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Lee, J.Y.,Lee, J.W.,Lee, M.G.,Barlat, F. Pergamon Press ; Elsevier Science Ltd 2012 International journal of solids and structures Vol.49 No.25
In this work, a constitutive model based on anisotropic hardening was used in the finite element (FE) simulations of springback and its performance was compared with that of conventional hardening laws. The homogeneous yield function-based anisotropic hardening (HAH) model (Barlat et al., 2011), considered in this work, describes a partial distortion of the yield surface under plastic loading. Although it does not use the concept of kinematic hardening, the HAH model was able to predict the complex material behavior upon load reversals such as the Bauschinger effect, transient hardening and permanent softening. For the application to springback, FE simulations were conducted for U-draw/bending of base (as-received) and pre-strained DP780 steel sheets, which was recently proposed as one of the Numisheet 2011 benchmark problems. The predictions with the HAH model, combined with a non-quadratic anisotropic yield function and a plastic strain-dependent unloading modulus, were in good agreement with experimental results for both as-received and pre-strained DP780 sheets.
Characterization of the post-necking strain hardening behavior using the virtual fields method
Kim, J.H.,Serpantie, A.,Barlat, F.,Pierron, F.,Lee, M.G. Pergamon Press ; Elsevier Science Ltd 2013 International journal of solids and structures Vol.50 No.24
The present study aims at characterizing the post-necking strain hardening behavior of three sheet metals having different hardening behavior. Standard tensile tests were performed on sheet metal specimens up to fracture and heterogeneous logarithmic strain fields were obtained from a digital image correlation technique. Then, an appropriate elasto-plastic constitutive model was chosen. Von Mises yield criterion under plane stress and isotropic hardening law were considered to retrieve the relationship between stress and strain. The virtual fields method (VFM) was adopted as an inverse method to determine the constitutive parameters by calculating the stress fields from the heterogeneous strain fields. The results show that the choice of a hardening law which can describe the hardening behavior accurately is important to derive the true stress-strain curve. Finally, post-necking hardening behavior was successfully characterized up to the initial stage of localized necking using the VFM with Swift and modified Voce laws.
Kim, H.,Lee, J.,Barlat, F.,Kim, D.,Lee, M.G. Elsevier Science 2015 Acta materialia Vol.97 No.-
<P>The effects of the stress state and temperature on the martensitic phase transformation behavior in a TRIP-assisted steel (TRIP780) were investigated using multi-axial experimental techniques. For this purpose, five different stress states were considered; i.e., uniaxial tension, uniaxial compression, equi-biaxial tension, plane strain tension and simple shear. A range of temperatures from room to 100 degrees C for each stress state condition except the simple shear test were investigated. In particular, for the equi-biaxial tension data in warm conditions, a specially designed hydraulic bulge experiment was adopted. In situ magnetic measurements were performed to monitor the evolution of the martensitic content throughout each experiment. A stress state and temperature dependent transformation kinetics law was proposed, which incorporates a non-linear function of the stress triaxiality, Lode angle parameter and temperature. This new model captures the measured martensitic phase transformation kinetics of TRIP780 steel over a wide range of stress states and temperature reasonably well. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.</P>
Kim, S.,Lee, J.,Barlat, F.,Lee, M.G. Elsevier 2013 Journal of materials processing technology Vol.213 No.11
Sheet formability, as determined by the limiting dome height (LDH) test, was evaluated for DP and TRIP steel sheet samples. The LDH test was also predicted with finite element (FE) simulations using various constitutive models. Three yield functions, von Mises, Hill's 1948, and Yld2000-2d, were considered to examine the effect of the yield criterion on formability. The anisotropy parameters were determined from different experimental tests and their influences on LDH predictions were analyzed. For Hill's 1948 model, the coefficients were calculated either using the yield stresses or r-values measured in different tension directions. The anisotropy coefficients of the Yld2000-2d were determined using in-plane biaxial test data in addition to the conventional uniaxial test-based data. The stress-strain curves for hardening characterization were measured using uniaxial and bulge tests. The latter provides the flow stress over an extended strain range, compare with uniaxial tension, without showing instability. The constitutive models were implemented in a FE code with a user material subroutine. They were evaluated by comparing the experimental and predicted punch load-displacement and sheet thickness variations after forming in the LDH test. The results for this particular example demonstrated that the non-quadratic yield function and the hardening curve of the bulge test improve the prediction accuracy for sheet forming and formability analyzes significantly.
Stress relaxation and its effect on tensile deformation of steels
Hariharan, K.,Majidi, O.,Kim, C.,Lee, M.G.,Barlat, F. Scientific and Technical Press ; Elsevier Science 2013 Materials & design Vol.52 No.-
The tensile deformation of metallic materials, when interrupted without unloading, exhibit relaxation of stress. The stress relaxation phenomenon can alter the mechanical behavior of the materials. Stress relaxation phenomenon during tensile test is studied in three steel grades with different microstructures. The influence of stress relaxation on uniform elongation has not been reported before. The uniform elongation varies with strain at which material relaxes and is found to increase upto 3.5%. Contradicting with the published results, the stress drop during stress relaxation varies with strain and the possible reasons are explained. The stress drop during relaxation is governed by strain hardening mechanism in low carbon steel and strain aging mechanism due to martensite in dual phase (DP) and transformation induced plasticity (TRIP) steels.
Properties controlling the bend-assisted fracture of AHSS
Lee, J.,Kim, J.H.,Lee, M.G.,Barlat, F.,Zhou, C.,Chen, Z.,Wagoner, R.H. Pergamon Press ; Elsevier Science Ltd 2015 International journal of plasticity Vol.75 No.-
Bend-assisted fracture, also commonly called shear fracture, is the splitting of metal sheets during forming in tight-bending regions. It has been shown to be predominantly a result of plastic localization for most advanced high strength steels (AHSS). Such fractures are poorly predicted by typical industrial methods involving finite element modeling (FEM) and forming limit diagrams (FLDs). In order to understand the source of the problem, the sensitivity of simulated shear-fracture formability to material and process parameters was determined using FEM in conjunction with a realistic range of constitutive models, element sizes, and friction coefficients. Two types of shear fracture process were simulated. (1) Draw-bend fracture (DBF) tests are laboratory analogs of industrial forming conditions producing shear fracture; they offer the opportunity of experimental validation but introduce complexity because of varying strain state and unavoidable transitions between shear fracture and tensile fracture. (2) Plane-strain (PS) draw-bend fracture simulations correspond more closely to industrial forming conditions; they simplify the modeling (fixed strain state, no transitions) but no corresponding full-scale laboratory experiments currently exist. The DBF test was found to be sensitive to every material and process parameter tested, with the largest factors being the form of 1-D hardening law and the yield function. Varying these quantities in ranges representing what practical measurements would produce showed variations in predicted formability of up to 80%. The PS simulations, which represent industrial practice more closely, showed large variations in predicted formability only for two variables: 1-D hardening law and friction coefficient. All other parameters were insignificant, except for thermo-mechanical effects, which were important for high-rate tests only. These results show why it is difficult or impossible to predict shear fracture using standard industrial techniques designed for traditional steels. They suggest ways to modify such techniques to accommodate advanced high strength steels. The results also give guidance to alloy designers in terms of which constitutive parameters are most important in inhibiting shear fracture, and which are relatively insignificant.