Novel Fatigue Crack Propagation Analysis of Solder Joint Using Singularity of Strain Energy Density in the Crack Tip Near Field

Abstract

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 L area . Therefore, the path-independent property was guaranteed using the proportional constant ¦W c of the inverse relationship. In contrast, the path-independent property of ¦W c 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, ¦W Near field , which was calculated by extrapolation from ¦W 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. ¦W Near 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 ¦W Near field .