PSI - Issue 39

O.N. Belova et al. / Procedia Structural Integrity 39 (2022) 761–769 Author name / Structural Integrity Procedia 00 (2021) 000–000

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that belong to isochromatic fringes with minimal light intensity. The analysis of the experimental data uses a Java application programmed for the advanced determination of the fracture characteristics: coefficients of the Williams series expansion for the stress field in the vicinity of the crack tip. The tool allows us to collect experimental points from the photoelasticity tests on the cracked specimens. An automatic routine implemented as a Java application permits to determine the values of coefficients of higher order terms of the WE that describe crack-tip fields. These values are calculated using the over-deterministic method which is also applied to the results of the finite element analysis of some mode I and mixed mode test geometry. Hence, the Java application provides an analytical reconstruction of the crack-tip stress field through the truncated WE and enables detailed analysis of the crack-tip stress field approximation. The tool proved to be an effective tool in increasing the accuracy of experimental data by sharpening the isodromes fringe loops. The developed procedures simplify the analysis of the description of mechanical fields at a greater distance from the crack tip considerably. The digital image processing with the aid of the developed tool is performed. The points determined with the adopted tool are used further for the calculations of stress intensity factor, T-stresses and coefficients of higher-order terms in the Williams series expansion. 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 algorithm based on the classical over-deterministic method and 2) the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for minimization of the objective function. The procedure of the over-deterministic method is based on the stress field only. It is demonstrated that this approach is characterized by simplicity and accuracy. It is also shown that the BFGS method has undeniable advantages over the classical over-deterministic method. One can conclude that the holographic interferometry technique and BFGS algorithm can be applied for the accurate determination of the coefficients of the Williams power series. The holographic interferometry makes it possible to determine from experimental data, fairly and rapidly, the coefficients of the Williams series expansion including the higher order terms. Acknowledgements The work was supported by Russian Foundation for Basic Research (project 19-01-00631). References Ayatollahi, M.R., Mirsayar, M.M., Dehghany, M., 2011. Experimental determination of stress field parameters in bi-material notches using photoelasticity. Materials & Design 32(10), 4901-4098. Dolgikh, V.S., Stepanova, L.V., 2020. 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