Modeling of Residual Stress Effects Using Eigenstrain

This paper discusses the modeling of residual stresses in fracture problems. Historically, residual stress effects in fracture have focused on the crack driving force, so that solely opening mode residual stresses are assumed to influence fracture. However, residual stresses can effect all components of stress at the crack-tip, and can thereby alter crack-tip constraint and influence material toughness. This paper discusses a modeling approach capable of revealing the effects of residual stress on both driving force and constraint. The modeling employs non-linear finite element analyses in which residual stresses are treated using eigenstrain. Eigenstrain is imposed to induce residual stress as an initial condition in a cracked geometry. Under subsequent applied loading, the stress fields due to applied and residual loadings are free to interact, with residual stress being potentially reduced by gross plasticity. In order to predict fracture independent from the level of crack driving force, the evolution of the crack-tip stress and strain with applied loading is monitored using any of various micromechanical fracture prediction schemes, which depend directly on the crack-tip conditions. Domain integral solutions for J , derived from the FEM results and properly corrected for the presence of initial eigenstrain, are computed. Constraint is quantified using J-Q theory. Together, J and Q allow comparison between the modeling approach pursued and more traditional global parameter approaches.