## 36

The adherends of the specimens were prepared using an acetone wipe, a base acid etch, or a P2 The adherends of the specimens were prepared using an acetone wipe, a base acid etch, or a P2 suggests an effect of interface properties on the locus of failure. For instance, when a more advanced surface preparation method was used, the carbon and silicon concentrations increased and the aluminum and oxygen concentrations decreased. These results suggest that advanced surface preparation methods...

## Info

On the shear rate, i.e. the materials' flow curve, to get reliable estimates of the volumetric flow rate under given pressure drops or vice versa. Several GNF models will now be covered since they are fairly important in engineering calculations ( 4 , Chapt. 4). However, we will limit our discussion of how other constitutive equations based on continuum mechanics can be constructed (using some of the ideas mentioned above) to merely a verbal sketch of the mathematical process. We will also not...

## 002

Non-dimensional plot of the load-displacement curves for a DCB specimen with different values of the fracture parameters 4 . is appropriate only when the normalized parameter Er 0 o2h is very small (i.e., a large cohesive strength, a low intrinsic toughness of the adhesive layer, or very thick adherends). In particular, it should be noted that if the peak load is used with Eq. 2.6 to calculate the energy-release rate at fracture, this value will result in an underestimate of the...

## 0 025 050 075 100 125 150

Distribution of radial stress along fiber fragment length 88 . the fiber axis. Depending on the amount of energy released upon fiber failure, this microcrack may or may not propagate into the matrix and or the interphase, depending on the level of adhesion between fiber and matrix. Then, the resulting stress distribution will depend on the mechanical properties of the fiber, the matrix and the interphase and the extent of the damaged zone around the fiber break. As pointed out by Ko et...

## 2 H

Where T0 is the (real) amplitude and 5 is the relative phase shift ( loss angle), then Eqs. 192 and 193 yield the components of the complex viscosity as ff 2HT0cos8 V V nR4co0o )' V V jz r4co0n ) If we want to find out how a fluid behaves under extension, we have to somehow 'grip' and stretch it. Experimentally, this is much more difficult than the shear arrangement, especially if the fluid has a low viscosity. Earlier (see Section 5) we saw that it is possible to classify steady extensional...

## Q

Ramberg-Osgood relation, 69 rate effects, 298 rate of debonding, 411 R-curve, 237 receding contact, 595 Reiner-Rivlin fluid, 463 relaxation, 451 relaxation function, 453 relaxation modulus, 453 relaxation spectrum, 460 relaxation time, 359 residual stresses, 32, 87, 124, 303, 318,398 in coatings, 318 compressive in coatings, 333 resistance to debonding, 501 resonance method, 706 retardation spectrum, 460 retardation time, 359 rheology, 443,504,513 rheometry, 483 Rivlin-Erickson tensors, 447...

## 7 Crack opening interferometry

One way of providing an overview of much of the foregoing material is to consider measurements of displacements near a crack front. It will also provide some points to ponder. A method that the author has used successfully is crack opening interferometry. This requires that at least one of the components of the bonded joint under consideration is transparent to the wavelength of the radiation being used. At first, especially considering the visible spectrum, this may seem to be rather...

## 2 7t

Again, it is the stress intensity factor that distinguishes the crack-tip stress distribution from one loading and crack geometry to another. A large variety of methods exist for determining the stress intensity factor associated with a particular configuration as can be seen from the compilation by Tada et al. 55 , When finite element methods are used for the stress analysis of cracked components, stress intensity factors may be extracted by examining the displacement solution near the crack...

## 0 9 0 7 Ii5 0 1 0 1 0 1 0 1 Os 0 7 0

Dependence of critical coating thickness ratio, r c on a, for fi 0 60 . design that avoids crack propagation does not always result in a design that avoids crack initiation. 1. Zozel, A., Prog. Org. Coat., 8(1), 47 (1980). 2. lkeda, K., Kolloid-Z., 160, 44 (1958). 3. Williams, M.L., Landel, R.F. and Ferry, J.D., J. Am. Chem. Soc., 77, 3701 (1955). 4. Achenbach, J.D., Wave Propagation in Elastic Solids, Elsevier North Holland, Amsterdam, 1984. 5. Papini, M. and Spelt, J.K., Wear, 222,...

## 1

And the complex stress intensity factor K K + iK2 has real and imaginary parts which are similar to the conventional mode I and mode II stress intensity factors in LEFM. In fact, were it not for the r' term, Eq. 26 would give the mode I (ct22) and mode II (o ) components of stress ahead of the crack, and K and K2 would reduce to the K and K of traditional LEFM. However, for f> 0, the rIE term in introduces an oscillating singularity and complicates the usual notions of stress intensity and...

## 7

Deformed shape of the elastic layer in an adhesively bonded butt joint with rigid adherends when subjected to a positive-shear loading. for uniform adhesive shrinkage. The solution for the uniform edge pressure can be thought of as providing the fundamental singular solution, and the characteristic stress defined in Eqs. 11 and 12 is the stress superimposed with the edge pressure to obtain a stress-free edge. The adhesively bonded butt joint's thin adhesive layer is sheared by...

## The durability of adhesive joints

Department of Mechanical Engineering, Imperial College of Science, Technology and Medicine, Exhibition Rd London SW7 2BX, UK One of the most important requirements of an adhesive joint is the ability to retain a significant proportion of its load-bearing capability for long periods under the wide variety of environmental conditions which are likely to be encountered during its service-life. Unfortunately, for the reasons outlined later, one of the most hostile environments for joints involving...

## Hzt

M 2M0k D , k-ko J h D )M(t -t')dt' where the characteristic time k has a rest value k0 and M(t t') is a memory function. The dimensionless function h is determined by D evaluated at t'. Eq. 164 is equivalent to models studied by Cheng and Evans 7 for any memory function M(t t') that corresponds to an evolution equation for k. For example, the equation is obtained for the exponential memory function M(t ') exp ( ' OAiL where k is a constant relaxation time. In these examples, the evolution...

## M

Simplified edge loading for a case where substrate is much thicker than coating. nut sandwich 95 , the indentation test and the modified DCB specimen (see Section 2.3.1). 4.2.3. Thin coatings and films with loading on coating only In many common cases (e.g. thin films), the coating is much thinner than the substrate, and the solution of the previous section is simplified by setting t 0. If we further restrict our discussion to cases where the only load is on the thin layer (Fig. 10),...

## 45

Crack growth rate as a function of strain energy 9, experimental results for compression, O theoretical results for compression, experimental results for simple tension. Redrawn from ref. 49 , be used to generate the characteristic fracture energy versus crack speed curves which can then be applied to very complicated real world parts by using numerical methods to map the strain energy in the part and using that data to determine if crack growth is likely. 5. Designing with elastomeric...

## 8m1m2

The subscripts indicate the upper (1) and lower (2) layers. Comparison of Eqs. 50 and 51 with Eq. 26 shows that the form of the singularity for the free-edge and steady-state cracking solutions is quite different. Notably, in the commonly encountered case of ft 0, the exponent of the singularity, A., depends on the material properties in the case of the free-edge solution, while it is always a square root dependence in the case of the steady-state solution. Also, the...

## P

Cross-sectional view of cone pull-out tests. Starter crack Fig. 25. Cross-sectional view of cone pull-out tests. inversely proportional to the maximum energy release rate for specimens with varying t D ratios. The failure behavior of a series of cone pull-out tests was also explained with the aid of fracturc mechanics and finite element analysis 23J. The specimens tested consisted of a truncated PMMA cone bonded into a matching hole in a PMMA plate using a dear...

## 644

Table 1 gives the range of tensile loads that were applied to the models. The loads were the mean values of the measured failure loads of these joints. Table 1 gives the range of tensile loads that were applied to the models. The loads were the mean values of the measured failure loads of these joints. 2.3. Adhesive properties used in the FE model Two commercial high-temperature adhesives were used in this set of results. This was because the most difficult case to model and to get agreement...

## G

Where G is the total strain energy release rate available and G is the strain energy release rate available for mode II crack propagation. When a debond is propagating cohesively within an adhesive layer, these relationships will prove useful in predicting the direction of cracking. For simple geometries, analytical solutions for the stress intensity factors, energy release rates, and mode mixities are possible, but for more complex configurations, numerical techniques are often required 14 ,...

## 0 a pdz

The simplified equation set that needs to be solved is therefore Eqs. 200, 201, 2102 with and 212. The boundary conditions that need to be satisfied are df dz 0, vz 0 at z 0 (symmetry) 0, vz dh dt h at z h (no slip) p pa at r R where pa denotes ambient pressure. To solve the set, we first differentiate Eq. 2IO2 with respect to z and use Eq. 212 to get which, combined with the two boundary conditions on , yield Next, integrating Eq. 201 with given by Eq. 215 we find, using the BC for v- at z 0,

## F z aw W o

Hence pressure and thrust measurements, via Eqs. 175 and 178, allow one to calculate N and While the cone and plate geometry is the preferred arrangement to obtain the steady viscometric functions, it is limited to low shear rates usually, to those less than 10 s '. At higher shear rates encountered in processing 10 106 s_l), it is customary to resort to capillary rheometry to measure the shear viscosity. Unfortunately, the normal stress differences cannot be obtained from this test. To get Ni...

## 34

The two representative specimens with different surface preparations revealed that the interface properties significantly affect the crack propagation behavior. Advanced surface preparation techniques enhance the adhesion between the adhesive and the substrates and consequently, the rate dependence of the locus of failure is reduced. Of particular significance, however, is that the debond did not propagate exclusively at the weaker interface. The stress state destabilized the debond, leading to...

## References

Anderson, G.P. and DeVries, K.L., Int. J. Fract., 39, 191-200 (1989). 2. Reedy Jr., E.D. and Guess, T.R., Int. J. Solids Struct., 30, 2929-2936 (1993). 3. Reedy Jr., E.D. and Guess, T.R., Int. J. Fract., 98, L3-L8 (1999). 4. Hart-Smith, L.J., In Kedward, K.T. (Ed.), Joining of Composite Materials, ASTM STP 749. American Society for Testing and Materials, Philadelphia, PA, 1981, pp. 3-31. 5. Adams, R.D. and Wake, W.C., Structural Adhesive Joints in Engineering. Elsevier, London, 1984. 6....

## Bgh

Algorithm possibility, of many that could be introduced in hardware or software to provide a total C-scan representation, hence allowing us to examine amplitude at a particular depth over the entire test structure being considered. For comparison purposes, Fig. 5b shows the representation of an A-scan, B-scan, and the popular C-scan. An A-scan is simply an amplitude versus time domain signal display. A rectified waveform is illustrated in Fig. 5. For a B-scan image, a cross-sectional image of a...

## 0 600 1200 1800

Stress-relaxation data for an Epon 828 T403 adhesive cured 18 h at 35 C and tested at three temperatures. Each specimen is loaded to yield at 0.0002 s_l prior to fixing the displacement. phase. Several recent studies have investigated the nature of the asymptotic, interface-corner stress field in a power-law-hardening material. Most of this work has concentrated on determining the strength of the stress singularity 73-78 , although there have been several studies where the associated...

## 12

Fracture envelope, Gc versus phase angle, V, for FPL-etched 7075-T6 aluminum ad-herends bonded with 0.4 mm Cybond 4523GB epoxv adhesive cured at 150C for 45 min 88 , Fig. 5 88 , In this case, the fracture parameter is expressed as Jc, the energy release rate, rather than Kc. Note that a relationship similar to that of Eq. 18, relates the energy release rate, J, to the stress intensity, K. In ref. 88 , J was used rather than G to emphasize that some of the specimens studied behaved in a...

## 4 Summary

This paper has provided an in-depth discussion on the fracture of adhesive joints with a focus on how to deduce the 'intrinsic' fracture parameters of the adhesive layer from experimental results. The approach of using these parameters in cohesive-zone models to predict the fracture of adhesive joints has been outlined. By using this approach, many important issues that are frequently encountered in the fracture testing of adhesive joints, yet are usually ignored by traditional fracture...

## Iio [1 W aln91

Various isothermal and non-isothermal flow problems have been solved with the above model fluids. Bird et al. 4 (p. 229) lists some of these solutions for rectangular slits and circular pipes. 5.2. Elastic and viscoelastic models We will now give a brief sketch of some of the other continuum models beyond the simple viscous ones considered above. The purpose here is to show how these models are interconnected and allow the reader to gain a broader scope of the subject without going into the...

## 2

The authors conclude that a combination of the flexure, torsion, and thermal bending tests can be used to accurately determine the Young's modulus, residual stress, and thermal expansion coefficient, if the Poisson's ratio can be estimated. Combinations of experimental parameters that give accurate results are presented The stiffness of inorganic films may also be determined from the measurement of the propagation velocity of surface acoustic waves, C, which, for a homogeneous material is...

## K iK pf HW 2V3 2315

If the crack is at the sub-interface, the local stress intensity factor Kx and Kv can also be expressed as a function of the external load by substituting Eq. 20 into Eq. 17 as K q IKI cos to + (j> + s In ( ) Ku q iT sin a) + 0 + eln(Sf O (21) and G 2P a E B H is the applied strain energy release rate in the specimen. Fig. 29 shows that due to the material mismatch, when the distance between the sub-interface crack and the interface St approaches zero, the corresponding component at the crack...

## 10

Peel stress at the first ply interface under load. can be of sufficient magnitude to cause interlaminar failure of the adherend prior to adhesive failure. Although such failure was not seen in these joints, probably because of the more brittle nature of the adhesive used compared with the rubber-toughened (CTBN) adhesive used by Adams et al., it was, nevertheless, important to consider the stress distribution within the adherend. As can be seen from Fig. 11,...

## 24

Fig. 3. 2024-T3 Aluminium adherend tensile stress-strain curves from ASM Metals Handbook Vol. 2, Properties and Selection, Non-Ferrous Alloys and Special Purpose Materials, 10th edn., ISBN 0871-703-785. were assumed as shown in Fig. 4 and all data for this alloy were again taken from the ASM Handbook. An elastic modulus of 110 GPa was assumed for the T -6A1-4V over the range of temperatures considered and a Poisson's ratio of 0.33 was used. The coefficients of thermal expansion are given in...

## O

Blistering of coating due to compressive residual stress inducing buckling. Note that edge normal load, the change in stress due to buckling, Act, is positive. originating in water clusters at microscopic voids. Blistering arises from the coating buckling (see Fig. 12), and an analysis similar to that used to study indentation induced buckling can be used to find the critical compressive stress. A delamination of length 2b is assumed present in the interface, and, in the absence of...

## P2

The Auger depth profiling method was then used for those specimens, in which the failure appeared to occur at or near the interface. As shown in Table 5, in the mode I test, the thicknesses of the residual adhesive layer on the failure surfaces were about 250 xm for all the specimens with different surface preparations, which indicated that the failures all occurred in the middle of the adhesive layer in the test regardless of the surface preparation method since the total...

## 08

Typical force-displacement plot from a pull-out experiment. both the free and embedded lengths of the fiber, the slope of a curve (i ) against pull-out distance gives only an approximate value of the interfacial shear stress ( xpo) where pQ is the pressure exerted by the matrix shrinkage at the moment the fiber emerges from the polymer. The experimental value for shear stress (rexp) obtained from the slope of the pull-out curve is related to the true value of zt xp0 by Eq. 9

## DS dP

This expression is a useful check on approximate relationships between C, 8' and P', given, for example, in the following section. Eq. 7 is a general expression that is valid for both the frictionless and full-friction boundary conditions. 2.2. Modifications due to finite size effects In the previous examples we have assumed that the thickness of the sample is much larger than the contact radius. Modifications to these expressions are necessary when the compliant material is reduced in...

## 14 Adhesive drag and hysteresis measurements

The problem of measuring adhesion, in general, is that the curves for peeling have a similar shape, with an apparent work of adhesion plus a large kinetic adhesion drag, but we are not sure exactly where the equilibrium is. So it is important to devise experiments to study both making and breaking the joint in order to define the precise equilibrium point. Three typical experiments are shown in Fig. 33 13 , Fig. 33a shows a wedging experiment, rather like that used by Obreimoff on mica. The...

## Ffo 7a2rsftr8

Tsf, is the stress free temperature of the adhesive, which was measured using a curvature measurement technique 37 for each adhesive, and was very close to the glass transition temperature of the respective adhesive (the results are also listed in Table 1). T is the test temperature (room temperature in this study). Since the coefficients of thermal expansion of the adhesives increased with rubber concentration and meanwhile the modulus and the glass transition temperature decreased slightly,...

## 243

The commonly held approximation that the behavior in peel at a given elongation rate is dominated by the viscoelastic properties at the equivalent frequency is shown to be crude at best and misleading at worst. The work of Piau et al. 23 follows a similar pattern. Modeling is done using the measured stress-strain behavior of the adhesive, the measured elongation at detachment from visualization of the peel front and the measured peel force. They show that the...

## Adhesive Shear Strain

Development of non-uniform shear stresses in double-lap and double-strap bonded joints. closed-form analysis, in ref. 9 , to have a constant width, independent of the total overlap. Most of the load is transferred there, with very little in the middle of the joint. However, the low-stressed interior is absolutely vital to the durability of adhesively bonded joint. The adhesive will creep, locally, at the ends of the overlap, at quite low sustained loads, because of the severity of the...

## Final Failure Of

NOTE THAT DESIGN PROCESS MUST ACCOUNT FOR NONLINEAR ADHESIVE BEHAVIOR, BUT A PRECISE STRESS-SRAIN CURVE IS NOT MANDATORY. AN APPROXIMATION, BASED ON A SIMILAR ADHESIVE, WILL U SUALLY SUFFICE. NOTE THAT DESIGN PROCESS MUST ACCOUNT FOR NONLINEAR ADHESIVE BEHAVIOR, BUT A PRECISE STRESS-SRAIN CURVE IS NOT MANDATORY. AN APPROXIMATION, BASED ON A SIMILAR ADHESIVE, WILL U SUALLY SUFFICE. Fig. 16. Adhesive shear design model based on restricting design limit loads below the adhesive elastic capability....

## 60

Experimental joint strengths of three steel adherends with AVI 19 adhesive. The predicted lines are from Eqs. 1, 2 and 3. Ciba, which has a measured maximum yield strength in shear of 49 MPa with about 30 shear strain to failure. In Fig. 16, line 1 applies to Eq. 1. It predicts reasonably the strength of the high-strength steel joints, although it is clear that, at high loads, the measured strength is below that predicted. A more brittle adhesive used with these high-strength adherends...

## Fully Plastic Adhesive Load Limited By Bond Area

Strength of double-lap bonded joints at minimum service temperature. limiting central adherend thickness and to compute the overlap needed to transfer the adherend ultimate strength (not any nominal design load, as explained above), using Eq. 6 and to add an appropriate manufacturing assembly tolerance. No greater overlap can ever add to the joint strength unless a more complex bonded joint geometry is adopted, as would be necessary for adherends thicker than the upper limit...

## The design of adhesively bonded joints

Phantom Works, The Boeing Company, Huntington Beach, CA, USA Designing successful adhesively bonded joints is straightforward, provided that one pays close attention to a small number of critical issues, none of which is difficult to comprehend and none of which is any more difficult to comply with than to ignore. The first is that the joint must never be designed to be weaker than the surrounding structure, unless one is deliberately planning a weak-link fuse with no damage tolerance. The...

## 10 10

The number, Nf, of cycles to failure for single-lap joints as a function of the maximum load, 7ma. , per unit width applied in a fatigue cycle. The lap joints were cycled at 5 Hz in water at 28 C. The points represent the experimental data filled points indicate where the test was stopped prior to failure whilst the lines are the theoretically predicted lifetimes 74 . and 6, for example for polymeric adhesives is often relatively steep. This implies that, for adhesive joints, the rate...

## 52

The microindentation technique seems to agree well with the results obtained from the single-fiber fragmentation method. An interfacial shear strength equal to rav 3870 750 psi 26.6 5.2 MPa was obtained for IM6 U fibers using the ITS. This value is slightly higher than the one obtained from the single-fiber fragmentation technique. For IM6-100 , rav 5400 1540 psi 37.2 11.0 MPa and for IM6-600 , rav 6200 1640 psi 42.7 11.3 MPa were obtained also using the ITS. The...

## Effect of rheology on PSA performance

Introduction to pressure-sensitive adhesives Pressure-sensitive adhesives PSAs have become familiar materials in our world. Most people have used tapes such as masking tape, electrical tape, or transparent tape, for example Scotch Magic Transparent Tape. All of these have pressure-sensitive adhesives of various kinds coated on a paper or polymeric film backing. The adhesive strength of such materials can vary widely from the easily removable Post-It note to the permanent bonds formed by the...

## 3 Adhesive cracking

In this case, cracks run along the interface between two materials due to interactions between the stress field in the adhesive layer and spatial variations in fracture properties. The cracks are not generally free to evolve as mode I cracks, as was the case for cohesive cracks, and mixed-mode fracture concepts combinations of tension and shear have to be considered. Mode II or shear components are induced, even in what appear to be nominally mode I loadings, due to differences in moduli about...

## Measurement methods for fibermatrix adhesion in composite materials

HERRERA-FRANCO b Departments of Chemical Engineering and Materials Science and Mechanics, Composite Materials and Structures Center, Michigan State University, East Lansing, Ml 48824-1326, USA h Centro de Investigaci n Cient fica de Yucat n, A.C., Calle 43 130, Col Chuburn de Hidalgo, C.P. 97200. M rida. Yucat n, M xico 1. Fiber-matrix adhesion measurement methods It is well known that the level of adhesion between fibers and matrix affect the ultimate mechanical...

## M M U

1E-4 1E-3 1E-2 1E-1 1E 0 1E 1 1E 2 r mm Fig. 11. Comparison of linear-elastic and elastic-perfectly plastic finite-element solutions with asymptotic solution for stress in front of an unbonded inclusion embedded, within an epoxy disk, with h 18 mm and AT -100 C. 6. Limits on the applicability of a Kac failure analysis Two basic requirements must be met before the Kac criterion can be applied. One obvious requirement is that failure must initiate at the interface corner. The other requirement is...

## Shear Lag Analysis Volkersen

X - transverse shear stress y - distance from neutral axis V - applied lateral shear load b - width of beam at section Q - 1st moment of area of partial section I - 2nd moment of area Fig. 9. When subjected to lateral shear loads, transverse shear stresses are required within the beam to allow buildup of axial stresses associated with changing bending moment. such lateral loads, the axial stresses vary not only from top to bottom of the beam, but also along the length due the change in bending...

## Peel Adhesive Joint

Which are the two boundary conditions that allow us to determine the final solution for the shear lag model of the lap joint where P is the axial load per unit width of the joint. For the balanced adherend case where the , t, products for the upper and lower adherends are the same, the coefficient for the hyperbolic sine term becomes zero, and the shear stress distribution is symmetric about the center of the joint. Adams and Wake 11 have provided insightful figures illustrating the shear...

## D

For peel loading, bending of the flexible adherend results in relative shear deformations within the bondline, again demonstrating coupling often seen between shear and peel stresses in bonded joints. the adherend results in a relative horizontal translation of the adherend surface with respect to substrate. Thus a peeling action produces not only peel stresses, but also shear stresses. Clearly, the stresses present within even the most simple joint configuration can be quite complex...