“…Gurson-like models are generally adequate to simulate predominate tensile fracture in moderate and high stress triaxiality conditions, but fail to predict fracture in the low and negative stress triaxiality domains [29]. However, recently, a modified GTN model [30,31] including a void shear mechanism emerged, enabling the analysis of ductile fracture behaviors under a wide range of triaxiality. Nevertheless, it is not easy to link FE analysis and MDM to produce results.…”
In this study, a 3D fracture locus of high-silicon steel strip was constructed through a series of fracture tests with specimens of various shapes and corresponding finite element (FE) simulations of the fracture tests. A series of FE analyses coupled with the developed fracture locus was conducted, and the effect of the secondary roll-bending ratio (defined as L2/R2, where L2 and R2, respectively, denote the secondary work roll barrel length and the radius of the convex curvature of the work roll surface profile emulating positive roll bending) and the initial notch length on edge cracking in the strip during cold rolling was investigated. The results reveal that the 2D fracture locus that does not include the Lode angle parameter (varying between −0.81 and 0.72 during cold rolling) overestimates the edge cracking in the range of 13.1–22.2%. The effect of the initial notch length on the length of crack grown in the transverse direction of the strip during cold rolling is greatest when the ratio L2/R2 is 0.12.
“…Gurson-like models are generally adequate to simulate predominate tensile fracture in moderate and high stress triaxiality conditions, but fail to predict fracture in the low and negative stress triaxiality domains [29]. However, recently, a modified GTN model [30,31] including a void shear mechanism emerged, enabling the analysis of ductile fracture behaviors under a wide range of triaxiality. Nevertheless, it is not easy to link FE analysis and MDM to produce results.…”
In this study, a 3D fracture locus of high-silicon steel strip was constructed through a series of fracture tests with specimens of various shapes and corresponding finite element (FE) simulations of the fracture tests. A series of FE analyses coupled with the developed fracture locus was conducted, and the effect of the secondary roll-bending ratio (defined as L2/R2, where L2 and R2, respectively, denote the secondary work roll barrel length and the radius of the convex curvature of the work roll surface profile emulating positive roll bending) and the initial notch length on edge cracking in the strip during cold rolling was investigated. The results reveal that the 2D fracture locus that does not include the Lode angle parameter (varying between −0.81 and 0.72 during cold rolling) overestimates the edge cracking in the range of 13.1–22.2%. The effect of the initial notch length on the length of crack grown in the transverse direction of the strip during cold rolling is greatest when the ratio L2/R2 is 0.12.
“…Pickett et al [23] suggest to add a nucleation mechanism controlled by the shear components of the plastic strain tensor. More recently Malcher et al [40] and Jiang et al [41] have used the GTN model in which the matrix flow stress (σ F ) is affected by shear damage following the Lemaitre approach [42]. The total void volume fraction is then defined as follows:…”
Section: Constitutive Equations For Damagementioning
Crack prediction is an important step of car design: its accuracy is crucial to avoid additional development costs and delays. The prediction of steel or aluminium sheets tearing is particularly challenging, and its simulation is not always reliable yet. This could be explained by the use of too simple fracture criteria based on a critical plastic strain that are uncoupled with the constitutive behavior (i.e. the material response is not affected by damage). To overcome this problem, coupled damage models are proposed in the literature. To select the appropriate constitutive equations to model the plastic and fracture behavior of a given material, various characterization tests are needed. A comprehensive experimental campaign that covers a wide range of stress states and loading rates was conducted. All tests can be performed on a tensile machine. From the results, an original set of constitutive equations was chosen from the literature to propose an extended Gurson-based damage model. A practical parameter identification procedure is proposed to calibrate the model on a few relevant specimen geometries. The model is then validated on another set of specimen geometries: comparisons between test results and simulations show a good agreement in terms of loaddisplacement curves for both quasi-static and dynamic loading conditions.
“…To analyze the strain distribution in this figure, an assumption, which was proposed by Chen and proved by Jiang, was introduced. 21,23 Namely, in the necking process, there is no shear stress in the principal stress plane, which means, the volume element surrounded by six adjacent principal stress surfaces can still maintain the shape of a cuboid after incremental deformation. Figure 6.The geometric relation on the principal stress plane.…”
In this study, the necking three-dimensional strain on minimum cross-section at room temperature was performed experimentally and analytically. A modified strain assumption was applied to overcome significant errors in calculating necking strain by Bridgman assumption. Then, one relatively simple strain distribution function was deduced based on equilibrium equation of necking element. To obtain the parameters in this function, the monotonic tensile tests in two kinds of carbon structure steels Q235 and Q345 were carried out. Meanwhile, the Aramis system based on digital image correlation method was adopted to measure the surface axial strain and deformation parameters during the loading process. The experimental and numerical results were compared with the traditional Bridgman strain assumption. The maximum axial strain calculation error the strain distribution function and experiment value was less than 8%, which was obviously less than that calculated by Bridgman assumption. Additionally, the variation law of the three-dimensional strain calculated by this function was consistent with that obtained by the macroscopic analysis of fracture surface. The application of traditional Bridgman formula can be expanded by this study. Meanwhile, it can provide a new idea to study the stress distribution characteristics and better understanding of ductile materials’ deformation properties.
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