Normal Anisotropy Coefficient Research Articles

DETERMINATION OF TECHNOLOGICAL CHARACTERISTICS OF PRESSABILITY

This article deals with the results of technological tests of pressability (Erichsen's - IE index and capping - limit drawing ratio (LDR)). It also presents on which material parameter (ductility, strain hardening exponent, coefficient of normal anisotropy...) should be given more emphasis when choosing a steel sheet, if stretching stress (uniaxial tension, biaxial tension) dominates during the production of stampings, or if dominates the “pull-pressure” technique (pulling out from under the flange).

Theoretical Forming Limit Diagram Based on Induced Stress in the Thickness Direction

The conventional theoretical forming limit diagram (FLD) based on the plane stress state has defects due to the neglect of the stress in the thickness direction of the sheet. It is urgent to study the FLD which considers the stress in the thickness direction. Through the finite element simulation, it is further confirmed that the stress in the thickness direction will be induced in the deformation process. At the same time, the effect of the induced stress in the thickness direction on FLD is not the same as that always applied stress in the thickness direction during the deformation process. Based on the Modified Maximum Force Criterion (MMFC) instability theory, C-H instability theory, Mises and Hill48 yield criterion, the effects of the two stresses on FLD are compared. The induced stress in the thickness direction also affects the sensitivity of the coefficient of normal anisotropy r, but does not significantly change the effect of the stress-strain index n on Forming Limit Curves (FLC). The theoretical calculations of the three materials TRIP780, AA5182, and 5754O are compared with the experimental data, which proves that the FLD which considers induced stress in the thickness direction is more accurate than the FLD of the plane stress.

Experimental investigation of hole expansion ratio for automotive-grade steels

Hole expansion ratio (HER) is widely used to quantify the stretch-flangeability of sheet metal. HER is determined from the maximum limit of successful expansion of a central hole by a conical punch. The central hole edge is prepared by the punching process. Around 45° cracks are noticed at the central hole edge after successfully completing the hole expansion test. HER of punched hole correlates with uniaxial tensile properties like yield strength, ultimate tensile strength, total elongation, post-uniform elongation, and coefficient of normal anisotropy. Comparisons of strength (yield strength, ultimate tensile strength), anisotropy (coefficient of normal anisotropy) and deformation (total elongation, post-uniform elongation) parameters among steel grades are essential to relate HER among steel grades. Interstitial free steel is the highest, and SPFH steel is the lowest HER among the four steel grades. HER correlates nicely with the notch mouth opening displacement at peak load.

3D DEM simulation of initial anisotropy in dredger fill soft soil

The initial anisotropy has a significant effect on the mechanical properties of the soft soil. Based on the initial anisotropy of the particles, the mechanical characteristics are analysed from a microscopic view, and the micro-macro relationship of the soil is established. According to the particle morphology of soft soil, the discrete element method is used to construct the flaky particle clusters, and seven sets of samples with different initial deposition angles are established for consolidation and undrained triaxial simulation tests. The results show that the strength of the sample decreases first and then increases with the increase of the deposition angle. When the deposition angle is 0°, the flaky particles mostly appear in a nearly horizontal suspension, and the sample has the largest shear strength. The distribution of the contact force chain formed by the particles in the shearing process is also related to the deposition angle. Different deposition angles form displacement fields of different shapes. When the deposition angles are 45° and 60°, there are obvious deformation displacement bands. At the same time, the initial deposition angle affects the particle coordination number. The higher the sample strength corresponding to the lowest average coordination number of particles. The contact normal anisotropy coefficient is related to the strain hardening and strain softening characteristics in the shearing process. The increase in the contact normal anisotropy coefficient shows the characteristics of hardening, and the smaller the contact normal anisotropy coefficient shows the characteristics of softening.

Determination of the Forming Limit for a ZIRLO™ Sheet with High Anisotropy.

In this study, the experimental two-dimensional forming limit diagram (FLD) data for a ZIRLO™ sheet, which is used in nuclear fuel rod support grids, were converted and presented as a triaxiality failure diagram (TFD). Most previous studies assumed ZIRLO™ to be isotropic when calculating the effective stress and strain. However, for highly anisotropic materials, the anisotropy should be considered for calculations of effective stress and strain; hence, in this study, they were calculated by introducing the normal anisotropy coefficient. To obtain this parameter of the ZIRLO™ specimens, tensile tests were performed on specimens with 0°, 45°, and 90° angles with respect to the rolling direction. It was observed that the average normal anisotropy coefficient measured during the tests was 4.94, which is very high. The von Mises isotropic and Hill 48 anisotropic yield criterion were applied to the FLD data that were experimentally determined using a limit dome height test and were converted into effective stress and effective strain. When the FLD is converted to TFD, the curve will increase in the top-right direction if the r-value is greater than 1, and this become more severe as the r-value increases. The TFD, which was converted considering the anisotropy, is almost the same to the TFD obtained using the digital image correlation method in the tensile tests of four specimens with different stress states. If anisotropy is not considered, then the formability is normally underestimated. However, a highly accurate TFD can be obtained with the method proposed in this study.

Исследование и оценка механической анизотропии сталей и сплавов магнитошумовым методом

The aim of this work is to experimentally study the relationship between mechanical properties using the example of the normal anisotropy coefficient of sheet metal, mechanical stresses during elastic deformation of electrical steel and anisotropy of the physical and mechanical properties of a set of steels and alloys with magnetic noise parameters.
 The mechanical anisotropy of the ferromagnetic materials properties predetermines the need for its study and evaluation, since it has a significant impact on the basic physical and mechanical characteristics of components, products and structures. Taking into account the relationship between the physical and mechanical properties of the material with the magnetic characteristics, to study the possibility of non-destructive testing of anisotropy the method of the Barkhausen effect was used, the informative parameters of which are magnetostructural and magnetoanisotropic. To study mechanical anisotropy a device for circular rotation of the Barkhausen transducer over the sample surface and a device for the production of elastic tensile / compressive stresses during static bending were made. Comparison of the results obtained using magnetic noises with the known coefficients of normal anisotropy of thin-sheet steel samples showed their qualitative and quantitative agreement, confirming the presence of a close relationship between them. It was found that elastic deformation in samples of anisotropic electrical steel leads to a sharp change in the level of magnetic noise and the type of circular diagrams, taking into account the sign of stresses. It is shown that as a result of cold rolling according to magnetic noise the samples have a pronounced texture due to the direction of rolling along the longest side of the sheet. The formed elastic deformation under tension and compression during static bending practically does not change the texture - the induced crystallographic anisotropy after rolling. The relationship between the intensity of magnetic noise and the degree of anisotropy is established and the possibility of evaluating the magnetic anisotropy in various steels and alloys using the Barkhausen effect method is investigated and confirmed.

The effect of grain size and initial texture on microstructure, texture, and formability of Nb stabilized ferritic stainless steel manufactured by two-step cold rolling

The present study investigated the influence of grain size and initial texture on the microstructure, texture, and formability of a niobium-stabilized ferritic stainless steel processed by two-step cold rolling. The characterization of the samples was performed by X-ray diffraction, electron backscatter diffraction, and tensile tests in order to evaluate the formability by the average normal anisotropy coefficient. The results showed that the reduction in grain size from 110 ± 21 to 50 ± 7 μm, in the hot rolled band, was favorable to obtain a more homogenous microstructure and smaller grain size after annealing. Coarse grain size and α-fiber (<110>||RD) favored a strong α-fiber after cold rolling. In addition, γ-fiber (<111>||ND) was more intense in the deformation texture of fine grain size samples. The recrystallization texture was constituted by intense γ-fiber (<111>||ND) and weak θ-fiber (<100>||ND) for both conditions. However, the reduction in grain size increased the γ-fiber fraction. Therefore, the r¯=1.92 and γ/θ = 8.12 were obtained to the sample originated from the initial fine grain size. The fine grain size and weak texture in the starting materials were effective in developing a high r¯ value in the samples manufactured by two-step cold rolling.

Microstructural characterization and mechanical behavior during recrystallization annealing of Nb-stabilized type ASTM 430 and Nb-Ti-stabilized ASTM 439 ferritic stainless steels

A comparison between the niobium-stabilized type ASTM 430, 430Nb, and niobium-titanium-stabilized ASTM 439 ferritic stainless steels with respect to their microstructure and texture at the different stages of recrystallization was performed. The annealed samples were subjected to tensile test and Swift test for evaluation of mechanical behavior and deep drawability, respectively. The heat treatment was carried out on lab-scale cold rolled sheets with 85% thickness reduction as an attempt to mimic the industrial process. Recrystallization occurred first for 430Nb steel with smaller recrystallized grain sizes, less pronounced γ-fiber texture, lower average normal anisotropy coefficient, R¯, and limit drawing ratio, LDR. On the other hand, ASTM 439 showed higher yield stress but better drawability. These results are presented and discussed based on microtexture evolution, precipitate characteristics and grain boundary character distributions.

Characterization of Plastic Anisotropy of AA5182-O Sheets During Prestraining and Subsequent Annealing

This paper described the effects of prestraining and annealing on plastic anisotropy (r-value) of aluminum alloy 5182-O sheets including two prestrain paths and two annealing conditions. During the prestraining and annealing processes, r-value changed depending on prestrain paths and annealing conditions. Although there were slight changes of the normal anisotropy coefficient, r¯, during prestraining and annealing processes, the planar anisotropy coefficient, Δr, increased significantly, especially for the uniaxial prestrain condition. This could accelerate the development of earing during a sheet forming operation. Also, the corresponding sheet textures in rolling direction (RD)/TD plane after prestraining and annealing processes were observed through electron backscatter diffraction (EBSD) analysis to explain the r-value changes, where the viscoplastic self-consistent (VPSC) model was used to correlate the determined texture to measured r-values. It is found that the sheet texture also had significant changes relating to the prestrain paths and annealing conditions resulting in varied r-values.

Microstructure, Texture and Microhardness Evolution during Annealing Heat Treatment and Mechanical Behavior of the Niobium-Stabilized Ferritic Stainless Steel ASTM 430 and Niobium-Titanium-Stabilized Ferritic Stainless Steel ASTM 439: a Comparative Study

A comparison of the influence of microstructure and texture on mechanical behavior between the niobium-stabilized ferritic stainless steel type ASTM 430, 430Nb, and the niobium-titanium-stabilized ferritic stainless steel type ASTM 439 was performed. The two steels were supplied as cold rolled thin sheets and the annealing was interrupted in different temperatures aiming the characterization of the microstructure and texture in different stages of recrystallization using optical microscopy, Vickers microhardness and Electron Backscatter Diffraction. The annealed samples were tensile tested to determine the mechanical properties and undergone to Swift test to evaluate the drawability. The steel 430Nb showed smaller grain size and greater yield stress. The steel ASTM 439 presented higher normal anisotropy coefficient, R, and higher Limit Drawing Ratio due to greater proportion of γ fiber. These results are presented and discussed in terms of precipitates and crystallographic texture developed in the recrystallization of both steels.

Evaluation of Intermediate Annealing on Nb-Stabilized Ferritic Stainless Steel

This study seeks to evaluate the effect of intermediate annealing on the microstructure, texture, and formability of Nb-stabilized ferritic stainless steel. Two routes - direct cold rolling and cold rolling with an intermediate annealing were performed. The total reduction was 80%, 3-0.6 mm and 3-1.2-0.6 mm. The characterization of the samples was conducted using X-ray diffraction, electron backscatter diffraction, and tensile tests to evaluate the formability by the average normal anisotropy coefficient, r value. The results showed that intermediate annealing promoted the strongest γ-fiber with peak at {111}〈112〉 and weak α-fiber after cold rolling. After the final annealing, it was observed that intermediate annealing reduces the banded microstructure and θ-fiber, and improves the γ-fiber uniformity and the r value. It is worth noting that the γ-fiber fraction was the same for direct reduction. The increase in r value was related to the reduction in θ-fiber and the uniformity of texture recrystallization.

Effects of Annealing Conditions on Recrystallization, Texture, and Average Normal Anisotropy Coefficient of a Niobium‐Stabilized Ferritic Stainless Steel

The present study investigates the influence of the heating rate on annealing, microstructure, recrystallization, texture, and the average normal anisotropy coefficient, value, of a niobium‐stabilized ferritic stainless steel (i.e., an ASTM 430‐type steel). Experiments with 0.10 and 41.5 °C s−1 heating rates are performed after 85% cold rolling. The sample's characterization is performed by optical microscopy, transmission electron microscopy, electron backscatter diffraction, and hardness tests. The tensile tests are performed to determine the value and the Δr value. The results show that the extent of recrystallization and the average grain size decreases significantly when the heating rate is raised. This increased heating rate causes a weakening of γ‐fiber and of the and components, and leads to an even more randomized recrystallization texture. The value after having achieved full recrystallization is improved when the heating rate is reduced. The is obtained for with a lower heating rate. These observed differences in recrystallization, grain size, and recrystallization texture are mainly related to the nucleation rate during annealing. The high intensity of the γ‐fiber is attributed to the number advantage of γ‐fiber grains after full recrystallization.

Prediction of complete forming limit diagram from tensile properties of various steel sheets by a nonlinear regression based approach

Experimental Forming Limit Curve (FLC) and tensile properties of various steel grades are collected from literatures to validate the proposed model. The experimental results show that the ultimate tensile stress (σUTS), total elongation (ɛt), coefficient of normal anisotropy (r), tensile strain hardening exponent (n) and sheet thickness (t) are strongly related to the plane strain forming limit (FLC0) values for steel sheets. A nonlinear regression equation is proposed to predict FLC0 from uniaxial tensile properties like σUTS, ɛt, r, n and t. To verify the predictive capability of the proposed equation, predicted FLC0 values for fifty six steel grades in various thickness and strength ranges are compared with experimentally measured FLC0 values. It is observed that the newly developed nonlinear regression equation predicts well the FLC0 values.Left side of the strain-based FLC is calculated from a criterion (a line with slope of –1) which is normally well matched with experimental observation. Right side of the strain-based FLC is calculated from modified Keeler–Brazier power equation. In the original Keeler–Brazier power equation for the right side of the FLC the exponent is considered as 0.5, while experimental finding revels that it varies systematically with FLC0. Complete strain-based FLCs calculated from proposed method are matched well with experimental FLCs for various automotive steel grades like IF, IF 340, DP 780, TRIP 780 and TWIP 940 steels.

Conditions Of Stability Loss During The Test Of Hydraulic Forming Of Drawpieces

The paper contains two parts. In the first part, basic relationships were derived and some problems connected with stability loss during hydraulic forming of round metallic drawpieces with liquid pressure were discussed. The aim of the considerations is to test drawability of sheets by estimation of acceptable values of plastic strains and the corresponding heights of spherical shells. The analysis was based on some selected real conditions of stability loss. The influence of the coefficient of material hardening for the drawpiece, the coefficient of normal anisotropy and coefficients of plane anisotropy on acceptable values of plastic strains and heights of the formed drawpieces corresponding to the given condition of stability loss was also tested.

EFFECT OF ASYMMETRIC ROLLING ON FORMABILITY OF PURE ALUMINIUM

Uniaxial tensile test was carried out at different loading direction (0o, 90o and 45o) on rolled aluminiumsheets. The anisotropic coefficient was analyzed to reveal formability characteristics. The shear strain that wasimposed during the ASR was extensive and the shear marks was inclined more or less linearly without beingzigzag or spiral lines. The ASRC improved the normal anisotropy coefficient compared to CR specimens. Thehighest normal anisotropy and the lowest planar anisotropy were observed by ASRC samples. Therefore, it wasfound that, asymmetric rolling especially ASRC can be used to improve the formability of aluminium thick sheets.

Non-linear Correlation Between Uniaxial Tensile Properties and Shear-Edge Hole Expansion Ratio

Stretch flanging of steel sheets is an important formability issue for automobile industry. Finite element simulation study confirms that the edge of the hole deforms in a uniaxial tensile manner during the hole expansion process. To understand the effect of various tensile properties on hole expansion ratio, current experimental data and collected data from published work have been used. Yield stress, ultimate tensile stress, coefficient of normal anisotropy, total elongation, and post uniform elongation are closely related to hole expansion ratio. A non-linear relationship between hole expansion ratio and tensile properties (ultimate tensile stress, coefficient of normal anisotropy, and total elongation) is developed in the present investigation.

Constrained tensile stretching of steel strips under different lubrication: predicting macroscopic strain distributions with microstructural inputs

Drawing Quality (DQ) and Interstitial Free (IF) steel strips, of identical specimen geometry, were uniaxially stretched using two servo hydraulic actuators moving in opposite directions at the same speed. Two strain levels were achieved, in a bending under tension testing setup, using a rigid cylindrical pin at the center of the respective strips. Different lubrication conditions brought into differences in microstructural developments and in macroscopic strain distributions. The latter was measured from digital image correlations, while measurements of in-grain misorientations and crystallographic textures were extrapolated into strain hardening exponent of Hollomon law (n) and normal anisotropy coefficient ( $$ \overline{r} $$ ). Finite element simulations were used to predict macroscopic strain distributions, assuming constant and varying (with strain) material properties of n and $$ \overline{r} $$ . Predictions with variable material properties, as estimated from experimental microstructural data, were superior, having the least mean squared error (MSE). This study not only reiterates clear possibilities of incorporating microstructural inputs in a continuum model, but establishes efficacy of the same in relatively complex forming environment.

Comparison between symmetric and asymmetric hot rolling techniques performed on duplex stainless steel 2205

The use of duplex stainless steel represents one possible efficient alternative of austenitic grade and an interesting resources for its high performance against stress corrosion cracking. Unfortunately such material shows some limitations in their use: for instance the sheets or plates of duplex stainless steels present anomalous and poor formability for plastic deformation processes. Such problems are mainly related to an unsuitable normal anisotropy coefficient, which might cause the “necking” and “earing” phenomena, especially during hot rolling. The study deals with the comparison of symmetric and asymmetric rolling technique on stainless steel duplex 2205 specimens. All the experiments were carried out using a laboratory mill, properly equipped with an individual engine for each rolling cylinder. The experimental parameters considered include three different pre-heating temperatures and two asymmetry ratios, while the reduction level is maintained constant for both rolling configurations. Moreover, the study involves also the analysis of the influence of solubilization quenching and the SEM, SEM-EBSD investigation dedicated to establish the microstructure modifications. The specimens were also studied through tensile tests to determine the influence of the rolling techniques on the mechanical properties of the product, focusing on the definition of the average anisotropy coefficient. The results of the experimental trials allow to conclude that the use of asymmetric rolling process induces an improved formability and increases duplex 2205 tensile properties.

Numerical Simulation and Optimization of Drawing for Shallow Tapered Surface

It was hard to predict crack and wrinkle which are the main failure modes when drawing for the shallow tapered parts. In this paper crack and wrinkle can be avoided effectively by using the software DYNAFORM in combination with orthogonal design of experiment method. The influence of normal anisotropy coefficient, friction coefficient, drawbead resistance and blank holding force on deep drawing shallow tapered surface was analyzed by numerical simulation. The results show that the minimum-wall-thickness was the main criterion for the drawing process but not the only criterion. Crack and wrinkle can be moderately eliminated finally after optimization of the parameters and following trim process in the drawing for shallow tapered surface.

Evaluation of the normal anisotropy coefficient in AZ31 alloy sheets

The Taylor-Bishop-Hill model of plastic deformation is used to determine the dependence of normal anisotropy coefficient R on angle α in the sheet plane (α = 0 in the rolling direction) from texture in the form of the coefficients of expansion of an orientation distribution function into a series in generalized spherical functions for AZ31 magnesium alloy sheets. The calculated values of R(α) are compared to the experimental values obtained during tensile tests under normal conditions (20°C) and at 180°C.