A rate-dependent constitutive model considering effects of temperature cycles for lead-free solders

The lead-free solders are adopted to avoid lead pollution in the past decades, however, the mechanical behaviors under complex loading are still requires further study. For example, change of environment temperature is one of the hazards affecting the electronics reliability, especially the temperature cycles which will increase the temperature damage rapidly and the working life could be reduced. In the current study, the rate-dependent Johnson-Cook model is modified, and the temperature cycle related damage model is proposed. The pre-damage caused by temperature is considered. With the modification of damage model, the full failure process of solder can be described. In order to verify the proposed model, the temperature cycling experiments were conducted at recycle temperature ranges from 77.15∼398K and 77.15∼293K with different number of recycle times. The model is implemented by UMAT and conducted by the finite element software ABAQUS. The simulation results are compared with the experiments, and the developed model can simulate the behaviors (such as the change of strength and the plasticity) of Sn3.0Ag0.5Cu lead-free solder after temperature cycles with reasonable accuracy. Besides, the proposed model can be applied to measure the temperature recycle damage of solder, which is useful to evaluate its reliability under complex working conditions.