Digital photoelasticity for calculating coefficients of the Williams series expansion in plate with two collinear cracks under mixed mode loading

Abstract

Photoelasticity method is used to study experimentally the complete Williams series expansion of the stress and displacement fields in the vicinity of the crack tip in isotropic linear elastic plates under Mixed Mode loading. The distribution of the isochromatic fridge patterns is employed for obtaining the stress field near the crack tip by the use of the complete Williams asymptotic expansion for various classes of the experimental specimens (plates with two collinear cracks under tensile loading and under mixed mode loading conditions). The higher order terms of the Williams series expansion are taken into account and the coefficients of the higher order terms are experimentally obtained. The stress field equation of Williams up to fifty terms in each in mode I and mode II has been considered. The comparison of the experimental results and the calculations performed with finite element analysis has shown the importance and significant advantages of photoelastic observations for the multi-parameter description of the stress field in the neighborhood of the crack tip.

Experimental and numerical analysis of size effects on stress intensity in anisotropic porous materials

“…The photoelastic fringe pattern has been used in previous research to experimentally estimate the stress intensity factor and indicate the need of the inclusion of non-singular terms in the estimation of the stress intensity factor in homogeneous specimens of varying sizes and configurations [25][26][27][28]. In porous materials, due to the widely irregular nature of the fringe pattern, the coefficients of the Williams series cannot be extracted.…”

“…The importance of the non-singular stresses in brittle materials can also be visually identified by observing the near-tip stress field by means of photoelasticity [25][26][27][28][29]. For homogeneous specimens, the photoelastic fringe pattern under mode I loading follows a concentric ellipsoidal pattern, originating at the crack tip.…”

Extraction of Fracture Mechanics Parameters From Fem Analysis: Algorithms and Procedures

“…Therefore, gaining insight on cracking processes is of crucial importance [1]. The first step in analyzing any fracturing process is to determine the crack tip asymptotic fields in order to characterize the stress, deformation and displacement near the crack tip, which requires the coefficients (unknowns) of the crack tip asymptotic field to be determined via reliable methods [1][2][3][4][5][6][7][8][9][10]. The first terms of the crack tip stress series expansion in isotropic linear elastic materials are singular, and, hence, dominant, in the proximate vicinity of the crack tip.…”

“…Therefore, in the singular dominant zone the first terms are sufficient to characterize the crack tip fields. However, at further distances from the crack tip, the importance of the higher order terms become evident [6][7][8][9][10][11]. Thus, precise and simple algorithms are needed to reliably calculate coefficients in the multi-parameter crack-tip fields.…”

“…Thus, precise and simple algorithms are needed to reliably calculate coefficients in the multi-parameter crack-tip fields. Numerical methods and in particular finite element method (FEM) [6][7][8][9][10][11] allow us to extract the crack tip parameters. Moreover, it is worth noting that even determining the stress in-tensity factor is still the subject of investigations.…”