A Unified Approach Toward Simulating Constant and Varying Amplitude Fatigue Failure Effects of Metals with Fast and Efficient Algorithms

A new finite strain elastoplastic $$J_{\mathrm {2}}$$ -flow model is established with an explicit formulation of work-hardening and softening effects up to eventual failure, in which both a new flow rule free of yielding and an asymptotically vanishing stress limit are incorporated. The novelties of this new model are as follows: (i) Fatigue failure effects under repeated loading conditions with either constant or varying amplitudes are automatically characterized as inherent response features; (ii) neither additional damage-like variables nor failure criteria need to be involved; and (iii) both high- and low-cycle fatigue effects may be simultaneously treated. A fast and efficient algorithm of high accuracy is proposed for directly simulating high- and medium–high-cycle fatigue failure effects under repeated loading conditions. Toward this goal, a direct and explicit relationship between the fatigue life and the stress amplitude is obtained by means of explicit and direct procedures of integrating the coupled elastoplastic rate equations for any given number of loading–unloading cycles with varying stress amplitudes. Numerical examples suggest that the new algorithm is much more fast and efficient than usual tedious and very time-consuming integration procedures.