Size effects and strain localization in atomic-scale cleavage modeling

Abstract

In this work, we study the adhesion and decohesion of Cu(1 0 0) surfaces using density functional theory (DFT) calculations. An upper stress to surface decohesion is obtained via the universal binding energy relation (UBER), but the model is limited to rigid separation of bulk-terminated surfaces. When structural relaxations are included, an unphysical size effect arises if decohesion is considered to occur as soon as the strain energy equals the energy of the newly formed surfaces. We employ the nudged elastic band (NEB) method to show that this size effect is opposed by a size-dependency of the energy barriers involved in the transition. Further, we find that the transition occurs via a localization of bond strain in the vicinity of the cleavage plane, which resembles the strain localization at the tip of a sharp crack that is predicted by linear elastic fracture mechanics.

A Molecular Simulation Approach to Bond Reorganization in Epoxy Resins: From Curing to Deformation and Fracture

“…The fracture of our samples is the combination of two processes: damage nucleation (which might be seen as crack-nucleation) and damage coalescence (which might be interpreted as crack propagation) and can therefore not be directly interpreted in terms of fracture mechanics. Furthermore, it must be noted that the peak-stress as well as the failure strain strongly depend on the sample, as (i) larger samples can contain larger pre-existing defects, which locally intensify the stress as described by the stress intensity factor K , thereby reducing the required external loading for crack propagation and (ii) the elastically stored energy available for crack propagation scales with the sample dimension along the loading direction, i.e., in computer simulations, larger samples fracture at smaller strains than smaller samples . The results presented in the manuscript can therefore not be directly compared to experimental results.…”

“…Furthermore, it must be noted that the peak-stress as well as the failure strain strongly depend on the sample, as (i) larger samples can contain larger pre-existing defects, which locally intensify the stress as described by the stress intensity factor K , thereby reducing the required external loading for crack propagation 38 and (ii) the elastically stored energy available for crack propagation scales with the sample dimension along the loading direction, i.e., in computer simulations, larger samples fracture at smaller strains than smaller samples. 39 The results presented in the manuscript can therefore not be directly compared to experimental results. However, our results can be used to inform continuum models like the cohesive zone model (CZM).…”

Fracture ab initio: A force-based scaling law for atomistically informed continuum models

“…If the theoretical strength is simply identified with the maximum of the derivative of the energy-displacement curve, it decreases with an increasing number of planes parallel to the cleavage plane. 37 However, the amount of energy that localizes and is subsequently released during the fracture process is in fact finite, 39 and the seemingly sizedependent fracture stress can be normalized to obtain the unique strength of the material. 40 Thus, a scaling approach via the elastic energy is practical, but not well justified, and a physically meaningful coarse-graining scheme providing an unambiguous connection between the macroscopic and microscopic stresses is still needed.…”

High-throughput screening of the static friction and ideal cleavage strength of solid interfaces

“…This approach is commonly known as rigid body separation and more information about its application can be found in the Supplementary Information. It provides reliable upper limits for the ideal tensile strengths of materials 37 and was shown to be well justified by comparison to a simulation of a crack tip under mode 1 loading 32 .…”