•Plasticity and fracture experiments are performed on AA6013.•The Yld2004-18p yield criterion is calibrated, including an evolving exponent.•The fracture strains are determined by a hybrid ...experimental-numerical approach.•The fracture strains are also estimated based on grain distortion and rotation.•Oyane, Johnson–Cook and Hosford–Coulomb fracture models are calibrated.
The anisotropic plastic flow and ductile fracture of AA6013 aluminum sheet is investigated under quasistatic conditions. The plasticity of the material is probed through uniaxial tension, plane-strain tension and disk-compression experiments, from which the Yld2004-18p non-quadratic 3D anisotropic yield criterion and the combined Swift-Voce hardening model are calibrated. The ductile fracture is characterized with two notched-tension (different notch radii), one center-hole tension and one shear experiment. These experiments cover a wide range of stress triaxialities, while requiring only a universal testing machine to be conducted. Digital Image Correlation is used throughout the experiments to assess the surface strain fields. The predictions of three plasticity models, i.e., von-Mises and Yld2004-18p with constant and with evolving exponents and the corresponding Swift-Voce curves, are compared to the measured force–displacement curves and surface strain histories. These models are then used to probe the stresses, strains, stress triaxiality and Lode angle parameter throughout the loading to fracture. It was found that this hybrid experimental-numerical approach for the fracture strain determination is very sensitive to the constitutive model adopted. As an independent assessment, a microstructure-based estimation of the fracture strains is described. This verified that the von–Mises yield criterion for this AA6013 aluminum sheet provides erroneous estimates of the fracture strains. The most suitable constitutive model is the Yld2004-18p with evolving exponent. Based on these results, the fracture loci are represented by the Oyane, Johnson–Cook and Hosford–Coulomb models.
•Experiments and analysis of hole expansion of aluminum alloy by a flat-headed punch•Digital Image Correlation is used to obtain the strain fields throughout the process•The hardening curve of the ...material is identified by probing the diffuse neck•Shell finite element model of hole-expansion using Yld2000-2D is developed•Both structural (force-displacement) and local (thinning) features are well predicted
The expansion of a circular hole in an orthotropic sheet of AA6022-T4 is examined using a combination of experiments and analysis. This deformation mode is accomplished by stretching a hole at the bottom of a cup during drawing in a hydraulic press with a flat-headed punch. The strain fields are acquired continuously throughout the hole-expansion experiment, using stereo-type Digital Image Correlation. This reveals that despite the axisymmetry of the set-up, non-uniform thinning is observed around the hole throughout the expansion, due to the anisotropy of the material. The greatest thinning occurs at ±45° from the rolling direction. The strains that develop at the hole periphery are significantly higher than the uniform elongation in uniaxial tension (true strain of 0.37 vs. 0.18, respectively). Furthermore, the strain paths change from uniaxial tension around the hole to plane-strain tension and biaxial stretching farther away. The experiments are simulated using finite element analysis. The orthotropy of the material is modeled with the non-quadratic anisotropic yield criterion Yld2000-2D, calibrated by uniaxial tension, plane-strain tension and disk compression experiments. Special attention is placed on the identification of the large-strain hardening curve, which is accomplished by acquiring the strain fields inside the growing neck in uniaxial tension, and using them to minimize the difference between internal and external work. For the material at hand, the Voce hardening law is found to provide the best fit, while the impact of plastic anisotropy on the identification is negligible. It is shown that this modeling framework not only reproduces the structural behavior (e.g., the punch force-displacement) very well, but it also provides accurate predictions of the thinning variation around the hole.
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•Plasticity and fracture of heat treated aluminum sheet is characterized.•New cruciform specimen is proposed that has proportional loading paths to fracture.•Fracture locus is determined by hybrid ...experimental-numerical method.•Plasticity modeling is critical for the fracture locus; Yld2004-18p criterion is used.
The ductile fracture of an AA6111 aluminum sheet after a thermal cycle typical of auto-body paint-baking is investigated with the hybrid experimental-numerical method. The plastic flow of the material is examined by uniaxial tension, plane-strain tension, disk-compression and notched-tension experiments, that are used to calibrate the Yld2004-18p anisotropic yield criterion and the combined Swift-Voce hardening model. Then, the fracture behavior under equibiaxial and plane-strain tension, as well as uniaxial tension and shear, is characterized using a specially-developed cruciform specimen, along with center-hole and shear specimens, respectively. The cruciform fracture specimen proposed here contains two shallow hemispherical depressions (dimples) in the test-section, to initiate fracture. For the fracture characterization, special emphasis is put on specimen design, so that the stress states developed at the neighborhood of the fracture initiation point remain proportional throughout the loading history. In all experiments, the surface strain fields are measured by a stereo-type digital image correlation system. This information is used to validate finite element simulations of the fracture experiments. It is found that the Yld2004-18p model provides a better agreement with experiments than von Mises does, which underscores the sensitivity of the hybrid method to the plasticity models adopted. Once validated, these simulations are used to obtain the fracture loci in terms of two stress-state metrics, i.e., the stress triaxiality and Lode angle parameter.
Micromechanical-based finite element simulations were carried out to investigate the transient plastic strain rate evolutions of ferrite and martensite dual-phase steel during strain path changes. A ...representative volume element (RVE) was generated through a three-dimensional (3D) reconstruction of microstructure images which were acquired from sequential polishing of a small material volume. The 10 × 10 × 10 μm3 3D RVEs consisted of martensite islands embedded in a ferrite base matrix. Each phase was assumed to exhibit distinct mechanical properties but the grain and phase boundary effects were ignored in this work. The effective mechanical properties for the constituent phases were assumed to be well defined by the von Mises or Hill 1948 yield criteria, the associated flow rule, and an empirical isotropic hardening equation based on chemical composition. This model was applied to investigate the transient behavior of the r-value (Lankford coefficient) in uniaxial tension when the loading direction changed. In addition to monotonic tension, compression-tension, and tension-orthogonal tension, sequences were considered. The simulation results captured well in a qualitative manner the experimental r-value evolutions in terms of a temporary transition and asymptotic limit. The evolutions of stress states in ferrite and martensite were analyzed to explain the r-value behavior that resulted from three factors: (1) r-value differences between ferrite and martensite, (2) martensite configuration-induced stress state in phases, and (3) stress partitioning and its evolution during non-proportional loading. Finally, an analytical relationship between the stress evolution in the constituent phases and the relevant r-value changes is suggested.
•A 3D representative volume element is generated from real microstructure of DP780.•The plastic strain dependent r-value evolution of DP780 is investigated.•The stress partitioning in ferrite and martensite are analyzed.•The analysis shows a strong correlation with r-value transition and loading history.•An analytical model for the stress redistribution and r-value change is proposed.
The plastic anisotropy and ductile fracture behavior of an Al–Si–Mg die-cast alloy (AA365-T7, or Aural-2) is probed using a combination of experiments and analysis. The plastic anisotropy is assessed ...using uniaxial tension, plane-strain tension and disc compression experiments, which are then used to calibrate the Yld2004-3D anisotropic yield criterion. The fracture behavior is investigated using notched tension, central hole and shear specimens, with the latter employing a geometry that was custom-designed for this material. Digital image correlation is used to assess the full strain fields for these experiments. However, fracture is expected to initiate at the through-thickness mid-plane of the specimens and thus it cannot be measured directly from experiments. Instead, the stresses and strains at the onset of fracture are estimated using finite element modeling. The loading path and the resulting fracture locus were found to be sensitive to the yield criterion employed, which underscores the importance of an adequate modeling of plastic anisotropy in ductile fracture studies. Based on the finite element modeling, the fracture locus is represented with three common criteria (Oyane, Johnson–Cook and Hosford–Coulomb), as well as a newly proposed one as the linear combination of the first two. However, beyond that, it is still questionable if all of these experiments are probing the same fracture locus, since the predicted loading paths of notched tension specimens are highly evolving compared to those of central hole and shear ones.
The influence of yield function parameters on hole-expansion (HE) predictions are investigated for an anisotropic AA6022-T4 aluminum sheet. The HE experiment is performed in a fully-instrumented ...double-action hydraulic press with a flat-headed punch. Full strain fields are measured by a stereo-type digital image correlation (DIC) system. The stress state gradually changes from uniaxial to plane-strain tension to biaxial tension in the radial direction. Besides HE, the plastic anisotropy of AA6022-T4 is characterized by uniaxial tension and plane-strain tension experiments. Uniaxial tension is considered as the most important, since it is the stress state along the hoop direction in the hole. For the finite element (FE) simulation, the Yld2000-2d non-quadratic anisotropic yield function is used with two different parameter sets, calibrated by: (1) uniaxial tension only (termed Calib1) and, (2) both uniaxial and plane-strain tension (Calib2). The strain field predictions show a good agreement with the experiments only for Calib2, which takes into account plane-strain as well uniaxial tension. This indicates the importance of biaxial modes, and in particular plane-strain tension, for the adopted yield function to produce accurate HE simulations.
In this study, the mechanical responses of Ti–6Al–4V alloy sheets at a high temperature under multi-axial loading were investigated using a micromechanics-based damage model within a continuum finite ...element (FE) framework. Tensile tests at three strain rates and a high temperature were conducted to analyze the plastic and ductile damage properties of the Ti–6Al–4V alloy sheets. Additionally, hot Nakajima tests were conducted on specimens with three different shapes to evaluate the improvement in formability at a high temperature. Moreover, the dimples on the fractured surfaces of the experimental samples were qualitatively analyzed. Simultaneously, corresponding FE simulations were conducted to predict the ductile damage behavior of the Ti–6Al–4V alloy sheets at a high temperature using a modified Gurson−Tvergaard−Needleman model. The predicted results and the displacements at the onset of failure were compared with the corresponding experimental data.
In this study, the ductile damage responses of high-strength 7000 series aluminum alloy (AA), AA 7075-T6 sheet samples, subjected to the plane strain deformation mode were investigated using finite ...element (FE) simulations. In the experiments, uniaxial tension (UT) and plane strain tension (PST) tests were conducted to characterize the plasticity and ductile damage behavior of the AA 7075-T6 sheet samples. The limiting dome height (LDH) and V-die air bending tests were conducted to evaluate the ductility of the material subjected to plastic deformation and friction between the tools, and the corresponding fractured samples were qualitatively analyzed in terms of dimples using fractography. FE simulations were performed to predict the ductility of the AA 7075-T6 sheet samples under plane strain deformation using an enhanced Gurson−Tvergaard−Needleman (GTN) model, namely the GTN-shear model. The model was improved by adding the shear dimple effect to the original GTN model. The predicted results in terms of the load–displacement curves and displacements at the onset of failure were in good agreement with experimental data from the aforementioned tests. Furthermore, virtual roll forming simulations were conducted using the GTN-shear model to determine the effect of the prediction on ductile behavior for industrial applications.
The plasticity and formability of a commercially-pure aluminum sheet (AA1100-O) is assessed by experiments and analyses. Plastic anisotropy of this material is characterized by uniaxial and ...plane-strain tension along with disk compression experiments, and is found to be non-negligible (e.g., the r-values vary between 0.445 and 1.18). On the other hand, the strain-rate sensitivity of the material is negligible at quasistatic rates. These results are used to calibrate constitutive models, i.e., the Yld2000-2d anisotropic yield criterion as the plastic potential and the Voce isotropic hardening law. Marciniak-type experiments on a fully-instrumented hydraulic press are performed to determine the Forming Limit Curve of this material. Stereo-type Digital Image Correlation is used, which confirms the proportional strain paths induced during stretching. From these experiments, limit strains, i.e., the onset of necking, are determined by the method proposed by ISO, as well as two methods based on the second derivative. To identify the exact instant of necking, a criterion based on a statistical analysis of the noise that the strain signals have during uniform deformation versus the systematic deviations that necking induces is proposed. Finite element simulation for the Marciniak-type experiment is conducted and the results show good agreement with the experiment.
Robustness of numerical models paves the way for efficient compensation of perturbations resulting in deviations from the nominal conditions. This is critical if the numerical simulations will be ...used to determine closed-loop process control adjustments to assure the final part quality. This work details the procedure to establish and validate numerical process models, through an investigation of deep-drawing of AA1100-O blanks using 3D Servo Press. Of particular interest is the robustness of the deep-drawing simulation models to different process variations and off-design conditions. The experiments are performed on a 3D Servo Press, used as a conventional press, and equipped with a spring-loaded blank holder. From the experiments, the punch force–displacement as well as local features, i.e., flange draw-in and wall-thinning, are obtained. Two types of finite element models of the drawing process are created, one using shell and the other using solid elements. Correspondingly, the plastic anisotropy of the blanks is modeled using the Yld2000-2d (2D) and Yld2004-18p (3D) yield functions. The friction coefficient between the blank and tooling is inversely identified by comparing the simulated punch force–displacement response, flange draw-in and thickness variations with the experimental ones. The robustness of the numerical and material models is confirmed by process variations on the geometry of the blanks, i.e., an initial offset of blank center and elliptical blanks. However, the wrinkling of the flange due to variation of the blank holder force is not captured by the model. A modification to the model, i.e., by introducing appropriate geometric imperfections to the blank, enables it to predict the flange wrinkling. This work investigates the robustness of numerical models to different types of process variations, which is vital in model-based control analyses.
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