Cyclic J-integral: Numerical and analytical investigations for surface cracks in weldments

The cyclic J-integral (ΔJ-integral) is a crack tip parameter of elastic-plastic fracture mechanics which can be used as governing parameter for the description of fatigue crack growth (FCG) in metallic structures. In this contribution, it is applied for modelling FCG in weldments. The ΔJ-integral is determined by means of analytical approximation formulas as well as numerical methods. An analytical solution, which takes into account effects of the local ligament plasticity, was derived. This solution is based on well established methods such as R6, BS7910 and SINTAP which were modified for cyclic loading. It incorporates methods for the description of short crack closure behaviour as well as the well known analytical (long) crack closure function of Newman. A specific code was written to evaluate the ΔJ-integral numerically in the course of finite element based crack growth simulations. The code was first validated for an infinite plate with centre crack by applying elastic and elastic-plastic material behaviour. Next, the ΔJ-integral was calculated for cracks in various butt and cruciform welded joints. The results were compared with the results of the derived analytical approximation formula. A good accordance was achieved between the results. Note that the work was part of the German research cluster IBESS the aim of which was the development of a method for fracture mechanics based determination of the fatigue strength of weldments. Since the question behind the present paper was restricted to the cyclic elastic plastic crack driving force needed for the short fatigue crack propagation stage, only the geometrical aspects of weldments (i.e. the weld toe notch) are addressed here whilst other characteristics such as material inhomogeneity (HAZ) or residual stresses are discussed by other papers of this special issue.