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Multi-scale modeling of thermo-mechanical dynamic damage in quasi-brittle materials

Abstract : Under impact mechanical loadings, structural components made of brittle materials may be exposed to dynamic failure. The appropriate modeling of the failure mechanisms at different scales of observation and the prediction of the corresponding thermomechanical damage evolution in such materials is essential for structural reliability predictions. Experimental observations on dynamic failure in brittle materials report important cooling and heating effects in the vicinity of the crack tip. Theoretical modeling of the thermo-mechanical coupling during fracture have been generally undertaken without accounting for microstructural aspects. The objective of the present thesis is to develop a procedure to obtain macroscopic thermo-mechanical damage laws in which the damage evolution is deduced from the propagation of microcracks and the associated small-scale thermal effects in the material. We use the asymptotic homogenization method to obtain the macroscopic thermo-mechanical and damage response of the solid. A Griffith type criterion is assumed for microcracks propagating in modes I or II. Heat sources at the tips of microcracks are considered as a consequence of the energy dissipated during propagation. Frictional heating effects are also considered on the lips of microcracks evolving in the shear mode. An energy approach is developed in combination with the homogenization procedure to obtain macroscopic damage laws. The resulting thermoelastic and damage system involves strong couplings between mechanical and thermal fields. Computation of the effective coefficients allowed us to study the local response predicted by the new models. The macroscopic response exhibits strain-rate sensitivity, microstructural size effects, degradation of thermoelastic properties and specific thermal evolutions due to microcracking and frictional effects at the small scale. Distributed heat sources are present in the macroscopic temperature equation linked to damage and frictional dissipations. The implementation of the proposed damage models in a FEM software allowed us to perform numerical simulations at the structural level. We reproduced numerically experimental tests reported in the literature concerning the rapid failure of PMMA samples impact. The results obtained in the simulations are in good agreement with the experimental observations.
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  • HAL Id : tel-02940741, version 1

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Kokouvi Gbetchi. Multi-scale modeling of thermo-mechanical dynamic damage in quasi-brittle materials. Mechanics of materials [physics.class-ph]. Université de Lorraine, 2020. English. ⟨NNT : 2020LORR0049⟩. ⟨tel-02940741⟩

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