Plasticity Characterization by Deriving Non-Linear Displacements for In-Plane Biaxial Cruciform Testing

In-plane biaxial testing using a cruciform type specimen is a useful experimental method to characterize the elasto-plastic material behavior under non-uniaxial conditions. Different stress states can be imposed to the specimen simply by varying loading ratios along two orthogonal axes. Experiments can be performed using one experimental setup and one specimen geometry. Among different control options for loading, the displacement control in each arm is a stable and consistent option to keep the static deformation rate. However, a non-linear relationship exists between the control parameter e.g., displacement, and derived quantities, e.g., stress and strain. Therefore, it is a challenge to achieve desired deformation paths in the main deformation area of the specimen. In this document, an interpolation method to systematically determine non-linear displacement paths is implemented using the finite element simulation method to produce linear stress and strain paths in the center of a cruciform specimen geometry. Interpolation is first applied to an AISI 1008 steel specimen, in which a previously interpolated linear strain path is improved with another iteration of interpolation. Interpolation is then expanded to produce displacement paths resulting in linear stress paths, having a constant stress triaxiality, for five different stress states of a SS304L cruciform specimen. The versatility of the interpolation method is displayed through the successful implementation for both strain and stress linearization as well as with two different materials and two specimen geometries