# Cohesive model approach to the nucleation and propagation of cracks due to a thermal shock

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## Abstract

This paper studies the initiation of cohesive cracks in the thermal shock problem through a variational analysis. A two-dimensional semi-infinite slab with an imposed temperature drop on its free surface is considered. Assuming that cracks are periodically distributed and orthogonal to the surface, at short times we show that the optimum is a distribution of infinitely close cohesive cracks. This leads us to introduce a homogenized effective behavior which reveals to be stable for small times, thanks to the irreversibility. At a given loading cracks with a non-cohesive part nucleate. We characterize the periodic array of these macro-cracks between which the micro-cracks remain. Finally, for longer times, the cohesive behavior converges towards that from Griffith’s evolution law. Numerical investigations complete and quantify the analytical results.

## Keywords

Thermal shock Cohesive surface energy Crack initiation Micro-cracks Stability## Notes

### Acknowledgments

C. Cyron and J.-J. Marigo were partially supported by the French Agence Nationale de la Recherche (ANR) under Grant T-Shock (OTP J11R087).

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