Papers by Keyword: Plastic Anisotropy

Abstract: Material Testing 2.0 (MT2.0) couples full‑field deformation measurements (Digital Image Correlation, DIC) with inverse identification methods (Virtual Fields Method, VFM) to extract constitutive parameters from a small number of heterogeneous experiments. This paper presents the Cut‑Clamp‑Play concept: an integrated industrial MT2.0 solution that unifies specimen design, automated testing hardware, and a computationally efficient VFM identification chain to deliver fast, user‑friendly sheet‑metal characterization. A perforated cruciform specimen is optimized for parameter identifiability of the Yld2000‑2d anisotropic yield function and used in a single biaxial test. A working prototype has been built at KU Leuven and used to collect representative DIC data; the measured displacement/strain response is double‑symmetric, confirming correct mechanical operation. Projected and early prototype results indicate that the Cut‑Clamp‑Play approach can reduce operator actions by roughly 70% and produce identification results within one hour for typical sheet‑metal cases, while further work is required to make the fully automated “Play” stage robust for industrial deployment.

Abstract: Accurate prediction of the forming limit curve (FLC) is critical for evaluating sheet metal formability, yet the influence of plastic anisotropy remains controversial. In this study, the yielding behavior, hardening response, and strain-rate sensitivity of DC01 steel are experimentally characterized. Different yield criteria combined with a Swift hardening law and the Marciniak-Kuczyński (M-K) model are employed to predict the FLC. The results show that the high-order non-quadratic Yld2k-2d yield criterion captures both the yielding behavior and the forming limits. Numerical experiments using this material framework are then conducted. Variations in r-values have a limited effect on the FLC, in contrast to the common notion that high r-values mean high formability, whereas the equibiaxial tensile yield stress strongly governs the right-hand side.

Abstract: Pure Niobium is a material of interest for high-energy-physics applications including superconducting accelerators. Cold-rolled sheets of Nb exhibit significant plastic anisotropy. Here we report on the mechanical and forming properties of 99.95% pure, 1.02 mm thin, cold-rolled sheet. Uniaxial tension, biaxial tension and disc compression experiments are performed, the first two at multiple angles to the rolling direction of the sheet. The material is very ductile (uniform elongation ~30%), and exhibits significant plastic anisotropy (e.g., the R-values range from 1.2 in 45^o to 2.5 in 90^o). The results are used to calibrate the Yld2000-2D anisotropic yield function, with an exponent of 6 as Nb is BCC. They are also used to extract the hardening curve beyond the limit load in uniaxial tension. Deep-drawing experiments are performed using a die of 27.6 mm dia. and a punch of 25.4 mm dia. Blanks of various diameters are used. The successfully drawn cups exhibit significant earing. The experiments are simulated using Abaqus/Standard and shell elements. It is shown that a properly calibrated material model enables the numerical simulations to match the experiments.

Abstract: The comprehension of the anisotropy impacts on mechanical properties of the rolled steel sheets was investigated using a non-quadratic anisotropic yield function. In this study, experimental and modelling determination of behavior of an industrial rolled sheets for a DIN 1623 St14 steel were carried out. The yield stresses and Lankford r-values in uniaxial were experimentally determined but the balanced biaxial tension stress states and rb were assumed. The parameters of the associated yield equation, derived from the three orthotropic yield functions proposed by Hill48 and Yld2000-2d, were determined. Predictions and the evolution of normalized yield stress and normalized Lankford parameters (plastic strain ratio) obtained by the presented investigative are considered. In order to describe the path of equivalent plastic behavior, the isotropic hardening function is described using the following various empirical standard formulae based on: Hollomon, Ludwick, Swift and Voce model.

Abstract: Mg alloy AZ31B is of interest for hot forming because it can achieve a superplastic response at high temperatures and slow strain rates. As temperature decreases and forming rate increases, its strain-rate sensitivity decreases and significant plastic anisotropy can arise. These effects are the result of a transition in deformation mechanisms from grain-boundary-sliding (GBS) to dislocation-climb (DC) creep. However, sheet production using warm rolling can produce a material with a smaller grain size and weaker basal texture. These microstructural changes promote GBS creep and decrease the degree of anisotropy under DC creep. Microstructural and tensile data are presented to show these effects at 350 and 450C through comparisons to a similar material having a more usual microstructure.

Abstract: Solutions for many rigid/plastic models are singular in the vicinity of maximum friction surfaces. In particular, the magnitude of the equivalent strain rate near such surfaces is controlled by the strain rate intensity factor. This factor is the coefficient of the leading singular term is a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Since the equivalent strain rate has a great effect of material properties, it is of important to reveal the dependence of the strain rate intensity factor on parameters characterizing material models. In the present paper, quite a general model of anisotropic plasticity under plane strain conditions is adopted. Then, using an analytic solution for instantaneous compression of a layer of plastic material between two parallel plates the effect of the shape of the yield locus on the asymptotic behavior of the equivalent strain rate in the vicinity of the friction surface is demonstrated.

Abstract: The present work deals with the calibration strategy of yield functions used to describe the plastic anisotropic behavior of metallic sheets. In this paper, Bron and Besson yield criterion is used to model the plastic anisotropic behavior of AA5086 sheets. This yield model is flexible enough since the anisotropy is represented by 12 parameters (4 isotropic parameters and 8 anisotropic parameters in plane stress condition) in the form of two linear fourth order transformation tensors. The parameters of this anisotropic yield model have been identified from a single dedicated cross biaxial tensile test. It is shown, from finite element simulations, that the strain distribution in the center of the cruciform specimen is significantly dependent on the yield criterion. Moreover, this cross biaxial test involves a large range of strain paths in the center of the specimen. The calibration stage is performed by means of an optimization procedure minimizing the gap between experimental and numerical values of the principal strains along a specified path in the gauge area of the cruciform specimen. It is shown that the material parameters of Bron and Besson anisotropic yield model can be determined accurately by a unique biaxial tensile test.

Abstract: Electro-deposited pure iron has a very sharp and isotropic <111>//ND fiber texture and a needle shaped grain elongated in the ND. This pure iron exhibits an r-value of over 7, and it is difficult to explain such a high r-value only from the texture. Specific {110} plane slips, which are perpendicular to the sheet surface, exclusively act in this material and this limitation of the active slip system is the main mechanism behind the extraordinarily high r-value. Thus, tensile deformation by this slip system doesn’t require a decrease in thickness. In this study, the mechanism of this slip system limitation is investigated. Because both the {110} slip plane and grain boundary are perpendicular to the sheet surface, the slip plane can easily connect with adjacent grains. This good continuity of slip plane with adjacent grain may have an influence on the choice of slip system.

Abstract: This paper presents two crystal plasticity based computational constitutive models for the intrinsic formation of plastic microstructure during monotonic loading and its altered evolution under strain path changes in metal forming operations. The formation step is modeled via a non-convex strain gradient crystal plasticity framework which could simulate the intrinsic development of the plastic microstructures. The evolution under strain path changes is modeled via phenomenologically based constitutive equations incorporated into crystal plasticity framework. The latter is capable of simulating the transient anisotropy effects (e.g. cross hardening, Bauschinger effect) depending on the change in the strain path. The paper discusses the unification of such models for the continuous modeling of microstructure formation and evolution processes.

Abstract: It is difficult to predict springback, particularly in torsion, with high accuracy by FE simulation. Generally, more accurate springback prediction havs been achieved mainly by the improvement of material modeling such as Baushinger effect and plastic anisotropy models. It is also proved that tool deformations can greatly influence on the accuracy of torsion springback prediction as shown in the authors’ study [Esaform 2012]. The study shows that FE simulation using elastic tool model has 30% more accuracy in predicting torsional spring back in a curved hat shape than that by rigid tool model. But full elastic tool modeling is tedious work and FE calculation with the elastic tool model needs enormous time.There are two kinds of tool deformation during a press forming: tool deflection as a whole, and surface deformation where the tool is in contact with the steel sheet. Three forming experiments were carried out with an insert block of different stiffness, which touch steel sheets directly, in this study. The results revealed that surface deformation of a tool has great influence on torsion springback of a curved hat shape. Based on the results, a new tool modeling is proposed in this study. In the model, the part of a tool in direct contact with a blank sheet is elastic and the other part is rigid. That means the model deals with only surface deformations of tools in FE simulation. By the new model, the accuracy of torsion springback prediction of a curved hat shape was improved with less calculation time.