Coefficient Of Plastic Anisotropy Research Articles

Analysis of distribution of deformations during tensile straightening of hot-rolled strips from aluminum alloys

In order to reveal the regularities of the change in the dimensions of strips of aluminum alloys during their straightening by stretching, an industrial experiment was carried out on a straightening-stretching machine with a force of 70 MN. Certain control points were assigned on the plate surface and strip thicknesses were recorded there before and after straightening. The measurements were made on 12 hot-rolled plates with a thickness of 25–130 mm from four types of alloys. The sample size is divided into two parts: measuring points located at the periphery, closer to the grippers, and points in the central part of the workpiece. The coefficients of plastic anisotropy are determined. It was found that the coefficient of plastic anisotropy takes on higher values in the peripheral part of the strip than in the central one. For alloys D16, 5083 and AMg6, respectively, there is a general tendency: with increasing thickness, the coefficient of plastic anisotropy increases. In the course of statistical processing, along with the average values, the dispersions of the strip thicknesses before and after straightening were also determined. In the range of thicknesses 20–60 mm, we can talk about the approximate equality of dispersions. However, above 80 mm, the indicator begins to grow, while at a thickness of 130 mm, the dispersion increases by about four times relative to this characteristic for small thicknesses. In general, the setting of the strip elongation parameters during tension straightening should lead to such a change in thickness, which should provide the value in the tolerance field. It is shown that the change in strip thicknesses depends on the initial one obtained during rolling. At thicknesses of 100–130 mm, plastic deformation approaches the conditions of isotropic material`s deformation. For thinner hot-rolled strips, the coefficient of plastic anisotropy varies in the range of 0.4–0.9, and the greater the strip thickness, the greater it is.This work was carried out with partial financial support from Decree No. 211 of the Government of the Russian Federation, contract No. 02.A03.21.

Assessing Material Properties of Commercial Magnesium Alloy with Digital Image Correlation (DIC) Technique for Forming Applications

The engineering field's main issues are often identified to be estimating the deformation and the strain measurements of the working material. Gauging displacements until the fracture more accurately is crucial in experimental procedures for assessing the chosen material properties. This research paper investigates the commercial magnesium alloy (AZ31B) material using digital images, often called Digital Image Correlation (DIC), which provides complete displacement and strain data information at each timestep rather than utilizing an extensometer. This method provides images taken during the deformation, and subsequently, the material properties computed using correlation software for tested samples. The plastic anisotropy coefficients are computed for test samples that cut down at angles of 0, 45, and 90 to the rolling direction. Also, the tensile test finite element model until the necking region was used to verify the fitted models such as Hollomon power-law and Ramberg–Osgood relationships to define the non-linear relationship between stress and strain. Hence, real models and numerical simulations of incremental forming are created to depict this research work's usefulness to the forming applications.

Analysis of the pre-straining effects on the limit strains of interstitial-free steel: experiments and elasto-plastic modeling of strain and stress-based forming limit curves

In this work, the limit strains under as-received and pre-strained conditions of an interstitial-free steel sheet were investigated by mechanical tests and numerical modeling. An original testing procedure was proposed to reproduce two equivalent pre-straining amounts under equibiaxial stretching (EB-PS) and uniaxial tension (UT-PS) deformation modes. The limit strains were defined from Nakajima’s hemispherical punch tests using digital image analysis according to the ISO 12004:2 standard. The plastic behavior of the interstitial-free steel sheet was evaluated by uniaxial tensile, disk compression, and hydraulic bulge tests. Moreover, an elasto-plastic framework based on the Marciniak–Kuczynski (M–K) model is proposed to forecast both the strain-based and stress-based forming limits. The parameters of the Yld-2000-2d yield criterion were identified using the plastic anisotropy coefficients with the flow-stress values determined from two distinct amounts of plastic-work per unit volume. For both deformation modes and pre-straining levels defined by the von Mises effective plastic-strain (4.8% and 9.0% EB-PS; 5.0% and 10% UT-PS), the transformed polar effective plastic-strain (PEPS) and forming limit stress (FLSC) results shown to be more strain-path insensitive than the conventional strain-based forming limit curve (FLC). The proposed elasto-plastic M–K model successfully forecasted the linear strain-path limit strains defined using the FLC, PEPS, and FLSC representations. The M–K model also provided quite conservative predictions for the pre-strained PEPS and FLSC. The Yld-2000-2d parameters identified using the flow-stress values defined from an upper-level of the plastic-work per unit volume proved to be the best choice in the present M–K modeling framework.

Some Practical Aspects of Digital Image Correlation Technique to Evaluate Anisotropy Coefficient and Its Comparison with Traditional Method

Abstract Digital Image Correlation (DIC) is a robust method that is used to evaluate full-field displacements. In this technique, images taken from the specimen are compared before and after deformation; this method provides an accurate displacement field as well as strain values. The objective of the present work is to examine the DIC method using the traditional method of calculating the plastic anisotropy coefficients. In this research, the DIC method has been applied on one side of the specimen, and the conventional circle grid analysis technique is performed on the other side. Results showed that the fully automated 2-D DIC method in MATLAB (MathWorks, Natick, MA) was verified and that it could replace the traditional technique of circle grid analysis, which is time consuming and incurs a lot of human errors.

Calibration of anisotropic plasticity models using a biaxial test and the virtual fields method

The aim of the present study is to explore the combination of a biaxial test with a cruciform specimen and the virtual fields method to develop an efficient strategy for simultaneous identification of material parameters related with hardening and anisotropy in plasticity. In a first step, three cruciform geometries are evaluated as potential candidates to generate an experimental database for the calibration of the classical Hill’48 yield criterion and Swift’s hardening law. In a second step, the geometry with the best results is used to calibrate YLD2000-2d yield criterion and Swift’s hardening law. Numerical results are used as virtual experimental full-field measurements, which allows the comparison of the identified solution with the input material parameters. The accuracy of the identified material parameters is thoroughly assessed through the analysis of flow stress curve evolution, normalised yield stresses and plastic anisotropy coefficients, and for the last step, yield locus prediction. The results show the potential of this combination to identify simultaneously the material parameters related to hardening and anisotropy with a single test.

On the ductility of alpha titanium: The effect of temperature and deformation mode

Single phase α-titanium shows anomalous warm deformation behaviour. As the temperature increases, ductility increases in uniaxial tension and decreases in biaxial stretching. Previously, this behaviour was attributed to an increase in strain rate sensitivity and a decrease in twinning activity with temperature. In this study, we show that it can instead be explained by an increase in slip anisotropy with temperature. Grade 2 CP-Ti sheet was tested in uniaxial tension at 20 °C and 300 °C to determine ductility, work hardening behaviour and the coefficient of plastic anisotropy (R-value). The increase in uniaxial ductility with temperature was found to be a consequence of an increasing rate of saturation work hardening with temperature. In the absence of significant twinning, this unexpected work hardening behaviour was attributed to an increase in slip anisotropy with temperature. This hypothesis was supported by crystal plasticity finite element modelling, which can also predict the observed increase in surface roughness with temperature. The increase in anisotropy leads to higher strain localization which, coupled with the increasing work hardening rate helps explain why biaxial ductility decreases with increasing temperature. In addition to explaining the limitations in warm forming of Ti, understanding the origins of these effects contributes to our general understanding of the deformation of other hexagonal metals like Zr and Mg.

Strain measurement and determining coefficient of plastic anisotropy using digital image correlation (DIC)

The deformation and strain measurements have always been one of the main issues in structural engineering. Measuring displacements accurately without damaging structures are an important aim in experimental analysis. For an example, the existing structures need to be evaluated whether they are still fit for purposes or not. To assess complex structures, we need an acceptable and enough amount of data Current strain measurement technologies are not capable of evaluating compounded structures. This paper investigates on an alternative method that uses digital images to provide a full displacement and strain field called Digital Image Correlation (DIC); This technique compares the digital images taken from digital cameras, before and after deformation. We also calculated the coefficient of plastic anisotropy. An aluminium 1050 specimen was loaded in tension according to ASTM E8 testing method while the Sony camcorder captured the video of the specimen being loaded. Once the video was captured, the images were snapshot from video strip using a built-in function of the camera. After that, the images were processed using the Matlab software. The results determined by the extensometer and the optical strain measurement method were compared to each other. This comparison shows that if the test’s setup could be configured in a good way, the error will be less than 2%.

Temperature-dependent anisotropic material modeling of the sheet metal component within the polymer injection forming process

In the course of this work, an extended material model for a carbon steel sheet metal has been developed based on Hill’48 yield criterion, considering temperature-dependent plastic anisotropy coefficients. This material model is applied on a polymer injection forming process in which the sheet metal heats up to a critical forming temperature through the contact with the plastic melt. At this temperature range blue brittleness occurs. The elastic properties, the yield stress as well as the plastic anisotropy coefficients of the sheet material become significantly different compared to those at room temperature. It should be emphasized that especially temperature-dependent anisotropy coefficients are not yet considered in most common material models. With the help of the presented modelling approach a more precise modelling of the temperature-dependent carbon steel material behavior can be realised.

Prediction of anisotropy and hardening for metallic sheets in tension, simple shear and biaxial tension

The mechanical behavior of mild and dual phase steel sheets is investigated at room temperature in quasi-static conditions under different strain paths: uniaxial tension, simple shear and balanced biaxial tension. The aim is to characterize both the anisotropy and the hardening, in order to identify material parameters of constitutive equations able to reproduce the mechanical behavior. In particular, a good description of flow stress levels in tension and shear as well as plastic anisotropy coefficients is expected. Moreover, the Bauschinger effect is investigated with loading–reloading in the reverse direction shear tests and the balanced biaxial tension test gives insight of the mechanical behavior up to very high equivalent plastic strains. Yoshida–Uemori hardening model associated with Bron–Besson orthotropic yield criterion is used to represent the in-plane mechanical behavior of the two steels. The identification procedure is based on minimization of a cost function defined over the whole database. The presented results show a very good agreement between model predictions and experiments: flow stress during loading and reverse loading as well as plastic anisotropy coefficients are well reproduced; it is shown that the work-hardening stagnation after strain path reversal is well estimated in length but Yoshida–Uemori model underestimates the rate of work-hardening.

Non-quadratic anisotropic potentials based on linear transformation of plastic strain rate

In this paper, anisotropic strain rate potentials based on linear transformations of the plastic strain rate tensor were reviewed in general terms. This type of constitutive models is suitable for application in forming simulations, particularly for finite element analysis and design codes based on rigid plasticity. Convex formulations were proposed to describe the anisotropic behavior of materials for a full 3-D plastic strain rate state (5 independent components for incompressible plasticity). The 4th order tensors containing the plastic anisotropy coefficients for orthotropic symmetry were specified. The method recommended for the determination of the coefficients using experimental mechanical data for sheet materials was discussed. The formulations were shown to be suitable for the constitutive modeling of FCC and BCC cubic materials. Moreover, these proposed strain rate potentials, called Srp2004-18p and Srp2006-18p, led to a description of plastic anisotropy, which was similar to that provided by a generalized stress potential proposed recently, Yld2004-18p. This suggests that these strain rate potentials are pseudo-conjugate of Yld2004-18.

Anisotropy of yielding in a Zr-2.5Nb pressure tube material

The anisotropy of yielding, as measured by the ratio of yield stress in the axial and transverse directions of Zr-2.5Nb pressure tubes used in Canada Deuterium Uranium (CANDU) nuclear reactors, was determined experimentally by testing samples in uniaxial tension. The yield anisotropy was measured in uniaxial tension in samples obtained from the three directions of a Zr-2.5Nb plate and in shear, by testing in torsion “mini” pressure tubes from the same material. From these experiments, the temperature and strain-rate dependence of the yield stress and the dependence of the anisotropy of yielding on temperature were also determined. It is shown that the yield anisotropy of pressure tube material is constant for temperatures up to about 800 K and that the strain-rate sensitivity is also constant up to about 700 K and is equal to ∼0.02. In addition, the activation energy (Q) of this material was estimated by using the temperature dependence and rate sensitivity of the yield stress. It was found to be of the same order of magnitude as that determined earlier by other investigators. A polycrystalline, nonlinear self-consistent model that takes into account the crystallographic texture of the material was used to derive the values of the critical resolved shear stress (CRSS) which are consistent with prismatic, basal, and pyramidal glide and the values of the Hill’s plastic anisotropy coefficients which are consistent with the observed anisotropy of yielding. The model provided an estimate of the complete stress tensor, describing yielding of a Zr-2.5Nb pressure tube material.