Experiments and simulations of uniaxial ratchetting deformation of Sn–3Ag–0.5Cu and Sn–37Pb solder alloys

This paper discusses uniaxial ratchetting deformation of lead-free solder alloy Sn–3Ag–0.5Cu and lead-containing solder alloy Sn–37Pb, which were subjected to tension–compression loading with several stress amplitudes and stress ratios, minimum stress over maximum stress. First the uniaxial ratchetting tests were conducted with three maximum stresses and four stress ratios. All tests were conducted using cylindrical bulk specimens of the solder alloys at 313 K. The test results show that there are differences in the ratchetting deformation behavior of the two solder alloys; the larger ratchetting strain occurs in the lead-containing solder alloy than in the lead-free solder alloy. The ratchetting deformation was simulated by the dislocation based constitutive model proposed by Estrin et al. (J Eng Mater Technol 118:441, 1996). The evolution equation of the back stress employed in the constitutive model was modified considering a dynamic recovery term. The effect of the modification of the back stress evolution is discussed by comparing the simulations with the corresponding experimental results. The simulations suggest that the recovery term in the kinematic hardening rule plays an important role in fitting the simulation to the experimental results of the ratchetting deformation of the solder alloys.