Shape optimization of a cruciform geometry for biaxial testing of polymers

The presented literature review of cruciform shapes used for biaxial characterization of materials indicates that the majority of shapes can be divided into two large groups when the following selection criteria are taken into consideration: (i) the shape of the outer boundaries and (ii) the load capacity needed to achieve failure in the biaxial region. Manipulation of the outer shape boundaries appears to be essential to bundle the applied loads to the central zone where failure is intended to be built up. For each group, one particular cruciform design is reported whereby the outer boundaries are based on a single curved shape. Although the use of discontinuous double radii edges should be avoided according to earlier reports [1,2], it is shown here through the construction of an optimization algorithm, that the use of a single curve for the outer boundaries leads to strains in the arms that are strongly dependent on these single curved edges. Numerical simulations based on the finite element method as well as experiments performed on polymeric test pieces in combination with DIC measurements, show good agreement on this matter and demonstrate this sensitivity very clearly.