Fatigue damage coupled constitutive model for 63Sn37Pb solder under proportional and non-proportional loading

In this paper, a series of low cycle fatigue tests under multiaxial non-proportional loading at constant room temperature is carried out. It is observed that 63Sn37Pb solder exhibits non-additional cyclic hardening effect under non-proportional loading compared with proportional loading. A damage coupled Ohno–Wang constitutive model is implemented to simulate stress strain loops of solder over a wide range of loading conditions with the consideration of peak stress sharp drop stage. The damage evolution equation proposed by Stolkarts et al. [Stolkarts, V., Keer, L.M., Fine, M.E., 1999. Damage evolution governed by microcrack nucleation with application to the fatigue of 63Sn–37Pb solder. J. Mech. Phys. Solids. 47, 2451–2468.] is modified, in which the sum of maximum shear strain range and normal strain range on the critical plane is adopted as the damage parameter to replace the uniaxial strain range. The reasonable substitution of damage parameter is capable of explaining the difference of damage evolution procedure of tin–lead under proportional and non-proportional loading. Comparison of the experimental results and simulation verifies that the stress strain hysteresis loops and peak stress decline curve of solder can be reasonably modeled with implement of damage coupled constitutive model under proportional and non-proportional loading. The lifetime estimation of 63Sn37Pb based on the assumption of microcrack nucleation governed damage is effective to provide a conservative prediction.