When crack tip constraint is high, the crack tip contour integral J characterises the asymptotic stress, strain and displacement fields of a stationary crack in an elastic-plastic material. In other cases, the crack tip fields can be related to J and a second parameter Q which governs the crack tip constraint. These observations are the basis of J-Q fracture mechanics assessments. In the most usual procedure J is compared to an effective, constraint-corrected fracture toughness Jc which is derived from Q and the fracture toughness of the material. The difference Jc – J is a measure of the margin of safety. The assessment procedure assumes there are no initial inelastic strains in the component or the fracture toughness specimen prior to introducing the crack and subsequent loading. However, plant components may contain inelastic strains prior to cracking arising from welding and other manufacturing or fit-up processes. This initial strain field can be established by a finite element analysis that simulates the welding and/or manufacture sequence. Weld residual stresses develop due to the accumulation of incompatible, inelastic strains, including thermal, plastic and transformation strains in the material. If a crack is inserted into an initial strain field, a procedure is required to calculate J by analysis of the resulting crack tip fields. Moreover, for the fracture assessment method to remain valid, it must be demonstrated that the values of J and Q continue to govern the onset of crack extension or fracture so that a meaningful comparison of J with Jc can be made. This paper describes a domain integral for calculating J when inelastic strains exist prior to cracking, and its implementation in the JEDI computer code. The code is used to determine J for a crack inserted into a three-point bend specimen containing an initial inelastic strain field representative of one that might develop during welding. The extent to which the crack tip stress field is characterised by J and Q is examined by comparing it to the field for high constraint, small-scale yielding conditions.
Effect of Bond Thickness on the Fracture Toughness and the Strain Field around a Crack Tip in Adhesive Joints Using Epoxy Resin Modified with Solid Rubber Particles