Abstract
In this work, we advocate using Bayesian techniques for inversely identifying material parameters for multiscale crystal plasticity models. Multiscale approaches for modeling polycrystalline materials may significantly reduce the effort necessary for characterizing such material models experimentally, in particular when a large number of cycles is considered, as typical for fatigue applications. Even when appropriate microstructures and microscopic material models are identified, calibrating the individual parameters of the model to some experimental data is necessary for industrial use, and the task is formidable as even a single simulation run is time consuming (although less expensive than a corresponding experiment). For solving this problem, we investigate Gaussian process based Bayesian optimization, which iteratively builds up and improves a surrogate model of the objective function, at the same time accounting for uncertainties encountered during the optimization process. We describe the approach in detail, calibrating the material parameters of a high-strength steel as an application. We demonstrate that the proposed method improves upon comparable approaches based on an evolutionary algorithm and performing derivative-free methods.
Highlights
To reduce the tremendous effort involved in experimentally characterizing the fatigue properties of components made from polycrystalline materials (Mughrabi et al 1981), complementary analytical (Stephens et al 2000) and computational strategies (McDowell 1996; Sangid 2013) are sought
The material parameters of the single crystal may be identified by comparing polycrystalline experiments to simulations on representative volume elements (RVEs) (Shenoy et al 2008), for instance based on static experiments (Herrera-Solaz et al 2014; Kim et al 2017) or in relation to hysteresis data (Cruzado et al 2017)
The final minimum error of 38.21 MPa is reached after 27 function evaluations, i.e., after 17 steps proposed by Bayesian optimization
Summary
To reduce the tremendous effort involved in experimentally characterizing the (high-cycle) fatigue properties of components made from polycrystalline materials (Mughrabi et al 1981), complementary analytical (Stephens et al 2000) and computational strategies (McDowell 1996; Sangid 2013) are sought. The material parameters of the single crystal may be identified by comparing polycrystalline (macroscopic) experiments to simulations on representative volume elements (RVEs) (Shenoy et al 2008), for instance based on static experiments (Herrera-Solaz et al 2014; Kim et al 2017) or in relation to hysteresis data (Cruzado et al 2017) Such inverse approaches were put forward for opencell metal foams (Bleistein et al 2020) and in the context of noisy thermal measurements (Sawaf et al 1995). Identifying material parameters in crystal plasticity by To overcome this intrinsic difficulty, inverse optimization techniques which build up a surrogate model (Zhou et al 2006; Sedighiani et al 2020) of the objective function turn out to be useful.
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