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Effects of plasticity on the anisotropy of the effective fracture toughness

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Abstract

This paper investigates the effects of plasticity on the effective fracture toughness. A layered material is considered as a modelling system. An elastic-plastic phase-field model and a surfing boundary condition are used to study how the crack propagates throughout the material and the evolution of the effective toughness as a function of the layer angle. We study three idealized situations where only one of the properties among fracture toughness, Young’s modulus and yield strength is taken to be heterogeneous and the others are assumed to be uniform. We observe that in the case of toughness and strength heterogeneity, the material exhibits anomalous isotropy: the effective toughness is equal to the largest of the point-wise values for any layer angle except when the layers are parallel to the macroscopic direction of propagation. As the layer angle decreases, the crack propagates along the brittle-to-tough interfaces, whereas it goes straight when the layers have different yield strength but uniform toughness. We find that smooth deflections in the crack path do not induce any overall toughening and that the effective toughness is not proportional to either the cumulated fracture energy or the cumulated plastic work. In the case of elastic heterogeneity, the material is anisotropic in the sense of the effective toughness, as the latter varies as a function of the layer angle. Four toughening mechanisms are active: stress fluctuations, crack renucleation, plastic dissipation and plastic blunting. Finally, we consider a layered medium comprised of compliant-tough-weak and stiff-brittle-strong phases, as it is the case for many structural composites. We observe a transition from an interface-dominated to a plasticity-dominated failure regime, as the phase constituents become more ductile. The material is anisotropic in the sense of the effective toughness.

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Notes

  1. Recall that these are non-dimensional quantities. The results presented in this paper are independent from the dimensions of the computational domain (see also Hossain et al. 2014; Brach et al. 2019a).

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Acknowledgements

I am delighted to acknowledge Profs. Kaushik Bhattacharya and Blaise Bourdin for their guidance and advices. I gratefully acknowledge the financial support of the U.S. National Science Foundation (Grant No. DMS-1535083 and 1535076) under the Designing Materials to Revolutionize and Engineer our Future (DMREF) Program. The development of the numerical codes used as part of this project was supported in part by a grant from the National Science Foundation DMS-1716763. The numerical simulations were performed at the Caltech high performance cluster supported in part by the Moore Foundation.

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  1. LMS, CNRS, École Polytechnique, Institute Polytechnique de Paris, 91128, Palaiseau, France

    Stella Brach

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Brach, S. Effects of plasticity on the anisotropy of the effective fracture toughness. Int J Fract 226, 181–196 (2020). https://doi.org/10.1007/s10704-020-00486-8

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