Sources of Fracture Toughness: The Relation Between KIc and the Ordinary Tensile Properties of Metals

Abstract

This paper examines crack extension from a metallurgical standpoint. Stress and strain intensification at the crack tip and the basic flow and fracture properties of the material are considered. Insights derived from etchpitting experiments are reviewed. These reveal the two characteristic types of local yielding: (1) plane strain or “hinge-type” relaxation and (2) plane stress or through-the-thickness relaxation. Two simplified elastic-plastic treatments that model plane strain and plane stress are identified. They offer approximate equations connecting K (the stress intensity parameter) with the plastic zone size and the crack-tip displacement, which are in good accord with experiment. They also help to define limiting conditions for plane strain and plane stress. A method of relating the crack-tip displacement to the peak strain is described, and this is combined with a critical strain criterion for ductile fracture. In this way, the plane strain fracture toughness parameter KIc is formulated in terms of ordinary tensile properties: KIc≈23EYn2ϵ¯* (E is the modulus, Y the yield stress, n the strain hardening exponent, and ε-* the true strain at fracture of a smooth tensile bar). This expression is shown to be in good accord with available data on a variety of titanium, aluminum, and steel alloys. Since the influence of composition and heat treatment on tensile properties is already established in many cases, the tensile properties can now serve as a link between fracture toughness and the backlog of metallurgical experience. This possibility is demonstrated for Type 4340 steel heat treated to different strength levels.