Size Effects in Solid Mechanics Due to Topology Transformation during Crack Growth

Abstract

A pseudo-elastic multi-damage analysis is carried out by utilizing the threepoint bending test as structural geometry and the strain energy density theory as crack growth criterion. An elastic-softening constitutive law is considered and the damage of the material is obtained by decreasing elastic modulus and fracture toughness in relation to the strain energy density absorbed in the volume element. In this way, the strain energy density factor S results to be a linear function of the crack length a when both crack growth and structural behavior are in their respective stable stages. The S-a straight line shifts upwards when the size increases. The non-similarity in the mechanical and fracture behavior, when the structural size varies, is due to the different physical dimensions of two parameters involved in the analysis: the strain energy density and the strain energy density factor. When the structural size is higher than a certain limit, the stable crack growth stage is impossible and only the unstable and brittle crack propagation can occur. Vice versa, when the structural size is very small, the unstable crack growth ceases to occur and the stable propagation corresponds to a global collapse of a different nature (ultimate strength or plastic flow).