The comparison of Qian-Liu model and Anand model for uniaxial tensile test of SAC305

The constitutive model of solder alloys is of great importance to describe the mechanical behaviors of solder alloys, which in turn affects the reliability evaluation of the electronic products. The Anand model is widely applied to describe solder alloys, which was initially proposed to analyze thermal deformation processing of metals. The Anand model employs one scalar internal variable, called deformation resistance, to describe the strain hardening/softening features of deformation behavior of materials. Besides, there is no explicit yield surface in Anand model and the anelastic and Bauschinger effect are ignored in Anand model. While, a unified viscoplastic constitutive model, coined as Qian-Liu model which was developed by Zhengfang Qian and Sheng Liu, employs back stress tensor to describe the kinematical hardening and cyclic hardening/softening effect based on dislocation dynamics framework. The Bauschinger effect of solder alloys was considered in Qian-Liu model. By using the least square method, the nine Anand parameters and nine Qian-Liu parameters of SAC305 were determined from a set of uniaxial tensile tests under different constant strain rates and different constant test temperatures. After obtaining the parameters of Anand model and Qian-Liu model respectively, the predicted stress-strain curves of SAC305 have been calculated. Results show that both Anand model and Qian-Liu model can be employed to describe the mechanical properties of SAC305 solder. Compared with Anand model, Qian-Liu model is a little better in describing the mechanical properties of SAC305 under uniaxial tensile test. The Qian-Liu model exhibits a great application prospect in the field of electronic packaging for the reliability evaluation of electrical products.