Novel fatigue crack propagation analysis of solder joint using singularity of strain energy density in the crack tip near field

This study investigated a singularity parameter of strain energy density by which the path-independent property is guaranteed in the analysis of fatigue crack propagation in a solder joint by using the finite element method. When plastic deformation was dominant, an inverse relationship obeying the HRR singularity theory held with the strain range W, which was calculated using the volume average of the element solutions in an area of arbitrary size around the crack tip and the size of the area Larea. Therefore, the path-independent property was guaranteed using the proportional constant Wc of the inverse relationship. In contrast, the path-independent property of ΔWc was lost under elasto-plastic deformation where the unloading effects could not be ignored or under creep deformation where the generalized Garofalo law was used for the constitutive equation. In this study, ΔWNear field, which was calculated by extrapolation from ΔW obtained in the first field around the crack tip and the second field inside the first field, was proposed as a new parameter in fatigue crack propagation analysis. ΔWNear field exhibited the pathindependent property for various loading conditions and it was demonstrated by FEM analysis using the fatigue data of Sn5.0Sb measured in a past study that highly accurate fatigue crack propagation analysis of solder joints is possible using ΔWNear field.