Computational and experimental identification of coefficients of the Williams series expansion by considering higher order terms in the cracked specimens through digital image analysis

Abstract

In the study, digital photoelasticity method is used for finding of the linear elastic fracture mechanics parameters for a plate of finite width with two inclined interacting cracks. The digital image processing tool for the whole set of experimental data namely isochromatic fringes and isoclinic phase maps obtained from the photoelasticity experiments is developed and exploited. The digital image processing tool is based on the well-known Ramesh technique but allows us to scan the image in any direction and to analyse the image after any number of logical operations. The performed digital image analysis allows us to extract photoelastic data from the whole field isochromatic and isoclinic fringe patterns. In the digital image processing fringe analysis, the optical data contained in the transmission photoelastic isochromatic fringe patterns near the crack tips were converted into text file and then the points of isochromatic fringes with minimum light intensity were used for evaluating fracture mechanics parameters. The multi-point stress field description is used. The mixed mode fracture parameters, especially stress intensity factors, T-stresses and higher-order coefficients of the Williams series expansion are obtained for specimen configurations like plates with two inclined interacting cracks using 1) the algorithm based on the classical over-deterministic method and 2) the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for minimization of the objective function. It is shown that the latter method has undeniable advantages over the classical over-deterministic method. The effects of higher-order terms in the Williams expansion were analysed for different the considered cracked specimen. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values, T-stresses and higher-order coefficients estimated using the proposed method are compared with finite element analysis (FEA) results, and are found to be in good agreement.