1、it,J i signifies simply that condi-tion (8) was violated. A negative value of Tav/T p indicates such severethermal mismatch between adherends that the joint will break apart prior toapplication of any mechanical loads.12Provided by IHSNot for ResaleNo reproduction or networking permitted without lic
2、ense from IHS-,-,-The computation of joint strength proceeding from the other end of the jointis effected by simply interchanging the subscripts l and 2 on all affectedquantities. With regard to adherend stiffness imbalance alone, it is alwayspossible to identify from equation (28) that the more cri
3、tical end (1) is thatfor which E_R(Z) .C): 1 - .(54)Cnl- (a/g)This can be differentiated with respect to (a/Z) so thata(Tav/T p) / d(a/C) = 0 whena &(1-_-)Cn(l-_-) =(_c)2e+ ,i+ ETR(1)CT_(1)i + ETR(1)CTHERM(1)i - ETR(1) -(_)Substitution of equation (55) into equation (54) yields, for the minimum(stat
4、onary) value of (Tav/_p)i+ ETR(1)CT_(1)a-tv = ETR(1)+T P(55)a _+ m_(_)CTHmM(_) 1+ - i - ETR(1) - . (56)c (_c)This is evidently consistent with the elastic solution (a/z) = 0 for largeoverlaps and, upon subsequent comparison with the more precisely estimatedjoint strengths, proved to be an extremely
5、close lower bound for all cases ofpractical interest. It is significantly conservative only for very short over-laps small values of (_c) or very brittle adhesives very small values of(yp/Ye). The adhesive shear strain capacity yp is involved in equation(56) implicitly through the extent (a/g) of th
6、e plastic zone. Equation (55)19Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-is solved by iteration to evaluate (a/L) and the result substituted intoequation (56) or (54). Appendix A2 contains a listing of the FORTRAN IYdigital computer program emp
7、loyed to solve equations (55) and (54), togetherwith sample outputs and brief user instructions. The iteration techniqueeventually adopted proved to be quite convergent, after other re-arrangementsof equation (55) demonstrated strongly divergent characteristics.This program in Appendix A2 served to
8、provide the initial estimates of (a/L)and (Tav/_p) in the more precise solution listed in Appendix A3. The sequenceof variables used in the solution is (a/L), (Tav/Tp) and (c/L) after which(_av/_p) is recomputed and the estimate of (a/L) adjusted until convergence isattained. In those cases in which
9、 the critical end is not evident by inspec-tion, the potential bond shear strength is computed from each end of the jointand the lower value adopted. Brief user instructions and sample outputs areincluded in Appendix A3.The analyses above for scarf joints pertain to adhesive shear stresses and itis
10、demonstrated that a small enough scarf angle can always be found to transferthe full adherend strength through the bond with an adequate margin. There is,of course, a potential problem with the adherend strength(s) if the scarf angleSpecifically, one adherend will fail if the scarf angle e is sois t
11、oo small.small thate T/Fu , (57)(where F is the ultimate adherend stress in tension, compression, or shear,Uas appropriate) at the more critical end of the joint (identified by the ad-hesive shear stress analysis). Should this situation arise, the solution isto decrease the adherend stiffness imbala
12、nce across the joint by local rein-forcement of the softer adherend. It is evident from equation (17) that thispotential problem of breaking off the tip of (usually) the stiffer adherendis more likely to arise with the brittle adhesives (higher values of peakadhesive shear stress _p) than with ducti
13、le adhesives. This is one importantreason for preferring to effect the load transfer with a shorter overlap ofductile adhesive than with a longer overlap of brittle adhesive. The extremecase of making the overlap so extremely long that the peak adhesive shear20Provided by IHSNot for ResaleNo reprodu
14、ction or networking permitted without license from IHS-,-,-stress actually developed is restricted to a small fraction of its capacitywhen adherend failure occurs outside the joint has theoretical appeal only,frequently being quite impractical.21Provided by IHSNot for ResaleNo reproduction or networ
15、king permitted without license from IHS-,-,-4. DISCUSSIONOFPARAMETRICEFFECTSRepresentative solutions from Sections 2 and 3 for unbalanced bonded scarfjoints are illustrated in Figures 3 through 7. Figures 3 and 4 showthe sep-arate effects of adherend stiffness and thermal mismatch, respectively, on
16、theelastic joint strength. The deviations from unity in the (TaV/Tp) ratio, fora given overlap (_), are proportional to the individual imbalances. Theeffect of stiffness imbalance is a smoothdecrease from a fully-efficient bond(T = T ) to a less efficient bond (T _ ) asymptoting towards the solution
17、av p av pgiven in equation (21). This diagram, more than any other, characterizes thedominant feature of the scarf joint behavior. This is that the potential bondstrength continues to increase indefinitely with increasing overlap. This isin marked contrast to the behavior of uniform lap joints Refer
18、ences (1) and(2), which develop maximum strengths which remain effectively constant beyondintermediate overlaps. The effect of this characteristic on the potential bondstrength of scarf joints is that, by making the scarf angle sufficiently small,one can always design a joint in which the potential
19、bond strength exceeds theadherend strength by any specified factor. This is amply demonstrated by curveD in Figure 4. While adherend stiffness and thermal mismatch combine to decreasethe bond efficiency below the unit value of curve A, the bond strength for longoverlaps ends up being proportional to
20、 the overlap. As a consequence of thischaracteristic, the elastic adhesive shear stresses play a far more importantrole in the strength of scarf joints than they do in the case of uniform lapjoints. Nevertheless, it would be erroneous to conclude that one could alwaysdesign an unbalanced scarf joint
21、 within the capabilities of an elastic adhesive.The limiting problem is that, as the scarf angle becomes very small, there isa strong probability of breaking off the tip of the stiffer adherend. Whilenot as acute a design detail problem as its counterpart for stepped-lap joints,this feature restrict
22、s the scarf angle to exceed the valuee : ARCTAN(Xp/F u) (58)in which Fu is the adherend ultimate strength (in tension, compression, orshear, as appropriate for the applied load).The effect of adherend thermal mismatch on the potential bond strength ofscarf joints is shown in Figure 4. It is clear that the effects are insigni-ficant for very short and very long overlaps, being significant only for those23Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
