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Using continuum damage mechanics (CDM) for lifetime prediction requires numerical integration of evolving damage until the onset of failure. The primary challenge for the simulation of structural fatigue failure is caused by the enormous computational costs due to cycle-by-cycle temporal integration throughout the whole loading history, which is in the order of 103–107 cycles. As a consequence, most approaches circumvent this problem and use empirical methods such as Wöhler curves. They are well suited for approximating the lifetime, but they are not capable to capture a realistic degradation of the material including redistribution of stresses. The main objective of the paper is to provide a technique for finite element (FE) simulations of structures under fatigue loading while reducing computational costs.
A Fourier transformation-based temporal integration (FTTI) scheme is proposed, which adapts the conventional FE method for modeling the viscoplastic deterioration in a structure subjected to cyclic loading. The response fields are represented by a Fourier series which assumes a temporal scale separation: a microchronological (short time) scale arises from the oscillatory loading and a macrochronological (long time) scale is due to the slow material relaxation resulting from yielding and damage evolution. The original dynamic boundary value problem (BVP) is approximated by the stationary BVP on the microchronological scale. Alternation of the displacement field on the macrochronological scale is correlated with evolution of the history variables by means of a high order adaptive cycle jump method. Performance and significant acceleration of the FE simulations is demonstrated at different loading scenarios for a constitutive damage model where the progressive damage accumulation is driven by viscoplastic yielding.
Computational methods for lifetime prediction of metallic components under high-temperature fatigue
(2019)
The issue of service life prediction of hot metallic components subjected to cyclic loadings is addressed. Two classes of lifetime models are considered, namely, the incremental lifetime rules and the parametric models governed by the fracture mechanics concept. Examples of application to an austenitic cast iron are presented. In addition, computational techniques to accelerate the time integration of the incremental models throughout the fatigue loading history are discussed. They efficiently solve problems where a stabilized response of a component is not observed, for example due to the plastic strain which is no longer completely reversed and accumulates throughout the fatigue history. The performance of such an accelerated Integration technique is demonstrated for a finite element simulation of a viscoplastic solid under repeating loading–unloading cycles.