Obtaining the J-integral by diffraction-based crack-field strain mapping

The analysis by diffraction of polycrystalline materials can determine the full tensor of the elastic strains within them. Point-by-point maps of elastic strain can thus be obtained in fine-grained engineering alloys, typically using synchrotron X-rays or neutrons. In this paper, a novel approach is presented to calculate the elastic strain energy release rate of a loaded crack from two-dimensional strain maps that are obtained by diffraction. The method is based on a Finite Element approach, which uses diffraction data to obtain the parameters required to calculate the J-integral via the contour integral method. The J integral is robust to uncertainties in the crack tip position and to poor definition of the field in the crack vicinity, and does not rely on theoretical assumptions of the field shape. A validation of the technique is presented using a synthetic dataset from a finite element model. Its experimental application is demonstrated in an analysis of a synchrotron X-ray diffraction strain map for a loaded fatigue crack in a bainitic steel.