Correction of post-necking stress–strain curve of copper using surface strain method

Correction of the stress–strain curve in the strained specimens after necking is one of the remarkable issues in mechanical engineering. The corrected curve strain–stress is needed to perform plastic or post-necking analysis in metals' large deformation issues. The stress becomes triaxle during the specimen's necking and includes tangential, radial, and circumferential stress components. The stress distribution is ununiformed in the necking area, and the actual stress is not obtained by dividing the force by the initial section surface. Instead, it is obtained by two different equations before and after necking. This research uses the surface strain method for a copper rod specimen on which several points are specified. The surface strain is obtained at any moment by measuring the distance between these points during the strain test using the image-processing technique. After computing the surface and radial strain, the correction factor is calculated using the relevant equations for determining the corrected actual stress values. The results are verified with the well-known results in the literature as presented by Davidenkov and Bridgham. Further, the finite element method is employed to perform numerical analysis. The commercial software ABAQUS is used to verify the results from image process analysis. The results show that determining the material model constants using the surface strain method does not require measurement of the necking radius at each moment during testing. Thus, this method outperforms the other ones in terms of simplicity, time, and accuracy. Additionally, the experimental and numerical are employed to present the corrected post-necking stress–strain curve.