Anisotropic constitutive model coupled with damage for Sn-rich solder: Application to SnAgCuSb solder under tensile conditions

Abstract

With the rapid development of microelectronics and nanoelectronics, Moore law has significantly slowed down and More than Moore based system in packaging (SiP) is expected to be more and more important, at least for next one to two decades. Mechanical behaviors of interconnect materials such as solders are critical for yield in processes and reliability in testing and operation. Based on the framework of crystal plastic theory and continuum damage mechanics, an anisotropic constitutive model coupled with damage was developed to describe the deformation behaviors of Sn-rich solder. In the proposed model, the inelastic shear rate function was presented by hyperbolic sinusoidal form and power law form. For the damage evolution law, the total shear strain was chosen as the damage function variable. The proposed model was implemented into the general finite element software ABAQUS by forward Euler integration procedure. Some simulation examples were performed to verify the proposed model by comparing the simulation results with the experiments at uniaxial tensile conditions with SnAgCuSb solder chosen as the Sn-rich solder. The tensile stress-strain curves of the simulation results agreed well with the experiments at small strain under different temperatures and strain rates. The simulated stress-rupture stages showed reasonable accuracy with the experiments under four representative tensile conditions. Different tensile stress-strain curves of single grains with orientation of (0-0-0)°, (0-45-0)°, and (0-90-0)° were obtained under the same loading conditions, with an inverse relationship between the tensile strength and elongation. This relationship was in accordance with a referable literature. All these results indicate that the proposed model can describe the deformation behaviors of SnAgCuSb solder well under the tensile conditions in consideration of the mechanical anisotropy and the damage evolution.

A thermomechanical constitutive model for investigating the fatigue behavior of Sn‐rich solder under thermal cycle loading

“…To couple thermal deformation into our previous proposed constitutive model, 35 the total deformation of Sn‐rich solder under TCL was assumed to be composed of three parts: elastic, inelastic, and thermal. The inelastic deformation was assumed to be caused by dislocation slip, with other deformation mechanisms neglected, such as diffusion, grain interface sliding, and twining 34 .…”

“…Then, other variables can be updated. More details about the update of variables and solution process can be referred to our previous work 35 …”

“…It is significant to contain enough grains on RVE model due to the mechanical responses being sensitive to grain number. Based on our previous analysis, 200‐grain number used in RVE model for material parameter obtaining is appropriate 35 . Therefore, in the RVE model, 200 grains were included, which were established by Voronoi tessellation polygon 45 with seed nodes randomly generated.…”

“…In order to make the simulations more consistent with the experiments, periodic boundary conditions were applied to the RVE model. The conditions are illustrated in Figure 3B, with the corresponding expressions of periodic boundary conditions as follows 35 : …”

“…A key objective in CPFEM is to adopt an appropriate constitutive model that can effectively describe the deformation behaviors of the material. To the authors' best knowledge, although some anisotropic mechanical constitutive models have been proposed for Sn‐rich solder, 31–35 no anisotropic thermomechanical constitutive model has been proposed. Based on our previous proposed mechanical constitutive model, 35 a thermomechanical constitutive model was developed in this work.…”