A probabilistic mesoscale damage detection in polycrystals using a random matrix approach
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abstract
This article is concerned with a probabilistic mesoscale damage detection in polycrystals. For this purpose, we make use of a stochastic model describing the linear elasticity matrix of material at the mesoscale. The model is constructed using a maximum entropy principle and random matrix theory and allows one to directly construct a probabilistic model for the system random matrices characterizing the constitutive behavior of the system. First, the theoretical framework and upscale scheme in the construction of the model are briefly reviewed. For each case of healthy and damaged materials, where the damage is introduced in the form of intergranular microcavities, the random matrix model is calibrated by performing simulations on an ensemble of statistical volume elements of microstructure. The calibrated models are then used in a simple coarse-scale simulation in order to explore the sensitivity of the model in detecting the location of mesoscale damages. The result shows that in most cases, one can identify the location of cracks by comparing the probabilistic description of a suitable response quantity of interest predicted for both healthy and damaged systems. Such a probabilistic description is suitable for detecting signature of fine-scale defects where the consequences are reflected at the coarse scale in the form of random fluctuations around the mean behavior. The model can be used as a predictive tool in the context of structural health monitoring and damage prognosis of metallic systems.
