Yielding and mechanical failure in (amorphous) solids

Recently, a Monte Carlo simulation study [1] has shown that yielding in crystalline solids is associated with an underlying quasi-static first-order phase transition. As a consequence, in the limit of a deformation with sufficiently low strain rate, the rigid response of a crystal due to a shape change of its boundaries corresponds to a metastable state that transforms to a stable state where internal stresses are eliminated, maintaining the crystalline order. A nucleation theory based on these findings predicts the yield point as a function of strain rate and shows agreement with data from experiment and molecular dynamics (MD) simulations over 15 orders of magnitude [2]. In the case of amorphous solids (glasses), a MD simulation study, using an athermal quasi-static (aqs) deformation protocol [3], have found a sharp stress drop in the stress-strain relation that marks the transition from an elastic response of the glass to plastic flow. In Ref. [3], this stress drop has been
interpreted as a non-equilibrium first-order transition, leading to the occurrence of shear localization, i.e. shear banding, after the drop. Using MD simulations of a glassforming binary Lennard-Jones (LJ) mixture under shear, we study the conditions for the occurrence of shear bands at finite temperatures [4] and discuss the response of the LJ glass to an external
shear in the limit of zero strain rate. We argue that there is no quasi-static first-order transition as in the case of crystalline solids.

[1] P. Nath et al., Proc. Natl. Acad. Sci. USA 115, E4322 (2018).
[2] V. S. Reddy et al., arXiv:1908.08829.
[3] M. Ozawa et al., Proc. Natl. Acad. Sci. USA 115, 6656 (2018).
[4] G. P. Shrivastav et al., Phys. Rev. E 94, 042605 (2016); J. Rheol. 60, 835 (2016).