Identification of friction coefficients and strain-compensated Arrhenius-type constitutive model by a two-stage inverse analysis technique

Abstract In this work, a two-stage inverse analysis technique is proposed to identify the friction coefficients during hot compression test of aluminum alloy 6N01 (AA6N01) and its material parameters in the strain-compensated Arrhenius-type constitutive model. Firstly, the minimal shape error between the measured and simulated specimen is set as the optimization objective. Based on the material parameters obtained by a traditional linear fitting method, the friction coefficient under each forming condition is obtained by the first-stage inverse analysis method. Secondly, on the basis of the obtained friction coefficients and taking the minimal error between the experimental and predicted forces as the optimization objective, 16 unified material parameters in the constitutive model are identified by the second-stage inverse analysis method. Then above two stages are combined together to realize loop calculation: the first-stage inverse analysis provides friction coefficients for the identification of material parameters while the second-stage updates new material parameters for identifying better friction coefficients. When the average error ( E r (friction)) between friction coefficients obtained at the current and last loop is less than 5%, the whole identification process comes to the end and the optimized friction coefficients and material parameters are obtained. Results show that the maximum shape error is only 2.48%, which indicates that the obtained friction coefficients can reflect the practical lubrication conditions between the tooling head and specimens. Additionally, at low strain rates (0.01, 0.1 and 1 s −1 ), the predicted forces have a good agreement with experimental ones. While at high strain rate (10 s −1 ), some discrepancy exists between the predicted and experimental results and the maximum error arrives at 8.58%. But the global predicted error is only 4.2%, which verifies that the proposed model and obtained material parameters can describe well the rheological behavior of AA6N01 at elevated temperatures. By comparing the predicted forces obtained by the inverse analysis and traditional linear fitting method, it is found that the predicted forces by the inverse analysis are more close to experimental data. Therefore, it can be concluded that more accurate material parameters can be obtained and provided for the numerical simulation of the extrusion process of AA6N01 using the two-stage inverse analysis technique proposed in this paper.