Procedure for accurate calculation of the J-integral from digital volume correlation displacement data

The application of digital image and volume correlation techniques to obtain displacement fields from images has become ubiquitous in experimental fracture mechanics. In this paper, a procedure to extract the J-integral (J) from three-dimensional displacement fields obtained using digital volume correlation is presented. The procedure has been specially adapted to allow for experimental noise and errors, such as poorly defined crack front displacements, smearing of the displacement field across the crack faces, and knowledge of the imprecise crack front location. The implementation is verified using analytical crack-tip fields perturbed with synthetic image correlation errors to characterise the response of J. The method is then applied to experimental results using a Magnesium alloy WE43 loaded elastically in mixed mode. The steps outlined are intended as a guideline for the application of the volume integral from displacement fields to allow for accurate calculation of J along a crack front embedded within the volume