24.4.1 Damage and failure for ductile materials in low-cycle fatigue analysis: overview
Product: Abaqus/Standard
References
Overview
Abaqus/Standard offers a general capability for modeling progressive damage and failure of ductile materials due to stress reversals and the accumulation of inelastic strain energy in a low-cycle fatigue analysis using the direct cyclic approach. In the most general case this requires the specification of the following:
the undamaged ductile materials in any elements (including cohesive elements based on a continuum approach) whose response is defined in terms of a continuum-based constitutive model (“Material library: overview,” Section 21.1.1);
a damage initiation criterion (“Damage initiation for ductile materials in low-cycle fatigue,” Section 24.4.2); and
a damage evolution response (“Damage evolution for ductile materials in low-cycle fatigue,” Section 24.4.3).
General concepts of damage of ductile materials in low-cycle fatigue
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,” Section 6.2.7) to model progressive damage and failure based on a continuum damage approach. The damage initiation (“Damage initiation for ductile materials in low-cycle fatigue,” Section 24.4.2) and evolution (“Damage evolution for ductile materials in low-cycle fatigue,” Section 24.4.3) 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, 
. At any given cycle during the analysis the stress tensor in the material is given by the scalar damage equation
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 
.Elements
The failure modeling capability for ductile materials can be used with any elements (including cohesive elements based on a continuum approach) in Abaqus/Standard that include mechanical behavior (elements that have displacement degrees of freedom).
Additional references
Darveaux, R., “Effect of Simulation Methodology on Solder Joint Crack Growth Correlation and Fatigue Life Prediction,” Journal of Electronic Packaging, vol. 124, pp. 147–154, 2002.
Lau, J., S. Pan, and C. Chang, “A New Thermal-Fatigue Life Prediction Model for Wafer Level Chip Scale Package (WLCSP) Solder Joints,” Journal of Electronic Packaging, vol. 124, pp. 212–220, 2002.