Application of configurational mechanics in characterizing contact fatigue life and its crack propagation: a numerical lattice-based approach

Abstract

A numerical lattice-based approach equipped with a brittle erosion algorithm and material forces in the context of LEFM and configurational mechanics is introduced to analyze contact fatigue life and crack propagation of brittle solids under low amplitude cyclic loading using the classical Paris’s law. Material force vectors at lattice nodes were employed in identifying potential crack path in high-cycle fatigue applications. A 2D plane strain pad-substrate system with contact formulations under constant compression and cyclic sinusoidal shear with constant amplitude was considered to investigate fatigue crack’s growth rate and its shape in the substrate, made of hydrided brittle Zircaloy-4 used in nuclear industry. The capability of the lattice in predicting the crack extension path using the material force vectors at the crack tip is verified by comparing with analytical solutions for a centered crack domain under pure shear and direct tension loading, and also for an initial small surface crack for the contact fatigue pad-substrate system. Obtaining the total fatigue life by assuming a failure value for the crack length and confirming the Paris’ law crack growth, the lattice results demonstrate that the fatigue crack path in the substrate is a curved trajectory which gradually reduces as the fatigue crack tip grows deeper into the substrate. Having simple constitutive formulation and straightforward erosion algorithm, this approach together with configurational mechanics implications can be employed in analyzing fretting fatigue problems.