• Strain Measurement;
  • Grid Technique;
  • Nonlinear Analysis of Strain;
  • Lagrangian Description of Material Flow


Plastic behavior and formability of materials are generally characterized by measured plastic strain remained in the deformed part. Thus the importance of determination of ultimate strain encourages researchers to reexamine available methods. The grid technique has been known as a suitable method for determination of strain distribution. Regardless of method used to emboss grids, formulation of the problem can directly affect accuracy of obtained results. Available methods only consider the displacements of nodal points in deformed grid to calculate the strains. This paper describes a modification to an embossed grid-based strain measurement technique in severe plastic deformation with especial application in machining processes. The idea is to drop the assumption that grid lines remain straight within the grid cell and to utilize information provided by curved grid lines to improve the accuracy of the method. The method has a mathematical base and is related to the use of polynomial shape functions in finite element method for isoparametric elements with mid-nodes. The results of this study indicate that in the case of large plastic deformation the strains calculated by existing linear formulation and the developed nonlinear formulation deviate significantly, with the nonlinear formulation predictions being much closer to the actual values.