Application of Inherent Stress Methodology to Linear Fracture Mechanics

Abstract

Linear fracture mechanics (LFM) is a powerful tool to describe the stress/strain field near a crack tip in an elastic body by means of the concept of stress intensity factor. However LFM being based on an elastic theory, there is limit in application of LFM to a real crack which has a plastic zone at the tip.An inherent stress methodology is one of the methods to calculate welding residual stress by an elastic theory. The concept of virtual external and body forces is used as operators for the calculation. These two operators are used basically to describe a welded deformation, but also are usuful to describe a plastic deformation by an elastic theory.Being represented plastic deformation of large scale yielding by virtual external and body forces, the application of LFM becomes wide because it is possible to adapt the theory of superposition for plastic problems.In this paper, above operators are introduced into a cohesive force model such as Dugdale model and new cohesive force model with consideration of inherent strain in a plastic zone is proposed, from the previous study of an inherent stress methodology on welded residual stresses and deformations. Then we calculate COD for center cracked tension specimens with various crack length by the new proposed model.It is seen that COD by the new model is almost the same as and slightly smaller than that by Dugdale model. However it is recognized that the hypothetical crack seems to reach the free edge of the specimen ahead of a crack for the specimen before applied stress comes to yield stress in Dugdale model. This may be because the decreased effect of K value due to plastic deformation is ignored in Dugdale model. On the contrary, it is recognized to show the tendency that the hypothetical crack tip approaches to the free egde of a center cracked plate in the new model, when the applied net stress comes to yield stress. It becomes also clear that the growth of plastic zone by the new model is equal to or less than that by Dugdale model.