Stretch forming of isotropic materials: Influence of the ratio between yielding in pure shear and uniaxial tension on the stress state

Abstract

Abstract. The formability of metallic sheets could be assessed by performing a hydraulic bulge test. For isotropic materials, interpretation of the bulge test is usually done using the von Mises yield criterion. F.E. simulations of bulge tests were conducted to study how the specificities of the plastic behavior of an isotropic material influences the strain paths and stress paths experienced during hemispherical and elliptical bulging. In this paper, we investigate the role played by the ratio between the yield stresses in pure shear and uniaxial tension of the material, τ_y \/σ_T on the mechanical behavior during hydraulic bulging. To this end, we make used of the Drucker yield criterion, which can describe the mechanical behavior of isotropic materials with different ratios τ_y \/σ_T with a unique parameter c. For c = 0, the Drucker criterion reduces to the von Mises yield criterion (i.e. τ_y \/σ_T=1\/√3 ) while for c ≠0, it involves dependence on the third invariant of the stress deviator, J_3. Finite element predictions using the yield criterion reveals a correlation between the ratio τ_y \/σ_T which is uniquely defined in terms of the parameter c and the level of plastic strains that develop in the dome, the thickness reduction at the top of the apex, and the strain paths achieved in an elliptical bulge test.