Nonlocal continuum damage mechanics approach in the Finite Element simulation of lead-free solder joints

Abstract

Realistic material modelling is at the heart of accurate reliability prognosis of electronics hardware by means of Finite Element (FE) calculations. It is usually achieved on the basis of material testing using standardized samples, where well defined, homogeneous stress states and loading conditions can be realized. Both the deformation behaviour in the initial state, as well as the materials degradation during repetitive loading can then be mapped by calibrated damage mechanics FE-models. Such models employ the calculation of internal damage state variables at integration point level, which are functions of stress, strain, time and temperature. However, in the simulation of real components accommodating inhomogeneous stress states due to their complex geometries, damage localization effects can take place. As reported in previous works, local enhancement of damage variables at integration points and significant impact of the FE-mesh quality on the results are commonly obtained in the simulations. Such numerical features can hamper the applicability of damage mechanics models derived from standard material testing samples onto real solder joints geometries. In order to overcome mesh dependency and localization of damage evolution, we adopt a spatial weighted averaging of the damage state variable in a visco-plastic Chaboche material model. This approach overcomes the numerical localization of damage on discrete numerical points and is often referred to as nonlocal damage concept. Here, we highlight the algorithm of nonlocal damage calculation at integration point level, which we implemented for the use in a commercial FE software package. We achieve a spatial damage distribution on a finite microscopic scale with the aim to resemble the physical material degradation, known to happen on the scale of microscopic cracks, grain and grain-boundary modifications. Finally, we discuss the advantages and implications of the nonlocal damage approach on the basis of the damage evolution obtained by simulations of a Low Cycle Fatigue (LCF) specimen.