Optimal Boundary Shape of the Center-Reduced Cruciform Specimen for the In-Plane Biaxial Test

Cruciform specimens are one of the most common used to measure the plane mechanical properties of materials. Two significant difficulties in designing cross specimens are reducing stress concentration at the intersection of cross arms and improving stress/strain uniformity in the gauge area. The shape of the border at the intersection of the cruciform specimen is tightly related to the above two. Due to the lack of guidelines for the design of cruciform specimens, optimizing the cruciform specimen border intersection is an urgent problem to be solved to increase the reliability of test results. By employing the finite element method and the shape optimization method, the boundary of the cruciform specimen is optimized, and the mathematical expression of the shape function at the intersection of the cruciform specimen’s boundary is obtained. Furthermore, experiments are used to validate the optimum border. The findings indicated that the stress concentration at the improved specimen’s boundary was reduced. The optimal shape of the cruciform specimen’s boundary intersection described in this study can be used as a reference for the structural design of the cruciform specimen and can be used for extensive strain testing of the cruciform specimen.