Composite Bolted Joints Analysis Programs

Bruce D. Snyder, t Joe G. Burns, 1 and Vipperla B. Venkayya ~

Composite Bolted Joints Analysis Programs

REFERENCE: Snyder, B. D., Burns, J. G., and Venkayya, V. B., "Composite Bolted Joints Analysis Programs," Journal of Compos- ites Technology & Research, JCTRER, Vol. 12, No. 1, Spring 1990, pp. 41-51.

ABSTRACT: Several different composite bolted joint analysis programs are now available to composite structures designers. All of the programs vary widely in the amount of input required, output re- ceived, and required user knowledge of composite materials. Six different bolted joint analysis programs will be examined. The various programs are (1) A4EJ, (2) BJSFM, (3) SASCJ, (4) SAMCJ, (5) SCAN, and (6) JOINT. Other analysis programs exist, but they apply many constraints on the problem definition and depend heavily on empirical test results. The relative merits of each program as well as their disadvantages will be discussed. The most appropriate ap- plications of each of the programs will be presented, and some nu- merical comparisons of the results will be made. Each of the programs has a useful place in the design and analysis arena. An examination of the programs will be made to help users determine which program will best suit their needs.

KEYWORDS: composites, bolted joints, analysis, design

Nomenclature

ai Complex coefficient a~j Series coefficients

Aq Laminate compliances b Radius of hole C Half-distance between outer rows of bolts (for single lap

joints) d Bolt hole diameter e Edge distance

E Modulus of elasticity F Complex stress function

F~. Ultimate bearing stress allowable F,. Ultimate joint shear stress allowable F,. Ultimate tensile stress allowable

Fo7 Stress value at .7 × E on the stress-strain curve K Bending moment coefficient for single lap joint Mo

K. Stress concentration factor for unloaded hole /(,2 Stress concentration factor for loaded hole

l Lap step length Mo Bending moment at edge of overlap

N Stress resultants N~ Allowable joint stress resultant p, Running shear load in member i Pb Bolt bearing load

1Aerospace engineer, aerospace engineer, Member AIAA Flight Dy- namics Laboratory, Wright-Patterson Air Force Base, OH 45433.

© 1990 by the American Society for Testing and Materials 41

P(k) Fastener load P, Bypass load

t Lap thickness t, Effective thickness reacting bolt hole T Temperature Ti Internal load in member i

AT (To..r.,,o.- T~se.,~,,.) u Displacement in the x direction v Displacement in the y direction w Lap width a Coefficient of thermal expansion

Displacement In-plane strains

v Poisson's ratio ~, Mapping function

ere Bending stress ~r, Bypass stress ~r Shear stress qb, Complex functions

Introduction

Composite materials possess both the qualities of light weight and high strength. Lightweight composite structures must be efficiently designed to take full advantage of their qualities. Building structures with composite materials is very different from building strictly with metals. Although composites offer high strength with less weight, an inefficiently designed composite structure can easily weigh more than an equivalent metal structure. Joints are key elements of composite structures and are the weakest links in the overall performance of a structure. Composite joints can cause problems because of delamination, anisotropy, absence of ductility and environmental effects when they are not properly designed. Methods of joining metal to composite and composite to composite in substructure is an area of increased emphasis [1].

The two most common ways of joining composite structures are adhesive bonding and bolting. Both joining methods have advantages and disadvantages associated with them. Bonded joints have their place in structures, but they have problems such as debonding, susceptibility to impact damage, higher construction costs, and inaccessibility after construction. Bolted joints also have problems that must be accounted for such as bearing failures, bolt pullout, and delamination. Bolted joints are gen- erally capable of carrying higher loads than an equivalent bonded structure. Bolted joints also tend to weigh more than bonded joints but for major structural components, the extra weight is

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42 JOURNAL OF COMPOSITES TECHNOLOGY & RESEARCH

worth the added strength. For major structural components, the joints are usually bolted together. Mechanically fastened joints can provide structures that are more reliable, maintainable, ac- cessible, and cost effective. When properly designed, composite layups and joints can be tailored to efficiently carry the structural design loads.

With the high costs associated with designing and testing composite materials, methods of analytically determining the strength of composite structures have been developed. Analytical methods are preferred because of their potential for generality, economy, and exactness, and are principally formulated from two-dimensional anisotropic elasticity theory. An examination of the analytical methods used to determine the strength of bolted composite joints will be performed. All of the analysis methods for bolted joints are in use in industry today [2].

Joint Analysis Code

JOINT is a composite joint analysis code developed by the Douglas Aircraft Company from 1976 to 1978 [3]. The code is capable of analyzing both bonded and bolted joints from an interactive graphics terminal. JOINT is based on a simplified theory that relies on empirical test data for its simplicity. JOINT is capable of analyzing the following types of joints: balanced double-lap, supported single-lap, stepped-lap, and unsupported single-lap. The code is capable of performing a limited type (brute force, trial, and error) of joint optimization on the following types of infinite width bolted joints: double-lap, supported single-lap, and unsupported single-lap. For the optimization, the code determines the number of bolt rows, bolt diameter, bolt spacing, and joint thickness for the lightest joint that will carry the applied load. The coupling effects of the bolt rows has been neglected, which can cause severe error for some types of joint analysis.

The code assumes a bypass stress equal to

/,, P~ ~, = g , , - + g,~ (1)

t(w - at) t~(w - d)

and a bending stress equal to

6Mo o-b = f (2)

and

1 k = 1 + ~C + 1,~2C~ (4)

(2 _ 12(1 - V2"N~] (5) E?

where the allowable joint stress resultant N~, depends on the failure mode. For a tensile mode of failure

N, = F,,t(1 - d/w) (6)

P, Ka + Pb~K~z + 3K(1 - d/w)

For a bearing failure

/~,t d N ~ -

P b w (7)

For a bolt shear failure

~r F~.(bolt)d d X~ - (8)

2 P~ w

For a bolt tear-out failure

,9, N~ = 2 - 0 . 5 Pb w

The analysis is performed for an infinite width plate with a specified bolt spacing through the width of the plate.

The JOINT analysis code makes several simplifying assumptions in the analysis. Test data must be used to obtain stress concentration relief data for the composite plates. After the experimental data are obtained, the stress concentration factors are found. These concentration factors are used to determine the stresses in the plate. Only uniaxial loadings can be applied to the joint. JOINT is not capable of analyzing compressively loaded joints, and the analysis assumes that the fasteners do not fail. For all of the different types of joints the JOINT program can analyze, the following restrictions apply

The stress concentration factors, K,1 and Ka, are derived from test data. K,1 and Ka are functions of the diameter of the bolt holes and widthwise bolt spacing w. The constants in the functions are determined for an AS/3501-6 graphite epoxy composite with different percentages of 0 ° plies. The code only has the concentration factors calculated for composites with 25 and 37.5%, 0 ° plies. The bolt load distribution depends on the bolt and joint flexibility, but bolt torque-up and bolt type are not accounted for. The code allows four different failure modes: (1) tension at the hole, (2) bolt bearing, (3) bolt shear, and (4) shear tear-out. The bearing stress is determined differently for each type of failure. With the bending stress equal to cr~ = 6Mo/f

Mo = kN~ 2 (3)

e w 3 D ~ m d 3 3 - < ~ - < 12 t - < d - d < 1½ row pitch = 6d

Other limitations are

• choice of two bolt materials, joint load limitation of 40 000 lb (18 144 kg)

• choice of two composite layups, limitation on the number of bolt rows

For a double-lap configuration, the thickness of the two outer splice plates must be one-half the thickness of the center plate. A stepped lap joint configuration assumes that the bolts are at the center of the steps. Varying step lengths, bolt diam- eters, and lengthwise spacing between bolts can be specified. All bolt row coupling effects are neglected and the bolts are assumed to be lined up one behind the other. For an optimization problem, the bolts must be the same size for every bolt row. Bolt


row spacing is assumed to be uniform for the whole joint. In summary, the code applies quite a few constraints to problem definitions and has a limited analysis and data output capability. Problems do run very quickly, which allows many design itera- tions to be performed in a short period of time.

A4EJ Analysis Code

A4EJ is a composite bolted joint analysis code developed by the Douglas Aircraft Company from 1979 to 1981 [4]. A4EJ has the capability to analyze multi-row joints having a nonlinear load- deflection characteristic for the fasteners, and linear or Ramberg- Osgood characterizations of the adherends. A4EJ accounts for nonlinearities in the joint because of (1) fastener load-deflection characteristics, (2) fastener clearance, (3) elastomechanical deformation of the members between the fasteners, and (4) inter- action between bearing and bypass loads. A4EJ is based on continuum mechanics techniques, requiring shorter computer run times than finite-element modeling techniques. A4EJ pro- vides a detailed definition of the internal load transfer within a joint and requires a large amount of input data.

The load transfer through the fasteners within a joint is char- acterized in terms of the relative displacement between the members at each fastener station. A4EJ assumes a bilinear elastic load deflection curve. The known boundary conditions are at both ends of the joint. The problem is solved iteratively by start- ing at one end of the joint and assuming a value for an unknown quantity. The user can assume the total joint strength or the

SNYDER ET AL. ON BOLTED JOINTS ANALYSIS PROGRAMS 43

displacement at the first fastener induced by a specified load. By calculating progressively along the joint and satisfying both equilibrium and compatability requirements, the reactions at the other end of the joint can be determined. The initial assumption can be modified until all the boundary conditions are satisfied at both ends of the joint. The initial assumption must be very close; otherwise the solution will diverge.

Figure 1 shows how the typical equations for each step of the joint are established. The conditions of equilibrium for Member 1 between stations k and k + 1 are

~'~l(k+l ) : Tl(k ) - - P(k)+ p l l ( k ) (10)

Similarly for Member 2

T~(,+,) = T~(k ) + h , ) -p2t(k) (11)

Figure i shows a joint in single lap shear. In a double shear joint, the two portions of Member 1 or 2 would be combined and the fastener load P would be changed from single to double shear values. To make sure the analysis complies with compatability requirements, the mechanical and thermal properties of the members must be used. The user must input the stiffness of each member between each adjacent pair of fastener stations, allowing variations in width and thickness. Provisions are also made for thermally induced strains. The nonlinear load-deflection behavior of materials is accounted for by using the Ramberg-Osgood model for loading beyond the material proportional limit.

o ! - = 1' ........ ' .... I b = t .

" - ' - 1 . . . . . . . . l ' - P( k)'~' ' STATION NO. k.2

- ~ j~ T2(k.2 )

~ "--'I~TI (k.2) ",,IP-'-- ,,ip-,..*

k.1 k;1 GEOMETRIC k÷2

A. GEOMETRY FASTENER DISCONTIN UITY STATION

t i '2 l

!L ' : -

J Pl ~ l, T I ( k + I ) ' T I ( k ) - P ( k ) + P l ~k) i k k+l B. FREE-BODY DIAGRAMS

REFERENCE REFERENCE

FIG. 1--Loads and deformations on elements of bolted joint [4].



The extension of the members between stations k and k + 1 is given by

and

~ l ( k + l ) - - ~l(k) : OtlATl(k) q- e~l(k)

~z(k+~ ) -- 82~k ) = et2ATl(k) + ¢2l(k)

Any running load is applied uniformly along the length of the joint, and in calculating the strains, the deformation is that which would be associated with the average member load in each seg- ment. The average loads causing the stretching of each member between stations k and k + 1 are

T~(k+x ~ = T~(~) - P(~) + pfl(k)/2

and

T2~+~ = T2 m + P~k~ - p2l~/2

The corresponding stresses are

T'fk) (16) ¢rl(k) : [Wl(k) tl(k)]

and

T2(k~

°'2(k) = [w2(k ) t2(k)]

For linear elastic materials, the equivalent strains would be

_ _ o r l ( k )

6~(k) -- Et(k )

and

_ _ O ' 2 ( k )

~2(k ) - - E2(k )

active input of the data. Data for composite materials is input on the laminate level. A4EJ does have short turnaround times and outputs joint failure load, fastener station loads, deflections

(12) and strains; however it is an iterative technique, and certain values must be checked and adjusted to get the solution to converge. Joints in compression as well as tension can be analyzed. A4EJ accounts for temperature effects, but only with respect to

(13) each material's coefficient of linear thermal expansion; A4EJ does not account for material strength degradation with temperature. Although A4EJ analyzes multi-row bolted joints, it is not capable of analyzing single fastener joints or joints with open holes. A4EJ performs the same analysis on single-lap and double- lap joints and does not account for single lap eccentricities. The exact fastener locations cannot be input, but are accounted for by inputting the distances between fastener stations. Fasteners

(14) are assumed to be evenly spaced throughout a row. A specific plate loading can be input, and A4EJ can account for running shear loads, but biaxial loadings cannot be specified. Boundary conditions can be input but are not required. A4EJ does not

(15) output the specific mode of failure, but the mode can be determined from the failure location and loads. A4EJ is not capable of calculating stress distributions around fasteners. A4EJ is effective in analyzing multi-row bolted joints; however users en- counter difficulties in obtaining and inputting the required data.

SASCJ Analysis Code

SASCJ is an acronym for Strength Analysis of Single Fastener Composite Joints. The code was developed by the Northrop

(17) Corporation from 1983 through 1985 [5,6]. As the name implies, the code can only perform an analysis on single- or double-lap joints connected with one fastener or plates with an open hole. SASCJ has the capability to perform a two-dimensional analysis of a finite bolted composite plate. The two-dimensional stress

(18) field in the finite bolted plate is expressed in terms of an Airy stress function, F(x,y), that automatically satisfies the equilibrium equations in the plate. The displacement solution satisfies the compatability equations when

(19) A2~ OAF 2Az6 04F 04F bx--; - 0x-~0y + (2A~z + A~6) Ox20y 2

For ductile materials, the Ramberg-Osgood model is incorporated and the equivalent strains are calculated to be

O" i O" i ~ = • 1 + (i = 1,2) (20)

After determining the member strains, the relative displacement between the members at the next station is

~(k+l ) : ~2(k+l ) - - ~1(k+i ) (21)

as shown in Fig. 1. This allows a new increment of fastener load transfer to be evaluated. After computing the bearing and bypass loads at each station, the failure criterion are checked to see if the combination of the two loadings is capable of causing joint failure.

A4EJ requires the user to input a relatively large amount of empirical data for the materials that are being joined. The input of the data is not user friendly, requiring formatted, noninter-

O'F OAF - 2A16 0 ~ y 3 + A~I--0y 4 = 0 (22)

is satisfied by the Airy stress function. The laminate compliance coefficients for the laminate are given by

= A N (23)

where the matrices ~ and N are the in-plane strains and stress resultants, respectively, in an anisotropic plate. The complex stress function can be written as

F(x , y ) = 2Re [F1(zl) + F2(zz)] (24)

The complex stress functions F~(zl) and F2(z2) are analytic functions of the complex characteristic coordinates, z~ and z2, respectively. The coordinates zl and z2 are given by

z~ = x + I~y z2 = x + txzy (25)



Using the complex stress function the complex functions

dF~ dFz (26) (1)l(Zl) = ~ 1 (~)2(Z2) = MZ----'7

are introduced. The above equations lead to the following expressions for stresses and displacements in the plate

rr~ = 2 R e [lx2m;(z~) + ~x~qb;(z2)l (27)

% = 2 R e [~b~(z~) + +;(z2)] (28)

%. = - 2 R e [IJLI(I);(z1) ~¢- ~J1~2(1)~(~#2) ] (29)

u = 2 R e [p1+~(z~) + pz+2(z2)] (30)

v = 2 R e [ql+~(z~) + q2+2(z:)] (31)

where p,, p2, q~, and q: are defined as

Pl = a111x~ + A12 - A 1 6 1 - 1 q (32)

P2 = Anl~ + A12 - AM.I,2 (33)

A ql = A121*1 + --2---2 - A26 (34)

tXl

A q2 = A12~2 + --2~ _ A26 (35)

~2

The complex functions, +1 and +~, automatically satisfy the governing equation. For a finite geometry problem with specified boundary conditions, the complex functions cannot be solved so a Laurent series expansion is used

+1(61) = e~o In ~1 + ~ (a-,,6;" + a.6]') (36) n=l

+~(62) = [3o In 62 + ~ ([3°62" + [3,67) (37) n=l

Mapping functions are incorporated into the expansions to make the series converge faster. The rigid body rotation constraint and single valuedness of the displacement constraint are imposed on the complex functions. The complex coefficients of the series expansions are determined, and the displacements and stresses can be calculated using Eqs 27 through 31. To get an accurate solution, approximately 100 collocation points are used in the expansion at the hole boundary. These points are sufficient to recover the imposed boundary conditions at the edges of the plate and at the hole boundary. With an open hole the imposed boundary conditions are self-equilibrating. With a loaded hole, a cosine bolt load distribution is assumed for the hole boundary. This bolt load distribution is equilibrated to the imposed exter- nally applied loads. The bolt in a loaded hole plate is modeled as a Timoshenko beam on an elastic foundation. A finite-difference approximation of the governing equation is used to determine the loading distribution and displacements on the plate.

SASCJ uses a progressive failure procedure that predicts local ply failures and combines them to get the plate strength.

The SASCJ analysis code considers many of the complexities of composite bolted joints. The symmetry of a double-lap shear problem is taken into account in the problem to reduce the amount of input required and computation time. Bilinear elastic ply behavior is assumed. No fastener friction effects are taken into account in the code, but an approximation to the fastener and plate contact is incorporated by an assumed radial stress distribution. The user must specify a bypass ratio for the joint. The bypass ratio is the ratio of load carried by the plates to the load carried by the fastener. This quantity is dependent on how much torque is applied to a fastener when it is tightened. An edge distance to bolt diameter ratio must be greater than 3, and the plate width to bolt diameter ratio must be greater than 4. SASCJ allows for protruding and countersunk head fasteners. The only difference the analysis makes between the two types of fasteners is in the determination of the boundary conditions for the bolt. The protruding head fasteners are given fixed boundary conditions at both ends. The countersunk fasteners are given a free boundary condition at the countersunk head and a fixed boundary condition at the bolted end. The analysis assumes that the fasteners do not fail. The failure criteria are checked at locations specified by the user. The input data for the failure criteria depends on the failure option chosen: point stress, average stress, maximum strain, or Hoffman/Tsai-ttill. The same failure prediction procedure is used for all of the plates in the bolted joint. The SASCJ analysis code outputs the following joint properties upon completion of the analysis: failure load, failure mode, joint loads at specified nodal points, and an echo of a limited amount of the input data. The SASCJ code at Wright- Patterson AFB has been modified to output the stresses, strains, and displacements at the hole boundary at the failure load. The code cannot determine stresses in a joint for a given load but a tensile or compressive loading can be specified. The analysis accounts for the actual laminate stacking sequence and asymmetric laminates can be input. SASCJ considers fastener bending, torque, and shear in the analysis. For most cases, the code runs relatively slowly. SASCJ is a versatile code that can analyze most single fastener joints.

BJSFM Analysis Code

BJSFM was developed by the McDonnell Aircraft Company from 1978 to 1981 [7,8]. BJSFM is an acronym for Bolted Joint Stress Field Model. BJSFM can predict stress distributions and perform failure analysis of an anisotropic double-lap plate with a single loaded or unloaded fastener hole. The analysis is based on (1) anisotropic theory of elasticity, (2) lamination plate theory, and (3) a failure hypothesis. The principle of elastic superposition is used to obtain laminate stress distributions as a result of the combination of bearing and bypass loading. The developed analysis can be used with various failure criteria to predict laminate load carrying capability. The derivation of the equations used in the BJSFM and SASCJ codes are identical up to Eq 35. BJSFM uses conformal mapping techniques to obtain exact solutions for an infinite plate with a circular hole and uniform stresses at infinity. A mapping function, used to map the circular boundary of radius b in the zk plane onto a unit circle in the ~k plane is given by



zk-+ X/z~ - b 2 - ~ b 2 ~ = ( 3 8 )

b(1 - i~k )k = 1, 2

The sign of the square root is chosen such that the hole is mapped to a unit circle. The equations used to this point contain complex stress functions qbl(Zl) and ~b~(z~), which for an infinite plate, will have the general form

(b l (Z l ) = B~z~ + al In G + ~ alml~; m (39) m=l

1~)2(Z2) = BeZ2 + a2 In ~2 -}- ~ a2m{2 m (40) m=l

For the stress to be uniform at infinity, z 1 and z2 must be linear. Terms with In El and In ~2 are present whenever the resultant of the applied stresses on the circular boundary are nonzero. The aim and a2,, coefficients are used to satisfy the boundary conditions on the circular hole. Only the linear terms and the first coefficient of the summation are used for the unloaded hole solution. For the loaded hole solution, a radial stress boundary condition is specified, which varies as a cosine over half the hole. The linear terms in the above equations are not required because the boundary conditions at infinity result in stress free conditions since the finite force, which balances the bolt load, is applied to an infinite boundary. The long-term coefficients are determined by impos- ing single valued displacement conditions since the specified hole loading is not self-equilibrating on the boundary. The following simultaneous equations are given for the a, and a~ complex coefficients

p 2 . ai - a l + a2 - a 2 = ~ "iT1 Z (41)

~ 1 a l - ~1al + 1,1,2a2 - l,£2a2 - Pa ¢ri (42) 2

2 - - t.L2a2 = ( 4 3 ) ixla 1 _ ~2al + 1.12a2 - - 2 - -A12P2 A16p1 2 T r / a 2 2

a_.zl _ -~_21 + a2 -d2 _ A12p~ + A26p2 (44) P~l al la,2 52 2"rriA22

The al,, and a2,, coefficients are determined .by expressing the radial stress boundary conditions on the hole in terms of a Fourier Series and equating the series representation of the solution. The coefficients are

bP,(1 + itx~) a12- [16(Ix:- p.1)] (45)

bPi(1 + itxl) a22 - [16(Ix2 - t*1)] for m = 4, 6, 8 . . . . (46)

aim = a2,, = 0 fo rm = 1, 3 ,5 . . . . (47)

b P i ( - 1 ) (m 1)/2(2 + imp.2)

al,,, = - [.rrmZ(m 2 _ 4)(ix2 - ~J~l)] (48)

b P i ( - 1 ) ( ..... '/2(2 + imp.a) (49) a2m = - [.rrm2(m: _ 4)(ix2 _ ~ll.1) ]

The above equations completely define the elastic stress distribution of an infinite, two-dimensional, anisotropic material containing a circular hole. Although the solutions are valid only for homogeneous materials, they are assumed to be valid for laminates that are symmetric. The laminate compliance coefficients A,k are derived using classical lamination plate theory with unidirectional material elastic constants, and ply angular orientations and thicknesses. The material compliance constitutive relations are used to determine the laminate strains. Strains for the individual plies along lamina principal material axes are calculated using coordinate transformations and by assuming that the laminate strain remains constant through the thickness. The principle of superposition is used to obtain stress distributions resulting from an arbitrary set of in-plane loads. The "characteristic dimension" hypothesis of Whitney and Nuismer [9] is used to model inelastic or nonlinear material behavior at the hole boundary. Various material failure criteria can be used with the characteristic dimension failure hypothesis. The failure criteria options are Tsai-Hill, maximum stress, maximum strain, Hoff- man, and modified Tsai-Wu. Finite width has a significant impact on the circumferential stress distribution around a loaded fastener hole. Finite-width effects are evaluated by superimposing stress distributions from loaded and unloaded hole infinite plate solutions. The bolt load is reacted by tensile and compressive loads of P/2 in the loaded hole analysis. The loading on the bolt and overall equilibrium is obtained by superimposing the solution for an unloaded hole under a remote tensile loading of P/2. The resulting stress distribution approximates the state of stress in a plate with finite width very well. The distribution differs from an exact solution by giving nonzero superimposed normal and shear stresses at the edge of the plate.

BJSFM does not require the user to input a large amount of data, and the input procedure is user friendly. The data are input interactively, but if a mistake is discovered after a response to a prompt is already entered, the user must start over from the beginning. BJSFM has a very short turnaround time and offers a variety of output options and failure criteria. BJSFM can account for material anisotropy, general in-plane loadings (tension, compression, biaxiality, and shear bearing), and different hole sizes. BJSFM can also account for composites that are made of more than one type of material. Only mechanical properties for the basic unidirectional ply lamina are required to obtain strength predictions. BJSFM does not account for compressive or temperature effects, and has joint geometry restrictions. When inputting the plate properties, BJSFM uses the thickness of each ply orientation normalized by the total plate thickness. BJSFM views a joint as a single plate with an equivalent loading from a second plate. The properties and geometry of the second plate never enter into the analysis. Although BJSFM accounts for the percentages of plies of different orientations for composite materials, it does not account for the ply layup sequence. BJSFM can output stresses, strains, and displacements at fixed distances and angular locations about the bolt hole. BJSFM is a useful tool that can produce a significant amount of information about a problem.



SCAN Analysis Code

SCAN is an updated version of the BJSFM composite joint analysis code. SCAN is an acronym for: Stress Concentrations ANnalysis. The code was developed by the McDonnell Aircraft Company from 1985 through 1986 [10,1I]. The code can only analyze joints connected with one fastener. Improvements have been made to the BJSFM code, which makes the analysis procedure closely match the SASCJ analysis. The analysis is based on anisotropic theory of elasticity, laminated plate theory, and a boundary collocation procedure. The SCAN and SASCJ analysis formulations are identical until the point where a Laurent series expansion is assumed for the complex functions +1 and +2. SCAN uses the following expansions

4,,(zl) = a, in zl + ~ a,,,z? (50)

+2(z2) = a2 In z2 + ~ a2,,z'2' (51)

where a, and a2 are determined by solving Eqs 41 to 44 simul- taneously. No mapping function for the z coordinates is used in the SCAN derivation. The constants a~,, and a2,, are determined by using a least squares boundary collocation technique similar to the one used in SASCJ. Using SCAN, the user can obtain the stresses at any point in a plate, given a set of internal and external boundary conditions.

SCAN is capable of handling joints in a double-lap configuration. The code can analyze a single plate with an unloaded elliptical hole. SCAN can account for any quadrilateral plate shape, and bilinear elastic ply behavior is assumed. A limitation on the dimensions of the quadrilateral plate is that the aspect ratio of the plate must be less than 2. The code assumes the bolt bearing load acts in a cosinusoidal distribution over one-half of the bolt hole. No fastener friction effects are considered in the code, but their effects on the joint can be approximated. You can specify a bolt load, axial load, transverse load, and shear loading. The loads are given in terms of stresses applied to the plate edges and the bolt hole. SCAN, like BJSFM, considers the force of the bolt to be just an input force on the hole. Typically the input loadings, especially the bolt loading, can only be determined experimentally. The user must also know how much load is transferred through the bolt and how much is bypassed around the bolt. The failure criteria are checked at a characteristic distance specified by the user. The failure criteria options are as follows: maximum strain, maximum stress, Tsai-Hill, modified Tsai-Wu, and Hoffman. The failure criteria is used at the ply level.

The SCAN analysis code has many different output options. The user can print out laminate and ply stresses and strains, failure criteria, and failure stresses. The analysis does not account for the actual laminate stacking sequence, and asymmetric laminates cannot be specified. Instead of inputting the stacking sequence, the user inputs the percentage of plies for each different orientation. The code is strictly valid for homogeneous anisotropic flat plates and is assumed to be valid for mid-plane symmetric laminates. The user can input stress or displacement boundary conditions for a plate edge. The boundary conditions can be input as a constant or as a quadratic distribution over the

length of the plate edge. To enforce equilibrium on a loaded hole joint, the bearing load P must be equal to the edge loading P,, divided by the plate width w. The user can input up to eight different ply angular orientations and can have up to three different materials for hybrid laminates. SCAN is a versatile code for singly fastened composite bolted joints. The code runs relatively fast compared to the SASCJ and SAMCJ codes and has many output options.

SAMCJ Analysis Code

SAMCJ was also developed by the Northrop Corporation from 1983 to 1985 [12,6]. SAMCJ is an acronym for Strength Analysis of Multifastener Composite Joints. As the name implies, the code can analyze joints connected by multiple fasteners. In ad- dition to this capability, the code can also effectively model a combination of loaded and unloaded holes and cutouts. SAMCJ also performs a two-dimensional analysis of finite bolted composite plates. SAMCJ is derived from SASCJ, so the basic analysis is the same. Many identical or slightly modified subroutines are used for both analysis codes. The main difference is that SAMCJ uses special finite elements to perform the analysis. The special finite elements include elements with loaded holes, elements with unloaded holes, regular plate elements, and beam elements to model the bolts. The user is required to input the geometry of the bolted joint, the type of elements, the material properties, loading condition, and fastener geometry. SAMCJ applies a 1-kip (4448 N) load to the joint and also applies the constraints. The code allows the user to take advantage of multiple elements with similar stiffness matrices to reduce run times. An average stress failure criteria is used for all joint types in SAMCJ. The failure criteria determines the joint failure load, the location of the failure, and the failure mode.

The SAMCJ analysis code has many of the same options as the SASCJ code. The code is capable of handling multiply fastened joints in a double- or single-lap configuration. The symmetry of a double-lap shear problem is taken into account to reduce the amount of input required and computation time. The code can not analyze a single plate with an unloaded hole, but it can analyze joints with only one bolt. A two-dimensional analysis is performed on any finite anisotropic joint. SAMCJ can account for finite geometries, which include cutouts, nearby free edges, and tapered or stepped plates. Bilinear elastic ply behavior is assumed. The code assumes the bolt bearing loads act in a cosinusoidal distribution. No fastener friction effects are taken into account, and there is no way to specify a bypass ratio in the SAMCJ code. The code internally calculates the bolt load distribution. The edge distance to bolt diameter ratio must be greater than 3. The plate width to bolt diameter ratio must be greater than 4. The user can specify a protruding or countersunk head fastener as in SASCJ. All of the fasteners are assumed to be made of the same material and are identical in type and size. The analysis assumes that the fasteners do not fail. The failure criteria are checked at locations specified by the user. The SAMCJ analysis code outputs the following joint properties upon completion of the analysis: failure load, failure mode, joint loads in the elements, element forces, and an echo of a limited amount of the input data. Like SASCJ, the code cannot determine stresses in a joint for a given load. The analysis accounts for the actual laminate stacking sequence and asymmetric laminates can



be specified. SAMCJ accounts for fastener bending, torque, and shear. Run times for the analysis can be very long depending on the number of elements that make up the joint.

Comparisons and Recommended Usage

The authors decided to examine and compare the six composite bolted joints analysis codes by performing analysis on various types of joints using as many different codes as possible. We began by selecting various joint test cases for which data from actual experimental strength tests already existed. A test program of joint geometries, which had already been experimentally tested in Refs 5 and 8, were compared to the calculations of each of the bolted joint analysis programs described above. Nine typical joint geometries were chosen to demonstrate some of the capabilities and limitations of each code. The assumptions that were made are as follows: (1) One of the plates being joined (inner plate for the double lap joints) is made of graphite/epoxy with the properties shown in Table 1. (2) The outer plate of each double-lap joint and one plate for single-lap joints is made of steel with the properties also shown in Table 1. (3) The fasteners used for each joint are steel bolts with protruding heads. Some of the fasteners had bushings, but they were not accounted for in the analyses. (4) The fasteners were assumed to fit exactly, and no fastener clearance was considered. (5) No fastener torque- up effects were considered; however it was experimented with in adjusting the bearing/bypass loads for some of the analysis codes. (6) For the experimental tests, the average of the failure loads for each joint geometry is considered to be the actual failure load for that geometry. (7) All joint loadings are uniaxial. SCAN, SASCJ, SAMCJ, and BJSFM check for joint failure at a characteristic distance, which is away from the edge of the hole. The standard distance that was used for this effort was 0.02 in. (0.51 ram). For all joints with bolts that carry a toad, the bypass ratio plays a role in the definition of the problem. SASCJ requires the user to input the bypass ratio; SAMCJ, A4EJ, and JOINT internally calculate a bypass ratio. The SCAN and BJSFM codes require that the user know the bolt loading, which in turn implies the bypass ratio for the joint. For the SASCJ code, the bypass ratio was adjusted to get a feel for the correct bypass ratio. The actual bypass ratio is a function of bolt torque and is not accu- rately known. For the JOINT analysis code, the percentage of 0 ° plies was assumed to be 37% instead of the actual 50% because of the limitations of the code. Table 2 gives the laminate ply orientations for the three layups used. The following discussion gives an explanation of" the results summarized in Table 3.

TABLE 2--Symmetric ply layups.

44-Ply Symmetric Laminate (45, 02, -45, (0, 45)2, 90, ( -45 , 0, 0, 45, 0, -45)~, 0)s

44-ply layup has 50.0%, 0 ° plies 22.7%, 45 ° plies

22.7%, -45 ° plies 4.6%, 90 ° plies

40-Ply Symmetric Laminate (45, 02, -45, 90, (0, 45)2, 90, -45, 04, 45, ( -45, 0)2)s

20-Ply Symmetric Laminate (45, 02, -45, 02, 90, -45, 45, 0)s

20- and 40-ply Layups 50.0%, 0 ° plies

20.0%, 45 ° plies 20.0%, -45 ° plies

10.0%, 90 ° plies

Open Hole

BJSFM, SCAN, and SASCJ are capable of analyzing open holes. The output from all of the analyses is very clos e as shown in the graph in Fig. 2, even though the composite laminate stacking sequence is not considered in the BJSFM and SCAN codes. The BJSFM and SCAN codes are quicker, require less, and more fundamental input data, provide more output data, and are unique in their capability to analyze biaxial loadings. SCAN is also the only code capable of analyzing elliptical holes and quadratic loadings, Both the SCAN and SASCJ codes can perform an analysis for a nonrectangular quadrilateral plate shape. SCAN or BJSFM are the recommended codes to use if you are analyzing plates with open holes.

Single Bolt, Double Lap

All of the codes except A4EJ are capable of analyzing double- lap joints with a single fastener. Actually the JOINT analysis code is not capable of doing an analysis of a single bolt joint either because the code assumes an infinite width plate with uniform bolt spacing through the width of the plate. The JOINT analysis was included in this section to give the user a feel for how the capabilities of the code can be stretched.

If the bolt loading is already known from another analysis or through testing, and stress or strain displacement data are desired, then BJSFM and SCAN are the recommended codes to use. If the bolt loading is not known, the user can took at trend data or case studies to get a feel for how the joint is reacting to varying loading conditions. SASCJ should be used if you simply want the failure load of the joint for a particular bypass ratio. The compressively loaded joint shows that SAMCJ tends to predict an unconservative value for the failure load.

TABLE 1--Material properties.

Graphite Epoxy Steel

E~ = 18.9 x I06 psi E~ = 18.2 x 106 psi E~ = 1.9 x 10 ~ psi G~2 = 0.85 x 106 psi v~2 = 0.3

E = 30.0 × 106 psi v = 0.3

Single Bolt, Single Lap

JOINT, SASCJ, and SAMCJ are capable of analyzing single- lap joints with a single fastener. Again, the JOINT analysis code performs an infinite width plate analysis so the results should be used with this in mind, The SASCJ and SAMCJ codes run relatively slowly, but they are the only codes capable of performing an analysis on single-lap joints. SASCJ requires the user to input



T A B L E 3---Composite bolted Joint problem results',

Bypass Ratio Joint Analysis 0-Full Bearing Type Code 1-Open Hole

Cross Actual Predicted Section Predicted Actual Failure

Failure Area , Failure Failure Failure % Differ- Load, Load, lbs in. 2 Mode Criteria Mode ences Ibs

OH" SASCJ N/A OH" SCAN N/A O I P BJSFM N/A

DL1 b JOINT 0.0 DL1 b BJSFM N/A DL1 b SCAN N/A DL1 b SASCJ 0.6 DL1 b SAMCJ N/A

DL1C b BJSFM N/A DL1C b SCAN N/A DL1C b SASCJ 0.5 D L I C b SAMCJ N/A SL1 JOINT 0.0 SLI SASCJ 0.6 SL1 SAMCJ O K DL2 J O I N T 0.0 DL2 SAMCJ N/A DL2C SAMCJ N/A DL4 J O I N T 0.0 DL4 A4EJ N/A DL4 SAMCJ N/A SL2 SAMCJ N/A SL2 J O I N T 0.0 SL4 J O I N T 0.0 SL4 A4EJ N/A SL4 SAMCJ N/A

Analysis Codes

1 - JOINT 2 - A4EJ

3 - BJSFM 4 - SCAN 5 - SASCJ 6 - SAMCJ

27 800 0.431 N/A H T H NS + 10 25 033 30 444 0.431 N/A t t T H NS + 18 25 033 24 138 0.431 N/A H T H NS - 4 25 033

16 753 0.9385 B N/A SO - 22 21 525 17 768 0.9385 N/A MS SO - 17 21 525 28 800 0.9385 N/A MS SO + 25 21 525 19 375 0.9385 B/SO AS SO - 1 0 21 525 20 956 0.9385 B AS SO - 3 21 525

22 636 0.938 N/A MS B - 10 25 183 26 100 0.938 N/A MS B + 4 25 183 25 595 0.938 SO/B AS B + 2 25 183 32 418 0.938 B AS B +22 25 183

5 072 0.467 TN N/A SO/B - 44 8 980 9 915 0.467 NS/B AS SO/B + 9 8 980

10 479 0.467 B AS SO/B + 14 8 980 15 392 0.626 TN N/A SO/B - 2 8 21 475 13 660 0.626 B AS SO/B - 36 21 475 18 721 0.312 NS AS B + 24 14 165 15 653 0.521 TN N/A NS - 3 9 25 6t3 6 786 0.521 N/A N/A NS - 74 25 613

14 236 0.521 B AS NS - 4 4 25 613 7 120 0.313 B AS SO/B - 3 9 11 640 4 141 0.313 TN N/A SO/B - 64 11 640 7 415 0.521 TN N/A SO/B - 7 0 24 963 6 859 0.521 N/A N/A SO/B - 7 3 24 963

14 258 0.521 B AS SO/B - 4 3 24 963

Failure Criteria Joint Types

H T H - Hoffman/Tsai-Hil l O H - open hole AS - average Stress DL1 - double-lap 1 bolt

MS - m a x i mum Stress DL1C - double-tap 1 bolt, compression SL1 - single-lap I bolt

SO - shear out DL2 - double-lap 2 bolts B - bearing DL2C - double-lap 2 bolts, compression

NS - net section DL4 - double-lap 4 bolts TN - tension at hole SL2 - single-lap 2 bolts

SL4 - single-lap 4 bolts

44 ply layup. b 40 ply layup.

NOTE: all others 20 ply layup. 1 in.: = 6.541 x 10 -~ m% 1 lb = 0.4536/kg.

5 0 O 0

4 0 0 0 <

Z

0 3 0 0 0 - O3

o I 20'%@ -

I O 0 0 -

X 0

1000

BdGFM ,,,f p t

- + - S~,SCJ W © = 8

- * . - * - SCaN V,,' r : ' :8

/%,.

20 40 60 80 1 O0 120 140 160

A N G L E ( d e g r e e s ]

O P E N H O L E I N T E N S I O N

FIG. 2--Comparison of analysis codes.

a b y p a s s ra t io o r to l o o k a t a w o r s t - c a s e s i t u a t i o n . S A M C J d o e s

n o t r e q u i r e t h e u s e r to i n p u t a b y p a s s r a t i o , a n d it i n t e r n a l l y

c a l cu l a t e s th is va lue . B o t h S A S C J a n d S A M C J do wel l at de -

t e r m i n i n g t h e f a i lu re l o a d if t h e u s e r h a s a g o o d u n d e r s t a n d i n g

o f t h e p r o b l e m a n d t h e j o i n t p a r a m e t e r s . T h e r e is n o cap ab i l i t y

to o u t p u t s t r e s s e s , s t r a i n s , o r d i s p l a c e m e n t s in t h e S A S C J o r

S A M C J codes .

Multiple Bolted Joints

A 4 E J , J O I N T , a n d S A M C J a r e c a p a b l e o f a n a l y z i n g m u l t i p l y

f a s t e n e d jo in t s . A 4 E J a n d S A M C J a r e c a p a b l e o f a c c o u n t i n g fo r

c o m p r e s s i v e l o a d i n g s . I n all c o d e s , t h e m a g n i t u d e o f t h e e r r o r

t e n d e d to i n c r e a s e as t h e n u m b e r o f f a s t e n e r s i n c r e a s e d . T h i s is

s h o w n in T a b l e 3 w i th t h e p r e d i c t e d fa i lu re l o a d g i v en in t h e

f o u r t h c o l u m n , a n d t h e ac tua l f a i l u re l o a d g i v e n in t h e t e n t h

c o l u m n . A 4 E J h a s a r e l a t i ve ly s h o r t r u n t i m e b u t c a n o n l y a n a l y z e



j o i n t s c o n t a i n i n g a t l e a s t t w o r o w s o f f a s t e n e r s w i t h a t l e a s t t w o

f a s t e n e r s p e r r o w . A 4 E J is r e c o m m e n d e d f o r u s e i n d e s i g n s t u d i e s

o f m u l t i p l y f a s t e n e d j o i n t s . J O I N T h a s a r e l a t i v e l y q u i c k r u n

t i m e , a n d a l t h o u g h t h e c o d e a s s u m e s a n i n f i n i t e w i d t h p l a t e , t h e

c o d e p r o d u c e d g o o d r e s u l t s f o r s o m e c a s e s . J O I N T is l i m i t e d i n

t h e a m o u n t o f o u t p u t i t c a n p r o d u c e so i t i s r e c o m m e n d e d f o r

p r e l i m i n a r y d e s i g n s t u d i e s . S A M C J is c a p a b l e o f a n a l y z i n g m a n y

t y p e s o f m u l t i p l y f a s t e n e d j o i n t s b e c a u s e o f i t s f i n i t e - e l e m e n t

b a s e d f o r m u l a t i o n .

T A B L E 4~Program capabilities.

P a r a m e t e r J O I N T A 4 E J S A S C J S A M C J B J S F M S C A N

O p e n H o l e x x x x Single- lap , 1 bol t x x Doub le - l ap , 1 bo l t x x x x Single- lap , mul t i a x × D o u b l e - l a p , mul t i a x x C u t o u t s x S tep- lap x x x Biax ia l load ings x x Mul t ip le fa i lure c r i t e r ion x x x x F in i te d imens ions x x x a x Di f fe ren t bol t types x x C o m p r e s s i o n and t ens ion x x x x x x Type of fa i lure x T o r q u e - u p effects x x a a Specific p la te load ings x x x x x Di f fe ren t ply ma te r i a l s x x x Di f fe ren t p la te m a t e r i a l s x x x Jo in t op t imiza t ion x x A s y m m e t r i c l a m i n a t e s x E l l ip t ica l bol t ho les x

Has some capabi l i ty .

T A B L E 5--Program required inputs.

P a r a m e t e r J O I N T A 4 E J S A S C J S A M C J B J S F M S C A N

Bypass ra t io x a a P la te th ickness x x x x a x Ply o r i en t a t ions x x x x S tack ing sequence x x Y o u n g ' s modu lus , m x x x Shear modu lus , m x x Poisson ra t io , m x x Y o u n g ' s modu lus , c x x x x x Shear modu lus , c x x x x Poisson rat io , c x x x x H o l e d imens ion x x x x x x Pla te coo rd ina t e s x x x P la te w id th a x x x a x Specif ic fa i lure c r i t e r i a x x x x C h a r a c t e r d i s tances (fail- u re ) x x x x Ma te r i a l s t r eng ths x a x x x U l t i m a t e s t ra ins x a x M o d u l u s r educ t ion fac tor a x Scale fac tors a Fas t ene r type x x Bol t loca t ions x x x N u m b e r of fas teners a x a x a a % ply o r i en t a t ions a x x x x P la te load ing x a x x Bol t load ing x x B o u n d a r y cond i t ions a x Bol t l oad ing angle x x O p e r a t i n g t e m p e r a t u r e a a

° R e q u i r e d wi th excep t ions NOTE: C is c o m p o s i t e p la tes , and m is m e t a l bol ts and plates .


SNYDER ET AL. ON BOLTED JOINTS ANALYSIS PROGRAMS

TABLE 6--Program output data.

Parameter JOINT A4EJ SASCJ SAMCJ BJSFM SCAN

Failure load x x x x x x Stresses at hole boundary a x x Failure mode x x x F. E. grid forces x Margin of safety x Optimized joint weight x Optimum joint configuration x Laminate properties Laminate stresses Laminate strains Circumferential stresses Circumferential strains Radial stresses Radial strains Displacements Strains per ply Stresses per ply Failure criteria Echo input data Carpet plot data

X X X X X

X X X

X X X X

X X

X X

X X

X X

X X X

a X x

x X

x x

X a X a

x

" Outputs with exceptions.

51

Conclusions

As increased emphasis is placed on the design of lighter, faster, more maneuverable, and less costly aircraft, there will be an increased emphasis on the reliability and accuracy of composite bolted joint design methods. In examining the relative merits of six composite bolted joint design computer codes, some conclusions were drawn. For all of the problems that are run, the user must check the input data against the problem definition. The user must also check the output to see that it is consistent and meaningful. The manner in which most data are input into the codes makes it easy for errors to occur. Usually, more than one analysis is necessary to completely solve a problem. The user must adjust some of the variables and look to see if the solution is appropriate for the given loadings, bypass ratios, and boundary conditions. In most cases the analysis codes tended to give conservative and, at times, overly conservative results. In general, most of the codes that were capable of predicting a failure mode did so correctly. With all of the analysis codes, it should be noted that only a few load cases were examined in this study and not all of the capabilities or limitations of the codes were exploited. A summary of the different programs, capabilities, required inputs, and the output data is given in Tables 4, 5, and 6. Accurate results can be obtained from all of the codes if the user has a good understanding of the problem and the desired results. In all cases, several different analysis methods should be used to confirm all results. With the increased application of composites that are arising, work in the area of composite joint analysis should continue.

References

[1] Venkayya, V. B., Ramkumar, R. L., Tischler, V. A., Snyder, B. D., and Burns, J. G., "'Recent Studies on Bolted Joints in Com- posite Structures," 64th AGARD SMP Meeting, Madrid, Spain, April 1987.

[2] Ramkumar, R. L., Saether, E. S., and Tossavainen, E., "Design, Fabrication Testing and Analysis of Bolted Structural Elements," AFWAL-TR-86-3033, 1986.

[3] Smith, M. K., Hart-Smith, L. J., and Dietz, C. G., "Interactive Composite Joint Design," AFWAL-TR-78-38, Parts 1, 2, and 3, April 1978.

[4] Hart-Smith, L. J., "Design Methodology for Bonded-Bolted Com- posite Joints," AFWAL-TR-81-3154, Vols. I and II, Feb. 1982.

[5] Ramkumar, R. L., et al., "Strength Analysis of Composite and Metallic Plates Bolted Together by a Single Fastener," AFWAL- TR-85-3064, Aug. 1985.

[6] Ramkumar, R. L., Saether, E. S., and Cheng, D., "Design Guide for Bolted Joints in Composite Structures," AFWAL-TR-86-3035, March 1986.

[7] Garbo, S. P. and Ogonowski, J. M., "Effect of Variances and Manufacturing Tolerances on the Design Strength and Life of Me- chanically Fastened Composite Joints," AFFDL-TR-78-179, 1978.

[8] Garbo, S. P. and Ogonowski, J. M., "Effect of Variances and Manufacturing Tolerances on the Design Strength and Life of Me- chanically Fastened Composite Joints," Vols. I, II, and III, AFWAL-TR-81-3041, April 1981.

[9] Whitney, J. M. and Nuismer, R. J., "Stress Fracture Criteria for Laminated Composites Containing Stress Concentrations," Journal of Composite Materials', Vol. 8, July 1974.

[10] Hoehn, G., "Enhanced Analysis/Design Methodology Develop- ment for High Load Joints and Attachments for Composite Struc- tures," NADC-87011-60, Nov. 1986.

[11] Buchanan, D. L., Ogonowski, J. M., and Reiling, H. E., Jr., "De- velopment of High Load Joints and Attachments for Composite Wing Structures," NADC-86007-60, Nov. 1985.

[I2] Ramkumar, R. L., Saether, E. S., and Appa, K., "Strength Analy- sis of Laminated and Metallic Plates Bolted Together By Many Fasteners," AFWAL-TR-86-3034, 1986.


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Composite Bolted Joints Analysis Programs