Fracture mechanics analysis of generalized compact tension specimen geometry using the mechanics of net-section

Abstract

Fracture mechanics analysis of a generalized compact tension specimen, on the basis of the mechanics of deformation of the net-section, is shown to provide a simple and a broadly useful expression for stress intensity factor calculations. A single analytical expression is found to be sufficient for the characterization of crack behavior in compact tension, extended compact tension and wedge splitting test specimens without any restriction on the specimen length (or height) and width. The analysis is enabled by the concept of the change in net-section energy, which is determined by summing the changes in strain energies of the net-section of the generalized specimen for tension and bending deformation modes, which result from the introduction of the crack. This is equivalent in concept to the increase in strain energy upon the introduction of the crack, as in the Griffith’s fracture theory. The square-root of the change in net-section strain energy parameter multiplied by the elastic modulus provides an expression that is equivalent to the conventional stress intensity factor expression. The application of the net-section based expression to the standard compact tension, the extended compact tension and the wedge-splitting test specimens shows very good agreements with the crack behaviors as expressed by the stress intensity factor expressions for the respective geometries. The proposed method enables easy analytical determination of stress intensity factors for any asymmetrically-loaded mode-I crack problem.