Shakedown and Fatigue Damage in Metal Matrix Composites

Abstract

Fatigue failure of metal matrix composite laminates is often preceded by a substantial loss of stiffness associated with cyclic plastic straining and subsequent low-cycle fatigue crack growth in the matrix. Experimental observations indicate that two damage patterns evolve under cyclic loading beyond the elastic range, one formed by cracks extending along the fibers in off-axis plies, and another consisting of cracks bypassing the fibers at an angle in axially loaded plies. Damage saturation is observed under constant load amplitudes. Guided by these experiments, the damage evolution process analyzed herein is regarded as a shakedown mechanism, and damage saturation as a shakedown state. For a given program of variable cyclic loading, evaluation of crack densities needed for shakedown is formulated as a nonlinear constraint optimization problem, where the total damage in a laminate is evaluated from the minimization of a cost function that corresponds to a measure of total damage. The associated nonlinear constraints are derived from the ply yield criterion, hardening rule, and physically motivated bounds on the damage parameters. Effective elastic stiffness reduction and local stress redistribution predicted by the optimization procedure are compared with experimental measurements on B/Al laminates.