Evaluation of stresses in a combined plane strain-simple shear test

A biaxial testing device for sheet metal has been developed that can impose a combination of plane strain and simple shear deformation. The specimen has a large width to height ratio and a small height to thickness ratio. The forces in tensile and shear direction are easily measured and the tensile stress and shear stress can easily be derived. For a full description of stresses, however, the stress in lateral direction should also be known. This stress is a result of the constraint, imposed by the large width to height ratio and cannot be measured directly. The strain in the specimen is measured on the surface. By imposing the Drucker normality principle, the direction of the tangent to the yield surface is known and the unknown stress increment in lateral direction can be obtained. Computer simulations are performed to test whether the intended approach can recalculate all stress components from measurement of 3 in-plane strains and just 2 stresses. Without hardening, good results are obtained for a complete interval between the pure shear point up to a point between uniaxial stress and the plane strain point on the yield locus. With hardening, the algorithm requires a lot of data points to avoid drifting from the exact solution. It is noted that, although the normality rule is used, it is not necessary to have an a-priori knowledge of the yield function