PSI - Issue 42

T. Fekete et al. / Procedia Structural Integrity 42 (2022) 1684–1691 T. Fekete et al.: Extending reliability of FEM simulations… / Structural Integrity Procedia 00 (2019) 000–000

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While FE models can be a very powerful tool for simulating the plastic behavior of materials, the accuracy of the calculations depends largely on the precision of input data. Consequently, it is essential that measurements required for plastic flow curves are carried out carefully and evaluated with the required accuracy. The increase of precision can be facilitated by evaluating the measurements using DT simulations, based on the above presented theoretical background that meets the needs of corresponding applications. Plastic flow curves are typically derived from evaluation of tensile tests. In the classic arrangement, the elongation of the specimen is measured with a longitudinal extensometer. Since the elongation of the specimen –along the gauge length– can be seen to be approximately homogeneous up to the onset of necking, the stress distribution in the material can be calculated well and accurately using the formula / 0 F S σ = , where F is applied force and S 0 denotes initial cross section of the specimen. After onset of necking, neither the strain nor the stress field can be determined by the elementary formula, because the average strain determined from the longitudinal extensometer data, differs from the local strain value in the necking area, and the stress state becomes triaxial. Necking is a typical nonlinear localization process characterized by an ever-increasing variation in the geometry of the test specimen over a shorter and shorter length. As far as necking is dominated by volumetric phenomena, it is called ‘diffuse necking’, and when the appearance of new surface becomes decisive, it is called ‘localized necking’, which then rapidly leads to ultimate failure. In the presented work, the main aim is to investigate the post-necking behavior of the specimens over the ‘diffuse necking’ regime. The experiments were executed using square cross-section tensile test specimens with a square grid printed on their surface. During the experiments, two perpendicular cameras were used to observe the changes on the specimen surfaces from two perpendicular sides simultaneously –see Fig. 1., left–. Forces, crosshead, and extensometer displacements were continuously observed. The cameras were operated synchronously by the test machine. In data processing, two pairs of contour curves were determined from each pair of images, representing the contour of the sample in two perpendicular planes. The contours permitted the determination of minimal thicknesses in the two planes. With these settings, the cushioning effect could not be observed. Each specimen DT has full 3D geometry, which is meshed using hexahedron elements, including increased mesh density around the zone of contraction. The mechanical behavior of a specimen is governed by the system of equations given in Eq. (5). The structural material is assumed to be initially homogeneous and isotropic. The von Mises plasticity theory is used to describe plastic behavior, with a strain-hardening material. Boundary conditions are provided by the appropriate kinematic constraints. The calculations were performed in updated Lagrange setting, using large strain large displacement formulation. Fig. 1., right, shows a specimen's DT in initial state and after the onset of necking. 3. Description of the experiments and the Digital Twin

Fig. 1. Experimental setup (left), and the geometry of a specimen’s DT in initial state and with necking (right).