Implementing multiple biaxial-tension proportional loading paths using double elliptical dies

Abstract

When sheet metals are integrally formed into complex thin-walled components, to determine the forming scheme, establishing an accurate material model is essential. Traditional biaxial loading experiments are used to test the properties of sheet metals. However, a single test can only obtain the deformation behavior under one stress state. Multiple experiments are required to realize different loading paths to fully test the mechanical properties of the sheet under various stress states. To simplify test procedure and obtain multiple loading paths on a specimen by one single test, a bulge test method for sheet metal using a double elliptical die is proposed. The study is carried out on a cold-rolled 304 stainless steel sheet. To assess the stress state at various points along the symmetry line of the bulging zone, a mechanical analysis model is established. The feasibility of the double elliptical die bulge test method for achieving multiple loading paths by both simulations and experiments. Furthermore, the effect of variations in the elliptical ratios of the double elliptical die on the bulging results is analyzed. The findings suggest that during the single bulging process with double elliptical die, the stress path of points on symmetry line of the bulging zone follows a linear trajectory. The relationship between the upper and lower limits of the stress ratio (α_max and α_min) on the symmetry line of the bulging zone and the first elliptical ratio of the double elliptical die (λ₁) is found to be: α_max=0.56λ₁+0.82, α_max−α_min=0.5λ₁. The stress ratio α is defined as a numerical result: the ratio of the in-plane principal stresses σ_RD and σ_TD. By adjusting the value of λ₁, biaxial loading experiments within a specific stress ratio range can be realized based on this principle.