Decohesion models informed by first-principles calculations: The ab initio tensile test

Abstract

Extreme deformation and homogeneous fracture can be readily studied via ab initio methods by subjecting crystals to numerical “tensile tests”, where the energy of locally stable crystal configurations corresponding to elongated and fractured states are evaluated by means of density functional method calculations. The information obtained can then be used to construct traction curves of cohesive zone models in order to address fracture at the macroscopic scale. In this work, we perform an in depth analysis of traction curves and how ab initio calculations must be interpreted to rigorously parameterize an atomic scale cohesive zone model, using crystalline Ag as an example. Our analysis of traction curves reveal the existence of two qualitatively distinct decohesion criteria: (i) an energy criterion whereby the released elastic energy equals the energy cost of creating two new surfaces and (ii) an instability criterion that occurs at a higher and size independent stress than that of the energy criterion. We find that increasing the size of the simulation cell renders parts of the traction curve inaccessible to ab initio calculations involving the uniform decohesion of the crystal. We also find that the separation distance below which a crack heals is not a material parameter as has been proposed in the past. Finally, we show that a large energy barrier separates the uniformly stressed crystal from the decohered crystal, resolving a paradox predicted by a scaling law based on the energy criterion that implies that large crystals will decohere under vanishingly small stresses. This work clarifies confusion in the literature as to how a cohesive zone model is to be parameterized with ab initio “tensile tests” in the presence of internal relaxations.