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Description
The classical phase-field approach [1] assumes a homogenized distribution of the critical energy release rate, which leads to catastrophic failure and brittle fracture [2,3]. However, experiments on the fracture behaviour of rubber-like materials imply the existence of a ductile-like progressive failure mechanism [4,5]. The sensitivity of the material parameters governing elastic mechanical response doesn't play a strong role on the the bulk response of test specimens. However, the crack initiation and crack path are more sensitive to perturbations on the fracture parameters. Exploring this behaviour is important, as progressive crack growth is crucial in understanding the fatigue failure of rubberlike materials.
This study institutes samplings in critical entropic energy and material parameters using various probability distributions to capture inherent stochasticity in rubber-like materials. To validate the concept, experiments were conducted on die-cut V-shaped, double-edge notched specimens of unfilled styrene-butadiene-rubber (SBR), revealing non-repetitive response of crack paths and varying load-displacement curves beyond the threshold for crack initiation. Results obtained using die-cut specimens demonstrated ductile-like fracture behaviour, whereas laser-cut specimens exhibited sharp brittle fracture behaviour, demonstrating the sensitivity of the crack initiation on the initial flaws and defects on the surface. In addition to in-house experiments, data obtained from the literature were used for validation. Analysis of the simulations and experiments have shown that ductile-like fractures grow in an irregular manner and follow ornate, non-linear paths for both asymmetrical and symmetrical specimens with the introduction of stochasticity in material and fracture parameters. The study challenges the classical approach in phase-field fracture mechanism for rubber-like materials and offers insights for future work on fracture and fatigue crack growth.
References
[1] Miehe, C., Hofacker, M., Welschinger, F. (2010). A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering, 199, 2765-2778.
[2] Açıkgöz, K., \& Dal, H., (2022). A generalized phase-field approach for the failure of rubberlike materials. Constitutive Models for Rubber XII, 312–320.
[3] Schänzel, L., Dal, H., Miehe, C., (2013). Phase field modeling of fracture in rubbery polymers. Constitutive Models for Rubber VIII, 335–341.
[4] Wu, J., McAuliffe, C., Waisman, H., Deodatis, G. (2016). Stochastic analysis of polymer composites rupture at large deformations modeled by a phase field method. Computer Methods in Applied Mechanics and Engineering, 312, 596-634.
[5] Açıkgöz, K., Tanış, B. E., Dal, H., (2024). A stochastic phase-field approach for the failure of rubberlike materials. Constitutive Models for Rubber XIII,accepted.
