Estimation of Material Model Parameter using Bayesian Data Assimilation and Biaxial Tensile Test
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Aluminum alloys are essential for automotive lightweighting. Realizing efficient plastic forming processes for aluminum alloys requires accurate prediction of deformation behavior during plastic forming using finite element (FE) simulation. To accurately predict the deformation behavior using the FE simulation, identifying the parameters of material models is necessary. The parameters of material models have been identified based on experimental data obtained from multiple material tests. However, the parameter identification based on the experimental data is a time-consuming task. This study proposes estimating all nine parameters of the Yld2000-2d yield function from the results of a single biaxial tensile test (BTT). In this method, strain distributions on a specimen, measured by Digital Image Correlation (DIC), are integrated into the FE simulation of BTT using Bayesian data assimilation to estimate the parameters. A Tree-structured Parzen Estimator [1] is used to determine the parameters (optimally estimated parameters) that minimize the difference between the experimental and BTT simulation results. To evaluate the accuracy of the optimally estimated parameters obtained in this study, the FE simulations of BTT are performed under two conditions: once with the optimally estimated parameters and once with the literature parameters identified through uniaxial tensile and hydraulic bulge tests [2], and the results of these FE simulations are compared with the experimental data. In the BTT, the specimen fractured 120 seconds after the start of the test (xx = yy =120 MPa). Comparison of the maximum principal strain distributions immediately before fracture (xx = yy =120 MPa) revealed that the FE simulation using the optimally estimated parameters reproduced the experimental results with an accuracy close to that of BTT simulation using the literature parameters derived from multiple tests. Consequently, this study confirms that the proposed data assimilation approach successfully estimates material parameters with sufficient accuracy while avoiding the need for multiple experimental calibrations.
