PSI - Issue 39

O.N. Belova et al. / Procedia Structural Integrity 39 (2022) 770–785 Author name / Structural Integrity Procedia 00 (2021) 000–000

784

15

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 proposed tool proved to be an effective tool in increasing the accuracy of photoelastic data by sharpening and thinning the isochromatic fringe loops. The developed procedures simplify the description and analysis of mechanical fields at greater distances 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. 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. A photoelastic and numeric study of the stress field in the vicinity of two interacting cracks: Stress intensity factors, T-stresses and higher order terms. AIP Conference Proceedings 2216, 020014. Ganesan, V.R., Mullick, S.K., 2008. Digital image processing of photoelastic fringes – a new approach. Experimental techniques 15(5) 41-46. Ham, S.-M., Kwon, T.-H. 2020. Photoelastic observation of toughness-dominant hydraulic fracture propagation across an orthogonal discontinuity in soft, viscoelastic layered formation. International Journal of Rock Mechanics and Mining Sciences 134, 104438. Hello, G., Tahar, M.B., Roeland, J.-M., 2012. Analytical determination of coefficients in crack-tip stress expansions for a finite crack in an infinite plane medium. International Journal of Solids and Structures 49(3-4), 556-566. Hello, G., 2018. Derivation of complete crack-tip stress expansions from Westergaard-Sanford solutions. International Journal of Solids and Structures, 144-145, 265-275. Hou, C., Wang. Z., Jin, X., Ji, X., Fan, X., 2021. Determination of SIFs and T-stress using an over-deterministic method based on stress field: Static and dynamic. Engineering Fracture Mechanics 242, 107455. Jobin, T.M., Khaderi, S.N., Ramji, M., 2020. Experimental evaluation of the strain intensity factor at the inclusion tip using digital photoelasticity. Optics and Lasers in Engineering 126, 105855. Karihaloo, B.L., Xiao, Q.Z., 2001. Accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity. Eng. Fract. Mechanics 68(15), 1609-1630. Li, Y, Zheng, K., 2021. Crack tip field coefficients analyses based on the extended finite element method using over-deterministic displacement field fitting method. Theoretical and applied Fracture Mechanics 113, 102971. Liu, P., Ju, Y., Fu, G., Ren, Z., 2020. Visualization of full-field stress evolution during 3D penetrated crack propagation through 3D printing and frozen stress techniques. Engineering Fracture Mechanics 236, 107222. Malikova, L., Vesely, V., 2014. Significance of higher-order terms of the Williams expansion for plastic zone extent estimation demonstrated on a mixed-mode geometry. Procedia Structural Integrity 2014, 3 1383-1388. Mirzaeri, A.M., Aytollahi, M.R., Bahrami, B., Berto, F., 2020. Elastic stress analysis of a blunt V-notches under mixed mode loading by considering higher order terms. Applied Mathematical Modelling 78, 665-684. Patil, P., Vysasarayani, C.P., Ramji, M., 2017. Linear least squares approach for evaluating crack tip fracture parameters using isochromatic and isoclinic data from digital photoelasticity. Optics and Lasers in Engineering 93, 182-194. Pirmoradian, M., Naeeni, H.A., Firouzbakht, M., Toghraie, D., Khabaz, M.K., Darabi, R. 2020. Finite element analysis and experimental evaluation on stress distribution and sensitivity of dental implants to assess optimum length and thread pitch. Computer methods and Programs in Biomedicine 187, 105258.