A basic ductile fracture testing program is carried out on specimens extracted from TRIP780 steel sheets including tensile specimens with a central hole and circular notches. In addition, equi-biaxial punch tests are performed. The surface strain fields are measured using two- and three-dimensional digital image correlation. Due to the localization of plastic deformation during the testing of the tensile specimens, finite element simulations are performed of each test to obtain the stress and strain histories at the material point where fracture initiates. Error estimates are made based on the differences between the predicted and measured local strains. The results from the testing of tensile specimens with a central hole as well as from punch tests show that equivalent strains of more than 0.8 can be achieved at approximately constant stress triaxialities to fracture of about 0.3 and 0.66, respectively. The error analysis demonstrates that both the equivalent plastic strain and the stress triaxiality are very sensitive to uncertainties in the experimental measurements and the numerical model assumptions. The results from computations with very fine solid element meshes agree well with the experiments when the strain hardening is identified from experiments up to very large strains.

Hybrid experimental–numerical analysis of basic ductile fracture experiments for sheet metals

We focus on the importance of accurately describing the flow behaviors of metallic materials to be cold formed; we refer to several valuable examples. We review the typical experimental methods by which flow curves are obtained, in addition to several combined experimental-numerical methods. The characteristics of four fundamental flow models including the Ludwik, Voce, Hollomon, and Swift models are explored in detail. We classify all flow models in the literature into three groups, including the Ludwik and Voce families, and blends thereof. We review the experimental and numerical methods used to optimize the flow curves. Representative flow models are compared via tensile testing, with a focus on the necking point and pre- or post-necking strain hardening. Several closed-form function models employed for the non-isothermal analyses of cold metal forming are also examined. The traditional bilinear C-m model and derivatives thereof are used to describe the complicated flow behaviors of metallic materials at cold forming temperatures, particularly in terms of their applications to metal forming simulations and process optimization.

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A Review of Flow Characterization of Metallic Materials in the Cold Forming Temperature Range and Its Major Issues

An advanced post-necking analysis methodology for elasto-plastic material models identification

An Advanced Post-Necking Analysis Methodology for Elasto-Plastic Material Models Identification

Nowadays, many studies concerning plasticity and numerical simulations indicate that the true stress–strain curve plays a prominent role in the analysis of metal deformation. Hence, a new method is considered to correct the stress–strain curve based on image processing. Since the axial stress mainly becomes triaxial in the neck zone, the relationship obtained from the engineering stress–strain curve is not reliable in terms of authenticity and accuracy. Accordingly, correcting this relationship is highly advantageous and necessary. Due to the triaxial state of stress in the plastic area, longitudinal and surface strains are calculated through image processing and the correction coefficient of the stress–strain curve is obtained based on them. The equation of the stress–strain curve is based on the Hollowman relation until the onset of necking and then becomes almost linear. The finite element method (FEM) is employed for validating the obtained results. Since the corrected stress and strain equation is linear, the objective function of optimization is considered. This optimization is based on minimizing the difference between the three diameters values of the specimen, which are observed through experiment and FEM. Besides, a statistical method with the help of the genetic algorithm is employed to minimize this difference. As a result, an optimal equation is predicted for the 2024 aluminum based on the stress–strain curve of the error rate. Finally, a comparison is made between the results obtained from the surface strain method and the results obtained from the classical methods of Bridgman and Davidenkov, and a good agreement is observed between them.

Correction of the stress–strain curve for 2024 aluminum alloy after necking using the new 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.

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

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