The digital photoelasticity method and finite element analysis for determination of the multi-point crack-tip field series expansions for notched semi-disks

Abstract

The digital photoelastic method for the construction of the multi-point crack-tip series expansions in isotropic elastic semi-disks is employed. The series of cracked specimens in the form of the semi-disk with vertical and inclined notches from optically active materials (polycarbonates) were produced and tested under three-point bending. The principal intent of this experimental procedure of the phototelasticity technique was estimation of the amplitude coefficients in the Williams expansion in which the non-singular high-order terms are taken into account. The first ten coefficients in the multi-point series expansion have been ascertained. To retrieve the points belonging to the isochromatic fringe patterns and having the minimum light intensity the digital image processing scheme was utilized. The scheme of the over-deterministic method for evaluation of the amplitude coefficients (fracture mechanics parameters) is applied. Additionally, the problem was reduced to the problem of minimizing the objective function which is the quadratic form for the stress field in terms of unknown fracture mechanics parameters. The finite element analysis for the same series of the notched specimens was performed. The demeanour of the stress field in the neighbourhood of the notch tip for different types of mixed mode loading was elucidated from finite element analysis. The coefficients of the asymptotic presentation of the stress and displacement fields are recovered from finite element results. It is shown that the multi-point coefficients are in good agreement with experimental observations.