Characterization and modeling of mixed-mode I+III fracture in brittle materials
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Mixed-mode I+III fracture in brittle materials presents spectacular, scale-independent pattern formation in nature and engineering applications; and it is one of the last remaining puzzles in linear elastic fracture mechanics. This problem has received much attention in the literature over the past few decades both from experiments and analysis, but there are still open challenges that remain. Specifically, the existence of a threshold ratio of mode III to mode I loading below which fragmentation of the crack front (formation of daughter cracks) does not occur and the length scale associated with the spacing of the fragments when they do occur are still under debate. The continued growth of cracks under remote mode I + III loading is also of interest; it is observed that in some cases the fragmented cracks coalesce, while in others they maintain their independent development. We approach this problem through carefully designed experiments to examine the physical aspects of crack initiation and growth. This is then explored further through numerical simulations of the stress state that explore the influence of perturbations on the formation of daughter cracks. We show that a parent crack subjected to combined modes I+III loading exhibits fragmentation of the crack front into daughter cracks without any threshold. The distance between the daughter cracks is dictated by the length scale corresponding to the decay of the elastic field; this decay depends on the characteristic dimension of the parent crack from which the daughter cracks are nucleated. As the daughter cracks continue growing, they coarsen in spacing also through elastic shielding. As the daughter cracks grow farther, the parent crack, pinned at the original position, experiences increased stress intensity factor and the bridging regions begin to crack and the parent crack front advances towards the daughter cracks. This establishes a steady state condition for the system of parent crack with equally spaced daughter cracks to continue growing together. Finally, direct numerical simulation of crack initiation and growth is explored using a phase-field model. The model is first validated for in-plane modes I + II through comparison to experiments, and then used to explore combined modes I + III in order to study the above mechanism of mixed-mode I + III crack growth.