Crack tip localization method based on Williams series and digital image correlation method
FENG Ruirui1, MAO Lingtao1, 2, LI Qingxiang1, YAO Yongzhou1, SONG Hongli1
(1. School of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China；
2. State Key Laboratory for Fine Exploration and Intelligent Development of Coal Resources, China University of Mining and Technology (Beijing), Beijing 100083, China)
Abstract：The stress intensity factors (SIFs) are critical parameters for evaluating crack propagation behaviour and rock mass stability. In order to improve the accuracy of SIFs determination based on Williams series and digital image correlation (DIC), this study proposes a regional search method combining displacement residuals and the Williams series term -1 to locate crack tip. Numerical simulations were conducted to systematically analyze the influence of calculation region parameters and the number of expansion terms. The variation of SIFs in mode I fractures were calculated and analyzed for polymethyl methacrylate (PMMA) and granite specimens with prefabricated cracks under three-point bending. The results indicate: (1) This method remedies the deficiency of the -1 term in the Williams series, which is only applicable to straight crack propagation, and resolves the issue of local optimal solutions encountered when using displacement residuals alone. (2) For SIF calculations, the recommended angular range for the sector region is 120°–170°. The inner radius should be 0.2 times the prefabricated crack length. The outer radius should be 1 to 2 times the prefabricated crack length, and the maximum expansion order should increase with expansion of the calculation regions. (3) In mode I rock fracture, tortuous crack propagation can be simplified to as straight crack propagation for analysis without significantly affecting SIF results.
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FENG Ruirui1, MAO Lingtao1, 2, LI Qingxiang1, YAO Yongzhou1, SONG Hongli1. Crack tip localization method based on Williams series and digital image correlation method. , 2025, 44(7): 1857-1868.
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2025, Vol. 44 
