Principle of Local Symmetry in Mixed-Mode Fracture in Hydrogels
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When brittle materials are subjected to uniaxial tensile stress, we observe planar crack propagation perpendicular to the loading direction. However, when additionally subjected to an out-of-plane shear stress (mixed mode), the crack front deviates, leading to fragmentation in the form of twisting facets [1]. Conventional linear fracture mechanics does not adequately describe this effect unless additional criteria are assumed [2]. Among these, the principle of local symmetry, which states that fractures propagate in shear-free directions, is prominent but lacks robust experimental validation [3]. Here, we study fractures in hydrogels under mixed loading by obtaining 3D tomographic images of the growing crack. From the geometry of the evolving crack coupled with finite element analysis, we deduce the stress field near the fracture front and find clear evidence that the principle of local symmetry governs the fragmentation. Our results indicate that the finite size of the fragmentation pattern's facets and their elastic interactions account for deviations from the principle of local symmetry, providing new insights into fracture mechanics. [1] Pollard, D.D., Segall, P., Delaney, P.T.: Formation and interpretation of dilatant echelon cracks. Geol. Soc. Am. Bull. 93(12), 1291–1303 (1982). [2] Lazarus, V. , et al.: Comparison of predictions by mode II or mode III criteria on crack front twisting in three or four point bending experiments. Int. J. Fract. 153, 141-151 (2008). [3] Pham, K., Ravi-Chandar, K.: Further examination of the criterion for crack initiation under mixed-mode I+III loading. Int. J. Fract. 189, 121–138 (2014).