About Damage and Failure for Ductile Materials in Low-Cycle Fatigue Analysis

Accurately and effectively predicting the fatigue life for an inelastic structure, such as a solder joint in an electronic chip packaging, subjected to sub-critical cyclic loading is a challenging problem. Cyclic thermal or mechanical loading often leads to stress reversals and the accumulation of inelastic strain, which may in turn lead to the initiation and propagation of a crack. The low-cycle fatigue analysis capability in Abaqus/Standard uses a direct cyclic approach (Low-Cycle Fatigue Analysis Using the Direct Cyclic Approach) to model progressive damage and failure based on a continuum damage approach. The damage initiation (Damage Initiation for Ductile Materials in Low-Cycle Fatigue) and evolution (Damage Evolution for Ductile Materials in Low-Cycle Fatigue) are characterized by the stabilized accumulated inelastic hysteresis strain energy per cycle proposed by Darveaux (2002) and Lau (2002).

The damage evolution law describes the rate of degradation of the material stiffness per cycle once the corresponding initiation criterion has been reached. For damage in ductile materials Abaqus/Standard assumes that the degradation of the stiffness can be modeled using a scalar damage variable, $D$. At any given cycle during the analysis the stress tensor in the material is given by the scalar damage equation

where $\overline{\mathit{\sigma }}$ is the effective (or undamaged) stress tensor that would exist in the material in the absence of damage computed in the current increment. The material has lost its load-carrying capacity when $D=1$.