Theoretical and experimental study on constitutive modeling of sheet metal under proportional loading path

Based on the principle of plastic work equivalent per unit volume, Drucker flow rule and isotropic hardening model, a new expression of stress-strain relationship of biaxial tension for different loading paths, which used firsthand uniaxile tension test data, were derived from existing yield criteria such as Hill48, Hill90, Barlat89, Hosford and Mises yield criteria. The true stress true strain curves of two kinds of steel sheet, BH220 and SPEN, for loading ratios 1 : 1 and 2 : 1 were determined from uniaxial tension and formulae obtained above. It is found that for steel sheet the calculated true stress-true strain curves based on the Hosford, Barlat89 and Mises criteria are much better agreement with the experimental data points, whereas Hill48 overestimates the values. This result is consistent with the result obtained in previous paper. It shows that the constitutive model presented here is useful and the isotropic hardening rule is correct in proportional loading path for sheet with in-plane isotropy.