Abstract
High-speed forming processes, such as electrohydraulic forming, have recently attracted attention with the development of forming technology. However, because the high-speed operation (above 100 m/s) raises safety concerns, most experiments are conducted in a closed die, which hides the forming process. Therefore, the experimental process can only be observed in a numerical simulation with accurate material properties. The conventional quasistatic material properties are improper for high-speed forming simulations with high strain rates (>102 s−1). In this study, the material properties of Al 6061-T6, which reflect the deformation behavior in the high-strain-rate region, were investigated in a numerical approach based on a reduced order model and a surrogate model in which the numerical results resemble the experimental results. The strain rate effect on the material was determined by the Cowper–Symonds constitutive equation, and two strain rate parameters were predicted. The surrogate model takes two material parameters as inputs and outputs a weighting coefficient calculated by the reduced order model. The surrogate model is based on the Kriging method to reduce the simulation cost. Next, the optimal material parameters that minimize the error between the surrogate model and the experiments are estimated by nonlinear least-squares optimization using a genetic algorithm and the constructed surrogate model. The predicted optimal parameters were verified by comparing the results of the experiment, numerical simulation, and surrogate model.
Highlights
Forming processes under quasistatic conditions have developed alongside many technological advances in sheet metal forming at high speeds, such as electrohydraulic forming (EHF), electromagnetic forming (EMF), and explosive forming (EF) [1,2,3]. ese forming processes deform a sheet metal within 1 ms by a high-energy pulse, such as a high-voltage discharge or a high-energy explosion
The material parameters for Al 6061-T6 under the electrohydraulic forming process were estimated by a surrogate model based on a reduced order model (ROM) and the Kriging method
Works and findings from this study are as follows: (1) Using 20 training samples extracted from a specific domain of the two material parameters C and p, we performed numerical simulations in LS-DYNA and extracted the eigenvectors and eigenvalues by principle component analysis. e first eigenvector represented the whole numerical model by preserving over 98% variance of the original simulation data, which was taken as the basis vector for the numerical simulation
Summary
Forming processes under quasistatic conditions have developed alongside many technological advances in sheet metal forming at high speeds (above 100 m/s), such as electrohydraulic forming (EHF), electromagnetic forming (EMF), and explosive forming (EF) [1,2,3]. ese forming processes deform a sheet metal within 1 ms by a high-energy pulse, such as a high-voltage discharge or a high-energy explosion. High-speed forming processes such as EHF cannot be observed during tests because the sheet deformation is finished within 1 ms and conducted in a closed room for safety purposes. To increase the reliability of the numerical model, the obtained material properties must minimize the error between the experimental and simulation results. The experimental approach directly obtains the material properties, it is both costly and time consuming To avoid this problem, we proposed a numerical approach that estimates the parameters in the material model by a surrogate model with nonlinear least-squares optimization.
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