Experimental and numerical investigation of fatigue damage development under multiaxial loads in a lead-free Sn-based solder alloy

Electronic devices for automotive applications undergo substantial thermo-mechanical cyclic loads during their operation. Within the phase of assembly, a large variety of passive and active electronic components are electrically connected by solder joints of complex geometrical shapes. As a consequence, external thermomechanical loads result in local multiaxial stress states in the solder material during their operation. In the past years, significant efforts were made in the characterization of solder materials and the accurate FE-modeling of their viscoplastic deformation behavior as well as the modeling of their damage behavior. However, material testing and numerical model calibration were focused on uniaxial tests, which result in a homogeneous stress state and a fixed ratio between its hydrostatic and deviatoric parts. Therefore, the correlation between varying multiaxial loads and cyclic damage evolution in solder alloys is still not understood. Here, we report on the experimental investigation of Low Cycle Fatigue (LCF) on bulk samples under uniaxial and multiaxial stress states realized by means of a pure tension-compression and superimposed tension-torsion loads. In order to describe the observed cyclic degradation behavior, a phenomenological fatigue damage model is modified incorporating the influence of multiaxial stresses in the damage development. The new damage model is implemented as a user-subroutine for Finite Element (FE) calculation supported by the commercial FE-package ansysTM. Uniaxial and multiaxial loads are simulated on the meshed specimen-geometry. The material model is able to describe the mechanical properties in the initial state of deformation. Besides, it shows numerical stability which enables the simulation of large number of cyclic loads. Based on the damage mechanic approach enhanced by multiaxial effects, this study contributes to the framework of solder joints modeling.