Nonlocal Damage Modeling of Solder Joint Failure Under Thermomechanical Cyclic Loading

The increasing electrified mobility poses a challenge on reliability prediction of automotive electronics, especially when safety systems are concerned. The use of finite element simulation for accurate end-of-life prediction of automotive electronic devices under harsh environmental loading condition is getting increasingly significant. In particular, solder interconnection failure is in focus when subjected to thermomechanical loads. During cyclic loading, the initial deformation behavior and subsequent solder degradation can be modeled within finite element simulations using material damage coupled deformation models. Such models employ the calculation of an internal damage state variable at integration point level as functions of time, temperature and governing stress-strain state. In this work, a thermodynamic consistent implicit nonlocal damage formulation is presented. This modeling approach allows absolute end-of-life prediction of different solder joint geometries under thermomechanical cyclic loading within finite element simulations. The presented nonlocal damage model consists of damage evolution with strain and stress state dependencies, such as stress multiaxiality. Furthermore, a numerical de-localization algorithm is proposed, in order to avoid instability of damage evolution caused by finite element mesh dependency. Finally, the advantages and implications of the nonlocal damage approach are discussed based on simulations of damage evolution in multiple solder joints of a QFN48 package under combined cyclic thermal and mechanical 4-point bending loading.

A thermodynamically nonlocal damage model using a surface-residual-based nonlocal stress

ABSTRACT In this research, a surface-residual-based nonlocal stress was introduced into nonlocal damage theory to describe the long-range actions among microstructures that were excluded in the definition of Cauchy stress. By using the surface-residual-based nonlocal stress tensor, a thermodynamically consistent nonlocal integral damage model was established to simulate the strain localization behavior for elastic-brittle damage problems. In this model, both the strain and the damage were taken as nonlocal variables in the free energy function, and the integral-type damage constitutive relationships and the evolution equation were derived via thermodynamic laws in order to ensure the self-consistency within the thermodynamic framework. Based on the nonlocal damage formulations using a real nonlocal stress concept, we simulated the strain localization phenomenon in an elastic bar subjected to uniaxial tension. The results showed clear localizing and softening features of strain in the damage zone, and the boundary effects arising from the nonlocal surface residual were illuminated. Furthermore, the strain localization behaviors for different internal characteristic lengths were simulated, through which we found that the characteristic length was comparable to the size of the strain localization zone.