Experimental study on the interaction between two cracks by digital photoelasticity method: construction of the Williams series expansion

Abstract

The multi-point Williams series expansions for the near-crack-tip fields in the vicinity of two interacting cracks in an isotropic linear elastic material are experimentally and numerically determined. The experimental method used to study the interaction of two cracks is the digital photoelasticity method which is applied for determination of coefficients of the higher-order terms of the Williams series expansion for a plate of finite width with two interacting cracks. The digital image processing tool for handling of the entire set of experimental data isochromatic fringes and isoclinic phase maps obtained from the photoelasticity experiments is developed and exploited. The digital image processing tool is relied on the classical Ramesh technique but enables to scan the experimental image in any direction and to analyse the image after any number of logical operations. The realized digital image analysis allows us to extract photoelastic data from the entire field isochromatic and isoclinic fringe patterns. In the digital image processing fringe analysis, the optical data contained in the transmission photoelastic isochromatic fringe patterns in the vicinity of the crack tips are converted into text file and then the points of isochromatic fringes with minimum light intensity are used for estimating linear elastic fracture mechanics parameters. The multi-parameter stress field description with the first fifteen terms 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 interacting cracks using 1) the classical over-deterministic method in the form based on the stress field and 2) the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for minimization of the objective function. It is demonstrated that the BFGS method has indisputable advantages over the classical over-deterministic method. The significance of higher-order terms in the Williams expansion is proved for 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. This verifies the experimental analysis