Holographic interferometry experiments and numerical analyses of the stress field on the Williams series expansion: higher – order terms

Abstract

The study is aimed at experimental and numeric determination of the higher order coefficients of the Williams power expansion for the near crack-tip fields in isotropic linear elastic materials by two approaches. The first one is based on the experimental method of holographic interferometry, the second one is relied on the finite element analysis. The main problem and difficulty are accurate extracting the coefficients from the whole set of experimental data. To obtain the higher order coefficients of the Williams expansion the program tool which is designed for digital image processing of the experimental fringe patterns. As the first step the plate with the horizontal central crack has been chosen since this cracked geometry is thoroughly studied and the coefficients of the higher order terms are known. The stress intensity factors, T-stress and higher order coefficients are extracted and compared with the theoretical values. Then the mixed mode loading is considered. Using holographic interferometry a lot of tests with the inclined cracks were performed. It is shown that the digital holographic method and the developed programming tool allow us to find the coefficients with high accuracy. The results of digital image processing of the experimental data have been verified and confirmed by the finite element analysis.