Fatigue failure in two-dimensional glasses under cyclic shear deformation

Abstract

We investigate fatigue failure in two-dimensional (2D) model glasses under cyclic shear deformation using atomistic simulations. We find that the number of cycles to failure diverges as a power law as the strain amplitude approaches the fatigue limit, with an exponent close to $-1$, in contrast to the exponent of $-2$ reported in three dimensions (3D). A failure exponent of $-1$ has also recently been observed in a 2D elastoplastic model, suggesting an interesting dependence on spatial dimensionality that needs to be rationalized. Measures of accumulated plastic activity, including dissipated work and non-affine displacements, exhibit scaling with the failure time that is consistent with results in 3D, and indicate a robust connection between damage accumulation and failure. To probe the origins of the variability of failure times, we perform isoconfigurational {\it seeded} simulations in which a localized soft region is introduced. While such seeding constrains the spatial location of failure, the distribution of failure times remains broad. These findings extend recent results in 3D concerning fatigue failure times to 2D glasses, including their relation to accumulated plasticity and apparent stochasticity, while also revealing a key difference, namely the exponent describing the divergence of the failure times.