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A multi-interpolation method is proposed to determine the displacement trajectory along each axis of a cruciform specimen with the goal of achieving a linear stress path, corresponding to a constant stress triaxiality, in the center of the custom-designed, non-standard specimen during in-plane biaxial testing. Finite element simulations are used to obtain the stress path from the given displacement trajectory, which is the displacement histories imposed on the specimen loading arms. In every iteration, the displacement trajectory is updated using the interpolation between the target stress path and adjacent ones on each side of the curve. The iterations are repeated until a linearity tolerance is satisfied. In this study, the material is an austenitic stainless steel, SS316L, with the Hockett–Sherby isotropic hardening model and Yld2004-18p non-quadratic anisotropic yield function. The method is demonstrated for five stress states between pure shear and equibiaxial tension. The results show the successful determination of a displacement trajectory for the non-standard cruciform specimen so that a linear stress path and constant triaxiality at the area of interest are achieved. 

Abstract The automotive industry relies heavily on sheet metal forming processes for many components. Material data solely from uniaxial testing is insufficient to fully define the material behavior of the complex plastic deformation during numerical simulations of the forming processes. In-plane biaxial testing using a cruciform type specimen is a more comprehensive representation than the traditional uniaxial testing alone. Wide ranging biaxial stress states can be imposed by applying different loading conditions on each cruciform axis. However, this can create a challenge to achieve desired deformation paths due to the non-linear relationship between the control parameter, e.g., displacement, and the output of interest, e.g., strain path. In this paper, an interpolation method to develop the displacement control that produces a linear strain path with a desired strain ratio is revisited and expanded upon from the authors’ previous work [1,2]. In the first iteration, linear biaxial displacements were applied to the specimen and the corresponding strain paths were obtained from the numerical simulations. The non-linear strain paths, due to geometry effects of the specimen, were used to reverse engineer a new displacement path that results in a linear strain path. Interpolation is revisited to show increased success with a second iteration. Analysis of the simulation results shows that linear strain paths of a given model can be determined and improved by successive iterations of interpolating the strain data from adjacent deformation paths.