Crack Opening Displacement, J Integral, and Resistance Curve

Abstract

Introduction The fracture mechanics based on stress intensity factor (SIF) helped to characterize fracture in terms of the critical SIF, or fracture toughness. The application of linear elastic fracture mechanics (LEFM) became very limited for metals, in which plastic deformation preceded any crack extension. Wells (1961) experimented with variety of metals. He observed that before the onset of extension, the crack-tip blunts and there is a definite opening at the original crack-tip location. The extent of the opening is dependent on the fracture resistance of the material. The opening increases as the resistance of the material to fracture increases. He estimated the crack opening displacement (COD) at the original crack-tip location and presented the condition of fracture in terms of this parameter. This forms the basis of COD criterion of fracture mechanics. For small-scale plastic deformation at the tip, this condition is equivalent to the fracture condition in terms of Griffith potential energy release rate G I for Mode I, that is, G I = G IC , where G IC is the fracture resistance of the material. In the presence of linear or nonlinear elastic deformation at the crack-tip, the deformation field is conservative. Stress—strain relation for a material showing plastic deformation at the crack-tip, under monotonically increasing loading, is very similar to that of a nonlinear elastic material. Provided there is no unloading or crack extension, the material obeys the deformation theory of plasticity, that is, the total strain at any stage is related to the total stress, and the relationship is path independent. Rice (1968) showed that under such an elastic (linear or non-linear) deformation of a component with a crack, there exists an integral, called J integral, which is path independent when calculated joining any two points on the opposite crack flanks. Further, this integral indicates the potential energy release rate associated with the crack extension. It can characterize the onset of crack growth in the same fashion as the SIF, but it is valid even beyond the linear elastic limit. The path independence of this parameter along with its energy release rate character is shown in this chapter. Further its graphical interpretation is also given. It has been shown in the Chapter 2 that the fracture resistance of a material is constant for a purely elastic material.