Three-dimensional shear angle determination with application to shear-frame test

The shear frame test is very often used in the context of plastics engineering to examine only the fiber construction for its deformability. Here, it is common to assume a homogeneous deformation, which apparently exists as a global deformation due to the shear frame. This results in the assumption of a constant overall shear angle. In this paper, we compare two analytical approaches to describe the deformation and the resulting strains in detail, particularly, the local shear angle calculation. As a second step, the extension of the shear angle computation based on curvilinear, three-dimensional surface deformations is applied to optical results of the experimental deformation behavior. For this purpose, a three-dimensional image correlation system is drawn on to determine the local, tangential shear angle even for folded fabrics. This requires an approach which is different to the classical digital image correlation method since the speckle varnish influences the deformation of the very compliant fiber bundles. In a third step, the same procedure is applied to the results of three-dimensional finite element computations since the programs do not provide the shear angle measure. The shear angle determination is discussed at various examples. As a side result of the investigations, the material parameters for orthotropic elasticity are determined using a representative volume element approach exploiting μ-CT data. Although the wrinkling prediction calculations depend on the pre-deformation, finite element discretization, and uncertainties of the specimens, calculation results might be used as an indicator to improve the specimen geometries.