38), with sufficient accuracy. In particular, Abolin'sh (ref.
53) presented in detail the derivation of eq. (38) where the major Poisson's
ratio of the fiber v, may be allowed to be transversely isotropic with the
plane of isotropy normal to the fiber. However, in his derivation, no
72
allowance was made for the actual fiber cross-sectional shape. Within the
context of mechanics-of-materials theory, Bert showed that eq. (38) holds
for circular cross-section fibers (reference 65). Halpin and Tsai (reference
66) devised an interpolation method and applied it to the elastic numerical
results in a graphical form obtained previously by Hermans (reference 67) to
show that the numerical data can be empirically approximated by eq. (38).
As a further verification of eq. (38), the numerical results for v, 7, as
obtained from the second of eqs. (36), are shown in table I for various
fiber volume fractions. It is observed that, for all practical purposes,
the rule of mixtures, eq. (38), may be used for estimating the major Poisson's
ratio Vj~- Unfortunately, comparison with the experimental result (ref. 64)
showed that the theory predicted a much lower value of 0.30 against 0.36
for Narmco 5505 boron-epoxy composite with a fiber volume fraction of 0.50.
This is attributed mainly to the discrepancies in the nominal constituent-
material data used for calculation.
Minor Young's modulus E_-. - The minor Young's modulus E.- as
calculated from the first of eqs. (36) and those obtained by other investi-
gators are plotted against Young's modulus ratio E../E for various fiber
volume fractions for comparison as shown in figure 11. Foye has summarized
the results of analytical investigations on the various estimates of the
transverse properties of filamentary composites (ref. 40). It was concluded
that, in general, the transverse stiffness is relatively insensitive to the
types of models chosen. The specific analytical results for E^j chosen
here for comparison are those due to Tsai (reference 68) and Adams and Doner
(ref. 56). In fig. 11, it is observed that the present theory predicts
values for £„„ which are consistently lower than those of Tsai and of Adams
73
and Doner. However, it must be.remembered that in their analyses, a
square-array composite model was used. Thus, the free-edge effect was
completely eliminated. In the present analysis, a single-layer model
was chosen in order to obtain a more realistic representation of the
layer property on the micro-scale. Hulbert and Rybicki (reference 69)
showed in their recent paper that the free-edge effect for some filamentary
composites may range from 9.870 (for boron-epoxy) to 5.0% (for boron-
aluminum) at a fiber volume fraction of 0.50. It is believed that this
accounts for the lower estimates of the present analysis shown in fig. 11.Chen
and Cheng (ref. 38) chose a hexagonal-array model and gave some numerical
results for an E glass-epoxy composite and showed that their result from
the elastic analysis is well within the previous results obtained by
Hashin and Rosen (ref. 35) and Dow and Rosen (reference 70). The present
analysis also gave a result that is bounded by the results of the above
two references (refs. 35 and 70).
In-plane longitudinal shear stiffness G,,. - Adams and Doner (ref.OP
46) determined the in-plane shear modulus G,, using a square-array model
and compared their results obtained from an over-relaxation procedure with
other analytical results (refs . 35, 38, and 71) and a limited number of
experimental resul ts . Excellent agreement was observed between their re-
sults and the complex-variable elastic solution of Wilson and Goree (ref .
71), whereas comparison wi th the analyt ical work of Chen and Cheng (ref .
38) and that of Hashin and Rosen ( re f . 35) showed some discrepancy due to
the hexagonal-array model used by these investigators. A fai r agreement
is observed between Adam and Doner 's results and that of experiment;
theoretical values being consistenly lower by 5.37» for boron-epoxy, 6.7%
74
for carbon-epoxy, and 13.5% for glass-epoxy composites. From ait engineering
design point of view, an explicit formula such as the one given by Hashin
and Rosen ( ref. 35) would be highly desirable. For this reason, an
empirical correction factor Cy*: was introduced in Hashin and Rosen's formula
in order to bring their results to coincide with that of Adams and Doner
(ref. 46).
Longitudinal flexural stiffness DI . - In eq. (48), it is observed
that the ratio E^. /E,, represents a measure of flexural stiffness ef-
ficiency which is less than unity for all realistic values of the parameters.
In effect, this means that, unlike those composites containing many small
fibers, the longitudinal flexural stiffness D.... calculated from eq. (4)
using the in-plane major Young's moudlus would be highly unconservative.
A lower bound for the equivalent Young's modulus can be estimated readily
from a "netting type" analysis in which the contribution of the matrix
material to the composite flexural stiffness is completely neglected. This
leads to the expression, originally derived by Margolin (reference 72).
Analysis (^) (186)
In table II are shown the flexural stiffness efficiency, E /E , for
various constituent-material combinations, aspect ratios 6 , and volume
fractions (reference 73) . It is noted that the effect of 6 on the flexural
stiffness efficiency is much stronger than those of a and V .
Flexural stiffness efficiencies for various constituent-material
combinations and fiber volume fractions are plotted as shown in figure 12
for square typical elements, i.e., a square array of fibers. For example,
75
in the case of a boron-epoxy monofilament composite with a fiber volume
fraction of 0.50, conventional theory, eq. (4), predicts a value for
flexural stiffness D... that is twice as large as the actual flexural
stiffness for a single layer. Also shown in the figure as dashed lines
are lower-bound estimates for fiber volume fractions of 0.20 and 0.70.
It is seen that the lower-bound estimate, eq. (186), increases in accuracy
as the fiber becomes stiffer (large Ef/E ratio), and as the fiber volume'
fraction increases.
Poisson flexural stiffness D 2> - The values of Poisson flexural
stiffness as calculated from the present analysis, eq. (50), are compared
with those calculated from eq. (4) by the use of in-plane stiffnesses and
Poisson ratios. Again, it is found that Poisson flexural stiffnesses cal-
culated in a conventional fashion are much greater than those of present
analysis as demonstrated in Table III. For all of the composites compared,
it is observed that for a low Ef/E ratio (<6) and low fiber volume fraction
(<0.40), Dj» as calculated from eq. (4) is in fair agreement, the difference
being less than 7%. However, for a high-stiffness-fiber composite such as
boron-epoxy, the conventional formula, eq. (4), over-estimates by as much
as 40% or more at a fiber volume fraction of 0.60.
Transverse flexural stiffness DO?- ~ 1° order to assess the trans-
verse flexural stiffness efficiency in an analogous manner as that of
longitudinal flexural stiffness, the ratio of the value of D~? as obtained
from eq. (59) and that obtained from eq. (4) is plotted against the Ef/Em
ratio for various fiber volume fractions as shown in figure 13. It is
observed that the conventional estimates from eq. (4) are again on the
unconservative side. However, variance in the transverse flexural rigidity
76
efficiency due to fiber volume fraction is relatively weak. This is
perhaps due to the rather insignificant stiffening effect that the fiber
has on the transverse in-plane and flexural stiffnesses. For a boron-
epox
to note the similarity and symmetry in the ¥ - value in the first and
the second quarter-sections. It is also of interest to note the decrease
in the V - value in the third quarter-section that is farthest from the
origin. This means that for a layer containing many fibers, the
torsional rigidity (not the layer twisting stiffness) can be approxi-
mated as the number-of-fiber multiples of the torsional rigidity of a
slqgle element.
Figure 16 shows the twisting stiffness ratio D,,/D,, for variousDO OO
values of fiber volume fractions and shear modulus ratio G./G .f m
Comparisons of the twisting stiffnesses for a square single
element cross section calculated from eq. (84) and eq. (4) are tabulated
as shown in Table IV. It is apparent that a twisting analysis is a must
in predicting the layer-twisting stiffness.
Longitudinal thickness-shear stiffness G ,.. - For a small-fiber
composite or parallel laminates consisting of many layers, it is generally
accepted that the longitudinal thickness-shear modulus G,.,- is equal to the
in-plane longitudinal shear modulus Gfi, (references 75 and 76). However,
in the case of a single-layer composite with only a single row of fibers,
the longitudinal thickness-shear modulus G,.,- is expected to be greater
than the in-plane shear modulus G,, due to the shear-stiffening effect of
the fiber. Bert used an approximate Jourawski-type shear theory to pre-
dict that the ratio G ,,/G,, may vary from 2.86 for boron-aluminum to 37
for boron-epoxy composites with a volume fraction of 0.482 (ref. 73). In
the present more refined analysis, this ratio is found to vary from 1.5
for boron-aluminum to 16.2 for boron-epoxy composites with a volume fraction
of 0.5 .78
Numerical results for the longitudinal thickness-shear imxlulu;;
are summarized as shown in figure 17 for various volume fractions and
constituent-material combinations.
Transverse thickness-shear modulus G... - The transverse thick-44
ness-shear modulus G,, is plotted against volume fractions for various
constituent-material combinations as shown in figure 18. Comparison with
the analytical results obtained by Heaton (ref. 75) showed that fair
agreement is observed for fiber volume fractions below 0.5, but at higher
fiber volume fractions, 0.6 say, the present estimate for boron-epoxy
composites gave a 14% higher value for G,,. The discrepancy is attributed
to the differences in the models chosen for the analyses; Heaton's model
being that of a multi-fiber square array.
4.2 Storage Moduli and Associated Loss Tangents.
Prior to evaluations of the dynamic stiffness and damping be-
havior of a layer of a monofilament composite characterized by nine
stiffnesses and a Poisson ratio with their respective associated loss
tangents, accurate dynamic constitutive properties of each constituent
material must be known. A survey of the literature revealed that
numerous experiments have been made to determine damping characteristics
of glass (references 77-80) , epoxy (ref. 9), and aluminum (references
81-83). However, apparently no such data are available on boron. Because
of different experimental techniques and perhaps slight differences in
material compositions in the specimens, the damping properties obtained
by these investigators do not always correlate with those obtained for
the composite specimens. Therefore, it would be necessary to have avail-
79
able good data for the constituent-material properties for the micro-
mechanics prediction of the composite macroscopic properties. However,
sometimes this may be difficult to obtain experimentally, for example
due to frailty of fibers in the filamentary composites or nonlinear
effects (see Appendix D) .
In view of this, a scheme for obtaining in-situ constituent
material properties from tests on composites may be necessary. Some
successful attempts at deducing such constituent-material properties
were reported by Papirno and Slepetz (reference 84) and Bert (reference
85) for static properties. Therefore, this deduction procedure was
used in the present investigation properties to obtain the dynamic
properties of some of the constituents from the test data on filamentary
composites when necessary.
To characterize the isotropic behavior of the material completely,
two independent moduli and their associated loss tangents must be known.
For the subsequent data deduction, it is assumed here that each material
behaves elastically in dilatation. With this assumption and the knowledge
of the Young's modulus and associated loss tangent, the second pertinent
modulus (shear modulus or Poisson's ratio) and its associated loss
tangent may be readily obtained.
The dynamic Young's modulus and associated loss tangent for boron,
epoxy, E glass, aluminum alloy 2024-T3, and aluminum alloy 6061 are
summarized as shown in figures 19-23. Data for E glass (fig. 21) were
obtained from ref. 79; for aluminum 2024-T3 (fig. 22), from ref. 81;
for aluminum 6061 (fig. 23), from refs. 81 and 8; and curve B for epoxy
(fig. 20), from ref. 9.
80
Curve A for epoxy (fig. 20) was deduced from the experimental
data on glass-epoxy filamentary composites by Mazza et al. (reference
86); and the data for boron (fig. 19) were deduced from curve A and the
experimental results on boron-epoxy filamentary composites of the
same reference.
A quick comparison showed that the prediction of the loss
tangent associated with the transverse Young's modulus for glass-epoxy
is in good agreement with the experimental results of ref. 9, both vary-
•
ing from 1% to 3% for the frequency range between 20 and 2000 Hz.
The same comparison for boron-epoxy filamentary composites also
indicated excellent agreement on the prediction of the loss tangent
associated with the transverse Young's modulus; in both cases, ref. 86
and the present analysis, the value of loss tangent varies between 1.6
and 2.0% in the frequency range 20-400 Hz.
Pertinent data for the complete characterization of the con-
stituent properties are summarized in Tables V-IX.
4.3 Design Curves and Tables - Storage Moduli and Associated Loss
Tangents Versus Frequency for Various Fiber Volume Fractions
The results of the present analyses are summarized in the form
of design curves for a boron-epoxy filamentary composite as shown in
figs. 24-33 for the frequency range 50-2000 Hz. and the fiber volume
fractions V = 0.4, 0.5, and 0.6. In application, the curve A series
should be used for better predictions of the composite stiffnesses
and associated loss tangents; the Curve B series is included for com-
parison purposes only.
81
In Tables X-XX1X are listed all the pertinent dynamic stiffnesses
and associated loss tangents for the characterization of the layer
properties of boron-aluminum and E glass-epoxy composites for the
same ranges of frequency and fiber volume fractions.
82
V. CONCLUSIONS
Elastic and damping analyses resulting in determination of
all pertinent stiffnesses and associated loss tangents for the
characterisation of the elastic and damping behavior of a mono-
filament composite were carried out.
The numerical results obtained for the stiffnesses and
associated loss tangents compared favorably with some existing
analytical and experimental results for some typical filamentary
composites, such as, boron-epoxy, boron-aluminum, E glass-epoxy.
The results of the flexural and twisting stiffness analyses
showed that these properties cannot be deduced accurately from the
in-plane-properties, and, thereby, the necessity for such analyses
for a monofilament composite layer.
The assumption of Kimball-Lovell type damping was shown to
be equivalent to the elastic-viscoelastic correspondence principle
for the case of the in-plane longitudinal stiffness.
The results of this investigation were summarized in a set
of design curves for a boron-epoxy composite, and in a set of design
data tables for boron-aluminum and E glass-epoxy composites. The
former were applied to the problem of predicting resonant frequencies
nodal patterns, and damping ratios for laminated boron-epoxy plates
83
(references 6k and 87) and achieved excellent agreement with available
experimental results, for six different plates (ref. lit).
Recommendations for future investigation. - For future re-
searches, the following topics are suggested:
1. Experimental characterization of the complete set of dynamic
stiffness and damping properties of various filamentary
composite materials of technological importance.
2. Analytical investigation of the viscoelastic behavior of
composite materials with thermo-mechanical coupling.
3. A unified viscoelastic analysis for filamentary composite.
84
APPENDIX A
BOUNDARY-POINT LEAST-SQUARE METHOD
Numerous approximate methods are available for the solution of
boundary-value problems. To name a few, there are the Rayleigh-Ritz,
Galerkin, Kantorovich, finite element, relaxation, and collocation
methods. Of these methods, especially with the availability of modern
digital computers, probably the boundary-point least-square version
(ref. 5) of the collocation method is the most efficient for solution of
mixed boundary-value problems, such as those investigated in Section
II. The main useful features of the method are:
1. It may be applied to mixed boundary-value problems with re-
lative ease.
2. The assumed solution may be made to satisfy the boundary conditions
at a set of sufficiently dense points in the sense of minimiz-
ing the square error; hence the solution may be made independent
of the number of boundary points chosen.
In general then, the solution is reduced to the satisfaction of a set
of overdetermined algebraic simultaneous equations
AX = B (A-l)
where 7( >mx ncoefficient matrix (m>n), X -• n-dimension column vector
of unknown coefficients, B = n-dimension column vector of prescribed
85
boundary values, m = number of chosen boundary points, and n = number
of unknown coefficients.
2Then the mean-square-error matrix (E ) for equation (A-l) is given
as
2 *+** *N* T1 ***** «•/
E = (AX-B) (AX-B) (A-2)
where the superscript T denotes the transpose of the matrix quantity
which it follows.
On minimizing equation (A-2) with respect to X, one obtains
(XTA)X = (ATB) (A-3)
or
A*X" = B* (A-4)
where A is an nxn matrix given' by
A = A1^ (A-5)
and B is an n-dimension column vector given by
B = Tk1"! (A-6)
Finally, the solution-coefficient vector X that minimizes the square
error is obtained readily from equation (A-4) by using a number of standard
computer scientific subroutines. However, care must be taken in the choice
86
of appropriate forms of the stress functions and in the choice of
boundary points to avoid any boundary points at which the prescribed
boundary values are identically satisfied.
87
APPENDIX B
MODELS AND MEASURES OF MATERIAL DAMPING
Bl. Mathematical Models for Material Damping
Internal friction or damping in materials can be caused by a variety
of combinations of fundamental physical mechanisms, depending upon the
specific material. For metals, these mechanisms include thermoelasticity
on both the micro and macro scales, grain boundary viscosity, point-
defect relaxations, eddy-current effects, stress-induced ordering, inter-
stitial impurities, and electronic effects (ref. 7). According to
Lazan (ref. 7 ), little is known about the physical micromechanisms
operative in most nonmetallic materials. However, for one important class
of these, namely polymers and elastomers, considerable phenomenolo^ical
data have been obtained. Due to the long-range molecular order associated
with their giant molecules, polymers exhibit rheological behavior inter-
mediate between that of a crystalline solid and a simple liquid. Of
particular importance is the marked dependence of both stiffness and damp-
ing on frequency and temperature.
The purpose of developing, a mathematical model for the rheological
behavior of a solid is to permit realistic results to be obtained from
mathematical analyses of complicated structures under various conditions,
such as sinusoidal, random, and transient loading. According to reference
7 , as early as 1784 Coulomb recognized that the mechanisms of damping
88
operative at low stresses may be different than those at high stresses.
Even today, after more than 2500 publications on damping have appeared,
major emphasis is placed on linear models of damping for several reasons:
they have sufficient accuracy for the low-stress regime and linear analyses
are computationally more economical than nonlinear ones.
The simplest mathematical models of Theological systems are single-
parameter models: (1) an idealized spring, which exhibits a restoring
force linearly proportional to displacement and thus displays no damp-
ing whatsoever, and (2) an idealized dashpot, which produces a force
linearly proportional to velocity. Obviously, neither of these models
are very appropriate to represent the behavior of most real materials.
The next most complicated models of rheological systems are the
two-parameter models: (1) the Maxwell model, which consists of a spring
and dashpot in mechanical series, as shown schematically in figure B-l(a);
and (2) the Kelvin-Voigt model, which is comprised of a spring in
parallel with a dashpot, as shown in figure B-l(b). The Maxwell model
is a fair approximation to the behavior of a viscoelastic liquid. How-
ever, as a model for a viscoelastic solid, it has several very serious
drawbacks (ref. 7) ; there are no means to provide for internal
stress and for afterworking. The Kelvin-Voigt model overcomes these
deficiencies and is a first approximation to the behavior of a viscoelastic
solid. However, it has the following disadvantages (ref. 7): there
is no elastic response during application or release of loading, the
creep rate approaches zero for long durations of loading, and there is
no permanent set irrespective of the loading history.
89
It should be mentioned that the Kelvtn-Voigt model is the simplest
one which permits representation as a complex quantity when subjected to
sinusoidal motion. To show this, one can write the following differential
equation governing the motion of a single-degree-of- freedom system con-
sisting of a sinusoidally excited mass attached to a Kelvin-Voigt element:
. . . . ,_ , >.mu+ cu + ku = Fe (B-l)
where m = mass, c = viscous damping coefficeint, k = spring rate, F H
exciting force amplitude, iu s circular frequency of exciting force,
u = displacement, i =/-\~ , t 2 time, and a dot denotes a derivative
with respect to time. Assuming that sufficient time has passed for the
"ktransients to die out, we can write the steady state solution of equation
(B-l) as follows:
u = u ei(U>t - *>- J [ (k-m*2) + iuc]'1 eiu)t (B-2)
where cp = phase angle between the response (u) and the exciting force,
and 7i £ displacement amplitude.
It is noted that the terms containing Kelvin-Voigt coefficients k and
iu)c can be grouped into a single Kelvin-Voigt complex stiffness (k) as
follows:
It can be shown that they do die out for a mechanical system, for which
c, m, and k are all positive quantities.
90
k = k + iiuc (B-3)
Alternatively, the Kelvtn-Voigt element coefficient could have
been grouped into a single complex damping coefficient (c ) as follows:
c = c - (i k/co) (B-4)
The force (F.) in a dashpot is given by
Fd = c u = icucuei(U)t ' *> (B-5)
The energy dissipated per cycle (U,) in a dashpot undergoing
sinusoidal motion can be calculated as follows:
f p - n u ) 2Fd du = Fd u dt = ncum (B-6)
In 1927, Kimball and Lovell (ref. 22) observed that many
engineering materials exhibited energy losses which were contradictory
to equation (B-6). Specifically, they found that U, was proportional
~2to u but independent of co, i. e.
(B-7)
~Later work by Wegel and Walther (reference _>8) also showed that U , « "u
but C, was a weak function of CD. Still later, for stresses below the
fatigue limit of the material, Lazan (references 7,89 ) showed that IK <* 7i
and C' was practically independent of to.
91
Equating the energy dissipated per cycle in the Kimball-Lovell
material, equation (B-7), to that in the dashpot, equation (B-6), one
obtains
C' = TTCU) (B-8)d
To utilize the Kimball-Lovell observation in practical structural
dynamic analyses, it was desirable to have an expression for the as-
sociated damping force, i.e. an equation analogous to equation (B-5),/
which governs a dashpot. According to Bishop (reference 90) this was
first done by Collar. Combining equations (B-5, B-8), one obtains the
following "frequency-dependent damping" relation:
Fd = (b/cu) u (B-9)
where b is a constant given by
b = CJ/TT (B-10)
The kind of damping represented by equation (B-9) has been called fre-
quency-dependent damping, since the usual dashpot coefficient c is now
replaced by the quantity b/tu.
For the damper represented by Eq. (B-9), it is convenient to replace
k in the undamped system by the Kimball-Lovell complex stiffness
(reference 91):
k' = k + ib (B-ll)
where it is now noted that both k and b are assumed to be independent of
frequency. This representation has been used extensively in aircraft
92
structural dynamic and flutter analyses (references 92,93).
An alternative to equation (B-ll), is to use the concept of a complex
damping coefficient, originated by Myklestad (reference 94), in which the
spring constant is replaced by
k" = Cieim (B-12)
where C, and tn are constants.
Although Kimball and Lovell's original work was based on data
obtained during steady-state sinusoidal motion, the models represented
by equations (B-9, B-ll, B-12) have been applied to free vibrations as
well (refs. 90, yi ,95). To alleviate the difficulty of the interpreting of
m in equation (B-9) for the case of free vibration or for multiple-fre-
quency forced vibration, Reid (reference 96) suggested the following form:
Fd - b| u/u| u (B-13)
where the bars denote that the absolute value of the quantity between
them is to be used.
In summary, four different versions of material damping have been
discussed. In terms of the differential equation for free vibration,
they may be written as follows:
mil + (b/iu) u + ku = 0 (B-14a)
mu + (k + ib) u =0 (B-14b)
mil + C^e^u = 0 (B-14c)
mu + b | u/u | u + ku = 0 (B-14d)
93
The models represented by equations (B-14) have been criticized
by many investigators for various reasons:
1. In equation (B-14a), the interpretation of uu is dubious (refer-
ences 96,98). Milne (reference 97) suggested that it is associated with the
imaginary part of the pair of complex roots, but went on to state that
there is no clear justification for this interpretation.
2. Equations (B-14b) and (B-14c) are equations with complex coef-
ficients and the meaning of this is not clear (refs. 95, 9/) . Further-
more, although they have complex exponential solutions, neither the real
nor imaginary parts alone are solutions (refs. 97, 9&).
3. Equation (B-14d) is a nonlinear differential equation, due to
the behavior of | u/ii | (ref. 97).
4. None of the models represented by equations (B-14) can be sim-
ulated, even on a conceptual basis, on an analog computer (refs.
96, 98 ).
5. The model represented by equation (B-14a) does not meet the
Wiener-Paley condition (references 99,100) of causality for physically
realizable systems, as was shown in references 98,102-103.
6. Equation (B-14b) fails to give the proper relations of a
damping force that is proportional to displacement and in phase with
velocity. This can be alleviated by use of a more unwieldy expression
proposed in references 104,105.
Incidentally reference 106 claimed that none of the equation
(B-14) models result in energy dissipation that is independent of
u) (the reason for abandoning the Kelvin-Voigt model) . However, an error
in this reasoning, which makes it invalid, was pointed out in reference 107.
94
It can be shown that the sinusoidally forced vibration version of
free vibration equations (B-14a,b,c) are exactly equivalent. Probably
the most popular form for writing this is as follows:
~- iu)tmil + (k 4- ib)u = Fe (B-15)
The major criticism of the use of equation (B-15) is that it results
in a conventionally defined magnification factor (see Section B2), correspond-
ing to zero frequency, which is not equal to unity for g 0 (ref . 90) .
This difficulty can be eliminated by redefining the magnification factor as
follows:
MF' =
where
u' =st
and k1 is the stiffness coefficient associated with the total in-plane force
amplitude, i.e.
k1 = (k2 + b2)^
Thus,
MF1 = (k2 + b2)%/[k-mu)2)2 + b2]^ = (1 + g2A[(lVVu>n2)2 + g2]^
The major advantages of using the equation (B-15) model for steady-
state yibrational and flutter analyses are as follows:
1. The analysis is considerably simplified in comparison with that
for viscous damping, as pointed out in reference 108.
2. The analysis is linear.
3. The complex-modulus concept has long been in common use, especially
95
in connection with measurement of the damping properties of elastomers,
polymers, etc. (reference 107).
4. The complex-stiffness approach has been used very successfully
in flutter analysis for approximately three decades (refs. 92,93 ,107 ,109 )
In view of these considerations, the complex-stiffness approach is
used in the main portion of the present report. However, for completeness
and comparison, a number of other more complicated approaches are also dis-
cussed in this section.
To overcome some of the deficiencies of the Kelvin-Voigt and Max-
well models, they were combined in various ways to obtain the three-para-
meter models shown in figure B-l(c) and (d). It can be shown (reference
110) that by properly selecting the values of the coefficients, the two
models can be used interchangably. In other words, the model repre-
sentation is not unique. In fact, both representations have been called
the "standard linear solid", "standard linear material," "simple an-
elastic model", or "standard model of a viscoelastic body" (references
111-114)- Unfortunately, few materials have been characterized by the use
of the standard linear solid. Perhaps the most extensive characterization
has been carried out for flexural vibration of 2024-T4 aluminum alloy:
by Granick and Stern (reference 82,115) in air and by Gustafson et al.
(ref. 81) in vacuo.
Obviously one can go on from a three-parameter model to a four-
parameter one, etc. Continuing this process, one obtains two well-
known models (ref. Ill): the Kelvin chain, shown in figure B-2(a),
and the generalized Maxwell model, shown in figure B-2(b). The be-
havior of such systems can be written in either differential or integral
form, as discussed in detail in reference 111. However, the complexity of
96
such a model has limited its use both experimentally (in characterizing
engineering materials) and analytically (in performing dynamic analyses).
Thus, for engineering applications, there is a continuing search for
models which are simple, yet represent the behavior of real materials
with sufficient accuracy.
A relatively simple model, which is somewhat similar to the generalized
Maxwell one, is due to Biot (reference 116);see figure B-2(c). The number
of simple Voigt elements in this model is allowed to increase without bound,
so that the damping force is represented by the following expression:
rtF = gj Ei [-e(t-T)](du/dT) dT (B-17)
where T is a dummy variable; e ,g = parameters, and Ei(u) is the exponential
integral
P~uEi(u) = (eJ o
Caughey (ref. 98) made a detailed study of Biot's model for both
free and forced vibration. He showed that for uu/e > 10, the energy dis-
sipated in Biot's model is within 4% of being independent of frequency (u>)
and thus essentially depends only upon the square of the displacement
amplitude. Milne (ref. 97) studies the Biot model by means of the con-
volution integral. . ..
Neubert (reference 117) introduced a variant of the Biot model, in
which a different distribution function for the local stiffness-damping
ratio is used. Milne (ref. 97) also studied this model via the convolution
integral. Milne introduced a new synthesized model of his own. However,
97
the main conclusion of his investigation was that, for practical engineer-
ing purposes, the choice of a rheological model is not critical, provided
that the range of constant damping is kept the same and the damping is
sma11.
The linear hereditary theory of material damping was originated in
1876 by Boltzmann (reference 118). In this theory, the energy loss is
attributed to the elastic delay by which the deformation lags behind
tne applied force. It is called a hereditary theory because the in-
stantaneous deformation depends upon all of the stresses applied to the
body previously as well as upon the stress at that instant. The damping
force is given by
• <J-r
u (T ) dr
where t = actual time, T = an instant of time (dummy variable), u =
displacement, and $ = hereditary kernel or memory function. Often the
hereditary kernel depends upon the difference (t-T) only; then equation
(B-19) becomes:
•r-J -00
Fd = I *(t - T) U(T) dT (B-20)
It is most advantageous to determine the hereditary kernel from^
experimental data. It has been found to be a monotonically decreasing
function which can be represented mathematically as follows:
n$(t) = £ A.e'V (B-21)
Such a system is said to have a heredity of degree n and A. and or.
98
are called heredity constants. Hobbs (ref. 112) lias shown that a first
degree hereditary model is equivalent to a simple anelastic model
(standard linear solid) .
Volterra (reference 119) has presented a method of determining the
hereditary kernel from material response to either suddenly applied
loading or to sinusoidal excitation. He also presented plots of mag-
nification factor and phase shift versus frequency for a wide range of
parameters of a single-degree-of-freedom system with first-degree
hereditary damping. For certain combinations of the parameters, the
magnification and phase characteristics are quite different from that
of a viscously damped system; yet for certain other combinations, the
characteristics are quite similar.
Numerous nonlinear mathematical models have been proposed to per-
mit better correspondence between theory and experiment. However, all
of them, by their very nonlinear nature, are more complicated to apply
in structural dynamic analyses of practical engineering systems. Perhaps
the simplest one is damping energy per unit volume and per cycle pro-
portional to stress to a power (ref. 7 ):
Ud = Cd^m (B-22)
where GJ and m are material constants and a is the cyclic stress
\amplitude. It is noted that m = 2 corresponds to the Kimball-Lovell re-
lation (linear theory) discussed previously. It has been found that m
varies from 1.8 to 6.0, generally being near 2.0 at low stress amplitudes.
Tne hysteresis loop associated with the complex-modulus model,
equation (B-ll), is elliptic in shape; see figure B-3(a). However,
99
the hysteresis loops determined experimentally have sharp corners at both
ends and are nearly linear in the low-stress, low-strain region, as shown
in figure B-3(b). According to ref. 7 (page 97), in 1938 Davidenkov
proposed a nonlinear mathematical model which results in a similar shape
of hysteresis loop. Further work on this class of model has been carried
out by Pisarenko (reference 120) .
Rosenblueth and Herrera (reference 121) proposed a nonlinear model
which eliminates the causality difficulties of the complex-modulus model.
Chang and Bieber (reference 122) introduced a nonlinear hysteresis model
in which there is no hysteresis damping unless the displacement amplitude
exceeds a certain threshold value.
B2. Measures of Material Damping
In this section, various definitions of damping are discussed in
the context of a complex-modulus material.
Energy Dissipation Under Steady-State Sinusoidal Vibration. - Energy
dissipated per cycle (U.) in the form of internal frictional heating is
one measure of damping. Howeve'r, this quantity depends upon the size, shape,
and dynamic stress distribution (which in turn, depends upon the particular
mode of vibration). In view of the above difficulties, the specific damping
energy (U, ) is usually considered to be a more basic property of the
material, rather than the structure. The U, is defined as the damping energy
per cycle and per unit volume, 'assuming a uniform dynamic stress distribution
throughout the volume considered. Thus, the total damping energy is
Ud = JV Udv dV (B'23)
100
where V = volume. The usual units of U, are in-lb/cvcle and of U, ,a • dv
3in-lb/in -cycle.
Resonant Magnification Factor Under Steady-State Sinusoidal Ex-
citation. - The resonant magnification factor (KMF) is defined as the
dimensionless ratio of the response at resonance to the excitation,
where both the response and the excitation must be specified in the
same units (see figure B-4) . These quantities may be in units of dis-
placement, velocity, acceleration, or strain. Unfortunately, the re-
sonant magnification factor is dependent upon the structural system con-
figuration as well as upon the damping property of the material, so that
it is considered to be a system characteristic, rather than a basic material
property.
Incidentally RMF is not applicable to nonlinear systems, since then
it depends upon the excitation level. (In a linear system, RMF is independ-
ent of the level of excitation.)
Bandwidth of Half-Power Points Under Steady-State Sinusoidal Excitation,
The separation (OJ^-ULJ,) between the frequencies associated with the half-
power points increases with an increase in damping (see figure B-5) and thus
can be used as a measure of damping. A more meaningful definition is to
normalize by the associated resonant frequency (UD ), i.e. use the dimension-
less bandwidth given by
Ttiis measure is the basis for determination of damping by the original
Kennedy-Pancu method (reference 123) .
The quality factor Q is defined as the reciprocal of the dimensionless
101
bandwidth.
Derivative of Phase Angle with Respect to Frequency, at Resonance. -
This measure is the basis for determination of damping by an improvement
(reference 124) of the Kennedy-Pancu method.
Loss Tangent Under Steady-State Sinusoidal Excitation. - Applying
the complex-stiffness (see Section Bl) to the material property represent-
ing stiffness, namely the Young's modulus (E), we obtain
E - ER(1 + ig) (B-24)
*Thus, the loss tangent is defined as follows:
g H E X /E R (B-25)
I ** R ***where E = loss modulus and E is called the storage modulus.
Referr ing .to figure B-6, we obtain the following relation:
g = tan y = E X / E R (B-26)
or
= arctan E /E (B-27)
*Also known as the "loss coefficient", "loss factor", or "damping
factor".
**Also sometimes called the "dissipation modulus."
***Also sometimes called "elastic modulus" or "real modulus."
102
The quantity y is called the loss angle and equation (B-26) explains
the origin of the term loss tangent for g.
,') Cyclic Decay of Free Vibrations. - In a linear system, free vibrations
decay exponentially (see figure B-7). The larger the damping, the faster
is the decay. Thus, the logarithmic decrement 6 is defined as follows:
6 s £n (a../a_. .,) (B-28)
where £n s natural logarithm.
For a power-law material, eq. (B-22), to have 6 independent of
amplitude, m must be 2 (see Section B3 for proof). When m=2, the follow-
ing means of calculating 6 is more practical, especially when damping
is small:
6 = (1/n) In (ai/a1_)fl) (B-29)
where n is any arbitrary integer.
Temporal Decay of Free Vibrations. - Another measure associated with
the decay of free vibrations is the temporal decay constant v , defined as
follows (reference 7 , foldout opposite p. 35):
Vt =' (-t2"tl)" ln t U(t1)/u(t2)] (B-30-)
where t. and t« are two different values of time, arbitrary except that
t_ > t. and (t_ - t.) must be an integer number of periods of damped
vibration. The quantities u(tj) and u(t?) are the respective displacements
at times t and t_. It is seen that the usual units for v are sec
103
An alternate way of specifying the temporal decay is the decay
rate y , which has units of decibels per second (db/sec) and is defined
as follows:
Yt = 20 (t2 - t L ) ~ l log [uCt^/uO^)] (B-31)
or
-1 Vt ( t2 ' h*Yt = 20(t2 - tL) log e = (20 log e)v f c *, 8.68 vt
where log s logarithm to the base 10.
Spatial Attenuation of a Plane Wave in a Slender Bar. - If
one propagates a plane, harmonic wave in a slender bar made of a homo-
geneous, linear material , the wave exhibits exponential decay with axial
position (x), analogous to the temporal decay of free vibration (which
may be considered as a standing wave). Analogous to the logarithmic de-
crement (see above), we have the logarithmic attenuation 6 , defined asS
follows in terms of amplitudes a(x.) and a(x?) at stations x1 and x_:
6g = In [a(x1)/a(x2)] (B-32)
Analogous to the temporal decay constant, we define the spatial
attenuation constant v as follows:•— s
vs = (x2 - x "1 In ra(x1)/a(x2)] (B-33)
The unit of v is in" .s
Finally, analogous to the decay rate, we define the spatial
attenuation rate y as follows:s
104
YS = 20(x2 - x^" log [aCx^/aCx.,)] w 8.68 vg. (B-34)
The unit of Y is db per unit length.s
It should be cautioned that the determination of damping by wave
attenuation requires that the cross section of the bar be compact (pre-
ferably round or square) and that the largest cross-sectional dimension
be very small compared to the wave length of the traveling wave. Further-
more, the two stations along the bar, at which the wave measurements are
made, must be: (1) sufficiently far from the point of impact that initial
transients have died out and (2) sufficiently far from each other so that
a measurable change in amplitude occurs. Kolsky discussed these points
in detail in reference 125.
B3. Inter-Relationships Among Various Measures of Damping for
Homogeneous Materials
Here we consider a single degree-of-freedom system consisting of a
mass supported on a mass less spring made of a homogeneous Kimball-Lovell
or complex-modulus material. Then the governing differential equation
for simple harmonic excitation is equation (B-15), which has the following
steady-state solution:
•" (B-35)
where
u *sj [(k-nxu2)2 +b2]~1/2 (B-36)
9 = arctan [b/(k-mu)2)] (B-37)
The magnification factor (MF) is defined as follows:
105
MF = u/u (B-38)s c
where u is the so-called static displacement, defined as follows:st
u ="F7k (B-39)S C
Combining equations (B-36, B-38, and B-39), one obtains the
following relation:
M F = { f l - (u)/tun)2]2+ (b/mu2)2]-"172 (3-40)
where u> is the natural frequency (i.e. the resonant frequency of the
undamped system), given by:
The critical material damping coefficient (b ) is the minimum value
of b for which the free vibratory motion is non-oscillatory. It is
obtained from the following relationship:
(bc/2roun)2 = k/m = u)2 (B-42)
or
bc = 2roa>2 (B-42)
The damping ratio £ is defined as follows:
C s b/bc (B-43)
Combining equations (B-40, B-42, and B-43), one arrives at the
following general, dimens ionless relationship:
106
MF = {[l-(u>/u>n)2]2 + 4£2}~1/2 (B-44)
! It Is seen easily that MF is a function of only two parameters: the fre-
quency ratio (uj/u) ) and the damping ratio (£). It should be mentioned
that equation (B-44) is somewhat different than the known relationship
for a single-degree-of-freedom Kelvin-Voigt viscously damped system,
even though the damping ratio £ is defined analogously ( = c/c ,
where c = 2mu> ).c n
The resonant magnification factor (RMF) is defined as the value
of MF at resonance, which is taken here to occur when <p = 90 . In view
of equation (B-37), this implies that the resonant frequency is m .
Thus, at resonance, equation (B-44) reduces to the following simple
expression:
RMF = ( 2 C ) " | (B-45)
Thus, it is seen that the same simple relationship between the damping
ratio and the resonant magnification factor holds as does for a Kelvin-
Voigt system. Although the resonant amplitude can be measured accurately,
there are problems in measuring the static deflection in complicated
structures (due to signal-to-noise rat io limitations of instrumentation).
For this reason, in s t ructural dynamics, RMF is seldom used as a measure
of damping.
The damping energy, i.e. the energy dissipated per cycle, can be
computed as follows:2rr/u>
(B-46)o p
Ud = i Fd du = Fdu dt
where F, is the damping force, given by
107
(B-47)
Substituting equations (B-35) and (B-47) into equation (B-46) and
integrating, we obtain the following result:
U, = nb H2 (B-48)a
To convert equation (B-48) to the form of equation (B-22), with
m=2, it is necessary to divide by the volume and to relate u to n.
Now the force amplitude is :
"F = Aa = ku . (B-49)
where A H cross-sectional area.
Assuming the spring is a mass less and uniform bar, we have
k = AE/L (B-50)
where L = effect ive length of spring and E = Young's modulus of the bar.
Combining equations (B-48, B-49, B-50), one obtains the following result:
"< = UJ/V = (nbL/A)(o/E)2 (B-51)dv d
Comparing the form of equations (B-22) and (B-51), we see that
for a Kimball-Lovell mater ia l , m = 2 and
Cd = nbL/AE2 (B-52)
It should be noted that -Lazan (reference 7 , chap. II) has shown
that these results are independent of the stress distribution and the
specimen geometry, provided that m = 2.
108
In view of equations (B-42, B-43, and B-44), equation (B-52) can
be expressed in the following more useful form:
(B-53)
According to equation (B-48), the damping energy (and thus,
excitation power) is proportional to the square of the displacement
amplitude u (and thus, the MF). Then the power is one half of what it
is at resonance when MF = RMF//2. In view of equation (B-45), the half
power magnification factor (HPMF) is related to the damping ratio as
follows :
HPMF = RMF//2 = (2/2 £)~l (B-54)
To determine the two sideband frequencies (to = (u and u> ) cor-
responding to ha l f power, we combine equations (B-44) and (B-54) to
2obtain the following quadrat ic expression in u) :
(2/2 O2 = [1 - (u>/u>n)2]2 + 4C2
which has the following positive roots:
O* (B-55)
It is interesting to note that equation (B-55) is identical to the analogous
2expression for the lightly damped Kelvin-Voigt system, i.e. (c/c ) «1.
For small damping (£ «%) ,
""n
109
Thus, we get Che following relation between the dimension less bandwidth
and the damping ratio £:
K (B-56)
In the original Kennedy-Pancu method (reference 123), this relationship is
used to determine the damping ratio from the geometry of an experimentally
determined Argand plot (a polar-coordinate plot of response amplitude
versus phase angle).
In terms of the quality factor Q, equation (B-56) may be rewritten
as follows:
(B-57)
It is interesting to note that in order for the half-power frequencies
to be real, the damping ratio £ must be no greater than f2/2 sa 0.707. How-
ever, this is not a severe limitation for actual structural materials .
The potential energy (strain energy) stored in our single-degree-of-
freedom mathematical model is given by:
Q ** (2C)-l
U = d> F du8
where F is the spring force, given bys
F = kus
(B-58)
(B-59)
Thus ,
u
U - k < [ « du = ku2 /2 (B-60)
Combining equations (B-48) and (B-60), we obtain
2nb/k (B-61)
110
Using equations (B-41, B-42, B-43), we can rewrite equation (B-61)
in the following more useful form:
U./U = 4Tr£
or
c = (l/4n)(Ud/U)
(B-62)
(B-63)
The loss tangent is defined as follows for the system considered
here:
g = b/k (B-64)
g " 2C
Inserting equations (B-41, B-42, B-43) into equation (B-64) we
obtain the following useful relationship:
(B-65)
The following useful relationship, which is sometimes taken as a
fundamental definition of damping (ref. 104), is obtained here by
combining equations (B-63) and (B-65):
(B-66)
Taking the derivative of phase angle cp with respect to frequency
U), one obtains the following result from equation (B-37):
g = ( l /2rr)(U d /U)
dep/dto = 2bmuj/[ (k-mu)2)2+b2] (B-67)
At resonance (subscript R), defined by u)=u) /k/m, equation (B-67)n
becomes:
(dcp/du>)_ = 2mu) /b (B-68)K n
Combining equations (B-42, B-43, and B-68), we obtain the following
111
very useful result:
[u> (dcp/du)) I"1 ! (B-69)n t\
It is interesting to note that although the MF vs. cu relation,
equation (B-44), is different than the corresponding relation for a Kelvin-
Voigt viscously damped system, equation (B-69) is identical to its cor-
responding relationship for a Kelvin-Voigt system. Equation (B-69) is used
to determine the damping ratio from an experimentally determined Argand
diagram in the improved Kennedy-Pancu method (ref . 124).
The transient solution of the system represented by equation (B-14a)
can be written as follows:
u- = 7J • e~Cu >n t sin ( /T^2 u, t - cp) (B-70)
From its definit ion in equation (B-28), the logarithmic decrement 6
can be determined as follows:
6 = In -— ^ = In e^nT = £u> T (B-71)e-On(t1+T)
where T is the period of damped oscillation, given by
T = (2nC/u)n)(l-C2)"1/2 (B-72)
Thus, we now have
6 = 2rrC (1'C )2 x - l / 2 (B-73)
2For small damping (£ «1), equation (B-73) can be replaced by the
following approximate expression:
! 6 w 2nC I (B-74)
112
Combining equations (B-65) and (B-74), one obtains the following:
6 = ng (B-75)
In view of equation (B-63) and since the specific energies are
given by;
we have
Udv S VV' Uv =
Udv/4TrUs
(B-76)
(B-77)
However, the specific strain energy is
Uy = a /2E (B-78)
A power-law-damping material is defined by equation (B-22).
Combining this relation with equation (B-78), one obtains:
(E (B-79)
Thus, it is clear that £ is independent of stress amplitude only for a
KL (Kimball-Lovell) material (m=2). Then
(B-80)C = E Cd/8TT
g = E Cd/4n
or, in view of equation (B-65),
(B-81)
Furthermore, since the logarithmic decrement of a KL material with
small damping is approximately proportional to the damping ratio as shown
by equation (B-74), the following approximate relation holds:
(B-82)6 «s E Cd/4113
APPENDIX C
DETAILS OF FORMULAS USED IN SECTION II
Cl. Airy Stress Function and the Associated
Stress, Strain, and Displacement Components
Some useful formulas pertaining to analyses carried out in Section
2.3 and 2.5 are summarized as follows. See the main text and the list
of symbols for the definitions of notations used. It is to be noted that
the same formula will apply to fiber as well as matrix regions with ap-
propriate interpretations of the material property values, E and v, etc.,
and choices of terms in the series. For example, in the fiber region,
terms containing negative powers of p must be omitted to prevent a
singularity in stress.
Polar stress components. - Stress components o , afl, and T -. are
given by:
-2 ' 10 = a p +2b + 2 b, p cos 9 - 2 a.p"J cos 0r o o 1 1
a n n - n " 2
nn=2,3,...
[a n(n-l)pn"2 + b (n-2) (n+1) pn
n n
+ a' n(n+l) p"n"2 + b' (n+2) (n-1) p"
n] cos n 9 (C-l)
114
-2 ' -3a_ =-a p + 2 b + 6 b, p cos 9 + 2 a.p cos 99 o^ o 1 1
00
+ I [an n(n-l) pn'2 + bn(n+2) (n+1) p
n+a^ n(n+l)p"n '2
I n=2,3 , . . .' -n-+ b (n-2)(n-l) p""] cos n 9 (C-2)
1 -3T Q ~ 2 b. p sin 9-2 a^p sin 9
+ T [a n(n-l)pn~2 + b n(n+l)pr
f^A n nn=2,3 , . .
-a' n(n+l) p"n"2 - b' n(n-l)p"n] sin n 9 (C-3)n n
Rectangular stress components. - Stress components o ,o , and Tx y xy
are given by:
o _3O = a p" cos 2 9 + 2 b + 2 b.p cos 9 - 2 a. 'p cos 3 9x o ^ o i l
00
-V I a n(n-l)pn"2 cos (n-2) 9 + b (n+1) pn[n cos (n-2) 9L> . \. n n
n=2,3, . , .
- 2 cos n 9] + a1 n(n+l)p"n"2 cos (n+2) 9
+ b ' (n- l)p" n [n cos (n+2) 9 + 2 cos n 9] ) (C-4)n J
a - -a ft'2 cos 2 9 +2 bQ+ 6 b^ cos 9 + 2 a^p~ cos 3 9
09
+ Y (a n (n-l)pn~2 cos (n-2) 9+b (n+1) p"[n cos (n-2) 9L> I n n
n=2 ,3 , . . .115
+ 2 cos n 9] + a' n(n+l)p~ cos (n+2) 0
3"nLn cos (n+2) 9 - 2 cos n 9] j (C-5)
-2 -3 2rx = aop Sln 2 6 ~ 2 biP sin 6 + 2 a]p sin 9 (1-4 cos 9 )
a n*.n-i;fn'2 ' ' ^ n ' ^ ~ n~ 2
n=2,3, . . .
[a n(n-l)pn"2 + b n(n+l)pn - a1 n(n+l) pn n
b', n(n-l)p"n] sin (n+2) 9 (C-6)n
Rectangular displacement components. - Displacement components u
and v are given by:
E (l+v)"1(u/R)=-a p"1 cos 9 + 2 b (l-2v)p cos 9
- bLp2 [3+4 (1+v)] cos 2 9 + a[p"2 cos 2 9
oo
+ ] |-a np cos (n-1) 9 + b p [-n cos (n-1) 9
n=2 ,3 , . . .
+ 2 (l-2v) cos (n+1) 9 - 2 sin n 9 sin 9]
+ a1 np"0"1 cos (n+1) 9
+ b^p"n+1 [n cos (n+1) 9+2 (l-2v) cos (n-1) 9
+ 2 sin n 9 sin 9] } (C-7)
116
E (l-fv)"1(v/R)= -aQp"1 sin 9 + 2 bo(l-2v)p sin 9 + 4 blP
2(l-v) sin 2 9
OB
+ ajp" sin 2 9 + Y |an np""1 sin (n-1) 9
n=2,3,...
+ bnpn+1[ n sin (n-1) 9 + 2 (l-2v) sin (n+1) 9-1-2 sinn 9cos9]
+ a' np"11"1 sin (n+1) 9
+ b'p"n+1 [n sin (n+1) 9-2 (l-2v) sin (n-1) 9-2 sin n 9 cos 9 ](•n J
(C-8)
C2. Details of Formulas Used in Section 2.6
Dirichlet torsion function ¥ (p.9) (i-f.m). - Torsion functions
Y and Y that satisfy Laplace equation in the fiber and matrix regions,
respectively are assumed to be:
OB
Yf(p,9) = a + Y a, pk cos k 9 (C-9)O £j K
oo
fm(p,9) = b + Y (b pk + b p"k) cos k 9 (C-10)
Relationships among fiber-region and matrix-region coefficients a
and b .- For the nth element, the distance of the fiber from the origin is
d = 2(n-l)p. The boundary conditions at the fiber-matrix interface are:
117
-i) (5on C,
dY f/dn = dVm/dn
(C-ll)
On the interface C..,p=l, hence, equations (C-ll) becomes
X(a +Y a. cos k 9) = b +7 (b. +b .) cos k 9o LJ k o L> k -k
k=l ,2 , . . . k=l ,2 , . . .
Z d c o s 9)
y k a, cos k 9 = y k (b - b . ) cos k
k=l ,2 , . . . k-1,2,...
(C-12)
(C-13)
Equating the coefficients of cos k 9 in equations (C-12 and 13), we
have:
[bo + <X-D(HO/2] /X
ak = 2 bk/(X+l) (k-2,3,. . .)
-l
b i= ^ibu- k I k(k-2,3,...)
(C-14)
where
= (x-D/(x+D (C-15)
118
Inter-element boundary conditions between the n-th and (n-H)-th
elements . - On the inter-face boundary C2 where £ = (2 n-1) u, the
local coordinate systems [p,.x, O/.v ] ,[|/ .\ , TL .-> ] (1=1, 2, ...n) are inter-
related as
p(n)=p(n+l) ' 9(n) = " ' 9(n+l) ' \u)' ^ 5(n)
(C-16)
Thus the boundary conditions = Y ,lNand M ^(n) (n+1) (n;
which warrant the displacement continuity and stress equilibrium on C_
become, respectively:
2 Xl(dHu) p'n) cos 9(n) (C-17)
and
(k-1) G^-X^^j1 cos (k+l) 9(n)]
-22\1u p cos 2 9(n) (C-18)
Shear stress formulas. - The shear stresses T ,T (i=f,m) in
the fiber and matrix regions of the n-th element are calculated from
equations (79 and 80) (Section 2.6) as follows:
119
Txf/((*XGmr) = (^f/^TD - Tl
CO
k a,n sin
k-1,2,...
ZK.~" J. ) £. 9 • • ,
bk ' - p ' Sin
V k-1= - ) k a, p cos (k-1) 9 + 5 (C-20)L J k K / a
+ (X,d)p" 2 sin 2 9 - 11 (C-21)
k bk[pk~ l cos (k-1) 9 - J^p"1*"1 cos (k+1) 9 ]
p"2 cos 2 9 + I (C-22)
Torslonal rigidity calculations for the nth element. - The torsional
rigidity D, ^ for the n-th element is calculated from equation (83 and 84)
as
120
D(n) / (Gm r > = X (2 W + (2 (C-23)
where
R2 = JJ dT] = TT
R = JJ Ym dP dT]
m
(C-24)
= b ( 4 u 6 - n) + b, [(4/3)o i ( 1 - 6 ) + X. (n - arctan 6) ]i
Z bk
k=4 ,6 , . . .
k=4,6 , . . .
R4 = (4/3) U46 (1+62) + 4u2 6 d2 + d
2]
s, =tan 6 k+2
sec 0 cos k 0 dQ
C(k+2)/2]
Im=l
n/2
csckH' 9 cos k 9 d9
tan"16 T121
/(k-2ori-3)
m=l
»= J
tan 6sec 9 cos k 9 d9
[(k-m+2)/2]
^y y <-i)l—> t->m=l n=l
k-1 [(k-2nri-3)/2]
n+l.-m 2 m-1,1.c2.m-k ^k-m+1I 5 (.l+o ; C_ ,2n-l
m-1 n-1
(k-2)/2 [(k-2m+3)/2]
Im=l
-2tn+2n-3
2n-l
J2(n-l)
) (C-25)
J
C3. Details of Formulas Used in Section 2.7
Saint-Venant flexural function \ (p,9) (i=f>ni).- Flexural functions
\ and x that satisfy the Laplace equation in the respective fiber and
matrix regions are assumed in series form as follows:
f V kX (P»e> = aP cos k 9
k=l,3
Xm(p,9) (bkpk + cos k 9
k=l,3
> (C-26)
Note that in equations (C-26), coefficients with even-numbered
subscripts are zero due to the anti-symmetry condition with respect to
the TV-axis.
122
Relationships among fiber-region and matrix-region coefficients.
a. and b,. - In view of the displacement-continuity and the stress-
equilibrium requirements at the fiber-matrix interface, where p = 1,
a. are related to b, , on substitution of eq. (C-26) into eqs. (109 andK K
110) , as follows:
akXa,
_k
(C-27)
+ b_k (k = 1,3,...)
(k = 5,7,...)
- (X - 1) (3+2 v)M
Xa, = b - b + (X - DM•j Z — Z
Equation (C-27) may be solved for a. and b in terms of b to yield:
2 b1/(X+D - X1(3+2v)/4
2 b3/(X+D
2 bk/(X+D (k-3,5,...)
• (C-28)
_3
-k
+ (1/4)]
(k=3,5,...)
where \. is as defined in eq. (C-15).
Longitudinal thickness-shear stiffness S,.,.. - In view of notations
in eq. (106), the longitudinal thickness-shear stiffness expression, eq.
(120), may be written as
123
4 6 U / 3 ] / P ' (C-29)
where
" - (2/3) 6u4 [0(62-1) -2 62]
jA). + JJ
m
II. ft'< -1tan" 5 - (n/4) + uV(6~ lH
m
tan"^)] -1- t a n 6 ) + ^n - 26/( l+6)]
• . t an - f i TT/2J G (9) d6 + 4
-1tan 6
G (9) d9
(bj/4) u sec20 + (b3/6) <a sec 9) 6 cos 0 cos 3 9
sec
cos 9 cos k 9
6 esc 0) cb.Qcsc
(C-30)
CdH-3)-1 <u6 csc 9)k+3csc
• cos 9 cos k
12
APPENDIX D
EXPERIMENTAL OBSERVATION ON THE
DAMPING BEHAVIOR OF A BORON FIBER
In the damping analysis of a monofilament composite, it was found that
the loss tangent gg,, associated with the in-plane Young's modulus is re-
lated to the volume fractions, stiffness ratio, and the loss tangents of
the. constituent materials by the equation, [eq. (156)]
g = (X1 V g -I- V g )/(\' V + V )Ell f Ef m Em f
In the case of boron-epoxy composite, the stiffness ratio \' is usually of
the order of 120; whereas the loss tangent of boron is expected to be about
one-tenth that of epoxy. The complete omission of the contribution of
the boron fibers to the damping of the composite will then lead to a com-
posite loss tangent which is unreasonably low.
Unfortunately, so far as known to the authors, no experimental data
dealing with the damping behavior of boron material alone are available
in the literature. In view of this, a crude exploratory experiment was
carried out on an Avco 4.5-mil-diameter boron fiber in order to assess
roughly the order of magnitude of damping in the boron material. A boron-
fiber cantilever with a concentrated mass attached at its tip was deflected
a certain prescribed distance and then released to oscillate in the vertical
125
plane. The profile of the oscillation was recorded by a 16-mm motion-picture
camera (set at 64 frames per second) until the motion of the fiber decays
and returns to its initial equilibrium position. The decaying sinusoidal
motion of the concentrated mass at the fiber tip is then reconstructed from
the frame-by-frame observation of the film. The experiment was repeated
several times with different initial deflections.
The logarithmic decrement was obtained from the displacement versus
time plots of the fiber tip (figure D-l) and then related to the loss
tangent using eq. (B-75) from Appendix B. Averages of several runs were
summarized as in figure D-2, where logarithmic decrements 6 based on the
number of cycles elapsed were calculated for three cases with initial
deflections equal to 1.5, 1.0, and 0.5 inch, respectively. These curves
show clearly the amplitude dependency of the logarithmic decrement which
is attributed mainly to the air damping. In view of the air damping which
predominated, the loss tangent at small deflections, as estimated from
this experiment, is of the order of 0.02 to 0.05, which is roughly ten
times that of the estimated loss tangent for boron in vacuum (see Section IV)
It is concluded that, in order to assess the material damping of a boron
fiber, the experiment must be carried out in vacuum to eliminate the
effects of air damping which is both nonlinear and amplitude-dependent.
126
APPENDIX E
COMPUTER PROGRAM DOCUMENTATION
The computer program for computing the stiffnesses and the
associated loss tangents consists of one lead-in program and ten
subroutine programs.
The lead-in program is concerned with the input of the material
data, calling of each subprogram, and the output of the computed
results.
The input data consist of various pertinent material data
such as Young's modulus, shear modulus, Poisson's ratio, and their
respective loss tangents for specific frequencies as listed in Tables
V-IX.
Each subprogram is concerned with the calculation of a
specific stiffness and associated loss tangent based on the input
data. For example, subprogram COMPE11 calculates the major Young's
modulus En and the associated loss tangent gg .
Each subprogram is designed to accomplish three functions:
1. Generation of the parameters necessary for solution,
2. Evaluation of the stiffness, and
3. Evaluation of the loss tangent.
The program was written in FORTRAN IV language as prescribed
127
in IBM System Reference Library Form C-28-6274-3.
A complete listing of the computer program is presented at
the end of this report.
128
REFERENCES
1. Ekvall, J.C.: Structural Behavior of Monofilament Composites. AIAA
6th Structures and Materials Conf., Palm Springs, Calif., Apr.
1965, pp. 250-263.
2. Lekhnitskki, S.G.: Anisotropic Plates, 2nd. ed., (English Translation).
Gordon and Breach, N.Y., 1968, p. 41.
3. Ashton, J.E.; Halpin, J.C.; and Petit, P.H.: Primer on Composite
Materials: Analysis. Technomic Publishing Company, Inc., Stamford,
Conn., 1969, Ch. 3.
4. Chamis, C.C.; and Sendeckyj, G.P.: Critique on Theories Predicting
Thermoelastic Properties of Fibrous Composites. J. Composite Matls.,
vol. 2, no. 3, July 1968, pp. 332-358.
5. Chambers, R.E.; and McGarry, F.J.: Shear Effects in Glass Fiber Re-
inforced Plastics Laminates. ASTM Bulletin, no. 238, May 1959,
pp. 38-41.
6. Khischenko, Yu M.: Effect of Shear on the Modulus of Elasticity of
Specimens of Glass Fiber Reinforced Plastics Tested in Transverse
Bending. Industrial Laboratory, vol. 30, no. 6, June 1964, pp.
937-939.
7. Lazan, B.J.: Damping of Materials and Members in Structural Mechanics.
129
Pergamon Press, 1968, Oxford, England.
8. Pottinger, M.G.: Material Damping of Glass Fiber-Epoxy and Boron
Fiber-Aluminum Composites. Rept. ARL 70-0237, Aerospace Re-
search Laboratories, Wright-Patterson Air Force Base, Ohio, Oct.
1970 (AD-721191).
9. Schultz, A.B.; and Tsai, S.W.: Dynamic Moduli and Damping Ratios
in Fibers-Reinforced Composites. J. Composite Matls., vol. 2, no.
3, July 1968, pp. 368-379.
10.. Schultz, A.B.; and Tsai, S.W.: Measurements of Complex Dynamic
Moduli for Laminated Fiber-Reinforced Composites. J. Composite
Matls., vol. 3, no. 3, July 1969, pp. 434-443.
11. James, W.L.: Calculation of Vibration Damping in Sandwich Construction
from Damping Properties of the Cores and Facings. Rept. 1888,
Forest Products Laboratory, U.S. Dept. of Agriculture, Madison, Wis.,
Dec. 1962. •
12. Nordby, G.M.; Crisman, W.C.; and Bert, C.W.: Dynamic Elastic, Damping,
and Fatigue Characteristics of Fiberglass-Reinforced Sandwich Struct-
ure. Rept. USAAVLABS TR 65-60, U.S. Army Aviation Materiel Laboratories,
Ft. Eustis, Va., Oct. 1965 (AD-623128).
13. Bert, C.W.; Wilkins, D.J., Jr.; and Crisman, W.C.: Damping in Sandwich
Beams with Shear-Flexible Cores. J. Eng. Industry, Trans. ASME, vol.
89B, no. 4, Nov. 1967, pp. 662-670.
130
14. Clary, R.R.: Vibration Characteristics of Unidirectional Filamentary
Composite Material Panels. Composite Materials: Testing and Design
(Second Conference), Amer. Soc. Testing & Mat Is., Spec. Tech. Publ.
497, 1972.
15. Bert, C.W.; Mayberry, B.L.; and Ray, J.D.: Vibration Evaluation of
Sandwich Conical Shells with Fiber-Reinforced Composite Facings.
Rept. USAAVLABS TR 68-85, U.S. Army Aviation Materiel Laboratories,
Ft. Eustis, Va., Dec. 1968 (AD-685318).
16. Ray, J.D.; Bert, C.W.; and Egle, D.M.: The Application of Kennedy-
Panchu Method to Experimental Vibration Studies of Complex Shell
Structures. Shock and Vib. Bull., Bull. 39, Pt. 3, U.S. Dept. De-
fense, Jan. 1969, pp. 107-115.
17. Bert, C.W.; and Ray, J.D.: Vibrations of Orthotropic Sandwich Conical
Shells with Free Edges. Int. J. Mech. Sci., vol. 11, no. 9, Sept.
1969, pp. 767-779.
18. Richter, H.P.H.: Photographic Method for Measuring Material Damping
and Dynamic Young's Modulus at Low Frequencies Applied to a Fiberglass
Reinforced Resin Structure. Proc. 18th Ann. Tech. & Mgt. Conf.,
Reinf. Plastics Div., Soc. Plastics Industry, Inc., 1963, sec. 4-D.
19. Kerr, L.; and Lazan, B.J.: Damping and Fatigue Properties of Sandwich
Configuration in Flexure. Rept. ASD TR 61-646, Aeron. Systems Div.,
Wright-Patterson Air Force Base, Ohio, Nov. 1961 (AD-272016).
131
20. Hashin, Z. : Complex Moduli of Viscoelastic Composites - I. General
Theory and Application to Particulate Composites. Int. J. Solids
& Structures, vol. 6, no. 5, May 1970, pp. 539-552.
21. Hashin, Z.: Complex Moduli of Viscoelastic Composites- II. Fiber Re-
inforced Materials. Int. J. Solids & Structures, vol. 6, no. 6,
June 1970, pp. 797-807.
22. Kimball, A.L.; and Lovell, D.E.: Internal Frictions in Solids.
Physical Review, ser. 2, vol. 30, 1927, pp. 948-959.
23. Miller, K.D., Jr.; and Breslau, S.M.: Fiber-Reinforced Plastic as a
Rocket Structural Material. Jet Propulsion, vol. 26, no. 11, Nov. 1956,
pp. 969-972.
24. Rosato, D.V.; and Grove, C.S., Jr.: Filament Winding: Its Development,
Manufacture, Applications and Design. John Wiley & Sons, Inc., N.Y.
1964.
25. Cutwater, J.O., Jr.: The Mechanics of Plastics Reinforcement in Tension.
Modern Plastics, vol. 33, no. 7, March 1956, p. 156ff.
26. Beer, F. : Die Festigkeitseigenschaften Kreuzweisebewehrter Kunstoffe.
VDI Zeits., vol. 101, Apr. 1959, pp. 463-468.
27. Brown, R.L., Jr.: Simplified Stress Analysis of Filament Reinforced
Plastic Pressure Vessels. Soc. Plastic Engrs. J., vol. 17, 1961, p. 989.
28. Ekvall, J.C.: Elastic Properties of Orthotropic Monofilament Laminates.
Paper 61-Av-56,ASME Aviation Conference, Los Angeles, Calif., Mar. 12-16, :
132
29. Greszczuk, L.B.: Theoretical and Experimental Studies on Properties and
Behavior of Filamentary Composites. SPI 21st Conference, Chicago, 111.
1966, sect. 5-B.
30. Nosarev, A.V.: Effect of Fiber Curvature of the Elastic Properties of
Unidirectionally Reinforced Plastics (in Russian). Mekhanika Polimerov,
vol. 3, 1967, p. 858.
31. Hill, R.: Theory of Mechanical Properties of Fiber-Strengthened Materials:
III. Self-Consistent Model. J. Mech. Phys. Solids, vol. 13, Aug.
1965, pp. 189-198.
32. Whitney, J.M.; and Riley, M.B.: Elastic Properties of Fiber Reinforced
Composite Materials. AIAA J., vol. 4, no. 9, Sept. 1966, pp. 1537-
1542.
33. Sokolnikoff, I.S.: Mathematical Theory of Elasticity, 2nd. ed.
McGraw-Hill Book Co., Inc., N.Y., 1956, Chapt. 7.
34. Tsai, S.W.: Structural Behavior of Composite Materials. NASA CR-71, 1964.
35. Hashin, Z.; and Rosen, B.W.: The Elastic Moduli of Fiber Reinforced
Materials. J. Appl. Mech., vol. 31, no. 2, June 1964, pp.
233-232; errata, vol. 32, Mar. 1965, p. 219.
36. Wu, T.T.: On the Parametrization of the Elastic Moduli of Two-Phase
Materials. J. Appl. Mech., vol. 32, no. 1, Mar. 1965, pp. 211-214.
37. Haener, J.; and Ashbaugh, N.: Three-Dimensional Stress Distribution
in a Unidirectional Composite. J. Composite Matls., vol. 1, no. 1, •,
133
Jan. 1967, pp. 54-63.
38. Chen, C.H.; and Cheng, S., Mechanical Properties of Fiber Reinforced
Composites, J. Composite Matls., vol. 1, no. 1, Jan. 1967, pp. 30-
41; errata, vol. 1, no. 2, Apr. 1967, p. 207.
39. Bloom, J.M.; and Wilson, H.B.: Axial Loading of a Unidirectional Compos-
ite, J, Composite Matls., vol. 1, no. 3, July 1967, pp. 268-277.
40. Foye, R.L.: An Evaluation of Various Engineering Estimates of the
Transverse Properties of Unidirectional Composites. SAMPE, National
Symposia, vol. 10, 1966, p. G-31.
41» Foye, R.L.: Structural Composites. Quarterly Progress Reports no. 1
and 2, AFML Contract No. AF 33(615)-5150, 1966.
42. Bolotin, V.V.: Basic Equations of the Theory of Reinforced Media.
Polymer Mechanics, vol. 1, no. 2, 1965, pp. 23-30.
43. Herrmann, G.; and Achenbach, J.D.: On Dynamic Theories of Fiber Re-
inforced Composites. AIAA/ASME 8th Structures, Structural Dynamics
and Materials Conference/ Palm Springs, Calif., Apr. 1967, pp. 112-118.
44. Chi, S.H.: Bibliography and Tabulation of Damping Properties of Non-
metallic Materials. Rept. WADD-TR-60-140, Wright Air Development
Division, Wright-Patterson Air Force Base, Ohio, Sept. 1962.
45. Hashin, Z.: Viscoelastic Fiber Reinforced Materials. AIAA J., vol. 4,
no. 8, Aug. 1966, pp. 1411-1417.
134
46. Adams, D.F.; and Boner, D.R.: Longitudinal Shear Loading of a
Unidirectional Composite. J. Composite Matls., vol. 1, no. 1,
Jan. 1967, pp. 4-17.
47. Hill, R. : Theory of Mechanical Properties of Fiber-Strengthened
Materials: I. Elastic Behavior. J. Mech. Phys. Solids, vol. 12,
1964, pp. 199-212.
48. Bloom, J.M.: Nonconservative Behavior of Composite Materials. Kept.
AFML-TR-68-10, Air Force Materials Laboratory, Wright-Patterson
AFB, Ohio, Jan. 1968 (AD-666676).
49. Timoshenko, S.; and Goodier, J.N.: Theory of Elasticity, 3rd. ed.
McGraw-Hill, New York, 1969, pp. 132-136.
50. Conway, H.D.: The Approximate Analysis of Certain Boundary Value Prob-
lems. J. Appl. Mech., vol. 27, no. 2, June 1960, pp. 275-277.
51. Conway, H.D.; and Leissa, A.W.: Application of the Point Matching
Method to Shallow Spherical Shell Theory. J. Appl. Mech., vol. 29,
no. 4, Dec. 1962, pp. 745-747.
52. Hulbert, L.E.; and Niedenfuhr, F.W.: On the Numerical Solution of Certain
Classes of Boundary Value Problems. Presented at the 19th Annual
Meeting of the Association for Computing Machinery, Denver, Colo.,
Aug. 27, 1963.
53. Abolin'sh, D.S.: Compliance Tensor for an Elastic Material Reinforced
in One Direction. Polymer Mechanics, vol. 1, no. 4, 1965, pp. 2.8-32.
135
54. Hill, R.: Elastic Properties of Reinforced Solids: Some Theoretical
Principles. J. Mech. Phys. Solids, vol. 11, 1963, pp. 357-372.
55. Paul, B.: Prediction of Elastic Constants of Multiphase Materials.
Trans. AIME, vol. 218, no. 1, Feb. 1960, pp. 36-41.
56. Adams, D.F.; and Doner, D.R.: Transverse Normal Loading of a Uni-
directional Composite. J. Composite Matls., vol. 1, no. 2, Apr.
1967, pp. 152-173.
57. Muskhelishivili, N.I.: Some Basic Problems of the Mathematical Theory
of Elasticity, 4th ed. P. Noordhoff, Ltd., Groningen, The Nether-
lands, 1963, sec. 139, pp. 609-626.
58. Timoshenko, S.: Strength of Materials, Part I, 2nd. ed. D. Van
Nostrand Co., Inc., New York, 1940, pp. 170-171.
59. Timoshenko, S.: On the Correction for Shear of the Differential
Equation for Transverse Vibrations of Prismatic Bars. Philosophical
Magazine, ser. 6, vol. 41, 1921, pp. 744-746.
60. Mindlin, R.D.; and Deresiewicz, H.: Timoshenko's Shear Coefficient
for Flexural Vibrations of Beams. Proc. 2nd. U.S. Nat. Congr. Appl.
Mech., 1954, pp. 175-178.
61. Roark, R.J.: Formulas for Stress and Strains, 3rd. ed., McGraw-Hill
Book Company, Inc., New York, 1954, pp. 119-121.
62. Cowper, G.P.: The Shear Coefficient in Timoshenko's Beam Theory. J.
Appl. Mech., vol. 33, no. 2, June 1966, pp. 335-340.
136
63. Bert, C.W.; and Siu, C.C.: Vibration and Damping of Laminated,
Composite-Material Plates Including Thickness-Shear Effects.
Final Report (Part II), NASA Research Grant NGR-37-003-055,
School of Aerospace, Mechanical & Nuclear Engineering, Univ.
of Oklahoma, Norman, Okla., Mar. 1972.
64. Hadcock, R.N.: Boron-Epoxy Aircraft Structures, Chap. 24 in Handbook
of Fiberglass and Advanced Plastics Composites, edited by G. Lubin.
Van Nostrand Reinhold, N.Y. , 1969, pp. 628-660.
65. Bert, C.W.: Lecture Notes on Introduction to Analysis and Design
of Composite-Material Structures. Univ. of Oklahoma, Jan. 1970.
66. Halpin, J.C.; and Tsai, S.W.: Environmental Factors in Composite
Materials Design. AFML-TR-67-423, Air Force Materials Laboratory,
Wright-Patterson AFB, Ohio, 1967.
67. Hermans, J.J.: The Elastic Properties of Fiber Reinforced Materials
When the Fibers are Aligned. Proc. Konikl. Nederl. Akad. van
Wetenschapp., Amsterdam, vol. B70, no. 1, 1967, pp. 1-9.
68. Tsai, S.W.: Mechanics of Composite Materials, Part I - Introduction.
AFML-TR-66-149, Part I, Air Force Materials Laboratory, Wright-
Patterson AFB, Ohio, June 1966.
69. Hulbert, L.E.; and Rybicki, E.F.: Boundary Point Least Squares
Analysis of the Free Edge Effects in Some Unidirectional Fiber
Composites. J. Composite Mat Is., vol. 5, no. 2, April 1971,
137
pp. 164-175.
70. Dow, N.F.; and Rosen, B.W.: Evaulation of Filament-reinforced
Composites for Aerospace Structural Applications. NASA Report
CR-207, April 1965.
71. Wilson, H.B., Jr.; and Goree, J.G.: Transverse Shear Loading in
an Elastic Matrix Containing Two Elastic Circular Cylindrical
Inclusions, Mathematical Studies of Composite Materials III.
Rohm and Haas Co. Report S-98, Huntsville, Alabama, June 1966,
pp. 30-38.
72. Margolin, G.G.: Elasticity Modulus in the Bending of Thin Speci-
mens of a Unidirectional Glass Reinforced Plastic. Polymer
Mechanics, vol. 3, no. 4, 1967, pp. 737-740.
73. Bert, C.W.: Flexural Micromechanics of a Composite Material
Containing Large-Diameter Fibers. Presented at the 60th Annual
Meeting of the Oklahoma Academy of Science, Norman, Okrla., Dec.
1971;.to be published in Proceedings, vol. 52, 1972.
74. Ely, J.F.; and Zienkiewicz, O.C.: Torsion of Compound Bars -
A Relaxation Solution. International J. Mechanical Sciences,
vol. 1, no. 4, July 1960, pp. 356-365.
75. Heaton, M.D.: A Calculation of the Elastic Contants of a
Unidirectional Fiber-Reinforced Composite. Brit. J. Appl.
Phys. (J. Phys. D.), ser. 2, vol. 1, 1968, pp. 1039-
1048.
138
76. Wu, C.; and Vinson, J.R.: On the Nonlinear Oscillations of Plates
Composed of Composite Materials. J. Comp. Matls., vol. 3, no. 3,
July 1969, pp. 548-561.
77. Gemant, A: The Measurement of Solid Friction of Plastics. J. Appl.
Phys., vol.11, no. 10, Oct. 1940, pp. 647-653.
78. Blum, S.L.: Some Physical Factors Affecting the Internal Damping
of Glass. J. Amer. Ceramic Soc., vol. 38, no. 6, June 1955,
pp. 205-210.
79. Tamchyna, J.; and V. Zvonar: Static and Dyanmic Properties of
Glass-Reinforced Plastics. Polymer Mechanics, vol. 1, no. 1,
Jan.-Feb. 1965, pp. 102-105.
80. Masri, S.F.: Cumulative Damages Caused by Shock Excitation.
Shock and Vibration Bull., Bull. 35, pt. 3, Jan. 1966, pp. 57-71.
81. Gustafson, A.J.; Mazza, L.T.; Rodgers, R.L.; and Mcllwean, E.H.:
Development of Test Methods for Measuring Damping of Fiber-
Reinforced Materials, USAAVLABS Technical Reprot 70-42, U.S.
Army Aviation Materiel Laboratories, Fort Eustis, Va., June 1970.
82. Granick, N.; and Stern, J.E.: Material Damping of Aluminum by
a Resonant-Dwell Technique. NASA TN D-2893, Clearing House
for Federal Scientific and Technical Information, Springfield,
Va., 1965.
83. Bodner, S.R.; and Fraser, A.F.: Vibrations and Wave Propagation in
139
Aluminum Alloys at Elevated Temperatures. Trans. Soc. Rheology,
vol. 6, no. 1, 1962, pp. 157-177.
84. Papirno, R.; and Slepetz, J.: Determination of Matrix and
Filament Stress-Strain Properties from Tests Made on Com-
posites, Composite Matls., Paris, Apr. 2-3, 1970), NATO,
Advisory Group for Aerospace Res. and Dev., AGARD-CP-83-71, Sept.
1971. AD-732741.
85. Bert, C.W.: Plasticity and Creep Analysis of Filamentary Metal
Matrix Composites SC-DR-720055, Sandia Laboratories, Albuquerque,
N.M., March 1972.
86. Mazza, L.T.; Paxon, E.B.; and Rodgers, R.L.: Measurement of
Damping Coefficients and Dynamic Modulus of Fiber Composites.
USAAVLABS-TN-2, (AD-8690 25) , U.S. Army Aviation Materiel Lab-
oratories, Fort Eustis, Va., May 1971.
87. Chi, C.C.: Forced Vibration of Laminated Anisotropic Plates
Including Thickness-Shear and Damping Effects. Ph.D. dissertation,
Univ. of Oklahoma, Norman, Okla., May 1972
88. Wegel, R.L.; and Walther, H.: Internal Dissipation in Solids for
Small Cyclic Strains. Physics, vol. 6, 1935, pp. 141-157.
89. Lazan, B.J.: A Study with New Equipment of the Effects of Fatigue
Stress on the Damping Capacity and Elasticity of Mild Steel.
Trans. Am. Soc. Metals, vol. 42, 1950, pp. 499-549.
140
90. Bishop, R.E.D.: The Theory of Damping Forces in Vibration Theory.
J. Roy. Aeron. Soc., vol. 59, no. 539, Nov. 1955, pp. 738-742.
91. Soroka, W.W.: Note on the Relations Between Viscous and Structural
Damping Coefficients. J. Aeron. Sci., vol. 16, no. 7, Jul. 1949,
pp. 409-410, 448.
92. Theodorsen, T.; and Garrick, I.E.: Mechanism of Flutter- A
Theoretical and Experimental Investigation of the Flutter Problem.
NACA TR 685, 1940.
93. Scanlan, R.H.; and Rosenbaum, R.: Introduction to the Study of
Aircraft Vibration and Flutter. Macmillan, 1951; Dover, 1968.
94. Myklestad, N.O.: The Concept of Complex Damping. J. Appl. Mech.,
vol. 19, no. 3, Sep. 1952, pp. 284-286.
95. Lancaster, P.: Free Vibration and Hysteretic Damping. J. Roy.
Aeron. Soc., vol. 64, no. 592, Apr. 1960, p. 229.
96. Reid, T.J.: Free Vibration and Hysteretic Damping. J. Roy. Aeron.
Soc., vol. 60, no. 544, Apr. 1956, p. 283.
97. Milne, R.D.: A Constructive Theory of Linear Damping. Paper C.4,
Symposium on Structural Dynamics, Loughborough Univ. of Tech-
nology, Loughborough, England, 1970.
98. Caughey, T..K.: Vibration of Dynamic Systems with Linear Hysteretic
Damping (Linear Theory). Proc. 4th. U.S. Nat. Congr. Appl.
Mech., vol. 1, 1962, pp. 87-97.
141
99. Paley, R.E.A.C.; and Wiener, N.: Fourier Transforms in the Complex
Domain. Am. Math. Soc. Colloquium Publicat., vol. 19, 1934.
100. Garcia - Moliner, F.; and Thomson, R.: Linear Response Functions
and the Phenomenological Equations of Internal Friction. J. Appl.
Phys. ,vol. 37, no. 1, Jan. 1966, pp. 83-89.
101. Fraeijs de Veubeke, B.M.: Influence of. Internal Dampikng on Air-
Craft Resonance. AGARD Manual on Elasticity, vol. 1, chap. 3, 1960.
102. Grandall, S.H.: Dynamic Response of Systems with Structural
Damping. Air, Space, and Instruments (C.S. Draper Anniv. Vol.),
S.Lees.ed. McGraw-Hill Book Co., 1963, pp. 183-193.
103. Crandall, S.H.: The Role of Damping in Vibration Theory. J. Sound
&Vib., vol. 11, no. 1, Jan. 1970, pp. 3-18.
104. Pinsker, W.: Structural Damping. J. Aeron. Sci., vol. 16, no. 11,
Nov. 1949, p. 699.
105. Scanlan, R.H.; and Mendelson, A.: Structural Damping. AIAA J.,
voLl, no. 4, Apr. 1963, pp. 938-939.
106. Naylor, V.D.: Some Fallacies in Modern Damping. J. Sound & Vib.,
vol.11, no. 2, Feb. 1970, pp. 278-280.
107. Scanlan, R.H.: Linear Damping Models and Causality in Vibrations.
J. Sound & Vib., vol. 13, no. 4, Dec. 1970, pp. 499-509.
108. Bishop, R.E.D.: The Behavior of Damped Linear System in Steady
142
Oscillation. Aeron. Quart., vol. 7, no. 2, May 1956, pp. 156-168.
., 109. Cunningham, H.J.: In Defense of Modern Damping Theory in Flutter
Analysis, J. Sound &Vib., vol. 14, no. 1, Jan. 1971, pp. 142-144.
110. Bland, D.R.: The Theory of Linear Viscoelasticity. Pergamon Press,
1960, pp. 3-4.
111. Parke, S.: Logarithmic Decrements at High Damping. Brit. J. Appl.
Phys., vol. 17, no. 2, Feb. 1966, pp. 271-273.
112. Flugge, W.: Viscoelasiticty. Blaisdell Publishing Company, 1967,
p. 14.
113. Hobbs, G.K.: Methods of Treating Damping in Structures. AIAA
Paper 71-349, presented at the AIAA/ASME 12th Structures, Structural
Dynamics and Materials Conference, Anaheim, Calif., Apr. 19-21, 1971,
114. Huang, T.C.; and Huang, C.C.: Free Vibrations of Viscoelastic
Timoshenko Beams. J. Appl. Mech., vol. 38, no. 2, June 1971,
pp. 515-521.
115. Granick, N.; and Stern, J.E.: Material Damping of Aluminum by
Resonance-Dwell Technique. Shock & Vib. Bull., Bull. 34, Pt. 5,
U.S. Dept. Defense, Feb. 1965, pp. 177-195.
116. Biot, M.A.: Linear Thermodynamics and the Mechanics of Solids.
Proc. 3rd. U.S. Nat. Congr. Appl. Mech., 1958, pp. 1-18.
117. Neubert, H.K.P.: A Simple Model Representing Internal Damping
in Solid Materials. Aeron. Quart., vol. 14, no. 2, May 1963, pp.
143
187-210.
118. Boltzmann, L.: Zur Theorie der elastische Nachwirkung. Annalen
der Physik und Chemie, suppl. 7, 1876, pp. 624-654. .
119. Volterra, E.: Vibrations of Elastic Systems Having Hereditary
Characteristics. J. Appl. Mech., vol. 17, no. 4, Dec. 1950,
pp. 363-371.
120. Pisarenko, G.S.: Vibrations of Elastic Systems Taking Account
of Energy Dissipation in the Material. Kiev, 1955; Engl. transl.,
WADD TR-60-582, Wright Air Development Div., Feb. 1962 (AD-274743)
121. Rosenblueth, E.; and Herrera, I.: On a Kind of Hysteretic Damping.
J. Eng. Mech. Div., Proc. ASCE, vol. 90, no. EM4, Aug. 1964, pp.
37-48.
122. Chang, C.S.; and Bieber, R.E.: Synthesis of Structural Damping.
AIAA J., vol. 6, no. 4, Apr. 1968, pp. 718-719.
123. Kennedy, C.C.; and Pancu, C.D.P.: Use of Vectors in Vibration
Measurement and Analysis. J. Aeron. Sci., vol. 14, no. 11,
Nov. 1947, pp. 603-625.
124. Pendered, J.W.; and Bishop, R.E.D.: A Critical Introduction to
Some Industrial Resonance Testing Techniques. J. Mech. Eng.
Sci., vol. 5, no. 4, Dec. 1963, pp. 345-367.
125. Kolsky, H.: Stress Waves in Solids. Oxford Univ. Press, 1963;
Dover, 1963.
144
TABLE I. COMPARISON OF LONGITUDINAL IN-PLANE POISSON'S RATIO.
Ef/Em
120.
5.3
24.1
Longitudinal In-Plane Poisson's Ratio v,«
Eq. (30)
0.331
0.317
0.316
0.292
0.286
0.273
0.260
0.299
0.284
0.269
Eq. (38)
0.322
0.311
0.300
0.288
0.282
0.270
0.258
0.294
0.282
0.268
Vf
0.3
0.4
0.5
0.6
0.4
0.5
0.6
0.4
0.5
0.6
145
TABLE II. LONGITUDINAL FLEXURAL STIFFNESS EFFICIENCY OF
MONOFILAMENT COMPOSITES.
Composite
Steel-Epoxy
S glass-Epoxy
Boron-Epoxy
Boron-Al.
E./Ef m
74
24
120
6
• 6
1.00
1.00
0.95
0.90
0.95
0.93
1.00
0.85
0.90
0.95
0.85
0.90
0.95
0.85
U
1.11
1.06
1.11
1.11
1.06
1.16
1.00
1.38
1.23
1.11
1.38
1.23
1.11
1.38
Vf
0.636
0.708
0.673
0.707
0.746
0.743
• 0.785
0.482
0.572
0.673
0.482
0.572
0.673
0.482
E ( b ) /E11 ' 11
Eq. (48)
0.616
0.683
0.683
0.755
0.755
0.730
0.755
0.578
0.636
0.697
0.549
0.614
0.681
0.678
Eq.(142)
0.608
0.677
0.677
0.750
0.750
0.725
0.750
0.542
0.608
0.677
0.542
0.608
0.677
0.542
146
TABLE III. COMPARISONS OF POISSON FLEXURAL STIFFNESS
FOR COMPOSITES HAVING SQUARE TYPICAL ELEMENTS.
Composite
Boron-Epoxy
Glass-Epoxy
Boron-Al.
FiberVolumeFraction
0.4
0.5
0.6
0.4
0.5
0.6
0.4
0.5
0.6
[D12]eq. (50) ' [D12]eq. (4)
0.725
0.593
0.567
0.780
0.657
0.638
0.930
0.835
0.833
147
TABLE IV. COMPARISONS OF IN-PLANE LONGITUDINAL SHEAR MODULUS AND
EQUIVALENT SHEAR MODULUS AS CALCULATED FROM THE TORSION ANALYSIS.
Composite
Boron-Epoxy
E Glass-Epoxy
Boron-Al .
Gf / Gm
135.
23.4
6.7
Fibervolumefraction
0.4
0.5
0.6
0.4
0.5
0.6
0.4
0.5
0.6
Ratio G,, /Gbo m
In-Plane
2.30
3.23
4.67
2.16
2.84
3.80
1.84
2.22
2.72
Equivalent in Torsion
25.30
38.98
55.66
5.04
7.34
10.13
2.01
2.58
3.29
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(a) Monofilament composite
(b) Composite with randomly distributed filaments
I. Filamentary composites.
214
(a) Uniaxial loading
x, •*
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215
Figure 3. L o n g i t u d i n a l shear loading of a typica l composite c lement ,
m
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(a) ( b )Figure- 4. Transverse tension loading of a typical composite element
(a) Pure bending of a typical element
dy
(b) One-quarter cross section
Figure 5. Longitudinal flexural loading of a typical mono-filament composite element.
2/7
(a) (b)
Figure 6. Transverse flexural loading of a typical monofilament compositeelement.
218
OOP OOP O OO
n th element (n-H)-th element Nth element
-\\
Figure 7. Torsional loading of a monofilament composite layer.
219
(a) Tip loading of a monofilament beam
(b) Cross-sectional view
Figure 8. Tip loading of a monofilament composite
element.
22C
(a) Transverse thickness-shear loading
(b) Equilibrium of stresses in atypical strip
Figure 9. Transverse thickness-shear loading of a mono
filament composite element.
221
IMAGINARY AXIS
REAL AXIS
Figure 10. Concept of complex moduli and
loss angle.
222
EUJ*x
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fTSAI (Ref. 68)ADAMS a DONER
(Ref. 56)PRESENT THEORY
GLASS-EPQXY
ALUMINUN
10 20 40 100 200 400
Figure 11. Transverse Young's modulus.
223
SQUARE TYPICAL ELEM
Eq. (48)Eq. (142)
100 200
Figure 12. Flexural stiffness efficiency.
224
100 200
Figure 13. Transverse flexural stiffness
efficiency.
225
(II90X (670)
0(0.012)
0(0.002)
0(-0.003)
(3650) (1400) (760)
(-0.001)
0(-0.001)
Figure 14. Comparisons of Prandtl torsionfunction (0x10 ) of a squarematrix with a circular insert.
Remarks; Numbers at the meshpoints denote the values ofxl(A obtained by Ely and?ienkiewics (ref. 75) andthose from the point-matchingmethod (in parentheses).
226
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08
Figure 16. Twisting stiffness versus fiber volume fraction
228
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20
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63
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FIBER VOLUME FRACTION V,f
Figure 17. Longitudinal thickness-shear modulus.
229
15
10
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Boron-Epaxy
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Gloss-Epoxy
Boron-Alum.
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74
24
6
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78
262
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FIBER VOLUME FRACTION Vf
Figure 18. Transverse thickness-shear modulus.
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