Tensile strength and fracture toughness of brittle materials

Abstract

The fracture properties of brittle materials under tension have been explained by many authors; however, questions such as the dependence of the tensile strength on the crack tip radius of curvature and the scatter of fracture toughness are still not well explained from fundamental principles. This work aims to address this question by using a force-atomistic approach: we analyze the forces that act in the solid down to the smallest dimensions in an atomistic context, verifying the satisfaction of the static equilibrium condition given by Newton’s second law up to the beginning of the rupture. We take into account the forces due to the applied stress, which may be very large at crack tips, and the material cohesion forces, particularly at the point of largest local strain and stress concentration, where the local hyperelasticity of the material plays a governing role. By considering and connecting microstructure and atomicity, and using an experimentally proved maximum tensile-stress criterion for fracture, here we obtain an expression for the tensile strength of the brittle materials, where an effective local cohesive stress is defined. Thus, we explain in a unified framework from fundamental principles a set of established experimental results of brittle fracture of materials under tension, including the dependence of the tensile strength on the crack tip radius of curvature and some scatter in reported values of fracture toughness and cleavage surface energy. This work can be useful to make more realistic predictions of fracture properties of brittle materials taking into account microstructure and atomicity.