Spatiotemporal Analysis of Nonaffine Displacements in Disordered Solids Sheared Across the Yielding Point
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THE atomic level understanding of the structure–property relationship of amorphous materials is important for numerous structural and biomedical applications.[1–3] By now it is well established that an elementary plastic event in disordered solids involves a collective rearrangement of a small group of neighboring particles, or the so-called shear transformation.[4,5] It was recently argued that mechanical yield in amorphous solids is a first-order phase transition from a limited set to a vast number of atomic configurations.[6] In the past, the yielding transition and the strain localization during startup deformation at a constant rate were repeatedly observed in atomistic simulation studies.[7–13] In particular, it was found that at the critical strain, the disordered systems exhibit a power-law distribution of mobile regions, which belongs to the universality class of directed percolation.[11] Remarkably, the percolation of clusters of nonaffine deformation at the yielding transition were directly observed in experiments on strained colloidal glasses.[14] More recently, molecular dynamics simulations of metallic glasses showed the exponential correlation of nonaffine displacements with a decay
NIKOLAI V. PRIEZJEV is with the Department of Mechanical and Materials Engineering, Wright State University, Dayton, OH 45435. Contact e-mail: [email protected] Manuscript submitted October 29, 2019. Article published online April 28, 2020 METALLURGICAL AND MATERIALS TRANSACTIONS A
length that was related to the size of shear transformation zones in the elastic regime of deformation.[13] Although the yielding phenomenon in deformed disordered systems is ubiquitous, the complete picture, including the exact form of spatial correlation of nonaffine displacements and the failure mechanism, remains not fully understood. In recent years, molecular dynamics simulations were widely used to examine structural relaxation and mechanical properties of amorphous solids subjected to time periodic deformation.[15–32] Most notably, it was found that in the athermal quasistatic limit, following a number of subyield cycles, the disordered systems reach the so-called limit cycle, a dynamic steady state of reversible particle dynamics, and, in addition, the size of clusters of particles undergoing cooperative rearrangements becomes comparable with the system size at the critical strain amplitude.[18] During periodic deformation at a finite temperature, the majority of particles undergo reversible nonaffine displacements with amplitudes that approximately follow a power-law distribution.[19,21] Interestingly, some particles were found to escape their cages temporarily while still undergoing periodic nonaffine displacements during several cycles at strain amplitudes below the critical value.[19] At sufficiently large strain amplitudes, the yielding transition occurs after a number of transient cycles for both slowly and rapidly annealed glasses, and the transition is associated with the formation of a shear band across the system and the
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