Abstract
Grating techniques are used to determine the three-dimensional deformation and the tangential strain of sheet metal. A grating is fixed on the surface and taken by stereo CCD cameras in different deformation states. By suitable line-following software, the grating coordinates in the images are determined with subpixel accuracy. Using photogrammetric methods, the three-dimensional coordinates are calculated from the image coordinates. The strain usually is determined by means of a deformation gradient, which is calculated from every deformed triangle. In this paper, the gradient is determined in the center of four neighboring meshes using a polynomial approximation of the displacement function in a reference position. The influence of the nontangential deformation is considered. By simulation, a flat sheet metal is deformed to a rotational symmetric surface. The difference of the known exact strain is compared with the numerically derived strain with respect to different grating pitches. The proposed method yields good results even in the case of large spatial deformation. It is applied to the deformation of a hatlike test specimen.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Sevenhuijsen, P.J., Sirkis, J.S., andBremand, F., “Current Trends in Obtaining Data from Grids,”Exp. Tech.,27,22–26 (1993).
Andresen, K., Ritter, R. andSteck, E., “Theoretical and Experimental Investigations of Fracture by FEM and Grating Methods, Defect Assessment in Components—Fundamentals and Applications,”Mechanical Engineering Publications, London, 345–361 (1991).
Sirkis, J.S. andLim, T.J., “Displacement and Strain Measurement with Automated Grid Methods,” EXPERIMENTAL MECHANICS,31,382–388 (1991).
Andresen, K. andHübner, B., “Calculation of Strain from an Object Grating on a Reseau Film by a Correlation Method,” EXPERIMENTAL MECHANICS,32,96–101 (1992).
Andresen, K., Hentrich, K., andHÜbner, B., “Camera Orientation and 3D-deformation Measurement by Use of Cross Gratings,”Opt. Lasers Eng.,22,215–226 (1995).
Andresen, K., Lei, Z., andHentrich, K., “Close Range Dimensional Measurement Using Grating Techniques and Natural Edges,”SPIE,2248,460–467 (1994).
Lei, Z. andAndresen, K., “Subpixel Grid Coordinates Using Line Following Filtering,”Optik,100,125–128 (1995).
Sowerby, R., Duncan, J.L., andChu, E., “The Modelling of Sheet Metal Stampings,”Int. J. Mech. Sci.,28,415–430 (1986).
Stickforth, J., “The Square Root of a Three-dimensional Positive Tensor,”Acta Mechanica,67,233–235 (1987).
Bredendick, F., “Methoden der Deformationsermittlung an verzerrten Gittern,”Wiss. Zeitschrift der Techn. Uni. Dresden,18,531–538 (1969).
Eberlein, L., Feldmann, P., andRy, V. T., “Visioplastische Deformations und Spannungsanalyse beim Fliesspressen,”Umformtechnik,26,113–118 (1992).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Andresen, K. Strain tensor for large three-dimensional surface deformation of sheet metal from an object grating. Experimental Mechanics 39, 30–35 (1999). https://doi.org/10.1007/BF02329298
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02329298