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Continuum damage modeling of dynamic crack velocity, branching, and energy dissipation in brittle materials

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Abstract

This study is aimed at evaluating continuum scale predictions of dynamic crack propagation and branching in brittle materials using local damage modeling. Classical experimental results on crack branching in PMMA and the corresponding nonlocal modeling results by Wolff et al. (Int J Numer Meth Eng 101(12):933, 2015) are used as a benchmark. An isotropic damage model based on a frame-invariant effective strain is adapted. Mesh objectivity is achieved by calibrating the damage model for a suitable element size and subsequently retaining that mesh size in all subsequent analyses. Crack propagation and branching are predicted by simulating accurately the test conditions. It is found that a local, rate-independent damage model considerably overpredicts the dynamic crack velocity and the extent of crack branching. Subsequently, the effect of various strain rate-dependent phenomena, viz. material viscoelasticity, rate-dependent strength, fracture energy, and failure strain is evaluated. Incorporating the material strain rate effects is found to improve the predictions and match the test data. In this regard, radially scaling the damage law is found to work the best. Despite an overprediction of micro-branching, the macro-crack branching is found to occur in agreement with the Yoffe instability criterion. Overall, various experimentally observed aspects of dynamic cracks are reproduced, including acceleration of cracks to a steady state velocity, increased micro-branching and macro-branching with increased strain rates, and crack velocity dependence of energy dissipation and fracture surface area.

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Acknowledgements

Research was sponsored by the Army Research Office and was accomplished under Grant number W911NF-19-1-0312. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

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  1. Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY, 11794, USA

    Taufiq Abdullah & Kedar Kirane

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  1. Taufiq Abdullah
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Correspondence to Kedar Kirane.

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Abdullah, T., Kirane, K. Continuum damage modeling of dynamic crack velocity, branching, and energy dissipation in brittle materials. Int J Fract 229, 15–37 (2021). https://doi.org/10.1007/s10704-021-00537-8

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