Cross section reconstruction during uniaxial loading

The inelastic response of materials to applied uniaxial loading is typically measured using tensile or compressive specimens of initially circular cross-section. Under deformation, this cross-section may become elliptical due to anisotropic material behaviour. An optical technique for measuring the elliptical deformation of anisotropic, homogeneous cylindrical specimens undergoing uniaxial deformation is presented. It enables the quantification of anisotropic deformation in-situ and provides data for material characterisation. Three or more silhouette views of a specimen are obtained using multiple cameras or mirrored views. The positions of the edges are computed using a sub-pixel edge detection method and 3D tangent rays from the camera through these positions are calculated. These bounding tangents are used as the basis for an elliptical fit by least squares at cross sections along the length of the specimen. Stochastic error estimates are performed by simulation of the experiment. Error estimates, for the experimental set-up used, are also calculated by reconstructing elliptical prisms of precisely measured dimensions. Example reconstructions from specimens of rolled titanium deformed plastically in tension at quasi-static (7 × 10 s) and high strain rates (3× 10 s) are presented.