Multi-interpolation Method to Linearize Stress Path in Cruciform Specimen for In-Plan Biaxial Test

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.