3D Strain measurement from gratings on both surfaces of sheet metal

Summary  The deformation of thick sheet metal is analyzed using 3D coordinates of cross-gratings on both sides of a specimen. The basic equations are presented for evaluating the 3D strain tensor from displacement functions. Provided the grating coordinates are measured in the undeformed and the deformed states, the difference of the coordinates yields displacement vectors. These are used to determine polynomial displacement functions, which approximate the displacement vectors in a least-squares sense. The condition of volume invariance at plastic deformation implies the strain in the direction of the thickness. The whole procedure is tested by a radial symmetric forming of a rectangular sheet metal into a half-tube, because it can be evaluated analytically, too. Finally, a real forming process of a plane circular sheet metal into a cup-like object is analyzed. Received 10 May 1999; accepted for publication 22 September 1999