A numerical lattice method to characterize a contact fatigue crack growth and its Paris coefficients using configurational forces and stress-life curves

Paris' law material constants have computationally been determined using the implications of Configurational Mechanics and total stress-life curves to characterize fatigue crack growth rate, which is a challenge in experimental programs for measuring these parameters. A 2D plane strain lattice approach with a brittle erosion algorithm was employed to characterize total fatigue life and fracture behavior of propagating cracks of a pad-substrate system under high-cycle fatigue loadings in the context of LEFM. The capability of the lattice in predicting the direction of crack tip extension was validated by comparing with the analytical results of a center inclined cracked domain under uniaxial direct tension and also the surface crack initiation angle of the contact fatigue pad-substrate system. The lattice not only does fairly predict the Paris' coefficients comparing to experimental measurements in literature, but also obtains total fatigue life by assuming a failure value for the crack length and demonstrates a curved fatigue crack. Having a simple constitutive formulation and a straightforward erosion algorithm, the numerical lattice can be integrated with the proposed fatigue fracture approach to obtain the Paris' material constants, contact fatigue life, and crack propagation path.