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EXPERIMENTAL MECHANICS - Experimental Characterization of Composite Materials - Ibrahim Miskioglu

Encyclopedia of Life Support Systems (EOLSS)

EXPERIMENTAL CHARACTERIZATION OF COMPOSITEMATERIALS

Ibrahim Miskioglu ME-EM Department, Michigan Technological University, Houghton, MI 49931, USA

Keywords : Composite materials, fiber reinforced polymers, material characterization.

Contents

1. Introduction2. Basics of Composite Materials2.1. Constitutive Relationships2.1.1. Constitutive Relationships for a Unidirectional Lamina

2.1.2. Constitutive Relationships for a Laminate3. Characterization of Composite Material Properties3.1. Constituent Properties3.1.1. Fiber Properties 3.1.2. Matrix Properties3.2. Lamina Properties3.2.1. Lamina Tensile Properties3.2.2. Lamina Compressive Properties3.2.3. Lamina Shear Properties3.2.4. Lamina Flexural Properties3.3. Lamina Hygrothermal Properties3.3.1. Lamina Thermal Expansion Coefficients3.3.2. Lamina Moisture Expansion Coefficients3.4. Interlaminar Testing3.4.1. Interlaminar Shear Strength3.4.2. Fracture Tests3.5 Testing of Sandwich Composites3.5.1. Shear Properties of Sandwich Core Material3.5.2. Flexural Properties of Sandwich Composite Construction3.5.3. Flexural Properties of Sandwich Composite Plate4. ConclusionGlossaryBibliographyBiographical Sketch

Summary

Composite materials (Fiber Reinforced Polymers) offer light weight and highstiffness/strength. Due to these attributes their use in structural applications hasincreased dramatically practically at every length scale. A successful design andanalysis of a composite structure requires knowledge of the material properties such asstrength and stiffness. Material properties are determined in general by experimental

methods. In the event the material properties of the composite are determined by

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micromechanics models utilizing the properties of the constituents, then experimentaldetermination of the constituent properties and experimental verification of the material

property is required. As a background, a brief introduction to the mechanics ofcomposite materials is presented which is then followed by the discussion of the

experimental methods to determine the basic properties of a typical fiber reinforced polymer.

1. Introduction

Lightweight structures that meet even exceed the performance and safety requirementsin the strictest sense are gaining more importance. Fiber reinforced polymer compositeshave been shown to perform successfully in many structural applications, and it isexpected their use will increase further in the upcoming years.

A typical composite material consists of at least two distinct phases when combinedoffer advantages which cannot be offered by any one of its constituents alone. Acomposite material is sought after when lightweight structures are needed withsufficient strength and stiffness. Application of composite materials can be found fromaerospace, marine, automotive areas to biomedical implants.

Composite materials fall into the general category of anisotropic materials, for whichthe material properties exhibit directional characteristics. On the other hand the mostcommon engineering materials such as steel etc., are considered isotropic for whichthere is no dependence of material properties on direction. Isotropic materials can becharacterized by two independent material constants only, but for anisotropic materials

the number of constants can be as high as 21depending on the number of planes ofmaterial symmetry the material possesses.

2. Basics of Composite Materials

2.1. Constitutive Relationships

The constitutive relationship for the anisotropic materials is obtained throughgeneralized Hookes Law and is expressed as

klijklij C = )3,2,1,,,( =lk ji (1)

And

klijklij S = )3,2,1,,,( =lk ji (2)

where ij and ij are stress and strain tensors respectively, ijklC is the stiffness matrix

and ijklS is the compliance matrix.

Generalized Hookes Law can also be expressed in terms of contracted notation as

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jiji C = ( 6,...,2,1, = ji ) (3)

and

jiji S = ( 6,...,2,1, = ji ) (4)

This notation is obtained by letting111 = 111 = 222 = 222 = 333 = 333 = (5)

234423 === 423232 ==

315531 === 531312 ==

126612 ===

612122 ==

and

111111 C C = , 121122 C C = ; 131133 C C = ; 141123 2C C = ; 151131 2C C = ; 161112 2C C = ; etc.

Both stiffness and compliance matrices are symmetric and the compliance matrix is theinverse of the stiffness matrix. These matrices contain 81 elastic constants which reduceto 36 due to the symmetry of stress and strain tensors and further reduce to 21 due to thesymmetry of stiffness and compliance matrices. Hence for a general anisotropicmaterial a total of 21 elastic constants are needed to fully characterize the material.Materials may exhibit planes of material symmetry which in turn reduces the number ofelastic constants needed to characterize the material. The direction perpendicular to the

plane of material symmetry is known as the principal material axes. Based on thenumber of planes of material symmetry that a material possesses, the materials areclassified as follows:

Monoclinic materials : These materials contain one plane of material symmetry andthe number of elastic constants needed is 13.

Orthotropic materials : Two mutually orthogonal planes of material symmetry existand the number of elastic constants needed to characterize the material reduces to nine.

Note that if there are two planes of material symmetry, then a third plane of materialsymmetry exists which is mutually orthogonal to the other two.

Transversely isotropic materials : These materials have one plane of symmetry and thenumber of elastic constants reduces to five.

Isotropic materials : Every plane is a plane of material symmetry and only two elasticconstants are needed to characterize the material.

The fiber-reinforced polymers (FRP) are in general considered as orthotropic or

transversely isotropic. The higher stiffness composites manufactured from

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unidirectional lamina are orthotropic and the short fiber composites are in generaltransversely isotropic. In this chapter the emphasis will be on the experimentalcharacterization of the unidirectional composites. The methods that will be presentedare based on the testing standards specified by American Society for Testing and

Materials (ASTM).

For an orthotropic material the stress-strain relationship with respect to its principalmaterial directions is

=

6

5

4

3

2

1

66

55

44

333231

232221

131211

6

5

4

3

2

1

00000

00000

00000

000

000

000

C

C

C

C C C

C C C

C C C

(6)

or

=

6

5

4

3

2

1

66

55

44

333231

232221

131211

6

5

4

3

2

1

0000000000

00000

000

000

000

S S

S

S S S

S S S

S S S

(7)

The compliance terms in terms of the engineering constants are expressed as

111

1 E

S = 1

12

2

212112 E E

S S ===

222

1 E

S = 1

13

3

313113 E E

S S ===

(8)

333

1 E

S = 2

23

3

323223 E E

S S ===

2344

1G

S = 13

551

GS =

1266

1G

S =

where i E ( )3,2,1=i are the moduli of elasticity associated with the principal materialdirections, ij )3,2,1,( = ji are the Poissons ratio (e.g. 1212 = is obtained from auniaxial test when the applied stress is in the 1-direction), and jiG , )3,2,1,( = ji are theshear moduli associated with the plane ij .

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Hygrothermal strains due to change in moisture and temperature can be evaluated as

cT MT

MT

MT

+=

3

2

1

3

2

1

3

2

1

(9)

where T is the change in temperature, c is the change in moisture content, i )3,2,1( =i are the thermal expansion coefficients and i )3,2,1( =i are the moisture

expansion coefficients. Note that the shear strains are zero due to the hygrothermaleffects.

2.1.1. Constitutive Relationships for a Unidirectional Lamina

The building block in a typical laminated composite is the unidirectional lamina. Once aunidirectional lamina is characterized, then the properties of laminates with differentarchitecture can be deduced relatively easily.

The thickness of a unidirectional lamina is very small compared to its in-planedimensions, hence for all practical purposes a state of plane stress can be assumed. If

03 = , 0423 == and 0513 == then the stress strain relations reduce to

=

6

2

1

66

2212

1211

6

2

1

00

0

0

Q

QQ

QQ

(10)

=

6

2

1

66

2212

1211

6

2

1

00

0

0

S

S S

S S

(11)

where ijQ are the reduced stiffness coefficients and they are given by

2112

1

33

13131111 1 == E

C C C

C Q

2112

212

2112

121

33

23131212 11

=

== E E C

C C C Q

(12)

2112

2

33

23232222 1

== E C

C C C Q

126666 GC Q ==

The compliance terms ijS are as before given by Eqs. (8).

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2.1.1.1 Transformation of Stress-Strain Relationships for Unidirectional Lamina

If the lamina is loaded in a direction other than the principal material directions, it ismore advantages to express the stress-strain relationship with respect to a coordinate

system more suitable to handle the problem in hand.

Consider that the x-y coordinate system is oriented with respect to the principal axes 1-2as shown in Figure 1. Then the stresses in the 1-2 and x-y coordinate systems are relatedto each other through

1

2

6

xx

yy

xy

=

T with

2 2

2 2

2 2

2

2

m n mn

n m mn

mn mn m n

=

T (13)

and 1

12

6

xx

yy

xy

=

T where

2 2

1 2 2

2 2

2

2

m n mn

n m mn

mn mn m n

=

T (14)

Figure 1. Coordinate system for transformation between the principal material axes andthe x-y coordinate system

Note that 1T is the inverse of the transformation matrix T and, )cos( =m and)sin( =n .

The strain transformations can be achieved through the use of the transformation matrixand/or its inverse, e.g.

1

2

1 162 2

xx

yy

xy

=

T and1

12

1 162 2

xx

yy

xy

=

T (15)

Using the transformation relationships Eqs. (12)-(14) together with Eq. (10) we canwrite

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11 121

12 22

166 2

0

0

0 0 2

xx xx

yy yy

xy xy

Q Q

Q Q

Q

=

T T (16)

which is reduced to

=

xy

yy

xx

xy

yy

xx

QQQ

QQQ

QQQ

666261

262221

161211

(17)

where

6622

1222

224

114

11 42 QnmQnmQnQmQ +++=

6622

1222

224

114

22 42 QnmQnmQmQnQ +++= 66

2212

4422

2211

2212 4)( QnmQnmQnmQnmQ +++= (18)

6633

1233

223

113

16 )(2)( QnmmnQnmmnQmnnQmQ ++=

6633

1233

223

113

26 )(2)( QmnnmQmnnmnQmQmnQ ++=

66222

1222

2222

1122

66 )(2 QnmQnmQnmQnmQ ++=

Note that in the x- y coordinate system, although the material is orthotropic, this is notevident from Eq. (17) since the transformed stiffness matrix ijQ has all non-zero

coefficients, the same as an anisotropic material. The coefficients given in Eq. (18) arenot independent; they are all functions of the four lamina stiffnesses with respect to the

principal material axes.

Alternatively the strains are expressed in the x- y coordinate system as

=

xy

yy

xx

xy

yy

xx

S S S

S S S

S S S

666161

262221

161211

(19)

where the transformed lamina compliances ijS are

6622

1222

224

114

11 2 S nmS nmS nS mS +++=

6622

1222

224

114

22 2 S nmS nmS mS nS +++=

6622

1244

2222

1122

12 )( S nmS nmS nmS nmS +++=

6633

1233

223

113

16 )()(22 S nmmnS nmmnS mnnS mS ++= (20)

6633

1233

223

113

26 )()(22 S mnnmS mnnmnS mS mnS ++=

66222

1222

2222

1122

66 )(844 S nmS nmS nmS nmS ++=

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In terms of engineering constants, the stress strain relationship becomes

=

xy

yy

xx

xy y xy y x xy x

xy y xy y x xy

xy x xy y yx x

xy

yy

xx

G E E

G E E

G E E

1

1

1

,,

,

,

(21)

From the symmetry of the compliance matrix we get

y

xy y

xy

y xy

x

xy x

xy

x xy

y

yx

x

xy

E G

E G

E E

,,

,,

=

=

=

(22)

The engineering constants are determined from simple uniaxial tests. For example if0 xx and all the other stress components are zero, then xx xx x E = is the modulus

of elasticity associated with the x-direction, xx yy xy = is the Poissons ratio, and

xx xy xy x =, is the shear coupling coefficient. Likewise if 0 yy and all the otherstress components are zero, then yy yy y E = is the modulus of elasticity associatedwith the y-direction, yy xx yx = , and yy xy xy y =, , and if 0 xy and all the

other stress components are zero, then xy xy xyG = is the shear modulus associatedwith the x-y directions, xy xx x xy =, and, xy yy y xy =, .

2.1.2. Constitutive Relationships for a Laminate

Composite materials are used by forming a laminate from individual lamina. Eachlamina is thin and may have different fiber orientation and in some cases may havedifferent materials (see Figure 2). The response of the laminates to loads depends on the

properties, fiber orientation and stacking sequence of its layers. Two laminatescomposed of identical lamina, with the same thickness will respond to loads differently

if laminae are arranged differently. Analysis of laminates is mostly restricted to flat panels with limited discussion on curved laminates which can be found in textbooks onmechanics of composite materials.

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Figure 2. Laminated structure

Analysis of flat laminates under in-plane and bending loads are based on the Kirchoff-Love hypothesis. Assuming that all layers are perfectly bonded (no slippage betweenthe layers), Kirchoff hypothesis state that a line perpendicular to geometric midsurface(reference plane) remains straight and does not change its length while the laminate isdeforming under the applied loading. This hypothesis results in 0= zz , 0== yz xz .Then the strain distribution in the laminate is expressed by

+=

xy

y

x

xy

yy

xx

xy

yy

xx

z

0

0

0

(23)

where z is measured from the geometric midsurface as shown in Figure 3. The straincomponents 000 ,, xy yy xx are the strains of the geometric midsurface (reference plane) and

xy y x ,, are the bending curvatures of the reference plane in the xz, yz and xy planes

respectively.

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Figure 3. Laminate with coordinate notation for individual lamina

Determination of the force, xy y x N N N ,, and moment, xy y x M M M ,, resultants yields

the following constitutive relationships

+=

xy

y

x

xy

y

x

xy

y

x

B B B

B B B

B B B

A A A

A A A

A A A

N

N

N

662616

262212

161211

0

0

0

662616

262212

161211

(24)

+=

xy

y

x

xy

y

x

xy

y

x

D D D

D D D

D D D

B B B

B B B

B B B

M

M

M

662616

262212

161211

0

0

0

662616

262212

161211

(25)

where

)( 11

=

= k k n

k ijij hhQ A , 1, 2,6 (Extensional Stiffness)i j =

)(21 2

12

= k k ijij hhQ B , 1, 2,6 (Coupling Stiffness)i j =

)(31 3

13

= k k ijij hhQ D , 1, 2,6 (Bending Stiffness)i j =

If temperature and moisture change is considered, then the force and moment results are

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MT1 1

1 1

( ) ( )n n

k k k k xy ij xy k k ij xy k k

k k

h h T h h c = =

= + N Q Q (26)

MT 2 2 2 21 11 1

1 1( ) ( )2 2

n n

k k k k xy ij xy k k ij xy k k k k

h h T h h c = =

= + M Q Q (27)

and these can be superimposed to the force and moment resultants given in Eqs. (24)and (25).

Load-deformation relationships can be inverted to express strains and curvatures interms of loads and moments, i.e.,

0

0

0

xx x x

yy y y

xy xy xy

N M

N M N M

= + A B (28)

x x x

y y y

xy xy xy

N M

N M

N M

= +

C D (29)

where the matrices A , B , C and D are computed as1 * 1 * = *A A B D C

* 1 *B = B D * 1 * = C D C

* 1 =D D with

* 1= B A B * 1=C BA * 1= D D BA B

it should be noted that B C

What are given above are the main constitutive equations for a single lamina and

laminates. More detailed analysis of lamina and laminates can be found in the textbookson mechanics of composite materials.

3. Characterization of Composite Material Properties

A lamina is the main building block of a laminate, and the properties of a lamina alongwith the stacking sequence of the lamina are used to predict the response of laminates toloading. These predictions need the basic properties of the constituents of the laminaand the lamina itself. Constituent properties are needed to design the lamina throughmicromechanical models that relate the constituent properties to the property of alamina. Of course experimental measurement of properties is needed at both theconstituent and lamina levels.

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Bibliography

Adams D.F. (2005). A comparison of shear test methods. High Performance Composites , 13(5), 9-10. [Asummary of shear test methods is presented]

Adams D.F., Carlsson L.A., Pipes R.B. (2003). Experimental Characterization of Advanced Composite Materials , Third Edition, CRC Press, Boca Raton, FL, USA [A comprehensive guide to forcharacterization of composites materials]

ASTM Standards (2008), Volume 8.01, Plastics (I) , ASTM International, West Conshohocken, PA, USA[ASTM Standards volumes where the standards mentioned in the text can be found]

ASTM Standards (2008), Volume 8.03, Plastics (III) , ASTM International, West Conshohocken, PA,USA

ASTM Standards (2008), Volume 15.01, Refractories: Activated Carbon; Advanced Ceramics , ASTMInternational, West Conshohocken, PA, USA

ASTM Standards (2008), Volume 15.03, Space Simulation; Aerospace and Aircraft; Composite Materials , ASTM International, West Conshohocken, PA, USA

Carlsson L.A., Gillespie, Jr. J.W., Pipes R.B. (1986). On the analysis and design of the end notchedflexure (ENF) specimen for mode II testing, J. Composite Materials, 20, 594-604. [Details f the ENFspecimen and mode II testing is discussed]

Daniel I.M., Ishai O. (2006). Engineering Mechanics of Composite Materials, Second Edition, OxfordUniversity Press, NY, USA. [General reference for mechanics of composite materials]

Gibson R.F. (2006). Principles of Composite Material Mechanics, Second Edition, CRC Press, BocaRaton, FL, USA. [General reference for mechanics of composite materials]

Hojo M., Sawada Y., Miyairi H. (1994). Influence of clamping method on tensile properties ofunidirectional CFRP in 0 and 90 directions-round robin activity for international standardization inJapan, Composites , 25(8), 786-796. [Effect of the specimens with tapered and untapered tabs on tensile properties is discussed]

Pagano N.J., Halpin J.C. (1968). Influence of end constraint in the testing of anisotropic bodies, Journalof Composite Materials , 2, 18-31. [Influence of clamping the off-axis tensile specimen on the state of thestress is discussed]

Tsai C.L., Daniel I.M. (1994). Method for Thermomechanical Characterization of Single Fibers,Composites Sci. and Technol. 50, 7-12. [Details of the fixture shown on Figure 5 and the correspondingtest method is discussed]

Tsai C.-L., Wooh, S.-C. (2001). Hygric characterization of woven glass/epoxy composites, Experimental Mechanics , 41(1), 70-76. [Measurement of moisture expansion coefficients using transverse deflection ofan axially constrained specimen is discussed]

Walrath D.E., Adams D.F. (1983). The Iosipescu shear test as applied to composite materials,

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Experimental Mechanics , 23(1), 105-110. [Adaptation of the Iosipescu shear fixture to composites isdiscussed]

Welsh J.R., Adams D.F. (1997). Current status of compression test methods for composite materials,SAMPE Journal , 33(1) 35-43. [A summary of compression test methods is presented]

Whitney, J.M., Daniel I.M., Pipes R.B. (1984). Experimental Mechanics of Fiber Reinforced Composite Materials, rev. ed., Society for Experimental Mechanics, Prentice Hall, Englewood Cliffs, NJ, USA. [Useof strain gages for the determination of thermal expansion coefficients is presented]

Yaniv G., Perimanidis G., Daniel I.M. (1987). Method for Hygrothermal Characterization ofGraphite/Epoxy Composite, J. Composites Technology Research, 9, 21-25. [Measurement of moistureexpansion coefficients using embedded strain gages is discussed]

Biographical Sketch

Ibrahim Miskioglu received his B.S. (1976) in mechanical engineering from Bogazici University, Istan- bul -Turkey and M.S. (1978) from Mississippi State University in mechanical engineering, and Ph.D.(1981) in engineering mechanics from Iowa State University.

He is an Associate Professor of Engineering Mechanics in the ME-EM Department of MichiganTechnological University (MTU). He has served on the Executive Committee of the ME-EM Departmentas the Director of Solid Mechanics Area a number of times during his tenure at MTU. His current/ recentresearch interests include: experimental stress analysis, composite materials, failure studies of randomfiber composites with applications to structural problems, study of equal-channel angular extrusion(ECAE) of metallic alloys and material characterization by nanoindentation.

Dr. Miskioglu has been an active member of Society for Experimental Mechanics since 1979. He hasserved as the Vice Chair/Chair of Application Committee between 1989 and 1995, and as an ExecutiveBoard Member between 1999 and 2001. He has also served as the Associate Editor/Editor ofExperimental Techniques between 1991 and 1997.

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