Metallurgical and Materials Transactions A

, Volume 44, Issue 9, pp 4346–4359

Asymmetric Rolling of Interstitial-Free Steel Using Differential Roll Diameters. Part I: Mechanical Properties and Deformation Textures


    • Department of Materials EngineeringMonash University
    • Research Organization of Science and TechnologyRitsumeikan University
  • Arnaud Pougis
    • Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux, UMR 7239, CNRS/Université de Lorraine
    • Laboratory of Excellence “DAMAS”: ‘Design of Alloy Metals for low-mAss Structures’Université de Lorraine - Metz
  • Rimma Lapovok
    • Centre for Advanced Hybrid Materials, Department of Materials EngineeringMonash University
  • Laszlo S. Toth
    • Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux, UMR 7239, CNRS/Université de Lorraine
    • Laboratory of Excellence “DAMAS”: ‘Design of Alloy Metals for low-mAss Structures’Université de Lorraine - Metz
  • Ilana B. Timokhina
    • Institute for Frontier Materials, GTP ResearchDeakin University
  • Peter D. Hodgson
    • Institute for Frontier Materials, GTP ResearchDeakin University
  • Arunansu Haldar
    • R&D Division, Tata Steel Europe
  • Debashish Bhattacharjee
    • R&D Division, Tata Steel Europe

DOI: 10.1007/s11661-013-1791-y

Cite this article as:
Orlov, D., Pougis, A., Lapovok, R. et al. Metall and Mat Trans A (2013) 44: 4346. doi:10.1007/s11661-013-1791-y


IF steel sheets were processed by conventional symmetric and asymmetric rolling (ASR) at ambient temperature. The asymmetry was introduced in a geometric way using differential roll diameters with a number of different ratios. The material strength was measured by tensile testing and the microstructure was analyzed by optical and transmission electron microscopy as well as electron backscatter diffraction (EBSD) analysis. Texture was also successfully measured by EBSD using large surface areas. Finite element (FE) simulations were carried out for multiple passes to obtain the strain distribution after rolling. From the FE results, the velocity gradient along selected flow lines was extracted and the evolution of the texture was simulated using polycrystal plasticity modeling. The best mechanical properties were obtained after ASR using a roll diameter ratio of 2. The textures appeared to be tilted up to 12 deg around the transverse direction, which were simulated with the FE-combined polycrystal plasticity modeling in good agreement with measurements. The simulation work revealed that the shear component introduced by ASR was about the same magnitude as the normal component of the rolling strain tensor.

1 Introduction

Steel in sheet form continues to be in a great demand for various applications. Among them, interstitial-free (IF) steel sheet plays a major role in the markets for car body panels and a variety of consumer products. However, increasing competition from other materials targeting weight and manufacturing cost reduction makes it important to find a cost-effective way to simultaneously improve both deep drawability and strength of IF steel sheet. Despite the significant optimization of thermo-mechanical processing,[13] the conventional symmetric rolling process (SR) used for the production of IF steel sheets cannot be improved further to generate the required increased levels of these properties. In the meantime, it has been shown that methods based on the severe plastic deformation (SPD) approach can create ultrafine-grained microstructures with significantly improved mechanical properties.[4] One such process—which does not exactly belong to the group of well-known SPD methods, but employs similar principles—is asymmetric rolling (ASR).

ASR, as shown by several studies, e.g., in References 5 through 10, is an alternative process to introduce more deformation in the form of simple shear (the main characteristic of SPD processing) through the thickness of a sheet. Shear deformation is introduced into the sheet by an asymmetry of the processing conditions applied on the two sides of the sheet. Asymmetry can be created by three different techniques: differential diameter of rolls (geometric asymmetry), differential rotation speed of the rolls (kinematic asymmetry), and differential friction on the roll surfaces (tribological asymmetry). It has been shown in our previous research for aluminum[10] that the formability characteristics are different for these different ASR techniques. It has been revealed that kinematic and geometric asymmetries in rolling provide better control over the microstructure parameters than tribological asymmetry.

Extensive experimental and theoretic studies on ASR of IF steel with geometric asymmetry have been carried out with respect to grain refinement and microstructure and texture development and have been presented in our previous publications.[1113] It has been shown that ASR with geometric asymmetry improves the r-values and the plastic anisotropy of the rolled sheet. It also results in a decrease of the dislocation cell size compared to symmetric rolling as well as in a shift of frequency of subgrain boundary misorientations toward higher angles. At the same time, our preliminary work[14] has shown that geometric asymmetry provides better control of rolling and leads to more effective grain refinement and improvement of texture, mechanical properties, and r-values. Our previous investigations have also revealed that the reversal of simple shear can play a significant role in the evolution of the microstructure,[15,16] the texture,[17] as well as in the stability of the γ-fiber and the r-values.[12]

This paper presents the results of a comprehensive experimental and theoretic study of the ASR of IF steel using differential roll diameters. The effects of strain level, strain history, diameters ratio, and subsequent annealing schedule on the microstructure, texture, and mechanical properties were investigated. The experimental investigation was based on tensile and microhardness testing, optical and electron microscopy, and electron backscatter diffraction analysis. The theoretic part includes finite element (FE) simulations and crystal plasticity modeling. The paper is presented in two parts. In this first part, the role of different rolling parameters on grain refinement, microstructure formation, texture development, and mechanical properties is discussed. In the second part,[18] the effects of annealing after rolling on texture and microstructure are discussed and the modeling results are presented.

2 Methods and Materials

2.1 Material and Processing Conditions

Hot-rolled and recrystallized IF steel plates (composition in wt pct: Fe-0.0017C-0.05Mn-0.011P-0.005Si-0.023Al-0.021Cr-0.052Ti-0.002N), 25.4 mm in thickness, were supplied for the investigation by Tata Steel Ltd. In order to produce samples with thickness and other dimensions required for our experimental program in the most economical material-saving way, while keeping the texture as random as possible, the as-supplied plates were further hot rolled to two different thicknesses of 6.5 and 16.5 mm (width × length: 50 × 100 mm2), annealed at 1323 K (1050 °C) for 1 hour, and cooled within the furnace to 923 K (650 °C) and then in air down to ambient temperature. Hereafter, the state of this material will be referred to as the initial condition.

The strips were symmetrically or asymmetrically rolled at ambient temperature down to a thickness of 2.0 mm. Two rolling schedules were applied (see Table I). In the first schedule, three passes were performed, while in the second six were performed. For each pass, a thickness reduction of 30 pct was applied. This came to a total reduction of 66 and 88 pct for the first and second schedules, respectively. The asymmetry was introduced by the geometric technique, that is, by using different roll diameters. The following diameter ratios (dr) were applied: 1:1.3 (ASR-13), 1:1.6 (ASR-16), and 1:2.0 (ASR-20), see Figure 1. The two processing schedules in ASR presented in Table I were carried out in two ways: (i) by maintaining monotonic rolling (ASRm) with the larger diameter roll being always on the same side of the strip and (ii) reversal rolling (ASRr) where the strip was flipped 180 deg around the rolling direction (RD) between each pass.
Table I

Parameters of Rolling Experimental Program














66 pct-3p*

66 pct-3p

66 pct-3p

66 pct-3p

66 pct-3p

66 pct-3p

66 pct-3p


88 pct-6p

88 pct-6p

88 pct-6p

88 pct-6p

88 pct-6p

88 pct-6p

88 pct-6p

*SR stands for symmetric rolling, while ASRm and ASRr are for asymmetric rolling with monotonic and reversal application of the asymmetry, respectively; dr denotes roll diameters ratio and Np is number of rolling passes
Fig. 1

Rolling mill designed for symmetric and asymmetric rolling with different roll diameter ratios

2.2 Characterization of Structure and Properties

All samples for the characterization of properties and microstructures were cut at least 5 mm away from the left/right sides and 20 mm away from the front/rear edges of the as-rolled sheet, so these areas can be considered to have undergone “steady flow.” Special care was taken to keep track of all directions and the top/bottom surfaces of the sheet. Specimens for tensile tests were cut from the as-rolled sheets by electric-discharge machining. Then, they were ground using SiC papers with grit 400 to remove scratches left on the specimen surfaces after rolling.

The microstructure and texture characterizations were performed by means of light optical microscopy (LOM), electron backscatter diffraction (EBSD) analysis, and transmission electron microscopy (TEM) on the plane perpendicular to the transverse direction (TD). The TD plane was selected for the analysis of microstructure evolution since it is a representative section for the assessment of plastic flow in rolling. It is common practice to use this plane for the observation of microstructure evolution in rolling, e.g., in References 19 and 20. It is also particularly useful in this study since extra shear due to the asymmetry in rolling takes place in the RD, i.e., within the observation plane. All specimens for metallographic analysis were ground on SiC paper and polished with cloth containing a diamond suspension to a mirror-like finish. For the EBSD analysis, the specimen surfaces were further electro-polished in a perchloric acid-based electrolyte at 248 K (−25 °C). For the LOM observations, the electro-polished samples were finally etched in a 3 pct Nital solution for 30 seconds. TEM samples were prepared by twin jet electro-polishing using a solution of 5 pct perchloric acid in methanol at 243 K (−30 °C) and an operating voltage of 50 V.

Mechanical properties were determined by tensile tests on flat samples scaled down by a factor of 2.5 from the ASTM E8M-08 standard and having a gage length and width of 10 and 2.4 mm, respectively. The samples were cut in the rolling direction. At least three specimens were tested in each condition. The tensile tests were carried out using an INSTRON 55R4505 testing machine operated at a constant cross-head displacement rate and equipped with a standard mechanical 10-mm clip-on extensometer. The initial strain rate was set to 8.3 × 10−4 s−1.

The LOM images were taken with polarized light using an optical microscope OLYMPUS PMG3 equipped with a digital camera. Grain boundary spacing was determined using the linear-intercept method with at least 100 intercepts recorded.

A high-resolution field-emission gun scanning electron microscope (FEG-SEM) FEI Quanta 3D fitted with Hikari High Speed EBSD Detector and EDAX-TSL OIM v.5 software package was used for the EBSD data acquisition and texture analysis. The EBSD scans were performed at an accelerating voltage of 20 kV with a step size of 10.0 μm to measure a large area at least 6 × 2 mm in size covering the entire thickness of sheets and containing at least 1000 grains. To achieve this, data from 3 to 4 scans were merged for each processing condition. Although such a coarse step size did not allow the obtaining of precise subgrain structure characteristics from EBSD data, the scanned areas were sufficiently large for a statistically reliable global texture analysis. Although a slight tendency of a decrease in indexing rate toward the periphery of the scan areas was observed, it was almost completely compensated by the ~0.2-mm overlapping of the scan areas. No “clean-up” procedure was used in the analysis to avoid possible significant alterations of the original data. Instead, a “cut-off” procedure was employed to remove low-fidelity points (CI < 0.1) from the dataset.

TEM was carried out using a Philips CM 20 microscope operated at 200 kV. Observations were made in both bright and dark field imaging modes and selected area electron diffraction (SAED) patterns were taken from areas of interest using an aperture of 1.1 μm nominal diameter.

3 Results

3.1 Mechanical Properties

The measured strength and ductility as a function of strain are displayed in Figure 2 and as a function of rolls diameter ratio in Figure 3. For ASR, the results obtained for the largest diameter ratio are shown in Figure 2. It can be seen in Figure 2(a) that both the yield strength, σYS, (dashed lines on the diagram) and the ultimate tensile strength, σUTS, (solid lines on the diagram) increased monotonically with the increase in total accumulated strain. For all processing conditions, the difference between σYS and σUTS—which is related to strain hardening—decreased significantly with the accumulated strain up to the total thickness reduction of 66 pct. Up to the total thickness reduction of 66 pct, both ASRm and ASRr led to nearly the same increase in strength, which was ~15 pct higher than that after SR. Further rolling to the total thickness reduction of 88 pct led to a more intensive increase in strength for ASRm, rather than ASRr, and the lowest increase in strength for SR. As can be seen in Figure 2(b), both the uniform (δu) and the total (δf) elongations drastically decreased up to the thickness reduction of 66 pct. Further rolling to the thickness reduction of 88 pct led to almost negligible change in δu, but resulted in a significant increase in δf. These results demonstrate that cold rolling of IF steel in all processing modes leads to the significant increase of strength and to a decrease in ductility. Plastic deformation in a tensile test after rolling quickly localizes by necking with reasonable post-necking elongation. These results are consistent with earlier investigations, e.g., in References 20 through 22.
Fig. 2

Tensile properties of IF steel after SR and ASR with diameter ratio of 2.0 in monotonic and reversal regimes vs reduction in thickness: (a) yield strength, σYS, and ultimate tensile strength, σUTS; (b) uniform elongation, δu, and elongation to failure, δf. The straight lines connecting the data points in the graphs are drawn as a visual aid only and do not imply specific dependencies of the respective quantities on the reduction in thickness
Fig. 3

Tensile mechanical properties of IF steel cold rolled to the total thickness reduction of 88 pct vs the roll diameters ratio: (a) yield strength, σYS, and ultimate tensile strength, σUTS; (b) uniform elongation, δu, and elongation to failure, δf. The straight lines connecting the data points in the graphs are drawn as a visual aid only and do not imply specific dependencies of the respective quantities on the diameters ratio

Figure 3 displays the dependence of mechanical properties in IF steel cold rolled to the total thickness reduction of 88 pct on the level of asymmetry and deformation history. As can be seen in Figure 3(a), the strength after SR was always lower than that after ASR. Comparing monotonic and reversal asymmetries, ASRm led to higher strength than ASRr, starting from the roll diameter ratio of dr = 1.6. With increase in dr from 1.0 (symmetric) to the value of 2.0, the yield strength increased monotonically, while the ultimate tensile strength reached a maximum value of 593 MPa already at dr = 1.6, and then slightly dropped to 589 MPa for dr = 2.0 in the case of ASRm. Concerning ASRr, the yield stress and ultimate tensile stresses reached their maximum values at 528 MPa and 569 MPa, respectively, already at dr = 1.3. These values almost coincide with those obtained after ASRm-13. However, contrary to the ASRm case, a further increase of dr did not lead to a steady increase in the strength values for ASRr.

Figure 3(b) demonstrates that the gain in strength due to asymmetry led to a reduction of total elongation compared to the symmetric counterpart. In the case of ASRm, δf decreased monotonically from 17 pct after SR to 14 pct after ASRm-20, while in the case of ASRr, δf dropped to 14.8 pct after ASRr-13 and then increased up to 16.6 pct after ASRr-20. ASR with dr = 1.6 led to similar total elongations (about 15 pct) for both ASRm and ASRr. In contrast to the variations in total elongation, the uniform elongation—which was equal to δu  = 1.2 pct after SR—was enhanced by ASR. In particular, δu reached the maximum of 1.8 pct in the case of ASRm-13 and a maximum of 1.9 pct in the case of ASRr-20.

3.2 Microstructural Analysis

The LOM micrographs in Figure 4 show the initial and representative through-thickness macrostructures of the steel strip after processing. The analysis of Figure 4(a) reveals that the initial microstructure consists of rather equiaxed ferrite grains with a mean boundary spacing in the normal direction (ND) of 143 ± 21 μm and of 157 ± 28 μm in the RD. After all rolling routes, the macrostructures consist of typical RD-elongated grains. The grains can be separated in two distinctly different populations: (i) weakly etched grains having very smooth and light contrast interiors and (ii) strongly etched grains having alternating dark/light gray contrasts interiors. At this level of strain, the boundaries between grains within each population are very blurry and difficult to resolve by LOM, while they are very distinct between grains belonging to the different populations. Therefore, the linear-intercept measurements of boundary spacing do not provide adequate estimates expected from the Polyani–Taylor principle at this reduction in thickness. Further details about the boundary spacing will be provided in the TEM results described below and the EBSD data analysis in Part 2 of our work.[18]
Fig. 4

LOM micrographs of IF steel in initial state and after cold rolling to 88 pct of total thickness reduction. (a) initial microstructure; (b) after SR; (c) after ASRm-13; (d) after ASRr-13; (e) after ASRm-16; (f) after ASRr-16; (g) after ASRm-20; (h) after ASRr-20

Similar microstructural features in conventionally rolled IF steel were reported by Vanderschueren et al.[23] where the first and the second populations were classified as α- and γ-fiber grains, respectively. The α (i.e.,\( \langle 110\rangle ||{\text{RD}} \)) and γ (i.e., \( \langle 111\rangle ||{\text{ND}} \)) fibers are the most common and pronounced texture components developing during rolling (or in plane-strain compression) of b.c.c. metals.[19,24] According to Reference 23, the near α-fiber grains are “soft” orientations having a rather weak tendency to rotations and to development of substructure. Grain orientations near the γ-fiber have a higher spread in orientations and are much more susceptible to the development of substructure. Therefore, the alternating dark/light gray contrasts for the γ-fiber (or the second population) grains can indicate the formation of shear/microbands. The intensive development of dislocation substructure in the γ-fiber grains also leads to a higher rate of strain hardening in these grains. As identified by arrows in Figures 4(b) and (g), the soft α-fiber grains are forced to flow around the harder γ-fiber grains.

Although the appearance of the two grain populations is common for all macrostructures in Figure 4, the frequency of the appearance of the second-population grains depends on the processing route. Namely, the microstructures of the samples processed by ASRm demonstrate a higher density of γ-fiber grains compared to their counterparts after ASRr or SR, with the highest density being in samples deformed by ASR with dr = 1.6 (see Figures 4(e) and (f)).

3.3 TEM Characterization of Dislocation Substructure Formed After Different Rolling Conditions

The micrographs of the most representative microstructures revealed by TEM observations are shown in Figure 5. After 66 pct thickness reduction in SR, two types of deformation microbands were formed (Figure 5(a)). Namely, there are microbands parallel to the RD and shear bands inclined to the RD by about 35 deg. To distinguish between microbands and shear bands, we follow the definition given in Reference 13. Both types of the deformation bands display a similar thickness of 0.4 ± 0.1 μm, Figure 5(a). However, the bands after SR to 88 pct reduction have a significant variation in their thickness, ranging between 0.16 and 0.6 μm, see Figure 5(b). Here, the microstructure is represented by (i) thicker microbands parallel to both the RD and {110} planes, indicated by white arrows in Figure 5(b), and (ii) two clusters of finer microbands, one parallel to the RD, shown by black arrows in Figure 5(b), and the second inclined to the RD by about 35 deg, shown by black arrows with open interiors in Figure 5(b). The microbands still have low-angle boundary misorientations and their average orientation indicates that they belong to the γ-fiber.
Fig. 5

TEM micrographs representing the microstructure after SR to 66 pct (a) and 88 pct (b) of total thickness reduction, ASRm-20 to 66 pct (c) and 88 pct (zone axis is [113]α) (d), and ASRr-20 to 66 pct (zone axis is [113]α) (e) and 88 pct (f)

The change in rolling condition from SR to ASRm leads to a decrease in the deformation bands’ spacing to 0.3 μm and to the development of sharper dislocation walls accompanied with a decrease in the dislocation density in the cell interiors, see Figures 5(c) and (d). The dislocation substructure formed after ASRm to 88 pct reduction is more complex. It reveals the formation of micro-cells and deformation microbands having two orientations. Based on the analysis of azimuthal deflection of SAED pattern and the contrast of bright field image, it was found that the cells show larger boundary misorientation angles compared to those after SR: 5 to 10 deg. Moreover, some cells display very low dislocation densities in their interior, see, e.g., the identified \( [1\bar{1}0] \)||RD-oriented cell in Figure 5(d).

The dislocation substructure after ASRr (Figures 5(e) and (f)) is even more complex than after ASRm. The formation of cells and microbands as lamellar shear bands with an average spacing of 0.3 ± 0.05 μm can also be seen here. In addition, deformation bands parallel to the rolling direction and crossing several ferrite grains can be found (see Figures 5(e) and (f)) with an average thickness of 0.5 ± 0.05 μm. The interaction between the two sets of deformation bands leads to the formation of a fragmented dislocation substructure with sharp dislocation walls and low dislocation densities within the cell interiors.

3.4 Texture Analysis

It is well established by now that the evolution of crystallographic texture can be conveniently described in terms of texture components typical for a particular deformation mode. For bcc metals, these texture components are well established for pure shear, which is the case in plane-strain compression and symmetric rolling, see for instance References 19, 24. Concerning ASR, we have found in a recent theoretic study carried out on the stability of orientations and the rotation field in Euler space[12] that the ideal components of ASR are the same as for SR; they are simply rotated around the TD axis with respect to SR as long as the shear component is not the major one. In the present work, the dependence of the variation of the typical rolling texture components on the parameters of asymmetry is examined experimentally and by FE simulations of the textures.

The textures measured in the present study are displayed in {110} pole figures (Figure 6) as well as in the φ2 = 45 deg sections of the Euler orientation space showing the orientation distribution function (ODF, Figure 7). The pole figure presentation is suitable to show the overall texture, while the φ2 = 45 deg section is ideal to show the main ideal orientations of rolling textures (the α- and γ-fibers) without overlapping. It should be noted that the symmetry is reduced in ASR because of the shear, so only a twofold symmetry applies on the ASR textures around the TD direction of the specimen. This is the reason why the ODFs are plotted between 0 and 180 deg along the φ1 axis. For the second Euler angle, φ, the length of the axis is in the usual 0 to 90 deg range in Figure 7. To ease the reading of the ODFs, the positions of the major rolling texture components and fibers are indicated.
Fig. 6

Experimental {110} pole figures showing the initial (a) and end textures after SR, ASRm, and ASRr. (b): cold rolled to the total reduction in thickness of e = 88 pct by SR, same by ASR (c to h) with diameter ratios of n = 1.3 (c, d), n = 1.6 (e, f), and n = 2.0 (g, h) with the asymmetry applied in monotonic (c, e, g) and reversal (d, f, h) regimes
Fig. 7

Texture represented by φ2 = 45 deg sections of ODFs in initial state and after cold rolling to the 88 pct of total thickness reduction. (a) initial microstructure; (b) after SR; (c) after ASRm-13; (d) after ASRr-13; (e) after ASRm-16; (f) after ASRr-16; (g) after ASRm-20; (h) after ASRr-20

As can be seen in Figures 6(a) and 7(a), the texture in the initial condition is rather weak; its maximum intensity is only 2.6 mrd. Even though the texture is weak, the γ-fiber is preferential. After SR (Figures 6(b) and 7(b)), the texture becomes quite strong with a maximum intensity of 11.7 mrd in the ODF. The crystal orientations spread predominantly along the α- and γ-fibers; the strongest ideal components are the \( (112)[1\bar{1}0] \) and the rotated cube \( (001)[\bar{1}\bar{1}0] \), both situated along the α-fiber.

The main feature arising with the introduction of asymmetry in rolling is a general rotation of the whole texture around the TD axis, apparent in Figures 6(c) through (h). The same effect in the ODF section is a shift of the texture in the φ direction, see Figures 7(c) through (h). Close inspection of the textures reveals, however, that the rotation angle is not the same for all ideal components. For example, ASRm-13 leads to a shift of the \( (001)[\bar{1}\bar{1}0] \) and \( (111)[0\bar{1}1] \) components by about 12 deg in the φ direction, while the \( (112)[1\bar{1}0] \) texture component remains stable in its unrotated “SR position,” see Figure 6(c). At the same time, the intensities of the former components rise significantly at the expense of a moderate decrease in the intensity of the α-fiber. Consequently, the general intensity of the texture remains similar to the SR case. Another particular feature of the texture development is that by increasing the level of the rolling asymmetry from ASRm-13 to ASRm-16, the shift of the \( (001)[\bar{1}\bar{1}0] \) and \( (111)[0\bar{1}1] \) components becomes smaller, the \( (112)[1\bar{1}0] \) component is slightly shifted now in the negative Φ direction, and the overall texture intensity increases (Figure 6e). Further increase of the rolling asymmetry using the ASRm-20 schedule results in a drop of the texture strength to a level which is slightly lower than after SR. At the same time, the shift of the \( (001)[\bar{1}\bar{1}0] \) and \( (111)[0\bar{1}1] \) components is similar to the ASRm-13 case and the \( (112)[1\bar{1}0] \) component is more rotated in the negative Φ direction (Figure 6(g)).

The reversal of the rolling asymmetry between each pass during processing in ASRr-13 leads to a sharp increase in the texture intensity compared to both SR and ASRm-13 (Figure 6(d)). An important observation is that in spite of the ASR process during each pass, the γ-fiber components appear in the ideal positions expected for SR. A difference between ASRm-13 and SR is that the intensity of the \( (111)[1\bar{1}0] \) orientation is moderately stronger. A new component located between the \( (001)[\bar{1}\bar{1}0] \) and \( (001)[1\bar{1}0] \) appears. Another feature is that the \( (001)[\bar{1}\bar{1}0] \) and \( (001)[1\bar{1}0] \) shift significantly along φ1 direction (Figure 6(d)). The increase of asymmetry amplitude in ASRr-16 results in a decrease of the texture intensity, see Figure 6(f). The intensity distribution along the γ-fiber is very different from the ASRm-13 case; the \( (111)[1\bar{2}1] \) component becomes strong. The \( (111)[0\bar{1}1] \)γ-fiber component and the \( (001)[\bar{1}\bar{1}0] \) component remain similar in intensity compared to both ASRr-13 and ASRm-16. At the same time, a spread of α-fiber orientations in the φ1 direction is noticeable. When the asymmetry level is increased further, i.e., in the ASRr-20 case (Figure 6(h)), the γ-fiber components are shifted from their SR stable positions to positions similar to the monotonic ASRm-20 case; the overall texture intensity is also similar.

4 Finite Element Modeling of SR and ASR

4.1 Modeling Conditions

Two-dimensional FE simulations were carried out assuming plane-strain conditions using the commercial package ABAQUS/Standard 6.10. The two rolls were treated as rigid bodies. The plate was a deformable body discretized by 4125 CPE4 elements with four nodes and four integration points. Coulomb friction was used between the rolls and the plate with the friction coefficient being 0.1. The modeling was restricted to the SR and ASRm-20 cases for up to six passes. In the ASR modeling, the smaller roll was on top.

Hardening was modeled with the help of a UMAT subroutine with isotropic plasticity; for the description of the simulation procedure and the hardening parameters, see Reference 13. Initial material points were followed along their flow lines. The deformation gradient \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{F} } \) was extracted along three flow lines using the UMAT subroutine. In subsequent rolling passes, the values of stresses and plastic strain components as well as the y-coordinates of the nodes obtained in the previous pass were used as initial conditions for all elements in the simulation of the next pass.

The deformation gradient along the flow line was used to calculate the velocity gradient \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{L} } \) from its definition: \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{L} } = \dot{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{F} } }\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{F} }^{ - 1} \). Here, the time derivative of \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{F} } \) was approximated by the incremental numeric time derivative using the time increment \( \Updelta t \) between positions: \( \dot{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{F} } } \cong {{\Updelta \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{F} } } \mathord{\left/ {\vphantom {{\Updelta \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{F} } } {\Updelta t}}} \right. \kern-0pt} {\Updelta t}} \). The calculation of the velocity gradient permitted to obtain the evolution of all strain components, particularly the two shears that appear in ASR: the RD-directed shear on the ND plane, \( \gamma_{\text{RD,ND}} \), and the ND-directed shear on the RD plane, \( \gamma_{\text{ND,RD}} \). This procedure is important in order to distinguish between these two shear components. Indeed, the strain rate tensor \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\dot{\varepsilon }} } \) as can be obtained from the velocity gradient by its definition \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\dot{\varepsilon }} } = \left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{L} } + \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{L} }^{t} } \right)/2 \) is symmetric giving the same values for the two distinct shears. In order to quantify the accumulated shears in the RD and ND directions, two kinds of integrals were carried out; one for their accumulated values and another for their accumulated absolute (by modulus) values:
$$ \gamma_{\text{RD,ND}} = \int\limits_{0}^{T} {L_{\text{RD,ND}} } dt,\quad \gamma_{\text{ND,RD}} = \int\limits_{0}^{T} {L_{\text{ND,RD}} } dt, $$
$$ \left| {\gamma_{\text{RD,ND}} } \right| = \int\limits_{0}^{T} {\left| {L_{\text{RD,ND}} } \right|} dt,\quad \left| {\gamma_{\text{ND,RD}} } \right| = \int\limits_{0}^{T} {\left| {L_{\text{ND,RD}} } \right|} dt. $$

Here, T denotes the total time of plastic strain. The calculation of both integrals of accumulated shears is important to see possible differences caused by shearing in opposite directions.

The velocity gradient was also used to simulate the evolution of the texture and the microstructure with the help of a recently developed polycrystal model[25] which is able to model in one single frame the evolution of the texture, the grain size distribution, and the misorientation distribution of the fragmented grain structure. The model is topological; it is based on the lattice curvature that develops in grains due to the slowdown of lattice rotation near grain boundaries; for more details, see Reference 25. In this first part, we present only the results of the texture simulations; the other features will be discussed in Part II of the present work.[18]

4.2 Strain Analysis

Figures 8 and 9 display the above-defined strain measures obtained from the FE simulations for the rolling strain and for the two shear strains for all six passes at three positions within the sample: bottom, middle, and top. The following major trends are important by comparing Figures 8 and 9 for the SR and ASR cases, respectively:
Fig. 8

The accumulated strains during rolling obtained by integration of the absolute values of the strains in SR (a) and in ASRm (b) as a function of pass number
Fig. 9

The accumulated strains during rolling obtained by integration of the real values of the strains in SR (a) and in ASRm (b) as a function of pass number

  1. 1.

    First of all, there is a perfect symmetry for the top and bottom cases with respect to the middle position for SR, while the strains are not symmetric for the same in ASR.

  2. 2.

    There is inhomogeneity in the rolling strain \( \varepsilon_{\text{RD,RD}} \) for both SR and ASR within the thickness. This strain component has a slight minimum in the middle section for SR, while it is minimal at the top for ASR and monotonically increasing toward the bottom. The maximum difference in strain reaches about 0.15 after six passes, which is not negligible. This effect can be explained by the effect of hardening. Indeed, the total equivalent strain is significantly larger in regions where the shear strain is large, which hardens the material more. In this way, a hardness gradient develops in the thickness of the plate, which leads to higher \( \varepsilon_{\text{RD,RD}} \) rolling strain in regions where the material is softer.

  3. 3.

    The absolute values of the accumulated strain are larger than the accumulated real values for the shear components. This means that the shears are changing sign during the process when the material is crossing the “neutral section.”

  4. 4.

    The \( \gamma_{\text{RD,ND}} \) and \( \left| {\gamma_{\text{RD,ND}} } \right| \) strains are generally higher than \( \gamma_{\text{ND,RD}} \) and \( \left| {\gamma_{\text{ND,RD}} } \right| \), respectively. Nevertheless, the latter shears are quite significant with respect to the former and thus cannot be neglected.

  5. 5.

    There is a variation in the \( \gamma_{\text{RD,ND}} \) component within the thickness. For ASR, the largest shear takes place in the top region of the sheet. This can be attributed to the effect of the smaller roll, which is above the sheet. There is a similar effect on the \( \gamma_{\text{ND,RD}} \) component for the same reason.


4.3 Simulated Textures

The velocity gradient obtained from the FE simulations along the trajectory of three material elements—near the top, at the middle, and at the bottom position within the thickness—was used in the grain refinement viscoplastic polycrystal model. Figure 10 displays the textures in the form of {110} pole figures for both SR and ASR and for the three positions within the thickness. As can be seen, the texture is symmetric with respect to the reference system only in the middle of the sheet for SR. In both the top and bottom positions, the pole figure is tilted in the RD and −RD directions, respectively. This tilt is due to the shears that rotate the texture: They change signs between the top and bottom positions, see Figure 9(a). Actually, the \( \gamma_{\text{ND,RD}} \) component is always smaller and opposite to the \( \gamma_{\text{RD,ND}} \) shear, so their effect on the tilt is the opposite. Nevertheless, the tilts are not canceled; the net rotation of the texture is quite significant and is about 10 deg.
Fig. 10

{110} pole figures obtained from the FE simulation after six passes for SR (a, b, c) and ASRm (d, e, f) at the top, middle, and bottom positions. Isovalues: 0.8, 1.0, 1.3, 1.6, 2.0, 2.5, 3.2, 4.0, 5.0, 6.4

In contrast to SR, the simulated texture for the ASR case is always tilted in the RD direction independent of the position within the sheet thickness, see in Figures 10(d) through (f). The amount of rotation is similar to the rotations obtained for the SR case and seems to be independent of the position within the sheet.

For comparison with the experimental textures, the three textures were integrated into one for both SR and ASR; see the resulting textures in Figure 11. Actually, the experimental textures were measured in the whole cross section of the TD plane, see in Figure 6, so they show average textures. As can be seen, the simulated texture for SR is perfectly symmetric, while significantly (about 12 deg) rotated in the RD direction for ASR. The positions of the maxima of the experimental pole figures of Figure 6 are marked by stars in Figure 11. Clearly, the symmetric nature of the SR texture in the whole TD section is a result of the opposite rotations of the texture in the top and the bottom regions of the sheet. For ASR, the texture is always rotated in the sense of the larger shear component (\( \gamma_{\text{RD,ND}} \)), so the average texture shows the same.
Fig. 11

“Average” {110} pole figures obtained from the FE simulation after six passes for SR (a) and ASRm (b) by integrating the three pole figures corresponding to the bottom, middle, and top positions. Isovalues: 0.8, 1.0, 1.3, 1.6, 2.0, 2.5, 3.2, 4.0, 5.0, 6.4

5 Discussion

5.1 Correlation Between Mechanical Properties, Microstructure, and Processing Variables

Summarizing the results reported in Section III, it can be concluded that the change of deformation mode from symmetric to ASR does affect both the microstructure evolution and the tensile properties in IF steel. Although the effects are not large, they are significant enough to be considered in the advancement of industrial technologies of IF steel sheet manufacturing.

In greater detail, ASR leads to faster development of the substructure compared to the SR case as evidenced by the results presented in Figures 4 and 5. Namely, the dislocation density is higher and the dislocation cells are smaller in ASR. Misorientations between cell boundaries are also higher after ASR and their geometrical orientation with respect to the rolling direction is different. When the geometry of asymmetry is reversed by rotating the sample between passes (ASRr), shear bands parallel to the RD are formed. As a consequence of such microstructure evolution, the samples deformed in ASR mode have higher strength for monotonic ASR. The strength difference is increasing monotonically with an increase of both the asymmetry level and the total accumulated strain (i.e., the number of passes). The reverse of asymmetry after each pass leads to smaller and non-monotonic increase in strength; nevertheless, it results in higher ductility.

It is important to point out that the maximum possible level of asymmetry is limited by the friction conditions between the roll and the sheet. When the imposed asymmetry is too high to be sustained by friction, the sheet slips on the roll’s surface. In our experiments, we occasionally observed linear marks perpendicular to the RD, which is evidence of a stick–slip behavior during processing. This might be the reason for the occurrence of the saturation in strength when the ASR diameter ratio is increased from dr = 1.6 to 2.0. Friction is also one of the most limiting factors in controlling the maximum possible reduction per pass in cold rolling processes, especially at the beginning of processing when the sheet is relatively thick.

The results reported in Section IV–B allow an explanation of the nature and scale of the effects of ASR discussed above. The moderate differences in grain refinement can be explained by the similar levels of the total accumulated equivalent strains after SR and ASR. Nevertheless, it was found that the shear component is generally higher in ASR and that the shear strain is more uniformly distributed across the sheet thickness which leads to more homogeneous microstructure and texture.

The present results are very much in agreement with earlier reports, e.g., in References 5, 6, 26 through 28. The theoretic works reporting higher shear strains at a higher reduction per pass in ASR are only possible in hot rolling due to softer material being processed and higher friction.[6,26] Those simulation works only considered rolling in a single pass, which is not always possible. In our multi-pass experiments and simulations in cold rolling conditions, the obtained effects are moderated by a lower friction and lower reductions per pass due to multi-pass processing. Compared to results obtained in other pure metals like fcc aluminum[5,27] and even bcc low-carbon steel,[28] the effect of ASR on the level of grain refinement in IF steel is lower. This can be due to the (i) easier cross-slip in IF steel which should lead to lower grain refinement and (ii) lack of interstitial atoms that could pin dislocations causing pileups. Pileups promote the increase of misorientations, which is an important ingredient in the grain refinement process.[25]

5.2 Dependence of Texture Development on Processing Variables

As has been reported in Section III–D, the main characteristic feature of ASR-induced texture is a rotation of the typical rolling texture around the TD axis. This feature is consistent with the results of other research available from the literature, e.g., in References 5, 7, 26, 27, 29. The tilt of the rolling texture in ASR is common for both fcc[5,7,27] and bcc[26,29] metals. However, the extent of this effect strongly depends on the material and on the processing variables.

In the present study, the tilt of the texture in IF steel was found to be independent of the level of total equivalent strain. However, it strongly depends on the level of asymmetry and on the processing route. The analysis of the texture in ODF form permitted the observation that the rotation angle of the typical rolling texture is different for different texture components. A schematic illustration of the directions and relative magnitudes of the shifts of the major rolling texture components due to the asymmetry in rolling is given for the φ2 = 45 deg section of the Euler orientation space in Figure 12. This effect leads to a significant redistribution in the intensity of the texture components, which ultimately affects the process of grain refinement and the final strength.
Fig. 12

Schematic illustration of directions and relative magnitude of shifts of major rolling texture components in φ2 = 45 deg sections of ODF due to the asymmetry in rolling. The symbols’ notation is same as in Fig. 7

It was also observed that the overall tilt of the texture increases with the increase of the differential diameter ratio. In ASRm (monotonic asymmetry), it reaches the maximum value of approximately 12 deg at diameter ratio dr = 1.6 and then remains nearly constant with further increase in dr. In the case of the asymmetry reversal after each pass (ASRr), the texture tilt is canceled after each even pass when the level of asymmetry is small, like in the ASRr-13 case. However, at high diameter ratios, like for ASRr-20, the amplitude of the forward shear is high enough not to be canceled in the subsequent pass. In that case, crystal orientations do not perfectly go back into the positions they had before the forward shear. Such behavior is found to be in good qualitative agreement with the theoretic predictions reported in Reference 12.

It has been clearly shown with the help of FE and the crystal plasticity simulations in Section IV that the tilt of the texture is caused by the extra shear strain, which is homogenously distributed across the sheet thickness in ASR. Comparing the simulated average textures of Figure 11 to the experimental ones (Figure 6(b) for SR and Figure 6(h) for ASR), one can see that the most important features of the texture are rather well reproduced by the FE simulation. For SR, there is perfect agreement for the positions of the maximum intensities, while for ASRm, there is a small difference in the tilt of the components. The main parameter in the simulation, which can influence the position of the maximum intensity, is the friction for which the value of 0.1 was used. Larger friction would give larger rotation, that is, more asymmetry in the pole figures. Nevertheless, the agreement between experiments and the simulation reveals the approximate value of the ASR-induced shear component with respect to the rolling strain, which is about as large as the symmetric rolling strain.

6 Conclusions

In this work, results of analyses on strength, texture, and microstructure obtained in IF steel sheets processed by conventional symmetric (SR) and asymmetric (ASR) rolling at ambient temperature were reported. The asymmetry was introduced in a geometric way using differential roll diameters with a number of different ratios. From the results obtained through tensile testing, optical and electron microscopy, and EBSD analysis as well as a theoretic study based on FE and crystal plasticity simulations, the following conclusions can be drawn:
  1. 1.

    Compared to SR, ASR leads to a significant redistribution of the strain tensor components. Namely, the shear strains significantly increase at the expense on the normal components. In contrast to SR, the shear is homogeneously distributed across the sheet thickness.

  2. 2.

    In the IF steel sheet, such redistribution of the strain tensor components leads to (i) accelerated development of substructure accompanied by more intensive grain refinement, (ii) increase of density of γ-fiber grains and homogeneity of their distribution, (iii) substantial increase of strength, and (iv) tilt of the rolling texture components around the transverse direction. These effects strongly depend on both the level of the total accumulated strain and the level of asymmetry (diameter ratio). In the present study, an increase in strength of the γ-fiber up to 20 pct and a maximum tilt of the texture up to 12 deg due to ASR were achieved.

  3. 3.

    The tilt of the texture solely depends on the asymmetry magnitude.

  4. 4.

    The reverse of the asymmetry after each rolling pass (ASRr) leads to complete canceling of the texture tilt and a reduction of the other above-mentioned effects when the asymmetry amplitude is small. However, the canceling effect is not full with substantial increase in the asymmetry amplitude.



The authors acknowledge the use of equipment within the Monash Centre for Electron Microscopy, including SEM FEI Quanta 3D, funded through the Australian Research Council grant LE0882821. The authors also gratefully acknowledge financial support of this work by a Linkage Industrial project LP0989455 of the Australian Research Council. This work was also supported by the French State through the program “Investment in the future” operated by the National Research Agency (ANR) and referenced by ANR-11-LABX-0008-01 (LabEx DAMAS). One of the authors (P.D.H.) also acknowledges the support of the ARC Laureatte Fellowship scheme.

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© The Minerals, Metals & Materials Society and ASM International 2013