An Efficient Algorithm for Damage-Coupled Visco-Plastic Fatigue Model

The paper describes the development of an efficient and robust numerical algorithm for a damage-coupled visco-plastic-fatigue material model. The material chosen for the investigation is a eutectic material, Sn-Pb solder, exhibiting strain-softening behavior. The numerical algorithms employs a modified explicit method with adaptive sub-stepping based on the local error control for which the stress (constitutive) Jacobian explicit solution is derived. The algorithm is implemented in a commercial finite element (FE) code ABAQUS (Version 6.2) via its user-defined material subroutine. The validity of the algorithm is examined with several numerical examples, including (i) single-element simulations for uniaxial test, tensile creep, and fatigue simulations to attain an optimized algorithm, and (ii) two three-dimensional analyses of a miniature specimen under monotonic tensile loading and fatigue loading. The numerical examples illustrate the effectiveness of the modified explicit algorithm in predicting cyclic thermoviscoplastic behavior of a solder material. The algorithm is considered a generalized methodology that can be readily applied characterize thermoviscoplastic behavior and fatigue life of similar materials.