**1. Introduction**

Asymmetric sheet rolling is a process used when there are differences in any technological parameters in the horizontal plane across the width of the deformation zone or in the vertical plane between the top and bottom surfaces of the deformation zone. Asymmetric rolling due to purposefully created differences in the circumferential speeds of the work rolls is also called "differential speed rolling". For such a process, a degree of asymmetry is defined by a ratio of circumferential speeds *V*1 and *V*2 of the work rolls according to Equation (1):

$$S\_R = \frac{V\_1}{V\_2} \tag{1}$$

where *SR* is the "speed ratio" and *V*1 > *V*2. The first theoretical description of the asymmetric rolling process was proposed in 1941 by Siebel [1]. Experimentation has been used to quantify rolling force and torque. In 1947, Sachs and Klinger [2] first identified the region of cross shear, due to the fact that friction forces act in opposite directions in the deformation zone. The first invention of a rolling process with high ratio of circumferential speeds of work rolls (*SR* = 3) was announced in 1940 in the USSR by Razuvaev [3]. He was the first to propose a rolling process at a circumferential speed ratio equal to the ratio of sheet thicknesses before and after rolling according to Equation (2):

$$\frac{V\_1}{V\_2} = \frac{h\_0}{h\_1} \tag{2}$$

**Citation:** Pustovoytov, D.; Pesin, A.; Tandon, P. Asymmetric (Hot, Warm, Cold, Cryo) Rolling of Light Alloys: A Review. *Metals* **2021**, *11*, 956. https://doi.org/10.3390/met11060956

Academic Editor: Nikolay A. Belov

Received: 10 May 2021 Accepted: 10 June 2021 Published: 13 June 2021

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where *h*0 is the thickness of the sheet before the rolling pass, *h*1 is the thickness of the sheet after the rolling pass. This rolling process was proposed to reduce rolling force, obtain thinner sheets and reduce the number of rolling passes by increasing the reduction in each pass.

In the 1950s and 1960s, the first laboratory and industrial experiments on asymmetric rolling were performed and technological results were published [4,5]. Between the 1970s and 1990s, many experiments and theoretical calculations were carried out and the development of asymmetric rolling processes was focused mainly on the improvement of sheet geometry and technological aspects of the hot and cold rolling processes [6–13]. Asymmetry was used to reduce rolling force, improve sheet flatness, minimize the ski effect and obtain thinner sheets. Thus, from the 1940s to the end of the 1990s, the development of asymmetric rolling processes took place in research, which can be named as the "geometry approach" (Figure 1). The introduced asymmetry was rather low. Usually, the *SR* value did not exceed 1.5. Since the end of the 1990s, a new direction in the research on the asymmetric rolling processes has occurred. The development of asymmetric rolling processes has taken place in research, which can be named as the "material approach". The introduced asymmetry is rather high. Usually, the *SR* value is more than or equal to 2.0.

**Figure 1.** Different research lines for asymmetrical rolling processes: "geometry approach" and "material approach".

The first work about using asymmetric rolling with a high speed ratio (*SR* = 2.0) to control the texture and mechanical properties of Al alloys was published in 1998 by Choi et al. [14]. It was shown that AA1100 and AA3005 sheets composed of only shear texture with high {111} components could be obtained by asymmetric rolling. A remarkable improvement in the average Lankford value was also obtained. In 2000, Cui and Ohori [15] demonstrated that the presence of shear strain is more important than the maximum level of thickness reduction, when considering grain refinement by asymmetric rolling. They achieved grain refinement (~2 μm) in high-purity Al by asymmetric cold rolling. Fine grains evolved during asymmetric rolling and were stable at temperatures below 423 K.

In 2007, Kim et al. [16] introduced and developed an asymmetric rolling process known as the severe plastic deformation (SPD) method. Differential speed rolling with a high speed ratio (*SR* = 3.0) between the top and bottom work rolls was applied to AZ31 sheets (2 mm thick and 140 mm wide). The diameters of the top and bottom work rolls were identical and equal to 300 mm. From a starting thickness of 2 mm, sheets were reduced to 0.6 mm (70% reduction) by a single pass without lubrication. The effective strain accumulated during asymmetric rolling was 3.53 on average [16], which was comparable to that obtained by ECAP on a rod after three pressings. A very fine grain size of 1.4 μm and a high yield stress of over 300 MPa were obtained after asymmetric rolling at 413 K. Significant grain refinement was achieved due to the introduction of high shear strain. The best compromise between strength and ductility was achieved at 433 K. This result indicated that SPD can be imposed by differential speed rolling with a high speed ratio. This process was called "high-ratio differential speed rolling" (HRDSR) [17–20]. In 2009, it was applied to obtain high-strength sheets from Al alloy 6061 [19], and in 2010, to obtain high-strength sheets from pure Ti [20]. Kim et al. [21] in 2011, Loorentz and Ko [22] in 2012 and Polkowski [23] in 2013 introduced differential speed rolling with speed ratio *SR* = 4.0 for improvement of the microstructure and texture in Ti [21], Al [22] and Cu [23] alloys.

Thus, from 1998 to the present, asymmetric rolling with the "material approach" has been applied to light alloys of Mg, Al and Ti, which are the materials selected for this review. These materials have very attractive features such as light weight and high specific strength. The development of asymmetric rolling technology, such as the severe plastic deformation method, for industrial production of large-scale sheets with ultrafine grain structure and enhanced mechanical properties has been the major research line for the last 20 years. Depending on temperature conditions, four asymmetric rolling processes can be implemented: (1) Asymmetric hot rolling, when the temperature of the sheet is in the range (0.6...0.8) Т*melt*, where Т*melt* is a melting temperature in K; (2) asymmetric warm rolling, when the temperature of the sheet is in the range (0.3...0.6) Т*melt*; (3) asymmetric cold rolling, when the temperature of the sheet is below 0.3 Т*melt*; (4) asymmetric cryorolling, when the sheet is cooled in liquid nitrogen until the temperature reaches −153– −196 ◦C. Asymmetric cryorolling was first proposed in 2012 by Yu [24] as a new technique that combines the features of asymmetric rolling and cryorolling [25,26].

Although some reviews of asymmetric rolling processes have already been presented [27,28], the purpose of this review is to analyze and summarize the most relevant information regarding the asymmetric (hot, warm, cold, cryo) rolling processes in terms of the effect of purposefully created asymmetry on grain size and mechanical properties of pure Mg, Al, Ti and their alloys. This work is divided into six sections. First, the classification of asymmetric rolling processes is presented. Secondly, the fundamentals of the mechanics of the asymmetric rolling process due to purposefully created differences in the peripheral speeds of the work rolls are presented. This is followed by an analysis of asymmetric (hot, warm, cold, cryo) rolling of Mg alloys, Al alloys and Ti alloys. The review ends with conclusions and future prospects for these technologies.

#### **2. Classification of Asymmetric Rolling Processes**

Asymmetry can either have random causes, or it can be created purposefully (Figure 2). Asymmetry in the horizontal plane along the width of the deformation zone due to random causes can be caused by differences in thickness, temperatures, friction, displacement of the sheet along the work roll length, skewed work rolls or incorrect setting of the right and left hydraulic pressure devices.

Asymmetry in the vertical plane between the top and bottom surfaces of the deformation zone due to random causes can be caused by inclined entry of the sheet into the roll gap, differences in temperatures, friction, differences in the work roll diameters at the same angular speeds or differences in the work roll angular speeds with the same diameters. In

any case, asymmetric rolling caused by random causes is undesirable. For example, a negative consequence of asymmetric rolling is the bending of the plate, usually in hot rolling mills, more often known as the "ski effect" [29,30]. The negative effect of such asymmetry is prevented by improving equipment, stabilizing technology and using automatic regulators. However, asymmetry can also be purposefully introduced to improve the rolling process, for example, reducing rolling force, improving sheet flatness, minimizing the ski effect, obtaining thinner sheets, grain refinement and improvement of the texture and mechanical properties of sheet metals and alloys.

**Figure 2.** Classification of asymmetric rolling processes.

Asymmetry in the horizontal plane across the width of the deformation zone can be purposefully created by rolling with cone-shaped work rolls [31]. A schematic illustration of this process is shown in Figure 3a. When the ratio of the largest diameter of the roll to the smallest one D/d = 1.5, shear strain increases by 1.5–2.0 times in comparison with conventional rolling [32].

A little asymmetry in the horizontal plane across the width of the deformation zone can be an effective tool to improve sheet shape. The continuous variable crown (CVC) system (Figure 3b) was developed by Schloemann-Siemag (SMS) as a powerful tool for sheet shape control. The work rolls have an "S" shape and are arranged asymmetrically [33]. Through the axial shifting of two work rolls towards each other, a continuously adjustable rolling gap contour can be obtained. The CVC system is employed in many cold rolling and hot rolling mills worldwide. A little asymmetry in the horizontal plane can also be obtained by crossed work rolls (Figure 3c). The first hot rolling mill with asymmetry due to crossed work rolls was used at Nippon Steel's Kimitsu Works in 1991 [34]. In the work roll crossed system, the axes of the top and bottom work rolls are crossed as shown in Figure 3c. Work roll crossing is designed to control the roll gap profile. This action provides control over the shape and profile of the sheet. Thus, a little asymmetry across the width of the deformation zone provided by CVC or crossed work rolls is used in industrial rolling mills to improve the shape and flatness of sheets.

**Figure 3.** Schematic illustration of asymmetric rolling processes with purposefully created asymmetry in the horizontal plane along the width of the deformation zone: (**a**) Rolling with cone-shaped work rolls; (**b**) rolling with CVC work rolls; (**c**) rolling with crossed work rolls.

Asymmetry in the vertical plane between the top and bottom surfaces of the deformation zone can be purposefully created by inclined entry of the sheet into the roll gap [35] (Figure 4a) or due to differences in temperatures, when one work roll is purposefully heated and the other one is cold (Figure 4b).

Asymmetry during rolling can be purposefully created due to friction differences [36,37]. This rolling process is called "differential friction rolling" [37]. To change the friction coefficients on the contact surfaces of the deformation zone, the lubricant can be supplied only from one side (Figure 5a). Another way to create friction differences is rolling with different roughnesses of the top and bottom work rolls (Figure 5b). Utsunomiya et al. [37] proposed a differential friction rolling process for improvement in the r-value of aluminum sheets. A two-high rolling mill with TiC-coated rolls 130 mm in diameter was used for rolling of commercial aluminum AA1050 sheets 3 mm thick and 30 mm wide. A single-pass thickness reduction of 50% was conducted at 473 K. Low friction was achieved by applying a thin polytetrafluoroethylene (PTFE) film on the sheet. Teflon (PTFE) was sprayed by aerosol on the upper surface of the aluminum sheet and dried. However, the lower surface remained unlubricated. Both the top and bottom rolls revolved at the same speed of 2 m/min. The shear strain introduced by differential friction rolling was comparable to that introduced by differential speed rolling [37]. The annealed sheet showed a higher r-value than the symmetrically rolled sheet.

**Figure 4.** Schematic illustration of asymmetric rolling processes: (**a**) Rolling with inclined entry of the sheet into the roll gap; (**b**) rolling with temperature differences.

**Figure 5.** Schematic illustration of asymmetric rolling processes due to friction differences: (**a**) Rolling with different lubrications for top and bottom work rolls; (**b**) rolling with different roughnesses of top and bottom work rolls.

Asymmetry during rolling can be purposefully created due to differences in the circumferential speeds of the work rolls. Asymmetric rolling can be implemented due to disconnecting one work roll to make another work roll the only driven work roll (Figure 6a). This process called "single-roll-driven rolling" [38]. Sakai et al. [39] proposed two-pass single-roll-driven unidirectional shear rolling. Shear strain greater than 1.0 was introduced throughout the thickness of the AA5052 sheet. A shear texture was developed throughout the thickness of the sheets. The average r-value equaled unity. These values resulted in a superior drawability of the unidirectionally shear rolled and annealed sheets to that of sheets fabricated by the conventional process.

**Figure 6.** Schematic illustration of asymmetric rolling processes due to different circumferential speeds of the work rolls: (**a**) Rolling with idle work roll ("Single roll driven rolling"); (**b**) rolling with different diameters of top and bottom work rolls.

Asymmetry can also be achieved by using work rolls with different diameters while rotating at the same angular speed (Figure 6a). Choi et al. [14] used asymmetric rolling with different diameters of 248 mm and 126 mm of the top and bottom work rolls to control the texture and mechanical properties of Al alloys. Pesin [40] developed an improved process of asymmetric rolling by using different diameters of work rolls in combination with a bending roll (Figure 7a). This process is called the "combined process of asymmetric rolling and plastic bending". This technology is used to produce segments of large cylinders (Figure 7b) as curved plates with an angular size of 45 ... 60 degrees, plate thickness of 40 ... 220 mm, a width of up to 4300 mm, a length of up to 5000 mm and a radius of curvature from 1850 to 5000 mm. Industry testing of the combined process of asymmetric rolling and plastic bending is shown in Figure 8.

**Figure 7.** Schematic illustration of combined process of asymmetric rolling and plastic bending (**a**) and a curved plate as a segmen<sup>t</sup> of a cylinder (**b**).

**Figure 8.** Industry testing on hot plate mill 4500 at OJSC Magnitogorsk Iron and Steel Works: (**<sup>a</sup>**,**b**) Combined process of asymmetric rolling and plastic bending; (**c**) finished curved plate.

Asymmetric rolling can be achieved by using a single driven work roll, when one of the rolls is kept stationary. In the late 1970s, Potapkin and Fedorinov [41] proposed an asymmetric rolling process called "deformation by a stationary and driven work roll" (Figure 9a). The process is carried out at a sufficiently high front tension of the strip. The diameter of the stationary work roll is 3–10 times smaller than the diameter of the driven work roll. This provides a significant reduction in rolling force due to a decrease in the contact area. The technological capabilities and advantages of this process increase with a decrease in the diameter of the stationary roll. However, this decrease is limited by a decrease in its strength and rigidity and complications of fastening (the possibility of work roll twisting). In the late 1980s, Pesin [42] proposed to use, instead of a stationary cylindrical work roll, a prism-shaped tool with a cylindrical part with a very small radius up to 5 mm (Figure 9b). This solves the problem of the strength and rigidity of the deforming tool in combination with ensuring a small radius of the contact surface of this tool.

**Figure 9.** Schematic illustration of asymmetric rolling processes: (**a**) Deformation by a stationary and driven work roll; (**b**) deformation by a stationary prism-shaped tool and driven work roll.

Asymmetric rolling can be carried out due to different angular speeds of the work rolls with the same diameters (both rolls are driven) (Figure 10a). The ratio of these speeds is one of the most important parameters of the process, since it will influence the velocity field along the sheet thickness (together with other parameters, such as contact friction and thickness reduction per pass). The asymmetric rolling due to purposefully created differences in the circumferential speeds of the work rolls is also called "differential speed rolling".

**Figure 10.** Schematic illustration of asymmetric rolling processes due to different circumferential speeds of the work rolls: (**a**) Rolling with different angular speeds of the work rolls; (**b**) "rolling– drawing" process.

In the 1960s and 1970s, the energy theory of the asymmetric rolling process was developed by Vydrin [43]. As a result, a new asymmetric rolling process called "rolling– drawing" (Figure 10b) was proposed in 1971 [44]. This process is carried out under the following kinematic conditions:

$$\frac{V\_1}{V\_0} = \frac{h\_0}{h\_1}, \ V\_{0s} = V\_0 \text{ and } V\_{1s} = V\_1 \tag{3}$$

where *V*0*<sup>s</sup>*, *V*1*s* are the circumferential speeds of the strip before and after the deformation zone, respectively; *V*0, *V*1 are the circumferential speeds of the work rolls; *h*0 is the thickness of the strip before the rolling pass; *h*1 is the thickness of the strip after the rolling pass. The rolling–drawing process is carried out at a sufficiently high front tension of the strip. Such kinematic conditions provide one-zone and counter-directional friction forces in the deformation zone. Since the rolling–drawing process requires a high front tension of the strip, the thickness reduction per pass should not exceed 10–40%. This limits the possibility of using this process.

Thus, different circumferential speeds of the work rolls can be created in the following ways: (1) due to different diameters of the work rolls at the same angular speeds (both rolls are driven); (2) when one work roll is driven and another work roll is idle; (3) when one work roll is driven and another work roll or tool is stationary; (4) due to different angular speeds of the work rolls with the same diameters (both rolls are driven). The main disadvantage of the first three ways is the low technological flexibility of these processes due to the impossibility to control the speed ratio *SR* of the work rolls when creating shear strain, which is necessary for grain refinement and improving the texture and mechanical properties of various metals and alloys. From an industrial point of view, rolling with different angular speeds of the work rolls with the same diameters (both rolls are driven) is the most suitable way to implement asymmetric rolling.

Asymmetry during rolling can be purposefully created due to differences in the surface geometry of the top and bottom work rolls. In 2014, Shimoyama et al. [45] proposed the new rolling process called "periodical straining rolling" that enables control of the microstructure and texture of Mg alloys sheets. The periodical straining rolling process consists of two deformation stages. At the first pass, the sheet is rolled with a grooved work roll with, for example, a sine profile of the surface, and a flat work roll (Figure 11a). As a result, small rack-like dimples are formed periodically on the sheet surface. At a subsequent rolling pass, the rack-like sheet is flattened by conventional flat work rolls. Finally, the smooth sheet surface is obtained. The objective of the proposed rolling process is to introduce localized strain, to cause microstructure and texture changes in the rolled sheet. Periodical straining rolling can be easily adapted in existing strip rolling mills by replacing the ordinary work roll profiles.

**Figure 11.** Schematic illustration of periodical straining rolling (**a**) and asymmetric roll bonding of bimetal layered composites (**b**).

Hot or cold rolling is widely used for the manufacturing of bimetal layered composites [46]. As a result of the difference between the flow stresses of the sheets to be bonded, this process belongs essentially to the category of asymmetric rolling. However, this process is usually simply called "hot or cold roll bonding". Additional purposefully created asymmetry due to different circumferential speeds of the work rolls can be introduced to the rolling process of bimetal layered composites [47]. In this case, the rolling process is called "asymmetric hot or cold roll bonding" (Figure 11b). The harder metal contacts the fast work roll and the softer metal contacts the slow work roll. The deformation zone of asymmetric rolling forms a cross shear zone, which increases the bonding strength.

In 2019, Wang [48–50] proposed the new asymmetric rolling process called "corrugated rolling and flat rolling" (Figure 12) to achieve strong interface bonding and substantial grain refinement in Mg/Al and Cu/Al layered composites. The surface of a corrugated work roll was designed as a sine curve with an amplitude of 0.5 mm and a period of 0.06 radians. The diameters of the corrugated and flat work rolls were both 150 mm [48].

**Figure 12.** Schematic illustration of corrugated rolling and flat rolling, reproduced from [50], with permission from Elsevier, 2021.

During the first corrugated rolling, compressive stress of various orientations is formed in the corrugated Mg/Al laminated composite [49]. This means that asymmetric deformation occurs, as shown in Figure 13 [49]. The upper corrugated roll results in an inhomogeneous local stress distribution at different positions. Thus, the grain structure of AZ31B might not be uniform and the microstructure might change with the curve of the corrugated roll. On the contrary, the lower conventional flat roll corresponds to 5052 aluminum and stresses on the aluminum sheet near the flat roll appear to be homogeneous. During the second flattened rolling process, the AZ31B metal at the peak position prepared by the first pass flows downward and sideways, enduring severe plastic deformation under the rolling force. The original coarse grain might be broken and recrystallize during the rolling process and subsequent heat treatment. Considering the matching of surface ripples between the corrugated Mg/Al composite and corrugated roll, the rolling force appears to be uniform along the width direction, which is different from the force along the rolling direction. Therefore, for the flattened as-rolled Mg/Al laminated composite, the longitudinal and transverse interfacial microstructures are significantly different. The Mg/Al laminated composites prepared by corrugated rolling and flat rolling exhibited outstanding tensile properties along both RD and TD, which can be attributed to the microstructure refinement induced by the severe shear strain. The tensile properties along TD were higher than that along RD in both the as-rolled and heat-treated state, and this significant anisotropy of the tensile property was mainly due to the microstructure spatial distribution and the interfacial intermetallic compound layer along the different directions [49].

**Figure 13.** Schematic illustration showing the shear stress during the corrugated rolling and flat rolling process [49].

Pesin et al. [51] proposed asymmetric rolling based on the corrugated rolling and flat rolling process for the manufacturing of Al–steel layered composites with improved bonding strength between the stacked layers. It was numerically shown [51] that mechanical clinching and elevated plastic strain at the interface due to the creation of wave-like contact surfaces between the Al and steel, with the mutual penetration of hard material into soft material when the shear strain is activated, can provide superior bonding strength.

In 2007, Hirt and Thome [52,53] proposed the new asymmetric rolling process called "riblet rolling", which is used to obtain specific functional surface structures. Before rolling, a fine high-strength steel wire is tightly wound around the upper roll to provide it with a negative riblet imprint. Afterwards, the riblet structure is formed on the sheet by riblet rolling (Figure 14). The aim is to approach the production of semi-circular shaped riblet structures with a spacing *s* of 90–100 μm. In the ideal case, the ratio of riblet height *h* to riblet spacing *s* should be about 0.5. Riblet spacing *s* is defined by the diameter *dw* of the used steel wire. This surface is characterized by almost perfect negative semi-circular riblet structures with very sharp ground radii. The accuracy of the winding process—i.e., a constant pitch *p* of the steel wire on the roll—must be very high.

**Figure 14.** Schematic illustration of riblet rolling, reproduced from [52], with permission from Elsevier, 2008.

Rolling of functional riblet structures allowing for significant drag reduction on surfaces in fluid dynamic applications like airplanes and trains can be applied for the manufacturing of aluminum alloy sheets. Polished cross-sections of structured clad and bare AA 2024-T351 sheets are shown in Figure 15 [54]. Rolling of uniformly shaped riblets with a lateral distance of less than 100 μm is assumed to be possible on large Al sheets.

**Figure 15.** Polished cross-sections. (**a**) A 2 mm thick AA 2024-T351 sheet combined with a clad layer of commercially pure Al (Alclad 2024-T351). (**b**) Structured sheet of Alclad 2024-T351 with 80 μm riblet diameter. (**c**) A 1.6 mm thick Alclad 2024-T351 sheet. (**d**) Structured sheet of Alclad 2024-T351 with 300 μm riblet diameter. (**<sup>e</sup>**,**f**) A 2 mm thick AA2024-T351/T4 bare sheet with 100 μm riblet diameter, reproduced from [54], with permission from Elsevier, 2014.

#### **3. Fundamentals of Differential Speed Rolling**
