Analytical Model of Quasi-Brittle Fracture of a Plate with Crack

Abstract

The paper considers a rectangular plate with the edge crack of mode I of normal separation from the elastoplastic material with the ultimate strain. This class of materials includes, for example, the low-alloy steels used in structures operating at temperatures below the cold brittleness threshold. The strength of the plate was studied within the framework of the Neuber --- Novozhilov approach. The crack propagation criterion was formulated using the modified Leonov --- Panasyuk --- Dugdale model using an additional parameter, i.e., the plasticity zone diameter (pre-fracture zone width). Under conditions of small-scale yielding in the presence of the stress field singular feature in the vicinity of the crack tip, the two-parameter (dual) criterion for quasi-brittle fracture was formulated for mode I cracks in the elastoplastic material. The fracture dual criterion included deformation criterion at the crack tip, as well as the force criterion at the fictitious crack tip. The lengths of the original and fictitious cracks were differing by the length of the pre-fracture zone. Diagrams of the plate quasi-brittle fracture under conditions of plane deformation and plane stress were constructed. The parameters included in the proposed quasi-brittle fracture model were analyzed. It was proposed to select model parameters according to the approximation (σ--ε)-diagram of uniaxial tension and the KIc critical stress intensity factor