MIL-HDBK-17-3F Volume 3.Chapter 6 Structural Behavior of Joints where tp is the adhesive yield stress and Bod is given by Bod=[2Gboto/Eotb]1/2 where Gbo is the initial shear modulus,tp the bond thickness and Eo and to the adherend axial modulus and thickness.Because sinh(3)=10,this amounts to a requirement that Bodle/2to be at least 3,i.e.,that the elastic zone length be greater than 6to/Bod.Since ce,is equivalent to the total overlap length,( minus twice the plastic zone length (p,then making use of the expression given in Section 6.2.3.4.3 for (p (p=(Ox/2 Tp-1/Bpd)to where ox is the nominal adherend loading stress,the criterion for elastic zone length reduces to a crite- rion for total overlap length corresponding to a lower bound on which can be stated as 6.2.2.7(b) Equation 6.2.2.7(b)for the joint overlap length is the heart of the Hart-Smith approach to durability of bonded joints for cases where adherend failure is enforced 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 sev- eral contexts.In Reference 6.2.1(s)for example,it becomes part of the requirement for acceptable void volume,since in this 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 stiffness adherends and uniform thickness.For more sophisticated joint configura- tions such as step lap joints,the A4EI computer code provides for a step length requirement equivalent to that of Equation 6.2.2.7(b)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 Mall(Reference 6.2.2.7(b))presented the data in Figure 6.2.2.7(a)which shows the effect of adherend taper angle on development of cracks at ends of test specimens consisting of compos- ite plates with bonded composite doublers,at 10 cycles of fatigue loading;here the open symbols repre- sent the highest load levels that could be identified at which cracks failed to appear,while the solid sym- bols are for the lowest loads at which cracks just begin to appear.The predicted lines consist of calcu- lated values of applied cyclic stress required to create a total strain energy release rate threshold value, Gah,at the debond tip for a given taper angle.The values of Guh for the two adhesives were experimentally determined on untapered specimens.The angle of taper at the end of the doubler was used to control the amount of peel stress present in the specimen for static loading.It is noted that even for taper angles as low as 5(left-most experimental points in Figure 6.2.2.7(a))for which peel stresses are essentially non- existent for static loading,crack initiation was observed when the alternating load was raised to a suffi- cient level.A number of factors need to be clarified before the implications 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 3x10cycles corresponding to expected lifetimes of typical aircraft.Effects of cycling rate and envi- ronmental exposure are also of interest.Nevertheless,the data presented in Reference 6.2.2.7(b)sug- gests 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 joints (see Reference 6.2.2.7(c)-(i)for example)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. 6-10MIL-HDBK-17-3F Volume 3, Chapter 6 Structural Behavior of Joints 6-10 where t p is the adhesive yield stress and β bd is given by bd b0 o o b 1/2 β = [2G t / E t ] where Gbo is the initial shear modulus, t b the bond thickness and E0 and t0 the adherend axial modulus and thickness. Because sinh(3) ≈ 10, this amounts to a requirement that β bd e A / 2t0 be at least 3, i.e., that the elastic zone length be greater than 6 0t bd / β . Since Ae , is equivalent to the total overlap length, A , minus twice the plastic zone length Ap , then making use of the expression given in Section 6.2.3.4.3 for Ap : Ap = / 2 -1/ d i σ x τ p β bd to where σ x is the nominal adherend loading stress, the criterion for elastic zone length reduces to a crite￾rion for total overlap length corresponding to a lower bound on A which can be stated as A ≥ F H G I K J x p bd + o 4 t σ τ β 6.2.2.7(b) Equation 6.2.2.7(b) for the joint overlap length is the heart of the Hart-Smith approach to durability of bonded joints for cases where adherend failure is enforced 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 sev￾eral contexts. In Reference 6.2.1(s) for example, it becomes part of the requirement for acceptable void volume, since in this 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 stiffness adherends and uniform thickness. For more sophisticated joint configura￾tions such as step lap joints, the A4EI computer code provides for a step length requirement equivalent to that of Equation 6.2.2.7(b) 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 Mall (Reference 6.2.2.7(b)) presented the data in Figure 6.2.2.7(a) which shows the effect of adherend taper angle on development of cracks at ends of test specimens consisting of compos￾ite plates with bonded composite doublers, at 106 cycles of fatigue loading; here the open symbols repre￾sent the highest load levels that could be identified at which cracks failed to appear, while the solid sym￾bols are for the lowest loads at which cracks just begin to appear. The predicted lines consist of calcu￾lated values of applied cyclic stress required to create a total strain energy release rate threshold value, Gth, at the debond tip for a given taper angle. The values of Gth for the two adhesives were experimentally determined on untapered specimens. The angle of taper at the end of the doubler was used to control the amount of peel stress present in the specimen for static loading. It is noted that even for taper angles as low as 5o (left-most experimental points in Figure 6.2.2.7(a)) for which peel stresses are essentially non￾existent for static loading, crack initiation was observed when the alternating load was raised to a suffi￾cient level. A number of factors need to be clarified before the implications 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 3x105 cycles corresponding to expected lifetimes of typical aircraft. Effects of cycling rate and envi￾ronmental exposure are also of interest. Nevertheless, the data presented in Reference 6.2.2.7(b) sug￾gests 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 joints (see Reference 6.2.2.7(c)-(i) for example) 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