40207_28

MECHANICAL FASTENING AND ADHESIVE 28 BONDING D. W. Oplinger

28.1 INTRODUCTION

It would be difficult to conceive of a structure that did not involve some type of joint. Joints often occur at a transition between a major composite part, where most of the structural performance is generated, and a metal feature, which is introduced to allow for very high localized bearing contact for which the composite has inadequate strength or durability. In aircraft such a situation is represented by artic- ulated fittings on control surfaces as well as on wing and tail components which require the ability to pivot the element during various stages of operation. Tubular elements such as power shafting often use metal end fittings for connections to power sources or for articulation at points where changes in direction are needed. In addition, assembly of the structure from its constituent parts will involve either bonded or mechanically fastened joints or both.

Joints represent one of the greatest chal- lenges in the design of structures in general and in composite structures in particular. The reason for this is that joints entail interruptions of the geometry of the structure and often material discontinuities, which almost always produce local highly stressed areas, except for certain idealized types of adhesive joint such as scarf joints between similar materials. Stress concentrations in mechanically fastened joints

Handbook of Composites. Edited by S.T. Peters. Published in 1998 by Chapman & Hall, London. ISBN 0 412 54020 7

are particularly severe because the load transfer between elements of the joint have to take place over a fraction of the available area. For mechanically fastened joints in metal structures, local yielding, which has the effect of eliminating stress peaks as the load increases, can usually be depended on; such joints can be designed to some extent by the 'P over A' approach, i.e. by assuming that the load is evenly distributed over load bearing sections so that the total load (the 'I") divided by the available area (the 'A') represents the stress that controls the strength of the joint. In organic matrix composites, such a stress reduction effect is realized only to a minor extent, and stress peaks predicted to occur by elastic stress analysis have to be accounted for, especially for one-time monotonic loading.

28.2 MECHANICALLY FASTENED JOINTS COMPARED WITH ADHESIVE JOINTS

In principle, adhesive joints are structurally more efficient than mechanically fastened joints because they provide better opportuni- ties for eliminating stress concentrations; for example, advantage can be taken of ductile response of the adhesive to reduce stress peaks. Mechanically fastened joints tend to use the available material inefficiently and are characterized by sizeable regions where the material near the fastener is nearly unloaded, which must be compensated for by regions where high stresses occur to achieve a particular

Mechanically fastened joints 611

required average load capacity. As mentioned above, certain types of adhesive joint, namely scarf joints between components of similar stiffness, can achieve a nearly uniform stress state throughout the region of the joint.

In many cases, however, mechanically fastened joints cannot be avoided because of requirements for disassembly of the joint, for replacement of damaged structure, or to achieve access to underlying structure. In addition, adhesive joints tend to lack structural redundancy, and are highly sensitive to manufacturing deficiencies, including poor bonding technique, poor fit of mating parts and sensitivity of the adhesive to temperature and environmental effects such as moisture. Assurance of bond quality has been a continu- ing problem in adhesive joints, primarily because, while ultrasonic and X-ray inspection may reveal gaps in the bond, there is no present technique which can guarantee that a bond which appears to be intact by ultrasonic or X- ray inspection does not lack load transfer capability, because of such factors as poor surface preparation. Surface preparation and bonding techniques have been well developed, but the possibility that lack of attention to detail in the bonding operation may lead to such deficiencies needs constant alertness on the part of those responsible for the bonding. Thus mechanical fastening tends to be preferred over bonded construction in highly critical and safety rated applications such as primary aircraft structural components, especially in large commercial transports, since assurance of the required level of structural integrity is easier to guarantee in mechanically fastened assemblies. Bonded construction tends to be more preva- lent in smaller aircraft however and for non-aircraft applications as well as in non-flight critical aircraft components.

28.3 MECHANICALLY FASTENED JOINTS

Mechanically fastened joints for composite structures have been under study since the mid 1960s when high modulus, high strength

composites first came into use. It was found early in this period that the behavior of composites in bolted joints differs considerably from that which occurs with metals, primarily because stress concentrations are much more of a factor in joint behavior of composite structures, and stress analysis to quantify the level of various stress peaks is more important. It was fortunate that significant computing power became available in this period to keep up with the need for the intimate details of stress conditions around mechanical fasteners.

The current approach to the design of mechanically fastened joints in composite structures evolved mainly out of a number of DoD, NASA and associated university programs aimed at providing a methodology which could be applied routinely to aircraft and other applications. Numerous stress analysis approaches to the mechanics of fastened joints have been conducted over the years since the introduction of 'advanced' composites in the mid-1960s. These have included: the work of Waszczak and Cruse' based on the boundary integral method; the use of two-dimensional complex variable elasticity solutions which treated the problem of variable contact around the fa~tenel-2-~; as well as recent work reported by Madenci and Illeri7; and a number of finite element approaches, especially the work of Crews and Naik8 which featured an inverse method for dealing with the contact problem. Hart-Smith9 developed an analytic approach based on the use of available solutions for isotropic plates with bolt-loaded holes as well as unloaded holes in plates under tension or compression which came out of classical efforts such as those reported in Petersonlo. The latter provided simple functional descriptions of the effect of joint geometry on peak stresses which, with various empirically derived correction factors introduced by Hart-Smith9, provided valuable insight into a number of trends in joint behavior.

In addition to the analytic efforts, several fairly extensive programs aimed at the development of design approaches for structural

612 Mechanical fastening and adhesive bonding

systems have been supported by DoD and NASA4r6. Numerous papers have been pre-

28.3.1 KEY FEATURES OF MECHANICALLY FASTENED JOINTS

~~

sented Over the years in a series Of

Composites in Structural De~ign~, '~- '~. Many of the design principles which have been devel-

characteristics of bolted composite structures have been described4, 6, 13.

It is not possible within the scope Of this discussion to describe all the details and

design of specific joints. The objective is rather

factors that control the behavior of mechani-

The behavior of mechanically fastened

Figure 28.1 represents a generic single fastener

tener configuration. Many of the most important features of joints are illus-

28.1. Key dimensions are D, the fastener diameter, t, the thickness of the joint structural elements, e, the edge distance (distance from the fastener center to the edge of the

the upper plate to the left of the fastener.

ment. Note that the Same load, p, is passed

joint, including the bearing section in front of

DoD/NASA/FAA 'Onferences On Fibrous joint, while Fig. 28.2 depicts a multiple fas-

'ped to take into account the trated in the single fastener case shorn in Fig.

Processes that are necessary for achieving the upper plate) and W, the width of the part of

to give the reader Some insight into the Similar featups apply to the lower plate ele-

fastened joints in structures' successively through various sections of the

joints is governed by (l) the features that

types Of information: the behavior Of the

the fastener of area Dt which is in compression, the b o shearout sections of total area 2et

joint around individual fasteners and; (2) the behavior of multiple arrays of fasteners. The behavior of individual fasteners can be considered in terms of a generic rectangular element surrounding each fastener (Fig. 28.1), whose length and width are represented as ratios

which are loaded in primarily in shear, the net section, (w - D)t which is in tension, the gross section wt which is also in tension.

The average stresses associated with these sections are:

wi& respect to the fastener diameter. The effects of the geometry of this element together with effects of the reinforcement arrangement used in the laminate for the element determine the structural conditions under which the element will fail. Once the characteristics of the rectangular element are selected, its deforma- tion characteristics can be combined with those of other rectangular elements making up the joint to obtain the performance of the joint as a whole. This discussion is organized in terms of these two aspects of joint design.

In addition to a preliminary discussion of general features of mechanically fastened joints, the discussion which follows also con- siders: (1) single fastener joints, including effects of joint geometry together with those of composite material behavior; (2) multi-fastener joints; (3) fastener effects, and (4) a discussion of test methods which provide empirically-based data needed for completing the joint design.

average bearing stress, ab = P/Dt ; average shearout stress, a,, = P/2et; average net section stress, aN = P/(W - D)t; average gross section stress, aG = P / Wt.

(28.1)

LOAD PATH

P t

I ' \ bearid section goss net sectiqn

section section Dt I w t (W-O)t I

I I I

I ,/-7-. I

c I ! : I J

Fig. 28.1 Single fastener joint.


Axit! Lateral w * Lateral Pi tch tit h P i tch eff

I

Fig. 28.2 Multi-fastener joint.

From the standpoint of the designer, the gross section strength is of primary interest since the objective of good design is to stress the gross section to its highest level. Structural performance of the joint can be rated in terms of joint efficiency, which refers to the ratio of average gross section stress at failure of the joint to the strength of the laminate in the gross section, essentially the strength achieved in coupon tests for tensile or compressive loading of unnotched specimens. For organic matrix composites, single fastener joints achieve joint efficiencies of less than 50%, while for multi- fastener joints the maximum achievable efficiency is of the order of 60%. In contrast, metallic joints can reach efficiencies of close to 80% because of the opportunity for taking advantage of local yielding around points of high stress, though even in metallic joints, design for avoidance of crack initiation in cases where long life under cyclic loading is required may force the joint efficiency to be lower than for single cycle loading.

28.3.2 EFFECTS OF JOINT GEOMETRY

The peak value of axial stress on the net section on,),,, (Fig. 28.3) is one of the key controlling parameters on joint performance. It is convenient to express this as a stress concentration factor, i.e. a ratio with respect to either the mean stress in the net section or the

-8-1

G

Fig. 28.3 Peak stresses around fastener.

gross section:

KGt = O,&JO~ (28.2)

or

qt = q J m x / o G

where a,),,, is the maximum axial stress on the net section. Predictions of the peak stresses in the joint can be made using continuum elasticity analysis1", 7, 12, photoelastic measurements'O or finite element methodsE.

The behavior of K$ as a function of D / W for isotropic joint elements is given in Fig. 28.4 which was obtained from photoelastic measurements of KNnt against D / W (note that Kgt = KNnt/(l - D / W ) ) given by Petersenlo. Similar curves for orthotropic plates were obtained by elasticity analysis2, 3, 12.


There is obviously a competition for space between the bearing section and the net section. Increasing the fastener diameter, D, to lower ab has to decrease (W - D)t, the net section, thereby increasing uN, and vice versa. Furthermore, if D / W is much less than 1, the case is similar to that of a fastener in an infi- nitely wide plate; in such a case all the peak stresses become a constant multiplier of the bearing stress ab, which becomes large for D/W<<l. If D is large enough to fill most of the available width, the net section becomes small, oN becomes large, and the peak net section and shear stresses become proportional to uN for this case. As seen in Fig. 28.4, is large for small D / W as well as for D / W approach- ing 1, leading to a minimum around D / W = 0.59J2. The quantity 0.89ub/uG + 1.8 uN/uG which is plotted in Fig. 28.4 gives a reasonable approximation to the curve of KGt against D / W, so that the use of eqn (28.1) to express ob and uN in terms of D / W, shows:

Kgt 0.89W/D + 1.8/(1 - D/W) (28.3)

' T Functional Fit, 0.89 %+ 1.8 oN

\

The behavior of this approximation empha- sizes the tradeoff between the effect of the bearing section and the net section on the peak net section stress. A similar functional fit to the curve of KNt (the stress concentration based on a,) against D / W was given for isotropic plates by Hart-Smith9, based on photoelasticity results reported in the literature; when stated in terms of Kgt, the Hart-Smith approximation leads to

K;t (bolt loaded hole) = W/D + 2/(1- D/W)

- 1.5/ (1 + D / W ) (28.4)

He also gave an expression for KNt for open, unloaded holes (i.e. with no load transfer between the fastener and plate) in isotropic plates; when the stress concentration is expressed as a ratio with respect to ac rather than uN the Hart-Smith open hole expression reduces to:

Kgt (open hole) = 2/(1- D / W )

+ (1 - D/W)* (28.5)

Y 4

3 --

--

elastic measurements)

0 1 I

0.1s 028 0.4 0.53 0.65

DIW ---31.-

Fig. 28.4 Predicted net section stress concentration against D/ W.


This is of interest in later discussions of combined bearing-bypass loads on bolted joints. As a means of predicting joint strength, we can equate the peak stress CTJ, , ,~~ to F'", the strength of the orthotropic laminate used in the joint. If the joint material acts purely elasti- cally, then the elasticity prediction of K$ gives F; which denotes the value of C T ~ when net section failure occurs, as F," = F'"/K,"'. The minimum in the KGnt against D/W curve of Fig. 28.4 will result in a maximum in the relationship between F," and DIW at D/W = 0.5.

However, joint strength is usually found to be considerably greater than that based on purely elastic behavior of the composite to failure, and it is appropriate to use the method developed by Whitney and NuismerI4 to cor- rect strength predictions based on linear elastic response to failure. The Whitney-Nuismer approach was developed for strength prediction of composite plates in the presence of circular holes, crack-like slits and other types of notches, and is meant to take into account the softening effect of local damage such as

delamination and fiber-separation around regions of peak stress. The method is applied by averaging the stresses predicted by two- dimensional elasticity analysis over a selected length a,, along a path lying normal to the load direction, in the vicinity of the peak stress. The failure load is obtained by equating the aver- aged stress to the laminate strength P, and u, is determined by an empirical fit of the mea- sured strength data. In an alternative version of the Whitney-Nuismer analysis, F'" is equated to the stress at a point spaced an empirically fit- ted distance do from the location of the stress peak. The latter approach has frequently been used for joint strength predi~tion'~, although the averaging and point stress versions of the Whitney-Nuismer analysis are equivalent.

Figure 28.5 illustrates the prediction of F; for net section tension failure as a function of D / W . The curves here were obtained from stresses given by elasticity analysis of 0/90° glass epoxy joint elementsI2, by averaging the predicted axial stress distribution ux in the net section (using the definition of x and y indicated

D = 0.63 cm (0.25 ") Laminate Tensile Strength 110 ksi (0.76 GPa)

45 ,-0.31 GPa Compressive Strength 100 ksi ( 0.69 GPa)

40

35

30

25

0-

vi

c

C 0

$ 15 5 20

g 10

a 5

v)

L

0 0.13 0.25 0.33

D I W

Fig. 28.5 Maximum gross section stress against D/ W.

0.5 0.63

616 Mechanical fasfening and adhesive bonding

by the coordinate axes centred at the hole in Fig. 28.3 from the edge of the hole to a point a distance u, from the hole, using the a, values listed in Fig. 28.5. The lowest curve of Fig. 28.5 which corresponds to a, = 0 represents purely elastic behavior of the joint material. It is clear that increasing the value of a, causes an upward shift of the predicted strength curve. Experimental joint strength datal2 gave an a, value of about 3.8 * 1.3 mm (0.15 & 0.05 in) for quasi-isotropic carbon epoxy laminates, for net section failure. Nuismer and Whi tne~ '~ suggested that a, and the corresponding d, are relatively constant for composite materials in general, although this is not always true. However, for a given material and stacking sequence, a, is independent of hole size; this has the effect that for large fastener diameters, the averaging effect is less important, and strength values tend toward those predicted by the elasticity analysis.

All the net section failure curves of Fig. 28.5 have the peak in the vicinity of D/W = 0.5 which was predicted by the linear elastic response analysis. This suggests that the joint strength is a maximum for bolt diameters near half of the plate width. For multi-fastener joints such as the one shown in Fig. 28.2, the length corresponding to W for the single fastener joint is replaced by WeE, the spacing of the dashed lines, which are lines of lateral symmetry; note that We* is also equal to the lateral s cing of the fasteners (the lateral pitch), so t t the peak strength value occurs

diameter. The experimental data of Fig. 28.612 confirms the occurrence of a strength maximum for D / W = 0.5 in single fastener joints. For multi-row joints (see Section 28.3.4) in which bypass load is present, the net section strength peak occurs for smaller values of D / W. High bypass loads give results similar to those for plates with unloaded holes, in which case large values of W / D corresponding to large fastener pitch are desirable.

In addition to the solid curves in Fig. 28.5 for net section failure is the dashed line designated

at a lateral \ pi ch of about twice the fastener

- M

Fig. 28.6 Experimental results on strength against D / W 2 .

'bearing failure', corresponding to compressive failure in front of the pin. Except for joints with short edge distance or multi-fastener joints where high bypass loads are present, the peak compressive stress in front of the fasteneP is found to be about 1.3 times ab, and uG for bearing failure can be estimated by setting ab equal to F" (compressive strength of the laminate) from which uG)max = F'" D/1.3W, a linear function of D / W. Although this result implies that the laminate compressive strength is the same as the bearing strength as is approximately true in some cases, the actual value of Fb" = ub)mm depends on the stacking sequence of the laminate as well as a number of details of the joint such as the type of fastener and whether the joint is in single or double shear (Section 28.3.5); thus Fbu has to be empirically determined for a given fastener, joint configuration and joint material selection by appropriate bearing strength tests (Section 28.3.6). Hart- Smith9J3 introduced a method of comparing bearing and net section tension failure similar to that given in Fig. 28.5 to show the trade off in failure modes for various values of D/W, and recommended selecting D/ W for the

design of the joint as the point at the intersec- tion of the bearing and tension failure envelopes. However, it was also pointed out in Nelson, Bunin and Hart-Smith13 that in multi- row joints in which the bearing load is distributed over several fasteners in a given column, the bearing stress is smaller than for the single fastener case and bearing failure may not occur in practical joint designs.

The value of the edge distance, e, is another critical parameter for bolted joints. While it has become customary to present joint strength as a function of e / D , in fact9,12 it is more a function of e/ W if e / D is much greater than 1, and plotting data on the effect of edge distance as a function of e / D is somewhat misleading even though it persists as accepted practice. Both stress analysis9, l2 and experimental results (Fig. 28.7) indicate that full joint

b I I I I 1 4

.W

Fig. 28.7 Effect of edge distance on joint strength W / D = 212.


strength will not be achieved unless e is at least as great at W. This is shown schematically in Fig. 28.8, which indicates that the minimum e for full joint strength over a wide range of fastener diameters remains equal to W. It is true that there is a tendency for bending failures to occur at the unloaded end of the joint (Fig. 28.9) for edge distances as small as 1-2 times D, which were shown in Op1ingerl2, in fact, to be a function of e / D; however, this type of failure is eliminated for e / D greater than about 2.

Fig. 28.8 Minimum edge distance is equal to W (independent of D).

y / I

high bending stress 0

Y

Fig. 28.9 Tendency for bending failure with small e/ D.


28.3.3 EFFECTS OF JOINT MATERIAL

Typical failure modes for mechanically fastened joints are shown in Fig. 28.10. Figure 28.11 indicates that shear-related failures may include what are usually 'shearout' failures such as the upper figure for 0,&5 reinforce- ments, which tend to lie along straight lines tangent to the bolt hole and to run to the end of the joint, as opposed to those for 0/90° laminates which originate at about 45" points around the bolt hole and run along curving lines to the joint end. Hart-Smith9 shows examples of 'shearout' type failures while the second type are demonstrated by experimental results for 0/90" glass epoxies12. Since the 90" points around the bolt hole are traction free, shear stresses cannot exist there, and 'shearout' failures are probably associated with fiber separation failures resulting from to a deficiency of 90" fibers in 0,&5 laminate, while failures originating at the 45" points in 0/90° laminates appear to be true shear failures. Chang and Hun@ provided an analytical approach which modelled progres- sive damage in 0/90° laminates that predicted the types of shear failures that are depicted in Fig. 28.11.

Fig. 28.11 Shear failures in bolted joints.

In addition to modelling shear failures, Chang and Hung16 also reported results related to bearing failure which show that these failures result from high out-of-plane shear stresses; the associated failure surfaces are oriented along planes at 45" to the x-y plane. In addition to clarifying the bearing failure modes, these results verified the importance of clamping pressure as a factor in achieving maximum bearing strengths. This is discussed further in Section 28.3.5.

It should be mentioned that the term 'bearing' strength, which is usually associated with the maximum achieved value of ab, does not necessarily imply that the joint fails by bearing failure, since, depending on the joint geometry

- l€NSlON FAIUIIL BO11 PULLING lHlOUGn U M I W T E

Fig. 28.10 Typical failure modes in composite joints13.


PEICfNTAGf W-DEGIEE PLIES

BEARING STRESS CONTOURS 651)

WLT DIUETER = 0.25 IN. (10RQUED WLW

O M Z O 3 D ~ S O ~ M ~ W l W

RKfNlAGE f4S-DEGltE PLIES

and reinforcement, failure may take the form of shearout or net tension rather than bearing failure; bearing strength only identifies the value of ab that occurs when the joint fails. The value of ab for the bearing failure mode can be looked on as a laminate material parameter, however, and can be obtained from appropriate single fastener strength tests, to be discussed in Section 28.3.6, in which e/ W (usually specified in terms of e / D ) and W / D are large enough to guarantee a bearing failure mode. The effect of the reinforcement configuration on the maximum achieved ab is an important factor in joint design. Note that for design purposes, the normal reinforcement arrangement includes only plies in the 0", 45" and 90" directions with respect to the load axis, implying that other orientations are not encountered; in addition, the 45" reinforcement is arranged symmetrically as double plies of k45" reinforcement. The notation com- monly used to describe the stacking sequence is condensed to reflect percentages of plies in the three customary directions, 25/50/25 rep-

Fig. 28.12 'Carpet' plot of maximum bearing stress vs. percentage of reinforcement in key directions4.

the reinforcement arrangement in the vicinity of the joint.

resenting 25% 0", 50% 45", and 25% 90", or 28.3.4 quasi-isotropic, reinforcement, for example.

The effects of reinforcement percentages on maximum achieved bearing stress are shown in Fig. 28.12, a three-parameter 'carpet plot' which is used to show the effect of percentage of reinforcement in the 0", 90" and 4 5 " directions on maximum achieved bearing stress for a fixed joint geometry. The contours of constant bearing strength indicate that maximum joint strength is achieved within a broad plateau lying between 3040% 0" and 1040% +45" reinforcement. To avoid low strength against shearout failure, it is generally agreed that a minimum number of 90" plies, at least lo%, should be included in the laminate. Laminates reinforced in fewer than three directions, i.e. 0/90° and k45" reinforcement, should be avoided if possible, since they respond ductiley with excessively low yield strengths. These recommendations may be difficult to follow if considerations other than maximum joint structural performance govern

Single fastener joints cannot generally achieve anything close to the strength of the laminate being loaded and are not usually encountered in structural joints. Single fastener coupons do, however, serve as building blocks for design of multi-fastener joints (Fig. 28.2) since stress analysis and strength test results on single fastener geometries provide data which translate directly to multi-fastener arrays in structures. There are two principal features that affect multi-fastener arrays; that of bearing-bypass load is illustrated in Fig. 28.13. The bypass load, Pb , can be considered as a load added at the d o a d e d (right) end of the upper element in the single fastener joint in Fig. 28.1. In the case of a multi-fastener array (Figs. 28.2, 28.14), Pbp for a given fastener is equivalent to the sum of the loads developed by the fasteners lying to the right of (i.e. those lying in the direction of the load from) the one under consideration. For each fastener, the load P, in


Pf +pbp

pN

Fig. 28.13 Definition of bypass load.

Fig. 28.13 (see also Fig. 28.14) is the load passed through the net section associated with that fastener and is the sum of P , the fastener load, and Pb ; P, is also equivalent to the total load at the feft end of the joint in Fig. 28.13. The situation in Fig. 28.14(b) shows the buildup of P, along a joint containing five fasteners for the hypothetical case of equal P, for each fastener, while Fig. 28.14(c) shows the distribution of Pb /PN for that case. It is important to realize that the net section stresses build up along with P,. If the joint design is such as to distribute the fastener loads P, evenly as in Fig. 28.14, the load on each fastener is then the total load divided by the number of fasteners, a fraction of 1/5 in Fig. 28.14, so that the bearing stress at each fastener is much smaller than for a single fastener joint.

On the other hand, the net section load on the last fastener is the sum of all fastener loads and is therefore the same as in a single fastener joint carrying the same total load. The benefit of multi-rowed fastener configurations is primarily because the stress concentration factor associated with pure bypass load (eqn (28.4)) is smaller than that associated with pure bearing load (eqns (28.7), (28.3)), and the load ratio for the most highly loaded net section (the left most in Fig. 28.14) tends toward the case of pure bypass loading for large numbers of fasteners. Stress analyses for combined bearing-bypass loading have been discussed7, *, 12, 17, la.

Figure 28.1512 gives the elasticity predictions of KEt for various ratios of Pbp to P,, indicating the KEt is a nonlinear function of P,/P . (The results in Fig. 28.15 are for a perfect fit fastener and for a joint under tension.) This nonlinearity is caused by the variation of angle of contact between the fastener and the plate with the load ratio; Fig. 28.16 illustrates the difference in the contact region for the extreme cases of pure bearing and pure bypass load. In the latter case the plate stretches in opposite directions along a line parallel to the load direction and contact splits into two regions centered about +90" and -90" with respect to the load direction, while for pure bearing load, a single contact region occurs ranging from about -100" to +loo" about the load axis for perfect-fit fasteners. (For clearance fits in the case of pure bearing load the

bF

Fig. 28.15 Net section SCF against bearing/bypass load ratio. Fig. 28.14 Bypass against bearing load.


contact (28.5)). The results, given in Oplinger12, indi- [AI cated that this will result in inaccurate

predictions, not only for the general bearing- bypass situation but also for the case of pure - - bearing load with small edge distances (Fig. 28.9). Currently available analytical and finite element tools are sophisticated enough to treat the contact problem routinely, and the 'cos 8' radial pressure distribution should be avoided, although the superposition method gives some useful insight into the situation if analytical tools for dealing with the contact problem are not available. Crews and Naiks obtained results which showed that the hoop stresses

WWS

ce) BEARING -

Fig. 28.16 Contact angles for pure bearing load and pure bypass load.

contact region varies with load and is smaller than that of exact-fit fasteners. Crews and Naik8 treated the case of 1.2% clearance, i.e. a hole diameter 1.2% greater than the fastener diameter, for which contact between the fastener and hole occurs from about -60" to +60° for typical loads.)

For intermediate bearing/bypass ratios, the contact region is a mix of the two situations. Oplinger12 gave the variation of the radial pressure distributions for exact fit fasteners, for joints in tension, which showed how the contact region is modified as the bearing/bypass ratio varies, while Naik and Crewss treated cases of both exact and clearance fits for both tension and compression loaded joints; in addition, Madenci7 gave comparable results for cases of shear loaded joints. A number of efforts have treated the contact problem for pure bearing by assuming a radial pressure distribution which varies around the hole as the cosine of the angle with respect to the load axis; in addition, for combined bearing and bypass loading (following industry practice) Hart-Smith9 and others have, as a matter of expediency, superposed the peak stresses predicted for pure bearing and pure bypass (i.e. the values of K:t predicted by eqns (28.4) and

around the bolt hole are predicted with reasonable accuracy by the superposition method, so that with judicious use of N~ismer-Whitney'~ correction factors, net section failure stresses can be reasonably well predicted by superposition; bearing failures cannot.

Naik and CrewsIs described test methods for joint strength under combined bearing- bypass loading, with compressive as well as tensile bypass loads. Typical results are given in Fig. 28.17 for a 1.2% clearance fit fastener in a quasi-isotropic carbon epoxy laminate. Failure modes here are designated 'TRB' ('tension reacted bearing', i.e. bearing failure with tension bypass loading), 'TRC' (bearing 'failure with compression bypass loading), 'NT' (net section tension), 'NC' (net section compression) and 'OSC' or 'offset compression' which refers to the failure mode illustrated in Fig. 28.18 for compression bypass load.

Although the load distribution for the five- fastener joint shown in Fig. 28.12 is represented as having the same P, for each fastener, this condition cannot be achieved for joints in general. As shown in Fig. 28.1913, there is usually considerable variation of fastener loads along the joint. In a two-fastener joint such as that shown in Fig. 28.20, the upper and lower plate elements ('U' and 'L') have to stretch equally under load if there are no fastener deflection effects (no fastener tilt- ing or bending).


Bearing stress, Sb, Wa

Bypass stress, S W a nP'

Fig. 28.17 Laminate strengths under combined bearing/bypass loading17.

Fig. 28.18 'OSC' failures for combined bearing bypass loading17.

With the average gross section stresses and strains for the two plate elements in Fig. 28.20 give by:

OGU = ( P - P, )/tuW;

and

EGL = g G L / E L ,

the elongations are:

6,= kGu and 6 , = ZE,,.

The condition that 6, = 6, requires that:

I(P - P,,)/E,t,W = lPf,/E,f,W.

Since Pp = P - P,,, this is equivalent to:

Pf, = (E,f,/E,t,)Pf,, If E,>>E, or tL>>t,, the resulting P,, will be small compared with P,, so that the second fastener will be nearly unloaded. In such a case the joint will be equivalent to a single fastener joint containing an unloaded hole at the location of the second fastener. On the other hand, the last equation showsthat if the stiffnesses of the upper and lower plates are equal, the two fasteners will be loaded equally. In general, fastener loads will be highly variable in a way that depends on the relative thicknesses and


moduli of adjacent plate elements in the regions around each fastener; fastener deflections due to beam-bending of the fasteners as well as clearance effects will add other complications to the situation. In Fig. 28.19, configuration A illustrates the behavior of joints with both elements tapered (i.e. scarf joints); due to load transfer between the elements by fastener load, the net section load P, decreases from the loaded (thick) end of each plate to its unloaded (thin) end, while the corresponding thicknesses decrease keeps the gross section stresses and strains and therefore the stretching deflections uniform along each element, providing for nearly equal load transfer at each fastener. For configuration B of Fig. 28.19, the case of uniform element thickness, the interior fastener loads are smaller than those at the joint ends, which is typical of this situation. Since the configurations shown at the right in Fig. 28.19 are arranged in order of increasing load capability (see the strains

BOLT LOAD DISTRIBUTIONS 4-ROW BOLTED NINT

Fig. 28.20 Two fastener joint.

listed under each configuration), it is noted that the scarfed configuration gives the lowest strength of the four, and is about 9% weaker than the uniform thickness configuration, B. It is usually expected that scarfing will lead to a way of keeping the bearing load minimized at the joint ends where the highest P,s are encountered, but other factors having to do with the balance between the effects of local

- CONFIQURATION A O----Q CONFIQURATION B 0- 4 CONFIGURATION C -1 n CONFIGURATION D

CONFIGURATION D E , - O11(#lNIIN.

CONFIGURATION C E- = 0A)OMINIIN.

CONFIGURATION B - 0#)46INIIN.

Ob0IN. 1 2 3 4 0251N. I

! i I - .'- - 1 2 3 4 BOLT NUMBER 1A 112. 112. 112 I '

CONFIGURATION A E, - O m 1 INAN.

Fig. 28.19 Effect of joint configuration on fastener load di~tribution'~.


element thickness and local bearing load pre- dominates here. Note that configuration D, the strongest, uses a combination of variable fastener diameter and element tapering to achieve a maximum thickness of the outer elements which is greater than that in configuration C, to obtain maximum joint strength. Thus, judicious use of element tapering and variation of fastener diameters as well as other joint parameters can improve joint performance. With untapered joints, the maximum benefit of additional rows of fasteners is not much more than 20% greater than that for single row joints. Joint tapering will provide some improvement over that figure, although the benefit is limited; it should be kept in mind that the net section load at the loaded end of a given element will be the same for single fastener and multi-fastener joints, so that the benefit of adding more than a few rows may not be great. The interaction of the effects encountered in multi-fastener joints is fairly complicated and requires the use of analyses which can take into account the stresses and strains in single fastener configurations with bypass loading present (Fig. 28.13), represent- ing 'unit cells' of the joint configuration, together with finite element calculations which evaluate the interactions among the various unit cells to provide the overall fastener load distribution. Computer codes have been developed under DoD and NASA spon- sorship to provide for this type of integrated joint design. For example, Nelson, Bunin and Hart-Smith13 discuss the application of the well-known 'A4EJ' codeI9 in conjunction with the code 'BJSFM' (Bolted Joint Stress Field Model15) which were developed by McDonnell Douglas under NASA and Air Force sponsor- ship for this type of joint design analysis. Northrop similarly developed codes 'SASCJ' (Stress Analysis of Single Fastener Composite Joints) and 'SAMCJ' (Stress Analysis of Multifastener Composite Joints) under Air Force Contract6, 20. For information on the theory and application of these codes, the reader is directed to the references.

28.3.5 FASTENER EFFECTS

Joint strengths for local areas (Fig. 28.13) around individual fasteners are affected by a number of parameters associated with the fasteners. Some of these include: whether the joint is in single or double shear (Fig. 28.21); the use of countersunk (flush head) compared with protruding head fasteners (Fig. 28.22); effects of fastener diameter; effects of fastener clamping; fastener clearance effects, and effect of fastener deflections on fastener load distribution. Bearing strengths are significantly affected by the use of single compared with

P p 7 = g = 7 p 2 p (A) Double Shear Configuration

P

~

I'2 (B) Single Shear configuration

Fig. 28.21 Single shear and double shear configurations.

+f- P

3 (A) Protruding Head Fastener

P

P

(B) Countersunk Fastener

Fig. 28.22 Countersunk and protruding head fasteners.


double shear configurations, bearing strengths for single shear joints tending to run considerably below those for double shear because of greater through-the-thickness variation of fastener-plate contact pressure. Bearing strength tests referenced in Section 28.3.6 include separate test configurations for the two situations. In addition, as indicated in Fig. 28.22(a), bending moments tend to occur in single shear joints which are not present with double shear arrangements. Fastener head pull through (Fig. 28.10) can be a problem in the presence of such bending effects, and special test methods for fastener pull-through strength are described in Section 28.3.6. Countersunk, or flush head, fasteners (Fig. 28.22(b)) are frequently encountered in exterior surfaces of aircraft components where avoidance of air flow disturbance is required. Countersunk fasteners for composites include (Fig. 28.23) 'tension head' fasteners having the larger head depths and therefore wider heads, and 'shear head' fasteners having smaller head depths, with head angles ranging from 100" to 130". Countersunk fasteners tend to bear against the surrounding element more unevenly through the thickness than protruding head fasteners do. Tension head fasteners are generally preferred over shear head fasteners because of greater strength against head pull-through; however, if the joint element is so thin that the countersunk depth is greater than 70% of the element thickness, the tendency toward uneven bearing pressure in tension head fasteners is too great and shear head fasteners are recommended in this case.

Fig. 28.23 Tension head and shear head fasteners.

The fastener diameter should be on the order of the thickness of the thicker of the plate elements making up the joint, or greater, ( D / t 2 1) to avoid excessive fastener bending. As in Fig. 28.10 (lower right-hand sketch) excessive bending can lead to failure of the fasteners, which is intolerable. In addition, fastener bending causes uneven distribution of bearing pressure through the plate element thicknesses, so that the full bearing strength is not available in such cases. The effect of large fastener deflections on the clamping pressure provided by the fastener is another adverse effect of fastener bending deflections. Figure 28.2413 illustrates the fact that bending deformations reduce the clamping pressure provided by fastener head, causing a reduction of bearing strength which is in addition to that caused by uneven bearing pressure through the thickness.

The beneficial effect of clamping pressure on bearing strength, discussed earlier, has been well established. Required clamping levels are usually described in terms of bolt torques, 'finger tightened' being the lightest level, and installation requirements specify torque levels which supposedly represent particular bolt tensions (and therefore clamping

- -

TENSION JOINT HlQH BEARING LOAD SIDE

- -

TENSION JOINT HlQH BEARING LOAD SIDE

LOELAMINATIONS DUE TO BEARING LOAD AND REDUCED

HlQH BEARINQ LOAD SIDE

- COMPRESSION JOINT w-

Fig. 28.24 Effects of fastener bending on joint fail- ureI3.


pressures) that can be calculated in terms of the pitch of the fastener threads from machine design formulas. Bolt tensions for a given torque level are notoriously variable because of friction effects in the bolt threads, but specified torque levels which have been determined empirically probably represent minimum clamping levels necessary to insure maximum bearing strengths that can be achieved when variations in service conditions are taken into account. Steps should be taken to avoid loss of clamping pressure due to through-the-thickness viscoelastic deforma- tion of the laminatez1” at elevated temperature and humidity.

Fastener clearances are typically on the order of 0.075 mm (0.003 in) or less for typical 0.635 mm (0.25 in) aircraft fasteners. Analytical studies have shown that bearing stresses increase significantly for such relatively small clearances since the angle of contract decreases rapidly as the clearance increases. Clearances also have a significant effect on the fastener load distribution since the last in a series of fasteners cannot take up load until all the clearances have been taken up.

In addition to the effect of clearances on fastener load distribution, effects of fastener bending deflections must be taken into account in load distribution calculations such as those provided by the A4EJ, SASCJ and SAMCJ codes described above. In the case of the two-fastener joint shown in Fig. 28.20, bending and rotational deflections of the fasteners will modify the load distribution described in the discussion of that figure for zero fastener deflection. For E,t,>>E,t,, in Fig. 28.20 for example, fastener deflections will allow some load to be transferred to the second fastener, as opposed to the case of no fastener deflections discussed earlier which led to Pf2 = 0. Fastener deflection effects can be inferred from bolt bearing tests which provide for deflection measurements. Alternatively, analytical approaches based on beam models for the fastener which include both bending and shear deformations have been used13.

Complications, such as the way in which the fastener head and nut/washer combination bears on the surfaces of the plate element will influence the outcome of such calculations and must be taken into account. In addition, the through-thickness distribution of bearing pressure between the fastener and the surrounding the plate element should be included in the calculations. The method of Harris, qalvo and Hoosonz3 which treats the bore of the fastener hole as an elastic foundation for the beam used to model the fastener has been applied6 for such calculations.

28.3.6 TEST METHODS

Joint strength tests are needed to establish certain key parameters of the joint as inputs to design analyses. Such data as failure stresses for pure bearing load as obtained from single fastener coupons, and open hole coupon strengths for both tension and compression loading, are needed to establish joint performance for pure bearing and bypass loads. Intermediate combinations of bearing and bypass load must also be considered to provide empirical curves for dealing with the general situation. Because of differences in the way the fastener contacts the surrounding plate materials, bearing tests have to be conducted to treat both single and double lap (single and double shear) configurations. In single lap joints in particular, tests are needed to establish the effect of fastener rotation and bending deflection. Fastener deflections must be determined in tests of the type just described for providing fastener response data in connection with predictions of load distribution in multifastener joints. In addition, fastener head pull-through strength tests have to be performed to allow for joint configurations in which overall bending takes place, in which case out-of-plane forces between the fastener and joint plates tend to be sigruficant.

The details of test methods for mechanically fastened joints are described by Shyprykevichz4 and in Mn-HDBK-1725.

Adhesive joints 627

28.4 ADHESIVE JOINTS

28.4.1 INTRODUCTION

Adhesive joints are capable of high structural efficiency and constitute a resource for structural weight saving because of the potential for elimination of stress concentrations which cannot be achieved with mechanically fastened joints. Unfortunately, because of a lack of reliable inspection methods and a requirement for close dimensional tolerances in fabrication, aircraft designers have generally avoided bonded construction in primary structure. Some notable exceptions include: bonded step lap joints used in attachments for the F-14 and F-15 horizontal stabilizers as well as the F-18 wing root fitting, and a majority of the airframe components of the Lear Fan and the Beech Starship.

While a number of issues related to adhesive joint design were considered in the earlier literaturezG3, much of the methodology currently used in the design and analysis of adhesive joints in composite structures is based on the approaches evolved by L.J. Hart- Smith in a series of NASA/Langley-sponsored contracts of the early 1 9 7 0 ~ ~ ~ ~ as well as from the Air Force’s Primary Adhesively Bonded Structures Technology (PABST) programw3 of the mid-1970s. The most recent such work developed three computer codes for bonded and bolted joints, designated ‘A4EG’, ’A4EI’ and ’A4EKW under Air Force Contract . The results of these efforts have also appeared in a number of open literature publi~ations~’-~. In addition, such approaches found application in some of the efforts taking place under the NASA Advanced Composite Energy Efficient Aircraft (ACEE) program of the early to mid- 198Os5O, 51.

Some of the key principles on which these efforts were based include: (1) the use of simple one-dimensional stress analyses of generic composite joints wherever possible; (2) the need to select the joint design so as to ensure failure in the adherend rather than the adhesive, so that

the adhesive is never the weak link; (3) recognition that the ductility of aerospace adhesives is beneficial in reducing stress peaks in the adhesive; (4) careful use of such factors as adherend tapering to reduce or eliminate peel stresses from the joint; (5) recognition of slow cyclic loading, corresponding to such phenomena as cabin pressurization in aircraft, as a major factor controlling durability of adhesive joints, and the need to avoid the worst effects of this type of loading by providing sufficient overlap length to ensure that some of the adhesive is so lightly loaded that creep cannot occur there, under the most severe extremes of humidity and temperature for which the component is to be used.

Much of the discussion to follow will retain the analysis philosophy of Hart-Smith, since it is considered to represent a major contribution to practical bonded joint design in both composite and metallic structures. On the other hand, some modifications are introduced here. For example, the revisions of the Goland-Reissner single lap joint analysis36 have been re-revised according to the approach presented in Refs. 53,54.

Certain issues which are specific to composite adherends but were not dealt with in the Hart-Smith efforts will be addressed. The most important of these is the effect of transverse shear deformations in organic composite adherends.

28.4.2 SUMMARY OF JOINT DESIGN CONSIDERATIONS

28.4.2.1 Effects of adherend thickness: adherend failures versus bond failures

Figure 28.25 shows a series of typical bonded joint configurations. Adhesive joints in general are characterized by high stress concentrations in the adhesive layer. These originate, in the case of shear stresses, because of unequal axial straining of the adherends, and in the case of peel stresses, because of eccentricity in the load path. Considerable ductility is associated


(0) 4--- 1

TAPERED SINGLE-UP JOINT

DOUBLE-UP JOINT

(F) 1 DUJBLE-STRAP JOINT

(0) 4 n f &

TAPERED STRAP JOINT

Fig. 28.25 Adhesive joint types”, 55.

with shear response of typical adhesives, which is beneficial in minimizing the effect of shear stress joint strength. The response of typical adhesives to peel stresses tends to be much more brittle than that to shear stresses, and reduction of peel stresses is desirable for achieving good joint performance.

From the standpoint of joint reliability, it is vital to avoid the condition where the adhesive layer is the weak link in the joint, i.e. that the joint be designed to ensure that the adherends fail before the bond layer whenever possible. T ~ E is because failure in the adherends may be controlled, while failure in the adhesive is resin dominated, and thus subject to effects of voids and other defects, thickness variations, environmental effects, processing variations, deficiencies in surface preparation and other factors that are not always adequately controlled. This is a significant challenge, since adhesives are inherently much weaker than the composite or metallic elements being joined. However, the objective can be accomplished by recognizing the limitations of the joint geometry being considered and placing appropriate restrictions on the thicknesses the adherends for any given geometry. Figure 28.26, which has frequently been used by Hart-Smith39, 55 to

illustrate this point, shows a progression of joint types which represent increasing strength capability from the lowest to the highest in the figure. In each type of joint, the adherend thickness may be increased as an approach to achieving higher load capacity. When the adherends are relatively thin, results of stress analyses show that for all of the joint types in Fig. 28.26, the stresses in the bond will be small enough to guarantee that the adherends will reach their load capacity before failure can occur in the bond. As the adherend thicknesses increase, the bond stresses become relatively larger until a point is reached at which bond failure occurs at a lower load than that for which the adherends fail. This leads to the general principle that for a given joint type, the adherend thicknesses should be restricted to an appropriate range relative to the bond layer thickness. Because of processing considerations and defect sensitivity of the bond material, bond layer thicknesses are generally limited to a range of 0.125-0.39 mm (0.005-0.015 in). As a result, each of the joint

ADHEREND THICKNESS

Fig. 28.26 Joint geometry effects39.

Adhesive joints 629

types in Figs. 28.25 and 28.26 corresponds to a specific range of adherend thicknesses and therefore of load capacity, and as the need for greater load capacity arises, it is preferable to change the joint configuration to one of higher efficiency rather than to increasing the adherend thickness indefinitely.

28.4.2.2 Joint geometry effects

Single and double lap joints with uniformly thick adherends (Fig. 28.25(b), (e) and ( f ) ) are the least efficient joint type and are suitable primarily for thin structures with low running loads (load per unit width, i.e. stress times element thickness). Of these, single lap joints are the least capable because the eccentricity of this type of geometry generates significant bending of the adherends that magnifies the peel stresses. Peel stresses are also present in the case of symmetric double lap and double strap joints, and become a limiting factor on joint performance when the adherends are relatively thick.

Tapering of the adherends (Figs. 28.25(d) and (g)) can be used to eliminate peel stresses in areas of the joint where the peel stresses are tensile, which is the case of primary concern. For joints between adherends of identical stiffness, scarf joints (Fig. 28.25(i)) are theoretically the most efficient, having the potential for complete elimination of stress concentrations. (In practice, some minimum thickness corresponding to one or two ply thicknesses must be incorporated at the thin end of the scarfed adherend leading to the occurrence of stress concentrations in these areas.) In theory, any desirable load capability can be achieved in the scarf joint by making the joint long enough and thick enough. However, practical scarf joints may be less durable because of a tendency toward creep failure associated with a uniform distribution of shear stress along the length of the joint unless care is taken to avoid letting the adhesive be stressed into the nonlinear range. As a result, scarf joints tend to be used only for repairs of very thin structures.

Scarf joints with unbalanced stiffnesses between the adherends do not achieve the uniform shear stress condition of those with balanced adherends, and are somewhat less structurally efficient because of rapid buildup of load near the thin end of the thicker adherend.

Step lap joints (Fig. 28.25(h)) represent a practical solution to the challenge of bonding thick members. This type of joint provides manufacturing convenience by accommodat- ing the layered structure of composite laminates. In addition, high loads can be transferred if sufficiently many short steps of sufficiently small ’rise’ (i.e. thickness increment) in each step are used, while maintaining sufficient overall length of the joint.

28.4.2.3 Effects of adherend stiffness unbalance

All types of joint geometry are adversely affected by unequal adherend stiffnesses, where stiffness is defined as axial or in-plane shear modulus times adherend thickness. Where possible, the stiffnesses should be kept approximately equal. For example, for step lap and scarf joints between quasi-isotropic carbon epoxy (Young’s modulus = 55 GPa = 8 x lo6 lb/in2) and titanium (Young’s modulus = 110 GPa = 16 x lo6 lb/in2) ideally, the ratio of the maximum thickness (the thickness just beyond the end of the joint) of the composite adherend to that of the titanium should be 110/55 = 2.0.

28.4.2.4 Effects of ductile adhesive response

Adhesive ductility is an important factor in minimizing the adverse effects of shear and peel stress peaks in the bond layer. If peel stresses can be eliminated from consideration by such approaches as adherend tapering, strain energy to failure of the adhesive in shear has been shown by Ha~?-Smith~~ to be the key parameter controlling joint strength; thus the square root of the adhesive strain energy


density to failure determines the maximum static load that can be applied to the joint. The work of Hart-Smith has also shown that for predicting mechanical response of the joint, the detailed stress-strain curve of the adhesive can be replaced by an equivalent curve consisting of a linear rise followed by a constant stress plateau (i.e. elastic-perfectly plastic response) if the latter is adjusted to provide the same strain energy density to failure as the actual stress-strain curve gives. Test methods for adhesives should be aimed at providing data on this parameter. Once the equivalent elastic- perfectly plastic stress-strain curve has been identified for the selected adhesive for the most severe environmental conditions (temperature and humidity) of interest, the joint design can proceed through the use of relatively simple one-dimensional stress analysis, thus avoiding the need for elaborate finite element calculations. Even the most complicated of joints, the step lap joints designed for root-end wing and tail connections for the F-18 and other aircraft, have been successfully d e ~ i g n e d ~ ~ , ~ ” ~ and experimentally demonstrated using such approaches. Design procedures for such analyses which were developed on Government contract have been incorporated into public domain in the form of the ’A4EG’, ‘A4EI’ and ‘A4EK computer codes- mentioned previously in Section 28.4.1. Note that the A4EK code permits analysis of bonded joints in which local disbonds are repaired by mechanical fasteners.

28.4.2.5 Behavior of composite adherends

Organic matrix composite adherends are considerably more affected by interlaminar shear and tensile stresses than metals, so that there is a significant need to account for such effects in stress analyses of joints. Transverse shear and thickness-normal deformations of the adherends have an effect analogous to thickening of the bond layer, corresponding to a lowering of both shear and peel stress peaks. On the other hand, the adherend matrix is often weaker than the adhesive in shear and

transverse tension, as a result of which the limiting element in the joint may be the interlaminar shear and transverse tensile strengths of the adherend rather than the bond strength. Ductile behavior of the adherend matrix can be expected to have an effect similar to that of ductility in the adhesive in terms of response of the adherends to transverse shear stresses, although the presence of the fibers probably limits this effect to some extent, particularly in regard to peel stresses.

The effect of the stacking sequence of the laminates making up the adherends in composite joints is sigruficant. For example, 90” layers placed adjacent to the bond layer theoretically act largely as additional thicknesses of bond material, leading to lower peak stresses, while 0” layers next to the bond layer give stiffer adherend response with higher stress peaks. In practice it has been observed that 90” layers next to the bond layer tend to seriously weaken the joint because of transverse cracking which develops in those layers, and advantage cannot be taken of the reduced stresses.

Large disparity of thermal expansion characteristics between metal and composite adherends can pose severe problems. Adhesives with high curing temperatures may be unsuitable for some uses below room temperature because of large thermal stresses which develop as the joint cools below the fabrication temperature.

Composite adherends are relatively pervi- ous to moisture, which is not true of metal adherends. As a result, moisture is more likely to be found over wide regions of the adhesive layer, as opposed to confinement near the exposed edges of the joint in the case of metal adherends, and response of the adhesive to moisture may be an even more significant issue for composite joints than for joints between metallic adherends.

28.4.2.6 Effects of bond defects

Defects in adhesive joints which are of concern include surface preparation deficiencies, voids

Adhesive joints 631

and porosity, and thickness variations in the bond layer.

Of the various defects which are of interest, surface preparation deficiencies are probably the greatest concern. These are particularly troublesome because there are no current non- destructive evaluation techniques which can detect low interfacial strength between the bond and the adherends. Most joint design principles are academic if the adhesion between the adherends and bond layer is poor. The principles for achieving good adhesion of the bond to the adherends (see Chapter 29) are well established for adherend and adhesive combinations of interest. Hart-Smith, Brown and Won$ give an account of the most crucial features of the surface preparation process. Results shown in that reference suggest that surface preparation which is limited to removal of the peel ply from the adherends may be suspect, since some peel plies leave a residue on the bonding surfaces that makes adhesion poor. (However, some manufactur- ers have reported satisfactory results from surface preparation consisting only of peel ply removal.) Low pressure grit b l a ~ t i n g ~ ~ , ~ ~ is preferable over hand sanding as a means of eliminating such residues and mechanically conditioning the bonding surfaces.

For joints which are designed to ensure that the adherends rather than the bond layer are the critical elements, tolerance to the presence of porosity and other types of defect is consid- erable45. Porosity'jO is usually associated with overthickened areas of the bond, which tend to occur away from the edges of the joint where most of the load transfer takes place, and thus is a relatively benign effect, especially if peel stresses are minimized by adherend tapering. In such cases6", porosity can be represented by a modification of the assumed stress-strain properties of the adhesive as determined from thick-adherend tests, allowing a straightforward analysis of the effect of such porosity on joint strength, as in the A4EI computer code. If peel stresses are significant, as in the case of over-thick

adherends, porosity may grow catastrophi- cally and lead to non-damage tolerant joint performance.

Bond thickness variations'jl usually take the form of thinning due to excess resin bleed at the joint edges, leading to overstressing of the adhesive in the vicinity of the edges. Inside tapering of the adherends at the joint edges will compensate for this condition; other com- pensating techniques are also discussed'jl. Bond thicknesses, per se, should be limited to ranges of 0.12-0.24 mm (0.005-0.01 in) to prevent significant porosity from developing although greater thicknesses may be acceptable if full periphery damming or high minimum viscosity paste adhesives are used. Common practice involves the use of film adhesives containing scrim cloth, some forms of which help to maintain bond thicknesses. It is also common practice to use mat carriers of chopped fibers to prevent a direct path for access by moisture to the interior of the bond.

28.4.2.7 Durability of adhesive joints

Hart-Smith45 discusses differences in durability assessment of adhesive joints between concepts related to creep failure under cyclic loading and those related to crack initiation and propagation which require fracture mechanics approaches for their interpretation. In summary, Hart-Smith suggests that if peel stresses are eliminated by adherend tapering or other means, and if the principle discussed in Section 28.4.2.1 of limiting the adherend thickness to ensure failure of the adherends rather than the adhesive is followed, crack- type failures will not be observed under time-varying loading, failures being related primarily to creep fatigue at hot wet conditions, in joints with short overlaps which are subject to relatively uniform distributions of shear stress along the joint length. Additional discussion of viscoelastic response of bonded joints is

There is an extensive body of literature6571 on fracture mechanics approaches to joint


durability, based on measurement of energy release rates for various adhesives together with analytical efforts aimed at applying them to joint configurations of interest. In particular, Johnson and Malln report fatigue crack initiation in bonded specimen configurations with adherend tapering aimed at reduction of peel stresses in varying degrees, in some cases prac- tically eliminating them; data in Ref. 92 indicate that crack initiation will occur even with the adhesive in pure shear, for cycling to lo6 cycles above loading levels which are probably considerably below static failure loads. The results given” suggest that for combinations of peel and shear stressing, total (mode 1 + mode 2) cyclic energy release rate can be used to determine whether or not cracking will occur. However, Hart-Smith reportedfi that in ’thick adherend‘ test specimens that provide a relatively uniform shear stress distribution in the adhesive (see MIL-HDBK-17, Vol. 1, Chapter 7, Section 7.3) which were subjected to fatigue tests in the PABST programM, cycling to more than lo7 cycles applied at high cycling rates (30 Hz) were achieved without failure of the adhesive, although in certain cases, namely those involving 6.27 mm (0.25 in) adherend thicknesses, fatigue failures of the metal adherends did result. More study is needed to resolve some of the apparently contradictory results which have come out of various studies.

28.4.3 STRESSES IN ADHESIVE JOINTS

28.4.3.1 General

Stress analyses of adhesive joints have ranged from very simplistic ‘P over A’ formulations in which only average shear stresses in the bond layer are considered, to extremely elegant elasticity approaches that consider fine details, e.g. the calculation of stress singularities for application of fracture mechanics concepts. A compromise between these two extremes is desirable, since the design of structural joints does not usually depend on the fine details of the stress distributions. Since practical consid-

erations force bonded joints to incorporate adherends which are thin relative to their dimensions in the load direction, stress variations through the thickness of the adherend and the adhesive layer tend to be moderate. Such variations do tend to be more sigruficant for organic composite adherends because of their relative softness with respect to transverse shear and thickness normal stresses. However, a considerable body of design procedure has been developed based on ignoring thickness- wise adherend stress variations. Such approaches involve using one-dimensional models in which only variations in the axial direction are accounted for. Accordingly, the bulk of the material to be covered here is based on simplified one-dimensional approaches characterized by the work of Hart-Smith. The Hart-Smith approach makes extensive use of closed form and classical series solutions since these are ideally suited for making parametric studies of joint designs. The most prominent of these have involved modification of Volkersen26 and Goland-ReissnerZ7 solutions to deal with ductile response of adhesives in joints with uniform adherend thicknesses along their lengths, together with classical series expressions to deal with variable adherend thicknesses encountered with tapered adherends, and scarf joints. Simple lap joint solutions described below calculate shear stresses in the adhesive for various stiffnesses and applied loadings. For the more practical step lap joints, the described expressions can be adapted to treat the joint as a series of separate joints, each having uniform adherend thickness.

28.4.3.2 Adhesive shear stresses

Figure 28.27 shows a joint with ideally rigid adherends in which neighboring points on the upper and lower adherends slide horizontally with respect to each other when the joint is loaded to cause a displacement difference 6 = uu - uL related to the bond layer shear strain by yb = 6 / f b . The corresponding shear stress, zb, is given by zb = Gbyb. The rigid adherend

Adhesive joints 633

assumption implies that 6, y, and t, are uniform along the joint. Furthermore, the equilibrium relationship indicated in Fig. 28.27(c), which requires that the shear stress be related to the resultant distribution in the upper adherend by

dTU/dx = zb (28.6)

leads to a linear distribution of Tu and TL (upper and lower adherend resultants) as well as the adherend axial stresses uxu and ax, indicated in Fig. 28.28. These distributions are described by the following expressions:

where ax = T/t. In actual joints, adherend deformations will cause shear strain variations in the bond layer which are illustrated in Fig. 28.29. For the case of a deformable upper adherend in combination with a rigid lower adherend shown in Fig. 28.29(a) (in practice,

one for which E,tL >> E&), stretching elongations in the upper adherend lead to a shear strain increase at the right end of the bond layer. The case in which both adherends are equally deformable, shown in Fig. 28.29(b), indicates a bond shear strain increase at both ends due to the increased axial strain in whichever adherend is stressed at the end under consideration. For both cases, the variation of shear strain along the bond results in an accompanying increase in shear stress which, when inserted into the equilibrium eqn (28.6) leads to a nonlinear variation of stresses. The Volkersen shear lag analysisz6 provides the simplest calculation of adhesive shear stresses for the case of deformable adherends. This involves the solution of the following differential equation:

B, = E&; B, = E,t, (28.8)

which applies to the geometry of Fig. 28.30

I I

[a RIGID KkU

f -

Fig. 28.27 Elementary joint analysis (rigid adherend model).


( A ) AXIAL RESULTANT DISTRIBUTION (a) AXIAL STRESS DISTRIBUTXOH

Fig. 28.28 Axial stresses in joint with rigid adherends.

[A) RIGID UIIW AaEml

T-

Fig. 28.29 Adherend deformations in idealized joints.

--f

- below. The solution for this equation which TL = T-TU provides zero traction conditions at the left end of the upper adherend and the right end of the lower adherend, together with the applied load T at the loaded ends gives the resultants as:

where

(28.9)

- tu + tL t = - ; PB = BL/B" 2

Using eqn (28.6) to obtain an expression for the shear stress distribution leads to: +-

1 +PB SinhPZ/t

Adhesive joints 635

I

I 0- I X

1

Fig. 28.30 Geometry for Volkersen solution.

. - . . . . . : : . . 4 U a.4 OS a.0 1 IS! 1.4 IJ 1.8 2

#-

+- PB ) (28.11) 1 + pB tanhpZ/T

b . . . . . . . . . . o) a4 w os 1 IZ 11) i g t i 2

I---

where

G x = T/t Also of interest in the discussion which follows is the minimum shear stress in the joint. This occurs approximately at x = 1/2, leading to:

I

B, 2 B,; to be discussed subskquently. Figure

I 0 44 &4 a6 Q1 t 1.2 1.4 1s 1 1 2 IS

28.31


Fig. 28.32 Comparison of average and maximum shear stress vs. l / t .

shows the distribution of axial adherend stresses and bond layer shear stress for two cases corresponding to E, = E , and E, = 10Eu with tu = t,, p = 0.387 and l / t = 20 for both cases (giving p l / t = 7.74) and a nominal adherend stress 0, = 10. As in the approximate analysis given earlier, the shear stresses given by eqn (28.10) are maximum at both ends for equally deformable adherends (B, = B,); for dissimilar adherends with the lower adherend more rigid (B, > E$,), the maximum shear stress obtained from eqn (28.10) occurs at the right end of the joint where x = I , again as it did for the approximate analysis.

Figure 28.32 compares the behavior of the maximum shear stress with the average shear stress as a function of the dimensionless joint length, l / t , for equal adherend stiffnesses. The point illustrated here is the fact that although the average shear stress continuously decreases as the joint length increases, for the maximum shear stress which controls the load that can be applied without failure of the adhesive, there is a diminishing effect of increased joint length when q = pl / t is much greater than about 2.

An additional point of interest is a typical feature of bonded joints illustrated in Fig. 28.31(d) which gives the shear stress distribution for equal adherend stiffness, namely, the fact that high adhesive shear stresses are concentrated near the ends of the joint. Much of the joint length is subjected to relatively low levels of shear stress, which implies in a sense that that region of the joint is structurally inef- ficient since it does not provide much load transfer. However, the region of low stress helps to improve damage tolerance of the joint since defects such as voids and weak bond strength may be tolerated in regions where the shear stresses are low, and in joints with long overlaps this may include most of the joint. In addition, Hart-Smith has suggested51 that when ductility and creep are taken into account, it is a good idea to have a minimum shear stress level no more than 10% of the yield strength of the adhesive, which requires some minimum value of overlap length. Equation (28.12) can be used to satisfy this requirement for the case of equal stiffness adherends. The two special cases of interest again are for equal adherend stiffness and a

Adhesive joints 637

rigid lower adherend, since these bound the range of behavior of the shear stresses. As a practical consideration, we will be interested primarily in long joints for which pZ/t >> 1. For these cases eqn (28.11) reduces to:

p1/t >> 1;

1 2 B, = B,; zJrnaX= -pax (28.13)

Thus, for long overlaps, the maximum shear stress for the rigid adherend case tends to be twice as great as that for the case of equally deformable adherends, again illustrating the adverse effect of adherend unbalance on shear stress peaks.

28.4.3.3 Peel stresses

Peel stresses, i.e. through-the-thickness exten- sional stresses in the bond, are present because the load path in most adhesive joint geometries is eccentric. It is useful to compare the effect of peel stresses in single and double lap joints with uniform adherend thickness, since peel stresses are most severe for joints with uniform adherend thickness. The load path eccentricity in the single lap joint (Fig. 28.33) is

, i

Fig. 28.33 Peel stress development in single lap ioints.

relatively obvious due to the offset of the two adherends which leads to bending deflection as in Fig. 28.33@). In the case of double lap joints, as exemplified by the configuration shown in Fig. 28.34, the load path eccentricity is not as obvious, and there may be a tendency to assume that peel stresses are not present for this type of joint because, as a result of the lateral symmetry, there is no overall bending deflection. However, a little reflection brings to mind the fact that while the load in the symmetric lap joint flows axially through the central adherend prior to reaching the overlap region, there it splits in two directions, flowing laterally through the action of bond shear stresses to the two outer adherends. Thus eccentricity of the load path is also present in this type of joint. As seen in Fig. 28.34(c), the shear force, designated as F,,, which represents the accumulated effect of zb for one end of the joint, produces a component of the total moment about the neutral axis of the upper adherend equal to FsHz/2. (Note that F , is equivalent to T/2, since the shear stresses react this amount of load at each end.) The peel stresses, which are equivalent to the forces in the restraining springs shown in Fig. 28.34(b)

\

Fig. 28.34 Peel stress development in double lap ioints. J


and (c) have to be present to react the moment produced by the offset of FsH about the neutral axis of the outer adhered. Peel stresses are highly objectionable. Later discussion will indicate that effects of ductility significantly reduce the tendency for failure associated with shear stresses in the adhesive. On the other hand, the adherends tend to prevent lateral contraction in the in-plane direction when the bond is strained in the thickness direction, which minimizes the availability of ductility effects that could provide the same reduction of adverse effects for the peel stresses. This is illustrated by the butt tensile test shown in Fig. 28.35 in which the two adherend surfaces adjacent to the bond are pulled away from each other uniformly. Here the shear stresses associated with yielding are restricted to a small region whose width is about equal to the thickness of the bond layer, near the outer edges of the system; in most of the bond, relatively little yielding can take place. For organic matrix composite adherends, the adherends may fail at a lower peel stress level than that at which the bond fails, which makes the peel stresses even more undesirable.

P t P

Bond

E@e Region (Distornal

Strains)

Fig. 28.35 Shear stresses near outer edges of butt tensile test.

It is important to understand that peel stresses are unavoidable in most bonded joint configurations However, they can often be reduced to acceptable levels by selecting the adherend geometry appropriately.

28.4.3.4 Effects of joint geometry

In this section the behavior of joints is considered with linear response of the adhesive in shear assumed. Effects of ductility will be considered later.

28.4.3.4.1 Single and double lap joints with uniform adherend thickness

Double lap joints will be considered first since they are somewhat simpler to discuss than single lap joints because of deflection effects in the latter. Shear and peel stresses in double lap joints with uniform adherend thickness were treated by Hart-Smith%. For the shear stresses, the type of analysis discussed in Section 28.4.3.2 can be applied with suitable changes in notation, i.e. the expressions for the shear stresses given in eqns (28.11) and (28.12) can be applied with subscripts 'i' and '0' ('inner' and 'outer') substituted here for 'L' and ' U ('lower' and 'upper') used in eqns (28.6-28.11); in addition, the outer adherend thickness in the earlier equations is now equivalent to half the thickness of inner adherend because of vertical symmetry of the double lap joint. However, we will also introduce the effects of thermal mismatch effects in the following expressions for later reference. The notation used here is:

Bo = toEo; Bi = tiEi;

B B. Bo + Bi pB = Bi/Bo; Tth =L (ao - a,)AT;

A -

ax = T / t ; &* =T,/t (28.14)

Adhesive joints 639

where a,, a, are thermal expansion coefficients and AT is the temperature change.

is related to the resultants (axial adherend stress times thickness) at the ends of the joint as shown in Fig. 28.36. The shear stresses are then given by:

Note that

[ 1 coshp(x - I ) / : Zb =/35 ~

+pB sinhBl/t

h

In the absence of thermal effects ( Tth = 0) and assuming that Bi 1 Bo, the maximum value of the shear stresses occurs at the right end of the joint as noted earlier (Fig. 28.31). With thermal effects present, the situation is complicated by the sign of &* which is positive if (a, - a,) and AT have the same sign and negative otherwise.

The peel stresses in the double lap joint are described by a beam-on-elastic foundation type differential equation of the form:

b + 4 - 0 = - f - dzb (28.18a) d40 ?d

d P t4 2 O dx

(28.15) Ebto 114 - coshp(Z - x ) / t ]

sinh pz /t y d = (3x) (28.18b)

(A) DOUBLE STRAP JOINT

2 T t **-- 2t

*’ (E) WUBLE LAP JOINT 1 1 Fig. 28.36 Symmetric double strap/double lap joints.

For the usual situation in which the overlap is long enough so that p l / t is greater than about 3, the peak shear stresses at the ends of the joint are given by:

x = 0; Zb, = B(& 5, - &&

and for the special case of equal adherend stiffnesses (Bi = Bo) we have:

The solution to eqn (28.18) depends on whether a strap joint or a lap joint is considered. The exact form of the solution contains products of hyperbolic and trigonometric functions but for the practical situation of joints longer than one-or-two adherend thicknesses and B << yd, are given by:

Double lap joint,

Double strap joint,

(28.19)

For the case of identical adherends, the maximum peel stresses, which occur at x = 0, are given by:

Ob)max = ‘b)max yd (28.20)

‘b)-x = P ax/2 - p (identical adherends)

Here z ~ ) ~ ~ is taken to be the peak stress at the left end of the joint, corresponding to the expression for x = 0 in eqn (28.16), since the out-of-plane normal stresses are compressive at the other end of the joint for a tensile load.

Bi = BJp, = 1);

1 (28*17) ‘b)-x = T p ax “*


For compressive loading, the situation would reverse for the double lap joint (Fig. 28.36(b)), with the positive out-of-plane stresses occurring at the right end of the joint ( x = l), in the case of the double snap joint (Fig. 28.27(a)), the peak out-of-plane stresses would be compressive at the left end of the joint and would not occur at x = 1, since the inner adherends butt against each other there and act as a continuous element.

Effects of thermally induced stresses will be discussed in a later section. Figure 28.37 compares the peel and shear stress distributions for 8, = 0, in a typical joint having balanced adherend stiffnesses (the sum of the outer adherend stiffnesses equal to the inner adherend stiffness) whose parameters are listed in Fig. 28.37(b). The diagram at the top indicates the origin of x at the left end of the overlap. The distribution of peel stresses is somewhat more concentrated near the ends than that of the shear stresses and the peel stresses at the right end of the joint are negative. In addition, the compressive peak at the right end is half as great for the strap joint as for the lap joint, which is the result of the restraint of bending rotations in the strap joint for a gap which is essentially zero. If the loading were compressive rather than tensile, the inner adherends would bear directly on each other and no shear or peel stress peak would occur at the gap, whereas in the lap joint the right end of the overlap would experience the same peak stresses for compressive loading as the left end does for tensile loading.

The situation for the single lap joint (Fig. 28.38) is complicated by the effects of lateral deflection which are indicated in Fig. 28.39. Literature for the following discussion on the single lap joint is given53,51,7*78.

The deflection effect is dependent on the joint load, given in terms of the quantity LIl/2(8)1/2tu, where

LI = tud( c) E {( 12%); D, = EEutA 1 (28.21)

Quarter Plane Symmetry

t / t b t

t p--' I 4

2.00 3

i ~ x - , - , , A -

0.00. : : : : : : 0.00 0.200.400.60 0.801 .OO 1.20 1.40 1.601.80 2.00

(a) X-

v) m

v) g o %-0.5 X-

Double strap joint

-1.5

(b)

Fig. 28.37 Bond stresses in double lap/strap joints; (a) bond shear stress distribution; (b) bond peel stress distribution.

The effects of lateral deflections on the bond stresses were first evaluated by Goland-ReissnerZ7 for the case of equal adherend thicknesses, so that tu and t , can be denoted by t in the following. The lateral deflections can then be stated in terms of a dimensionless ratio, k, with respect to the adherend thickness, and are of the following form:

Adhesive joints 641

- - I -

E

wL" DI PLACEMENTS

Fig. 28.38 Single lap joint geometry.

Fig. 28.39 Effects of bending deflections in single lap joints.

t" = t, = t;

sinh[ U/.IS(X - L M ] sinh[Ulfl8t] l o ~ x < l + l o ; w = w,

t 2 2 L 2

+-- - - tu + tb x ; W, = -(1 - k) (28.22)

The Goland and Reissner (GR) expression for the parameter k has been re-examined by Hart-Smith% and more recently by Oplinger", based on the discussion in Ref. 74, the Goland-Reissner expression appears to provide adequate accuracy unless the adherends are excessively thin, not more that one or two times the bond layer thickness, in which case the expressions given in Refs. 73, 74 and provide corrections for bond layer thickness

effects. The most accurate expression (given in Ref. 74) is fairly elaborate and will not be repeated here; an expression of intermediate accuracygiven in Ref. 74 retains the essential form of the GR result but gives considerable improvement over the GR expression for thin adherends:

tanhLUo tanhLUo + d8C,tanh(LU/2Cp)

(28.23a) k =

where

The original GR expression for k is recovered if Cp is set equal to 1 corresponding to tu >> t, (i.e. relatively thick adherends) and tanh LUo is like- wise set to 1 corresponding to very long outer adherend lengths. A plot of k against the adherend loading stress is is given in Fig. 28.40 for two different values of adherend thickness corresponding to bond thickness-to-adherend thickness ratios (p, in eqn (28.23b)) of 0.5 and 0.1. This plot suggests that k is fairly constant at a value of about 0.25 for a wide range of applied stress values once the initial drop has occurred. The effect of bond-to-adherend thickness ratio is not particularly great and can perhaps be ignored for the most part.


1

a9

ae

a7 I 0.6

* a5 0.4

a3

0.2

ai

0

Fig. 28.40 k parameter vs. adherend loading stress.

The lateral deflections of the joint have a significant influence on the stresses in the

x - l o - l + ucos y,

bond layer, which show this through the presence of the k parameter in expressions for them. The shear stress is given by: "-") x - lo

cos y , t - sin y , t

cash [@(x - L ) / t ] x - lo lo - x Zb = 0, B(l + 3k)

I 4 sinh @A/)

'Osh iu(' - ')/.lst1 where y, = (6 Ebt/Extb)1/4 (28.26)

3 + mu(' - k, sinh (d/2&)

where B and U are given in eqns (28.14) and (28.21). Equation 28.24, which represents a slight modification of the GR expression, reduces to the latter for small values of LIl/t. In addition, the peel stresses, for joints in which

adherend thicknesses (essentially the only case

The maximum stresses in the bond layer are given by:

Maximum bond shear stress,

the overlap length is more than one or two zb)- = 0; of practical interest) are given by

a =a,- - b s (28.25) b - + m U(l - k)/tanh ($)I (28.27)

L Maximum bond peel stress,

1 l o + l - x l o + l - x t B ([YS(COS Y, t + sin y,

Adhesive joints 643

Figure 28.41 gives a comparison of the maximum bond stresses as functions of the loading stress ax for two different adherend thicknesses in a joint with a bond layer thickness of 0.01. It is interesting to note that the peel and shear stresses take on quite similar values. Since the maximum peel stress varies approximately as y i according to eqn (28.27) (the contribution of U being relatively minor), the relationship for ys given in eqn (28.26) suggests that the peel stresses should be expected to vary as (t/tb)1/2, while the same variation is seen from eqn (28.27) for the maximum shear stresses since p also contains (t/t,)'/* as a factor. Thus both stresses should vary with the thickness ratio by the same factor. The fact that they are numerically close together for all stresses is partly due to the effect of other parameters that enter into eqns (28.27) and (28.28) and partly due to the fact that k does not vary much with load for ax greater than 5. A slight nonlinearity can be observed in the curves of Fig. 28.41 for the lower loading stresses.

Figure 28.42 gives a comparison of maximum bond stresses in single and double lap joints for a fixed value of the loading stress ax. For loading stresses above this value the bond

stresses vary essentially in proportion to the load even in the single lap joint, as just discussed. The stresses are plotted in this figure as a function of adherend thickness with the adherend axial modulus as a parameter. The trend toward higher bond stresses and therefore a greater tendency toward bond failure with increasing adherend thickness which was discussed in Section 28.4.2 is clearly borne out in these curves. Note also that reduction of the adherend modulus tends to aggravate the bond stresses. In addition it is apparent that there is considerable separation between the peel and shear stresses in the case of the double lap joint, the peel stresses for the latter case being smaller. This reflects the fact that the peel stresses vary linearly as yd defined in eqn (28.18b) and therefore vary as (t/tb)1/4 rather than as (t/tb)l/* as in the single lap case. Thus, peel stresses for double lap joints are not as much of a factor in joint failure as they are in single lap joints, although they are still large enough relative to the shear stresses that they can not be ignored.

Failure characteristics of single and double lap joints will be discussed below. If the adherends are thin enough, failure in double lap joints should be in the form of adherend

'4 I &=looOO, Gb=150, %=SO0 M.02; (52, g=10

12

4 lo

E " s i 3

/

0 10 20 - 30 40 =* -

Fig. 28.41 Maximum bond stresses in single lap joint, bond thickness = 0.01.


Double Lap Joint Single Lap Joint

0'5 0 ' 0.08 0.1 0.02 0.04 0.06

AdherendThickness -

peel strau Shear Stress 4 -

Ex = 10,OOO 3.5 -.

Ex = 5,wO 3 -

2.5 - 2 -

1.5 - 1

0.5

0 0.02 0.04 0.06 0.08

AdherendThickness +

------- 0-O

Ex I20,oOo

0.1

CTx= 10 Gb= 150 E,= 500

l,,= 50 1 = 10

Fig. 28.42 Maximum bond stresses in single and double lap joints, fixed vx = 10.

axial (tensile or compressive) failure. For single lap joints, adherend bending stresses are significant at the ends of the overlap as indicated in Fig. 28.39; using standard beam formulas, the maximum axial stress for combined bending and stretching (the latter stress corresponding to the single lap joint in tension loading) for the bending deflection given in eqn (28.22) can be expressed as

QJrnax = OX3(1 + t,/t)k (28.29)

The maximum adherend axial stress is largest for adherends which are particularly thin with respect to the bond thickness; these will be prone to brittle bending failures for composite adherends or to yielding associated with bending for metal adherends. Hart-Smith discusses difficulties with the use of standard single lap shear test specimens50. The problem is that adherent bending failures are likely to occur with such specimens rather than bond failures and test results obtained in such cases tend to be irrelevant and misleading.

One additional characteristic difference between single and double lap joints should be discussed. The effect of lateral deflections

-

on single lap joint performance is quite long range. Figure 28.43 shows that for a joint with an adherend thickness of 2.54 mm (0.1 in) the bond stresses do not reduce to their minimum values until the overlap length reaches a value in the range of 10-12.7 cm (4-5 in), for a loading stress of 69 MPa (10 ksi). Double lap joints also require some minimum length before stresses settle out as a function of overlap length, but in this case the stresses reach minimum values with respect to overlap length for lengths on the order of 5 to 10 adherend thicknesses, in the present case amounting to 1.3-2.5 cm (0.5-1 in).

28.4.3.4.2 Effects of adherend tapering

In this section we will consider joints with adherend thicknesses which vary along the joint length. These include the configurations shown in Figs. 28.44 and 28.45, namely, double strap joints with tapered outer adherends and scarf joints as well as step lap joints. As discussed in Section 28.4.2.2, tapering the outer adherends of strap joints as in Fig. 28.44(a) is beneficial mainly for reducing or eliminating

Adhesive joints 645

1

0.5

t m e w - 0.7 m 1.6

Signmba--lO .'

Gb--160 Eb--500 Er--S.OOO tb- - 0.01 Mc~ all- ht@h -- 20

..

Fig. 28.43 Effects of overlap length in single lap joints.

(A) PARTIALLY TAPERED STRAP JOINT Qf-

I am i nat e meta 1 I I

Triangular Elewnt

I + * B (E) SCARF JOIN1

I I

Bond

Fig. 28.44 Tapered double strap and scarf joints.

peel stresses, while scarf and step lap joints (Figs. 28.44@), 28.45) can eliminate shear stress peaks as well as peel stresses.

With both tapered outer adherends and scarf joints, it can be shown that the bond stresses can be related to the ratio of taper length to thickness by

zb = axt/Z ; ab =ax t 2 / P (28.30)

Fig. 28.45 Generic step lap joint.

(axial modulus times maximum thickness) in each adherend. For tapered portions of strap joints it is fairly accurate for the peel stresses, and holds approximately for the shear stresses if the tapered portion is not too long. Note that eqn (28.30) implies that the bond stresses are constant along the length of the joint and can be reduced to any arbitrary level by making t/Z small enough, i.e. making the joint long enough with respect to the adherend thickness.

Moreover, the effect of t/Z on the peel stresses is quite strong, being governed by the square of the thickness-to-length ratio. This is especially important in the case of outer adherend tapering in strap and lap joints as a means of reducing peel stresses to a manage- able level.

This relationship is quite accurate for scarf joints having the same maximum stiffness

Step lap joints (Fig. 28.45) represent a compromise version of the scarf joint which can


take advantage of the layered structure of the composite adherend. The average slope of the region represented by the line through the steps in Fig. 28.45 tends to control the average shear stresses developed in the bond. Within each horizontal section, equivalent to the tread of a staircase, the behavior is analogous to a joint with constant adherend thickness, and the differential equation given in eqn (28.10) (Section 28.4.3.2) applies locally when tu and tL are adjusted to match the local situation. An expression similar to eqn (28.12), i.e. for thejth step,

PB +-

gives the maximum shear stresses within each step, and the overall solution is a chain of such expressions with allowance for continuity of the shear strain and resultants, Tuj and TLj at the points where neighboring steps join. In each step of the joint the shear stresses will have a distribution similar to that of Fig. 28.36, the size of the peaks being governed primarily by the length of the step through the parameter P.Z./t. The aspect ratio for the step, Zj/t, can in prmciple be kept small enough to almost completely avoid any peaking by using a large number of steps and keeping the length of each one small. In practice, the number of steps is governed by the number of plies in the laminate. In addition, if the joint is used to connect a composite adherend to a metal component, machining tolerance requirements and cost considerations for the metal part enter into the selection of the number of steps.

The following discussion will address the specific benefits of adherend tapering in

1 1

tapered double strap joints, scarf joints and step lap joints. The overall approach is to aim for a highly efficient joint which reduces the effects of shear and peel stress concentrations at the ends of the joint. Ideally we would like to achieve the joint strength provided by the 'P over A' concept obtained with the case discussed in Section 28.4.3.2 for perfectly rigid adherends (Fig. 28.27), in which increasing the joint length indefinitely brings the shear stress in the bond down to any required level regard- less of the magnitude of load being supported by the joint. While tapering does reduce the peel stresses markedly in the tapered strap joint as will be seen below, shear stress peaks can not be avoided, and the law of diminishing returns continues to prevail with regard to increasing the joint length to obtain greater load capacity; however, adhesive ductility will enhance the strength beyond what elastic analysis suggests.

Double strap joints with tapered outer adherends are considered in Figs. 28.46 to 28.48. Figure 28.46 indicates the tapered configurations that are considered. Figure 28.47 gives some shear stress predictions for joints with uniform adherend thickness for comparison with the tapered cases which are considered in Fig. 28.48.

Figure 28.46 defines the notation used in Fig. 28.45 in terms of 'fully tapered' outer adherends (Fig. 28.46(a)), partially tapered adherends in which the taper extends only part of the length of the joint (Fig. 28.46@)) and fully tapered adherends with an 'initial rise', i.e. in which the thin end of the adherend does not come to zero thickness. (The term '% initial rise' implies that the rise is expressed as a percentage of the maximum adherend thickness.)

The three cases considered in Fig. 28.48 can be compared with the case for uniform adherends with equal upper and lower adherends modulus (E, = EL) in Fig. 28.47. For the situation of no initial rise, two cases are considered in Fig 28.48, the case of 50% taper and that of full taper. There is an appreciable difference in the shear stress distribution at the

Adhesive joints 647

(A) F u l l y tapered - - no i n i t i a l r i s e

(@ 5G% tapered j o i n t

---I 1 .0 I.c I

---- I

(C] F u l l taper - - 25% i n i t i a l r i s e

/ 0 . 0 5 i n i t i a l r i s e

\'T

-==E==- I

left end of the joint for these two cases, but the peel stress distribution is essentially unaffected. For both the full taper and 50% taper cases, a minor tensile secondary peel stress peak is present at the right end of the region under consideration (near the midpoint of the strap joint). The peel stress expression in eqn (28.30) gives a good estimate of the peel stress level at the left end of the joint, and the result of the estimate is so small for both cases that the difference is not distinguishable in Fig. 28.48. However, in the case of an initial rise of only 1/4 of the maximum outer adherend thickness (25% initial rise), significant peel stresses arise at the left end of the joint, in fact, about 80% of the level occurring for the case of no tapering. The initial rise also causes a greater increase in shear stress at the left end of the joint than in the case of 50% taper. Thus, tapering is advantageous mainly as a way of eliminating the effects of peel stresses in double strap joints. Once this is accomplished, the effects of peel stress peaks can be controlled to a significant extent by taking advantage of adhesive ductility. Tapered strap joints can not achieve the ideal behavior which is possible with scarf or step lap joints, but they provide a simpler solution to good joint performance if the adherends are thin enough.

Shear stress distributions in scarf joints (Fig. 28.49) are given in Fig. 28.50. Practical scarf

Fig. 28.46 Tapered strap joints under consideration.

Shear strws - - Uniform Adhemd l h l c k m u e T

: I : I

0 0.2 0.4 b.r 0.8 1 1.2 1.4 1d 1.8 2 Fig. 28.47 Shear stresses in untapered strap joints. X


- -

(A) Shear stresb - - Double Strap Tapered Adherends 5 T

--Es

Fig. 28.48 Stresses in tapered double strap joints.

joints are arranged in a symmetric double lap configuration which avoids bending effects. Figure 28.49 represents a balanced stiffness design for dissimilar materials, by achieving a continuous thickness change over the length of the joint. The most important parameter for

/

0 . 2 , 0 . 4 TI, E.16 f f i i QI graphite epoxy

E.8 msi

Fig. 28.49 Stiffness-balanced scarf joint configuration.

the scarf joint is the effect of adherend stiffness unbalance ( E , # Ei; ’0’ and ‘i’ refer to the outer and inner adherends as in Fig. 28.36). The results given in Fig. 28.50 represent the effect of varying degrees of stiffness unbalance. The ratio of peak-to-average shear stresses compare well with the values given by Hart-Smith37, although the latter did not give the distribution of stresses along the length of the joint. For fairly sizeable unbalances, up to 4:1, the maximum shear stress peak is not as great as that observed in Fig. 28.47 for the uniform adherend case. However, it is clear that a stiffness unbalance will increase the shear stress peak and weaken the joint. For the equal stiffness case the shear stress is constant and equal to the average stress at all points.

Adhesive joints 649

EL I EU = 4 EU = 8,000 tu = n = .2

Gb=l60 Eb-600 t b = O . O l

Sigma - x = 10

2

0 0.2 0.4 0.6 0.8

Fig. 28.50 Shear stresses in scarf joints.

If there is no reason why the joint cannot be configured as in Fig. 28.49 for dissimilar materials so as to take advantage of the benefits of the balanced stiffness case, then in principle, the scarf joint provides a near ideal solution to achieving as much load capacity as is required in any situation without overstressing the bond layer. However, the dimensions of the joint may grow too large to be practical for high joint load. In addition, an extremely good fit, for example, to tolerances on the order of the bond thickness over large lengths, has to be maintained to ensure that the joint can maintain uniform load capacity over its length. Thermal stresses will also be a factor in various combinations of dissimilar materials which will prevent the ideal form of behavior from being achieved. In terms of the Hart- Smith approach to avoiding creep failure under slow cyclic loading, the balanced scarf joint is at a disadvantage in not providing a shear stress minimum. For this situation the allowed load would have to be limited to prevent environmental conditions corresponding to hot wet exposures; thus the advantage of the scarf joint in eliminating stress peaks

1 1.2 1.4 1.6 1.8 2

X

might be lost if performance in hot wet environments is required.

Step lap joints798o are treated in Figs. 28.51 to 28.53. Figure 28.51 shows a generic joint configuration that is introduced to illustrate some of the effects of design parameters on stresses in the joint. The results presented in Figs. 28.52 and 28.53 were generated for this discussion using a linear elastic response model for the adhesive; in practice, considerable strength capability of the adhesive is unused if elastic response of the adhesive is assumed; Fig. 28.54 taken from the discussion by Hart-Smithso is an example of joint design using elastic-plastic response for the adhesive. The elastic adhesive model used in Figs. 28.52 and 28.53 is adequate for illustrate some of the controlling parameters on joint design. These results are based on the classical Volkersen- type analysis with provision for resultant and shear strain continuity at the interfaces between neighboring steps, as discussed previously. The 5-step design in Fig. 28.52 and the 10-step design in Fig. 28.53 were chosen with the following characteristics:


I I / / V I

Quasi-Isotropic Carbon @OXY, Fig. 28.51 Step lap joint

As discussed above, the joint design shown in Fig. 28.5437 represents a practical joint design which accounts for several considerations that the simplified elastic analysis approach used for Figs. 28.52 and 28.53 neglects. The neglect of ductility effects has already been mentioned. In addition, the use of as large a

X configuration. E = 8 n s i

Except for the first and last steps, the adherend thickness was equal for each step. The first and last thickness increments were half those of the generic steps. The lengths of each step were chosen with - a fixed value of the parameter qs, = pirj/fj, where lj is the length of step j .

The half-incremented end steps gave a more uniform shear stress distribution than maintaining the same increment for all steps. The symmetric joint configuration shown in Figs. 28.51 and 28.54, the thickness increment for the outer adherend (composite) was greater than that for the inner adherend by the inverse of the modulus ratio, to achieve the desired stiffness balance for the dissimilar adherends. The parameter ETA listed in Figs. 28.52 and 28.53 is equivalent to qs, defined above. This parameter essentially controls the length of the joint; both Figs. 28.52 and 28.53 show an increase in joint length with qsl ('ETA' in the two figures). Note further that the load capacity of the joint in terms of the allowed resultant, 5, listed as "BAR in Figs. 28.52 and 28.53, which provides for the required bond shear stress limitation of 5 (ksi for the units mentioned earlier) shows a general increase with joint length, but with diminishing increase when vsl gets much beyond 3. Table 28.1 gives a summary of the results shown in the two figures. Fig. 28.52 Shear stresses in 5-step joint.

Adhesive joints 651

C L : : : : : : : : : : : : : : : : 0 u y a a 1 m k L 1 1 u n u u u r

I

Fig. 28.53 Shear stresses in 10-step joint.

number of steps as 10 in Fig. 28.53 may not be practical. The joint design shown in Fig. 28.54 represents the evolution of steplap joint design over many years. Early analytical work was

presented by Corvelli and Saleme79; this was later enhanced by Hart-%~ith~~, under NASA funding, to provide for elastic-plastic response, culminating in the A4EG and A4EI programs-, to allow for variations in thickness, porosity, flaw content and moisture content in the bond layer. Hart-SmithsoI8l notes that in mathematical treatments of step joints, all properties have to be constant within each step; however, in an actual joint such as that shown in Fig. 28.54, artificial breaks may be inserted to permit changes in porosity of bond thickness.

28.4.4 MECHANICAL PERFORMANCE OF ADHESIVES

28.4.4.1 Ductile response of adhesives

Figure 28.55 taken from the 1983 edition of the DoD/NASA Advanced Composites Design Guides1 show shear stress-strain response characteristics of typical aerostructural adhesives. Figure 28.55(a) represents a relatively ductile film adhesive, FM73, under various environmental conditions, while Fig. 28.55@) represents a more brittle adhesive (FM400) under the same conditions. Similar curves can be found in other sources62. Temperature dependence and strain rate dependence of the stress-strain characteristics are important characteristics; these are also addressed in the results shown in Ref. 62. Even for the less ductile material such as that represented in Fig. 28.55@), ductility has a pronounced influence on mechanical response of bonded joints, and design only for elastic response deprives the

Table 28.1 Summary of step lap joint results (Figs. 28.52 and 28.53)

No. of steps 10 10 10 5 5

V7sl 1 2 3 3 6

Joint length, cm 4.44 8.89 13.33 6.05 12.5

Allowed resultant, kN/cm 12.03 18.78 22.05 12.35 13.43 (103 lb/in) (6.87) (10.72) (12.59) (7.05) (7.67)

(in) (1.75) (3.5) (5.25) (2.47) (4.93)


7

6

5

4

3

2

1

0 1 2 3 4 5 6 1 2 3 4 6 6

0- 1 2 3 4 5 6

0 I 1 2 3 4 6 6

Fig. 28.54 Practical step lap joint designs0.

( A ) FM78 NON POROUS

0 0.2 0.4 0.8 0.8 1 1 .z f .4

S hesr 8 traln

6o LT = -55 d q C 46 RT = Room Temp

H T M = 60 degC1100%RH $ I: -aa

I$ F m o o ~ a m u r b m d 2 16 5 10

6 0

o om om 001 om ai a12 0.14

Mr-

Fig. 28.55 Typical stress-strain characteristics of aerospace adhesivess1.

Adhesive joints 653

application of a significant amount of available structural capability.

The work of H a r t - S ~ n i t h ~ ~ ~ emphasized the importance of ductile adhesive response and introduced the relationship between the strain energy to failure of the adhesive and the load capacity of the joint. As a means of simplifying the stress analysis of the joint in the presence of ductile adhesive response, Hart-Smith showed that any bilinear stress-strain curve which has the same ultimate shear strain and maximum strain energy as that of the actual stress-strain curve will produce the same total load in the joint. Figure 28.5681 gives an example of the method for fitting a bilinear curve to the actual stress-strain curve of the adhesive in shear. With the strain energy of the adhesive given by

SE = rJmax - zp2/2Gb0 (28.32)

where GbO! yma, and SE are the initial modulus of the stress-strain curve, the maximum strain and the strain energy of the adhesive at ymaX respectively, then the equivalent bilinear curve consists of an initial straight line of slope Gbo together with a horizontal part at an abscissa

zp, which can be obtained by solving for zp from eqn (28.32), leading to

'p = Gb$max - d[(GbOYmax)2 - 2GboSEl

(28.33)

Hart-Smith has also used an equivalent bilinear representation in which the horizontal part of the curve is set equal to zmax, the maximum shear stress of the actual stress-strain curve, and the initial modulus Gbo adjusted to give the strain energy match, using the expression:

Gbo = 'ma:('maxYmax - /2 (28'34) which is also obtained from eqn (28.32) when rmax is substituted for zp. In either case the use of a bilinear representation of the stress-strain curve for the response of the adhesive in shear makes it straightforward to obtain one dimensional stress distributions in various types of joint geometry with adhesive ductility accounted for; solutions are given for single and double lap joints with uniform and tapered adherends, as well as more sophisticated joint designs such as scarf and step lap

Fig. 28.56 Elastic-perfectly plastic adhesive response model (Fh473)*'.


geometries (Hart-S~ni th~~~). These have sub- sequently been incorporated in the 'A4Ex' series of computer programs- mentioned previously.

Figure 28.57 (see notation of Fig. 28.36) shows an example of the use of the bilinear stressstrain curve approximation, in this case for predicting the stresses in a symmetrical

4.5

f 4

0

double lap joint with equal adherend stiffnesses (i.e. Eo = Ei; to = fi/2). Figure 28.57(a) gives the distribution of upper adherend axial stress resultant while Fig. 28.57@) gives the shear stress distribution in the bond layer. The linear portions at the ends of the resultant distribution in Fig. 28.57(a) correspond to the ends of the shear stress distribution in Fig. 28.57@)

(A) Upper adherend resultant distribution ( 1 k-lblln = l.762 kNlom)

Axial load 310 MPa (46 ksl)

0 0.6 1 1 .I 2

K

l e

(6) Shear stress distribution (1 ksi= 6.896 MPa)

Axial k a d 310 MPa (45 ksi)

0.5 -- o i I

0 0.c z 1 .Q 2

Fig. 28.57 Stress distributions in double lap joint - ductile adhesive response.

Adhesive joints 655

where the shear stress is a constant because of the plateau in the bilinear representation of the stress-strain curve, in agreement with the equilibrium relation given in eqn (28.6). Following the analysis developed by Hart-Smith, the lengths of the plastic zones designated in Fig. 28.57(b) as Ip are given by

lp = (aX/2zp - l/pbd)to ; p,, = [2Gbflto/EotbI’/*

(28.35)

Here p,, (subscript ’bd’ denoting balanced double lap) is equivalent to p given in eqn (28.14) when the latter is specified for the case of equal-stiffness adherends, while 5, is the nominal loading stress at either end of the overlap. The expression for Ip given in eqn (28.33) is valid only if greater than 0, of course, negative values of plastic zone length not having any meaning. Thus if /33,/2 < zp, no plastic zone is present and the behavior of the joint can be considered to be purely elastic. The maximum value of 5, for this case can be expressed by inverting the shear stress expression in eqn (28.17) with oth = 0, for the case of equal adherend stiffnesses and setting zb)max to zp. For the case of pax/2 2 zp which corresponds to ductile response of the adhesive (the plateau of the bilinear stress-strain curve), the Hart-Smith analysis35 provides the required expression for 0, The two cases are summa- rized as follows:

pbdSX/2 < zp (elastic response):

‘x)max = 2zp/pbd E (28.36a)

PbdCx/2 2 zp (ductile response):

(28.36b)

If y,,, = zp/GbO, which is the maximum strain in the elastic part of the bilinear representation,

then eqns (28.36a, b) give the same value. The factor (2GbOymax/zp - 1)1/2 in eqn (28.36b) acts as a load enhancement factor and represents the increase of joint load capacity due to ductile adhesive response over the maximum load allowed by elastic response of the adhesive. Note that eqn (28.36b) can be rearranged to express 5x)ma, in terms of the maximum strain energy of the adhesive:

where ye = zp/Gb, (28.37)

then eqn (28.3613) can be written: 2

(28.38)

The Hart-Smith analysis based on the equivalent bilinear stress-strain law was shown in Ref. 35 to give the same joint load capacity as the solution for the problem using the actual stress-strain curve of the adhesive. The convenience of the bilinear stress-strain description is in the simplicity of the solutions it allows; once the length of the plastic zone at each end is determined, the same types of solution apply for the elastic zone as were given in eqns (28.9) and (28.10) for the resultant and shear stress distributions, together with linear resultant and constant shear stress distributions in the plastic zones.

The most obvious effect of ductility in the adhesive behavior is the reduction of peak shear stresses. In addition, there is a beneficial effect on reduction of peel stresses. For the double lap joint considered in Fig. 28.57, the maximum peel stresses denoted by ob),ax which occur at the ends of the joint, are given39 by:

- = p’(2Gb()SE)

Ob)max = F b ) m a x ; (28.39)

y = ( 3- i’” ; E, = peel modulus of adhesive


where z ~ ) ~ ~ ~ is the maximum shear stress, either /?OX/2 for the elastic case or zp for the case of ductile response. The maximum peel stresses are thus reduced by the same ratio as the maximum shear stresses in the case of ductile response of the adhesive.

Even though ductile response of the adhesive provides additional load capacity of the joint over what is provided by purely elastic response, it is advisable to keep the load capacity of the joint low enough to ensure purely elastic response for most practical situations where time-varying loading is encountered. Some damage to the adhesive probably occurs in the ductile regime which would degrade the long-term response. The main benefit of ductile behavior is to provide increased capacity for peak loads and damage tolerance with regard to flaws - voids, porosity and the like - in the adhesive layer. In addition, calculations of the plastic zone length play a part in the avoidance of creep failures which can constitute a major consideration for slow cyclic loading in hot wet environments.

28.4.4.2 Effects of bond layer defects

Defects in adhesive joints include surface preparation deficiencies leading to low strength interfaces between the adhesive and adherends, voids and porosity, and lack of bond thickness control. Surface preparation effects were discussed in Section 28.4.2.6 and will be treated in considerable detail in Chapter 29. However, it should be kept in mind that adhesive joints will not succeed in providing dependable performance if good surface preparation procedures are not maintained.

Bond layer thicknesses of 0.12-0.25 mm (0.005-0.010 in) are typical of structural bonded joints. There appears to be a tradeoff between negative effects which occur when the bond is too thin and those occurring for too thick bond layers. Thinness in bond layers

leads to high shear and peel stresses at the ends of the joint, and may inhibit desirable flow characteristics of the adhesive. On the other hand, thick bond lines tend to generate porosity which weakens the bond. Data presented in Ref. 83 show a fairly persistent tendency for lap shear strength to drop off somewhat as the bond thickness is increased above 0.12 mm (0.005 in).

In addition to effects of bond thickness per se, Hart-Smith60 discusses the effect of bond thinning at the ends of the joint which is caused by resin flow during curing. Figure 28.58 illustrates the tendency toward bond thinning at joint edges together with some manufacturing techniques for avoiding the situation. Loss of bond thickness may cause considerable elevation of shear and peel stresses in the bond. In addition to the approaches shown in Fig. 28.58, tapering of the adherends near the ends will help to alle- viate the situation; tapering from the inside surface of the adherend will also provide a local thickening of the bond line to compensate for thinning due to resin loss.

Effects of porosity in the bond layer are illustrated in Fig. 28.59(j1 which compares the response of FM73 for porous and non porous bond layers for various environmental conditions. The data6' indicate that porosity is mainly a characteristic of thickness of the bond layer. There is some loss of structural capability in the presence of porosity in the bond, but there may still be adequate strength for the bond to function as required if the joint is designed adequately. Since porosity is associated with thickened regions of the bond which tend to occur away from the edges, porosity tends to be confined to the interior of the joint where the stresses are relatively small, and may not be objectionable in many cases. The main focus in Ref. 61 is the effect of adherend thickness with regard to damage tolerance in the presence of bond layer defects. The issue has to do with the design principle discussed in Section 28.4.2.1 of keeping adherend thicknesses within limits which ensure that the

Adhesive joints 657

n

Fig.

V

4. NIIOIQFfCERVVACVUWMQ

28.58 Manufacturing techniques to relieve bond pinch-off 51,

6 0

50

I 40 2 Y

67 67 E 3 0 5 2 0

1 0 5

I rLT /Stress VQ. Strain -- FM731

LT - - -55dqC RT - -room temp. H/w - - 60 degC/lOo% rh

2.

0 0.5 1 1.5 2

Shear Strain

o $ I

Fig. 28.59 Effect of porosity on adhesive stress-strain characteristicss1 x : porous; : non porous bond layers.

adherends fail rather than the bond. Ductile response of the adhesive has an important influence on the situation. By making use of eqn (28.36b) above, together with the defini-

thickness limit for a double lap joint,

tJc,which ensures adherend failure can be expressed by restating eqn (8) of Ref. 52 as follows:

tion of p,, given in eqn (28.35), the adherend -


which is equivalent to:

t, = 4 {Max adhesive strain energy] / {Max adherend (elastic) strain energy] (28.41)

Hart-Smith states that for to not greater than to),, given in eqn (28.40), joint performance will be relatively insensitive to bond flaws provided there is adequate ductility in the adhesive response. Problems may arise with high temperature adhesives such as the FM 400 considered in Fig. 28.55(b), since these tend to have limited ductility. As indicated in eqn (28.36b), limited ultimate strain capability (y,,,) will reduce margin of ultimate strength over elastic response of the joint.

28.4.4.3 Durability of bonded joints

Two major considerations in the joint design philosophy of Hart-Smith are: (1) either limiting the adherend thickness or making use of more sophisticated joint configurations, such as scarf and step lap joints, to ensure that adherend failure takes precedence over bond failure; (2) designing to minimize peel stresses, either by keeping the adherends excessively thin or, for intermediate adherend thicknesses, by tapering the adherend. In addition, it is essential that good surface treatment practices be maintained to ensure that the bond between the adhesive and adherends does not fail. When these conditions are met, reliable performance of the joint can be expected for the most part, except for environmental extremes, i.e. hot wet conditions. The Hart- Smith approach focuses primarily on creep failure associated with slow cyclic loading (i.e. one cycle in several minutes to an hour) under hot wet conditions, this corresponds, for example, to cyclic pressurization of aircraft fuselages. In the PABST program4143, 18 test specimens used for characterizing adhesives (so-called 'thick adherend' specimens) which are designed to produce essentially uniform shear stress along the bond were tested at high cycling rates (30 Hz) and were able to sustain more than 10 million loading cycles without

damage, while tests conducted at one cycle per hour produced failures within a few hundred cycles. On the other hand, specimens repre- sentative of structural joints which have the characteristic shear stress trough seen in Figs. 28.37 and 28.57 are able to sustain hot wet conditions even at low cycling rates if the length of the elastic region (Ie in Fig. 28.57) is long enough. Based on experience of the PABST program, the Hart-Smith criterion for avoidance of creep failure requires that t,),, be no greater than t p / l O . But the stress analysis for the elastic-plastic case using the bilinear adhesive response model leads to an expression for the minimum shear stress equivalent to eqn (28.12) with 2 replaced by Ze:

,I- ' - - P (28.42)

*b)& sinh PbdZe/2fo

do,, - see eqn (28.35)). Since sinh (3) = 10, this amounts to a requirement that PbdZe/2to be at least 3, i.e. that the elastic zone length be determined by Ze 2 6to/Pbd. Since le is equivalent to the total overlap length, 1, minus the sum of the plastic zone lengths, i.e. 21, then making use of the expression for ZP m eqn (28.33), the criterion for elastic zone length reduces to a criterion for total overlap length corresponding to a lower bound on 1 which can be stated as

P

- 4 1 2 - + - t o (28.43) ( p b d )

Equation 28.43 for the joint overlap length is the heart of the Hart-Smith approach to durability of bonded joints for cases where adherend failure is ensured over bond failure for static loading and in which peel stresses are eliminated from the joint design. This type of requirement has been used in several contexts. For example60, it becomes part of the requirement for acceptable void volume in the bond layer, since in th s case the voids, acting essentially as gaps in the bond layer, reduce the effective length of the overlap. The criterion has to be modified numerically for joints other than symmetric double lap joints with equal

Adhesive joints 659

stiffness adherends and uniform thickness. For more sophisticated joint configurations such as step lap joints, the A4EI computer code provides for a step length requirement equivalent to that of eqn (28.43) for simple double lap joints.

In addition to creep failures under hot-wet conditions, the joint may fail due to cracking in the bond layer. Johnson and Mall7* presented the data in Fig. 28.60 which shows the effect of adherend taper angle on development of cracks at ends of test specimens consisting of composite plates with bonded composite doublers, at lo6 cycles of fatigue loading; here the open symbols represent the highest load levels at which cracks fail to appear while the solid symbols are for slightly higher loads at which cracks just begin to appear. It is noted that even for outer adherend taper angles as low as 10” (left-most experimental points in Fig. 28.60) for which peel stresses are essentially nonexistent for static loading, crack initiation was observed when the alternating load was raised to a sufficient level. A number of factors need to be clarified before the impli- cations of these results are clear. In particular it is of interest to establish the occurrence of bond cracking at shorter cycling times, say less than 3 x lo5 cycles corresponding to expected lifetimes of aircraft. Effects of cycling rate and environmental exposure are also of interest. Nevertheless, the data presented in Ref. 65

FM-XII M B O N D D NO MBOND

PREDlClED

,,.* - - APPLIED CYCLIC S I A E S S , IM ~ 5 , MPa

0 M 60 Po TAPER ANGLE. 0. deg

Fig. 28.60 Crack development in bonds of tapered composite doublers at lo6 loading cycles7*.

suggest the need for consideration of crack growth phenomena in bonded composite joints. Indeed, a major part of the technical effort that has been conducted on the subject of durability of adhesive joints6”” has been based on the application of fracture mechanics based concepts. The issue of whether or not a fracture mechanics approach is valid needs further examination. Apparently, no crack-like failures occurred in the PABST program, which was a metal bonding program, even when brittle adhesives were examined at low temperatures. The amount of effort which has been expended by a number of respected workers on development of energy release rate calculations for bonded joints certainly suggests that there is some justification for that approach, and the results obtained by Johnson and Mall appear to substantiate their need for composite joints in particular.

28.4.5 MECHANICAL BEHAVIOR OF COMPOSITE ADHERENDS

28.4.5.1 Joint failure characteristics

Typical failure modes in structural joints are illustrated in Fig. 28.61 which are indicative of adherend rather than bond failures. In the case of single lap joints (Fig. 28.61(a)) bending failures of the adherends will occur because of high moments at the ends of the overlap. For metal adherends, bending failures take the form of plastic bending and hinge formation, while for composite adherends the bending failures are brittle in nature. In the case of double lap joints, peel stresses build up for thicker adherends causing the types of interlaminar failures in the adherends illustrated in Fig. 28.61 (b) .

28.4.5.2 Thermal stress effects

Thermal stresses are a concern in joints with adherends having dissimilar thermal expansion coefficients. Figure 28.62 illustrates the


A. c

A 0. AND C INDICATE FAUURh I - E

(B) Double Lap hints

Fig. 28.61 Failure modes in composite adherends49, 50.

E; = E, 68.97 GPa (10000 ksi); G, = 1.04 GPa (150 ksi); f1/2 = f, = 2.54 mm (0.1 in); fb = 0.254 mm (0.01 in); a, = 23.4 x lo4 "C-'(13 x 1 O4 OF-'); a. = 1.8 x 1O4"C (1 x

). 10-6°F-1

Cure temperature 121.1"C (250°F); Application temperature 23.9% (75°F) Loading stress 68.97 MPa (10 ksi).

Fig. 28.62 Thermal shear stresses in double lap joints: outer adherend 0/90 carbon epoxy; inner adherend aluminum.

Adhesive joints 661

effect of thermal stresses in a double lap joint consisting of an aluminum inner adherend and a 0/90° carbon epoxy outer adherend. The stresses due to thermal mismatch between the aluminum and composite arise if the cure temperature of the bond is substantially different from the temperature at which the joint is used. The case considered here represents a 121°C (250°F) cure temperature for the adhesive and a room temperature application, a temperature difference of -79°C (-175"F), which (see Tables 28.2 and 28.3) would result in a strain difference of 0.002 between the aluminum and composite if no bond were present. (The material combination considered here, aluminum and carbon epoxy, represents the greatest extreme in terms of thermal mismatch between materials normally encountered in joints in composite structures.) Thermal stresses in bond layers of double lap joints can be determined from the expressions given in eqns (28.14-28.20). (These calculations are all based on an assumed elastic response of the adhesive.)

Hart-Smith3"39 provides corrections for ductile response in the presence of thermal effects. Figure 28.62 illustrates how the thermal stresses combine with the stresses due to structural load to determine the actual stress distribution in the adhesive. The thermal stresses in themselves develop an appreciable fraction of the ultimate stress in the adhesive, and although they oppose the stresses due to structural loading at the left end, they add at the right end and give a total shear stress that is somewhat beyond the yield stress of typical adhesives, even with as small a structural

loading stress as 69 MPa (10 ksi). Similar effects occur with the peel stresses, although the peel stresses due to thermal mismatch alone have the same sign at both ends of the joint; with a composite outer adherend the thermally induced peel stresses are negative, which is beneficial to joint performance.

Peak peel and shear stresses obtained from these relationships for various combinations of metal and composite adherends whose properties are given in Tables 28.2 and 28.3 are shown in Table 28.4. For joints with an aluminum inner adherend, the difference in thermal expansion between the adherends is relatively large, giving considerably higher thermal stresses for the most part. In addition, carbon epoxy has a particularly low thermal expansion, which tends to produce higher thermal stresses with carbon epoxy adherends in combination with metals than do other composites. Note that boron epoxy in combination with titanium gives particularly small thermal stresses because of similarity of the thermal expansion coefficients shown in Tables 28.2 and 28.3 for these materials. As

Table 28.3 Generic metal properties (MIL-HDBK-5 1983)

Ti6-Al4-4V 1025 2014 Steel Aluminum

Young's 110.3 206.9 69.0 modulus, GPa

Poisson 0.3 0.3 0.3 ratio

a, 10" OC-1 8.82 10.26 23.4

Table 28.2 Generic mechanical properties of composites (C.C. Chamis NASA Lewis Research Center, NASA TM-86909,1985)

Unidirectional lamina 0/90 Laminate

Composite E,, GPa E , GPa vLT aL, 10-6 "C-' aT, 1 P O C - l E x GPa ax 1 k6 O C - I

Boron epoxy 201 20.1 0.17 11.7 30.4 113.8 8.6 S-glass epoxy 60.7 24.8 0.23 3.78 16.7 43.72 7.92 Carbon epoxy 137.9 6.90 0.25 0.72 29.5 72.6 2.34


Table 28.4 Bond layer thermal stress in double lap joints (0/90 composite outer adhered, metal inner adherend)

Boron epoxy Glass epoxy Carbon epoxy -

Titanium Shear stress, MPa 0.419 2.33 15.64 (ksi) 0.061 0.338 2.27 Peel stress, MPa -0.465 -3.73 -19.43 (ksi) -0.067 -0.541 -2.817

Steel Shear stress, MPa 5.44 7.99 26.22 (ksi) 0.789 1.16 3.80 Peel stress, MPa -6.30 -15.0 -38.1 (ksi) -0.914 -2.17 -5.52

Aluminium Shear stress, MPa 27.7 28.2 40.47 (ksi) 4.02 4.08 5.86 Peel stress, MPa -24.4 4 0 . 1 -44.6 (ksi) -3.54 -5.82 -6.47

t, = 5.08 mm (0.2 in); to adjusted for equal adherend stiffnesses; t, = 0.253 nun (0.1 in). Adhesive properties: shear modulus, 1.03 GPa (150 ksi); peel modulus, 3.49 GPa (500 ksi). Give temperature, 121°C (250°F). Application temperature, 24°C (75°F).

discussed earlier, the 'peel' stresses shown in Table 28.4 are all negative (i.e. compressive) because of the location of the composite on the outside of the joint, although the shear stresses are unaffected by this aspect of the joint. Composite repair patches on aluminum aircraft structures benefit from this type of behavior, in that peel stresses are not a problem for temperatures below the cure temperature. Placing the metal rather than the composite on the outside of a double lap joint would reverse the signs of the peel stresses making them tensile and aggravating the effects of differential thermal expansion of the adherends.

28.4.5.3 Transverse shear and stacking sequence effects in composite adherends

Classical analyses such as the Volkersen shear lag model for shear stresses in the bond layer (Sections 28.4.3.3 and 28.4.3.4.1) are based on the assumption that the only significant deformations in the adherends are axial, and that they are uniformly distributed through the adherend thicknesses. This is a good assump-

tion for metal adherends which are relatively stiff with respect to transverse shear deforma- tion, but for polymer matrix composite adherends which have low transverse shear moduli, transverse shear deformations are more significant and can have an important influence on bond layer shear stresses. A useful correction to the classical Volkersen solution which allows for transverse shear deformations in the adherends can be obtained by modifying the shear modulus of the adhesive from its actual value, Gb, to an effective value, Gb)eff, given by

(28.44)

where Ksh = 1 +

Here GUo and Gxzi are the transverse shear moduli of the adherends. For the double lap joint, the parameter /? appearing in eqn (28.14) (see the third equation of the top row of eqn (28.14)) is then modified by replacing Gb by Gb/K,,, using the value for Ksh given in eqn (28.44), and all the expressions in eqns

References 663

(28.15-20) for stresses in the bond layer are modified by the resulting alteration of p. The correction given here amounts to treating 1 / 3 the thickness of each adherend as an extension of the bond layer, and assigning the shear stiffness of the adherend for that part of the effective bond layer. The factor 1/3 corresponds to a linear distribution of shear stress through the adherend thicknesses, which is consistent with the assumption that the axial deformations are approximately uniform through the adherend thickness.

As an example, consider joint with a 0/90 carbon epoxy outer adherend joined to an aluminum inner adherend, with adherend thicknesses of 2.53 mm (0.1 in) and 5.06 mm (0.2 in), respectively, and a 0.253 mm (0.01 in) bond thickness. Assume a shear modulus of the bond layer of 1.06 GPa (150 ksi) and transverse shear moduli of 4.82 GPa (700 ksi) for the composite adherend and 26.5 GPa (3800 ksi) for the aluminum. A value of 1.839 is then obtained for Ksh, and the value of p and the maximum shear and peel stresses which depend on it are reduced by a factor of (Ksh)1/2 or 1.36 for this case. The shear and peel stresses are therefore approximately 30% lower than the values predicted with the unmodified bond shear modulus. This type of correction can be shown to give relatively good predictions of the adhesive stresses in comparison with finite element analyses. In addition, the departure of Ksh given in eqn (28.44) from 1 gives a good indication of the range of joint parameters for which adherend shear deformations are important.

REFERENCES

3. Oplinger, D.W. and Gandhi, K.R., Analytical studies of structural performance in mechanically fastened fiber-reinforced plates. In Proc. A r m y Solid Mechanics Conf. 1974, Army Materials and Mechanics Research Center Manuscript Report AMMRC MS 74-8 (1974).

4. Garbo, S.P., Ogonowski, J.M. and Reiling, H.E., Jr, Effect of variances and manufacturing tolerances on the design strength and life of mechanically fastened composite joints. v2 Air Force Wright Aeronautical Laboratories Report AFWAL-TR-

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