Flow and Fracture in Strip Rolling

Transcription

1 Flow and Fracture in Strip Rolling Foreword. In Section and the analysis was performed under the assumption that the strip maintains a perfect rectangular cross section without changing its width. This assumption was necessary in order to obtain the analytical solutions. The solutions presented (and others which were not) are realistic and of immense value to the strip-rolling industry. However, the behavior of the workpiece is far from the ideal picture assumed for the basic analysis, and our treatment will not be complete unless the modes of deformation and of failure are presented. The treatment of these modes will be descriptive. Only the major modes will be presented, while some of the infinite number of possible flows that may be intriguing but less common will be omitted. The following flow phenomena are covered: 1. Thickness nouniformities and strip flatness control. 2. Spread and barreling. 3. Edge cracking. 4. Alligatoring, stringing, and herring shape. 5. Internal defects and gauging Longitudinal Variations in Thickness a. The Phenomenon. Nonuniformity of thickness is evident along the length of the strip as well as across its width. Length- and width-related thickness changes result from different sources. Their ill effects are different. Measures to minimize the thickness changes and their ill effects have had various degrees of success. Longitudinal changes in thickness are caused by variations in incoming thickness, friction, hardness, temperature, speed, etc. along the rolled strip. Variations in these factors cause variations in roll separation force. The rolling mill with all its components can be considered as an elastic system, because the roll separation force causes the system to flex. In rolling individual coils, it is observed that both ends of each coil are of heavier gauge than the rest of the coil if no setting of the mill except the rolling velocity is changed. Feeding the front end of the coil is done slowly and carefully. After the front end is secure on the coiler, the mill increases in velocity. Toward the end of the strip the mill is slowed down again to prevent damage by the tail end of the coil which might occur if it were relieved from the last set of rolls at full speed. If the rolling velocity is high enough to provide hydrodynamic lubrication during most of the operating time, then the strip thickness is smaller than the gap between the rolls by twice the lubricant thickness Є f. With the commencement of hydrodynamic lubrication, the friction drops appreciably, causing the roll force to drop. With lower roll separation force, the bending and flattening of the rolls and the elastic stretch of the frame of the rolling mill also 64

2 decrease; the gap between the rolls thus becomes smaller. Increased roll separation force causes more flexing and a consequent increase in roll gap, which leads to an increase in the thickness of the outgoing strip. From this cause the thickness of the strip varies by P t f = (a) K 1 Normally, the roll separation force P is proportional to the pressure on the strip, which can be approximated by Eqs. (13.5) and (13.6) b. Prestressing of the Mill. Prestressing of the mill frame is a very effective way to minimize the variation in thickness in outgoing strip. The vertical columns of the frame can be bored and tie rods passed through the holes. The rods are tightened so that the columns are placed under compression and the rods under tension even before the strip is inserted between the rolls. The rods, rather than the columns, carry the roll separation force. In Ref. 17 the columns of the frame of the mill are cut horizontally into three sections each to permit rapid disassembly for roll changing. Also, Ref. 17 (Fig ) describes a sophisticated design for prestressing by tightening the tie rods. Prestressing can also be provided by removing the screwdown mechanism and replacing it with bolts between the working rolls. The gap is controlled by pushing the two rolls apart, using the threaded bolts rather than the conventional screwdown mechanism. Design considerations dictate that the frame support the rolls through a hydraulic system. The prestressing of the frame (and compression of the bolts) is controlled independently of the steady-state strip pressure. The added separation or tightening force can be regarded as an elastic system. When rolling proceeds, variations in roll gap cause variations in the prestressing force P 2 : 2 P2 = K t (b) f The negative sign indicates that an increase in the gap between the rolls will relieve the prestressing pressure. The stretching force acting on the mill is the sum of the forces exerted on the strip by the rolls and the prestressing force: P = Lwp + (c) ave P 2 This increase in force is beneficial in that it provides a more uniform outgoing thickness. An increase in the pressure between the strip and the rolls (caused, for example, by an increase in the thickness of the incoming strip) causes in this case 65

3 a milder increase in the gap between the rolls and therefore in the thickness of the outgoing strip. Figure is a schematic representation of the effect of prestressing. The abscissa is the thickness of the outgoing strip, while the ordinate denotes mill forces. Lines 1 to 4 describe the components of mill force versus outgoing thickness when no prestressing is employed. Lines 5 to 7 describe the mill behavior with prestressing. Line 1 describes the roll force on the strip according to Eqs. (13.5) and (13.6). Line 4 describes the elastic behavior of the mill according to Eq. (a) when the screwdown mechanism on the upper rolls is set for a uniform thickness t f with the incoming strip of thickness t 0. The slope of line 4 is the elastic constant of the mill, K 1, by Eq. (a). If the incoming thickness changes to a higher value (or if the friction or hardness increases), the force on the strip described by Eqs. (13.5) and (13.6) increases too, and it is described now by line 2. The intersection of line 2 with line 4 is now the equilibrium point for the mill, and the outgoing thickness increases by t f. When the mill is prestressed, the prestressing according to Eq. (b) is described by line 3. The slope of line 3 is given by the coefficient of Eq. (b), which is - K 2. The mill force by Eq. (a) is now expected to counter the strip pressure (line 1 or 2) and the prestressing force. Adding the prestressing to line 1 yields line 5, and adding the same prestressing to line 2 yields line 6. The vertical distance between lines 5 and 6 is identical with the vertical distance between lines 1 and 2. The screwdown mechanism on the upper rolls is so readjusted that, for a uniform incoming thickness of t 0, the outgoing thickness is t f. Line 7 now describes the elastic behavior of the mill by Eq. (a) with the same slope K 1, but at a higher force level. Now, when the incoming thickness increases, line 5 is replaced by line 6. The new equilibrium of the mill introduces a change in the outgoing thickness t f, which is much smaller than the change without prestressing. Notice that the absolute level of the prestressing is not crucial. It is the slope (-K 2 ) that maintains the rigidity. The higher the absolute value of K 2, the more nearly uniform is the outgoing strip. Prestressing of the mill, in effect, increases the overall modulus of elasticity and thus dampens, but does not eliminate, variations in wall thickness. It employs no gauge or pressure measurement or external control system. The gauge control is provided by the construction of the mill c. Hydraulic Control of the Roll Gap. Use of hydraulic cylinder that replaces the screwdown mechanism has been adopted by many mill manufacturers. (See Refs. 18 and 19.) Direct gauge measurements, or measurements of the roll separation force translated to gauge, can provide information on drift changes caused by temperature variation in rolls and lubricant and on other slow-developing trends. These changes can be compensated through a feedback system that constantly controls the hydraulic cylinder. Automatic gauge control (AGC) is now standard in the operation of tandem mills in Japan

4 d. Front and Back Tension. An alternative feedback system for gauge control utilizes the control of front and back tension. The higher the applied front or back tension, the lower is the roll separation force [See Eq. (13.5)], the less stretching the mill experiences, and the thinner the strip is. Front and back tensions can be introduced through payoff reels, through tension rolls between stations on a tandem mill, or even through the relative rolling speed between consecutive rolling stations. (See Section ) FIGURE Gauge control by prestressing. 67

5 Variations in Thickness across the Width and Loss of Flatness a. The Phenomenon. Thickness variations across the width of the strip are more troublesome and are harder to eliminate. These variations are caused because of roll flattening (Section ) and roll bending under load. Bending is shown in Fig , exaggerated for illustrative purposes. The thickness variations are typically a fraction of a percent of the nominal thickness. They are, however, of concern, because they cause waviness and loss of flatness, as is discussed presently. The extent of bending and flattening depends on the geometry and strength of the rolls, and on the roll separation force. The roll separation force can be reduced by reducing roll diameter. Smaller roll diameter reduces roll flattening, which is one of the less significant causes of variations in thickness across the width. However, small roll diameter weakens the bending resistance of the rolls. To obtain the benefits of lower separation force by smaller roll diameter and still maintain stiffness against bending, the four-high rolling mill (see Fig b) is most commonly used. The larger-diameter backup rolls support the smaller-diameter working rolls, which are in contact with the strip. Cluster rolling mills, including the Sendzimir cluster rolling mill, are described in Section b. Roll Crown and Strip Loss of Flatness. Since roll bending is expected, the thickness of the strip on the edges is expected to be thinner than in between. Thus, rolls generally are machined with a crown, the middle of the rolls being slightly larger in diameter, with tapering off toward the ends. For some value of the roll separation force, the crown is so designed that the facing lines of both rolls are parallel and the expected strip thickness is uniform. However, since the crown on conventional rolls cannot be varied, while the roll separation force does vary with reduction, strip-thickness-to-roll-radius ratio (t 0 /R 0 ), strip width, and temperature and strength, it follows that flat strip is rarely rolled. Because of the crown on the rolls, some strip, rolled with high roll separation force, is convex (thicker in the middle), and other strip, rolled with low roll separation force, is concave (thinner in the middle). Variations of thickness across the width correspond to variations in reduction in thickness. If, for example, a flat strip of uniform thickness is rolled to a concave shape (thinner in the middle), then the middle experiences larger reduction than the ends. Thus the middle elongates more than the ends, and the strip wrinkles. If a concave strip is rolled to be flat or convex, the ends undergo larger reductions and elongate more than the middle, and again the strip wrinkles. Strip rolling is always done with front and back tension which helps to even out the elongation and minimize wrinkles even when the strip is not flat. The ill effects of variations in thickness across the width are costly. At the extreme, excessive nonuniformity results in a rejection, loss of customers, or sale at a loss. The producer has incentive to take some trouble to salvage a wavy strip or to prevent waviness in the first place. 68

6 FIGURE Rolling bending. The main incentive for gauge control across the width of the strip is the desire to produce flat strip. It is to be emphasized here again that gauge control and flatness control are not synonymous. If the strip emerging from each individual stand were perfectly uniform in thickness across the width of the strip, then the final strip might also be expected to emerge flat. However, in practice, it is only at the last stand that gauge is measured and means to effect uniformity in thickness are provided. Thus, if the incoming strip at the last station is nonuniform and the emerging strip is uniform, it may not emerge flat. Given the choice, flatness should be preferred over uniformity. Flatness or uniformity can be controlled at the rolling mill, while tension levelers (Section f) are used to correct flatness after rolling is completed. Since a gram of prevention is better than a kilogram of cure, it is preferred to control gauge and flatness at the rolling mill, eliminating the need for the extra leveling operation. 69

7 FIGURE (a) Two-high and (b) four-high rolling mills. Uniformity to within (say) a few tenths of a percent of thickness across the width is aimed at by gauge control. Flatness can then be achieved by superposition of changes in thickness that amount to a fraction of the thickness nonuniformity, namely a few hundreds of a percent. Sometimes the strip may come flat out of the mill, but after cooling or on removal from the coil waviness may return. This phenomenon may be explained by cooling of a strip that had a nonuniform temperature gradient across the width and thickness. The rest of Section is devoted to measures taken to prevent such defects by roll bulge control through internal pressure, roll bending, six-high rolling mills, and leveling. 70

8 FIGURE (c) Variable-crown control c. Variable-Crown Sleeve Roll. A variable crown (VC) control, fashioned after paper-mill practice, is described in Fig c, taken from Figs. 1 and 2 of Ref. 21a. A hollow sleeve is mounted (by interference fit, along the ends of the sleeve only) over a shaft. The gap between the shaft and the sleeve is supplied through a central hole in the shaft with liquid under pressure. The pressure of the liquid controls the crown. In a two-high rolling mill one or both rolls may be designed with a variable crown. In a four-high mill, the backup roll(s) (usually, for convenience of roll changing, the bottom backup roll) are designed with VC. The variable curvature of the crown can be effected through the design of the contour of the cavity in the sleeve as shown in the inset in Fig c. Variable-crown (VC) roll provides a very effective means for strip flatness or shape control, both for hot and cold strip rolling. Its effectiveness has been demonstrated at Sumitomo Metal Industries Ltd. 21 In the rolling of aluminum and steel. In a four-high mill, the VC backup roll design can be combined with forced bending of the working rolls for a most effective combined strip flatness or shape control. VC rolls can be installed on existing mills very easily. The concept is also attractive for the crown control during leveling d. Working Roll Bending. Roll bending is exercised to control the shape of the gap between the facing rolls. A moment is applied at both ends of the working rolls to affect the concavity or convexity of the emerging strip. Only general trends from the middle to the edge of the strip can be modified in a more 71

9 or less symmetric fashion; control of separate zones or selective control of each end of the strip is not possible by this technique. The signal to control the moment is provided through strip gauge measurement or flatness measurement devices, as described in Section g e. Six-High Rolling Mill. An alternative method utilizing roll bending is offered by the six-high rolling mill in Ref. 22 and Fig Here an intermediate roll is placed between each working roll and its backup roll. The working rolls are controlled by a bending force as described in Section d. The curvature of the bending at each end of each working roll is controlled by the positioning of the intermediate roll. Thus, each end of the strip can be controlled individually for a more uniform thickness t hroughout f. Leveling. A common defect in strip products after rolling is lack of flatness. The strip emerging from the last stand may be wavy or bowed, and sometimes contains kinks. These irregularities are usually controlled at the last stand of the finishing mill or by an additional leveling pass through a leveler. The process of leveling utilizes a series of rollers alternately displaced from a common plane in a manner that forces sharp bends in opposite directions on the strip that is drawn through the leveler (see Fig ). In order to be effective, the bending and unbending have to be done over a small bending radius. In addition, a tensile force is employed to cause about 1% of permanent elongation of the emerging strip. The desired amount of elongation and flattening can be achieved through a range of combinations of roll diameter and tension level. The smaller the roll diameter and bend radius, the lower is the required tension. If the roll diameter is too large, the required tension approaches the flow strength of the strip, and instability by necking result. At present, moderately small-diameter rollers serve to effect the bending, and the speed of the strip is limited by the practical rotational speed of the rolls. While rolling mills today may operate at emerging speeds of up to feet per minute (2,000 meters per minute, or 30 meters per second), the levelers still are restricted to speeds of a few hundred feet a minute (100 meters per minute). The leveling operations are therefore performed as a separate operation, and extra handling and reeling are involved. The actual size of the rolls is thus a compromise. Small-diameter rolls are desired for stability, but the smaller the roll diameter, the slower the leveling speed is. If leveling speeds could be increased to match the exit speed from the last stand of the tandem rolling mill, leveling could be made on line with rolling to streamline the mill operation. If, furthermore, these speeds could be reached with small bend radius, then low tensions would be required, the process would become more stable, and it would be possible to level a thinner strip. This possibility, through the introduction of thin-film lubrication, is described next. Both hydrostatic and hydrodynamic lubrication are considered. 72

10 FIGURE Six-high rolling mill. An alternative design, with rigid wedges to replace the rollers of the levelers, is described in Fig The wedges are more rigid than small-diameter rolls. For best control of the flattening effect, these wedges are designed so that they can be forced to bend in a controlled manner. Unless a full film of lubricant is FIGURE Leveling. FIGURE Leveling with wedges. 73

11 maintained between the edges and the strip, wear on the wedges and scratching of the strip will prevent the use of this design. In patents assigned to Toyo Kohan of Japan by Kiyoshi Kawaguchi et al. 23a and Yasunori Miyamatsu 23b et al., 24 forced lubrication between the strip and the wedge or rolls was introduced. The equipment is described in Ref. 24. When rolls are used, they are supported by hydrostatic bearings. Full separation between the workpiece and the tool, created by a thin film of the liquid lubricant, can be effected either by high hydrostatic pressure imposed by external pumping or through high workpiece speeds. These two means are called hydrostatic and hydrodynamic forced lubrication respectively. 1. Hydrostatic Film. Hydrostatic lubrication is effected through a system of orifices inserted into the wedges as shown in Fig Liquid under pressure is pumped to reach the recessed pool of liquid at the end of each orifice at the interface between the workpiece and the wedge. When the pressure is high enough, the workpiece is lifted from the tool, although the tension forces it to stay very close to the wedge. The film of lubricant on which the workpiece floats is very thin, and the volume of lubricant that flows through the orifices and escapes through the gap between the workpiece and the tool is under control. The diameter of the orifices is kept small to control this flow. When the strip is stationary, the pumped liquid emerges equally, from each side of the wedge. As the speed increases, the strip drags the liquid with it; more and more liquid exists downstream and less and less escapes upstream. At and beyond a critical speed of the strip, no liquid escapes from the incoming side of the strip and the lubrication film is broken. An advantage of hydrostatic lubrication over hydrodynamic lubrication is that full separation between the workpiece and the tool can be effected even when there is no relative motion between the workpiece and the tool. See, for example, the work on deep-drawing with hydrostatic lubrication. 25 A disadvantage of the design in Fig is that at too high speeds the film breaks. This disadvantage can be partially remedied by skewing the recesses towards the entrance side. 2. Hydrodynamic Film. The need to supply liquid under pressure by external means can be dispensed with when the workpiece is moving fast over the tool, as in strip rolling (see Section and Chapter 16). The higher the speed, the easier it is to effect hydrodynamic lubrication, as evidenced in many metalforming operations, e.g., wire drawing (Chapter 3), hydrostatic extrusion (Chapter 7), and strip rolling. When the strip is moving very fast, it is sufficient to supply liquid in quantity at the point of initial contact between the strip and the wedge (see Fig ). Layers of lubricant adhere to the surface of the strip and are dragged by the fastmoving strip into the interface between the strip and the wedge. The faster the strip moves, the more lubricant passes with the strip from the entrance side to the exit. At a critical speed, enough lubricant is dragged through to form a thin layer, 74

12 FIGURE Leveling with hydrostatic lubrication. fully separating the strip from the wedge, and causing the strip to float over this film. (See Ref. 26.) The critical speed is a function that can be presented symbolically by v cr ( η, σ, t, α, T R ) = f (a) 0, 0 where η is the viscosity of the lubricant, σ 0 is the flow strength of the strip, T is the tension on the strip, α is the bend angle, t is the strip thickness, and R 0 is the radius of the wedge. As the speed of the strip increases above the critical speed, the thickness of the film of lubricant increases. The characteristics of Eq. (a) are complex and beyond the scope of this book. Thus, comparing hydrostatic with hydrodynamic lubrication, a hydrostatic film prevails at speeds only below a critical value, while a hydrodynamic film prevails at speeds above another critical value. 3. Combination of Hydrodynamic Lubrication with Hydrostatic Bearing. A schematic of a solid cylinder resting in the wedge is described in Fig The liquid, coming through the orifice under pressure, lifts the roller, which then floats on fluid. When the strip is standing still, fluid emerges equally from both sides of 75

13 FIGURE (Continued). FIGURE Leveling with hydrodynamic lubrication. 76

14 the roll. As strip starts to move, the roll rotates with it. The roll drags liquid to one side, and gradually, with increasing speed, more liquid escapes from one side and less from the other. At high enough speed, the film on the deficient side breaks, and the roll stops rotating and scratches the strip. If, however, at this stage, the escaped liquid is made to enter the gap between the strip and the roll, a hydrodynamic effect may be introduced g. Gauge and Flatness Measurement. Means for dealing with the phenomena of gauge variation along and across the strip and of waviness are described in Sections a to f. The present section deals with the measurement of these phenomena. If a uniform gauge were achieved through any cross section (through the width) at any mill station, the strip might then also be flat. If the strip coming from intermediate stations is not uniform in thickness across the width, flatness will not be assured by achieving uniform thickness at the last station. Normally, controlling the last station to achieve flatness leads to nonuniform thickness. Thus, uniform thickness and flatness are not synonymous. Means to measure thickness and those to measure flatness are listed below. Mechanical thickness gauges are ineffective at the high rolling speeds. Gauge measurements are usually performed at the last station by X-rays, γ-rays, etc. The degree of waviness can easily be observed by the naked eye when the strip, free of tension, is laid horizontally over a flat platform. Instrumented measurement of flatness is based on applying tension to the strip in the longitudinal direction. The segments that are shorter (originally under tension) and the segments that are longer (originally buckled) experience different tensile stresses under load. The shorter segments are now under higher tension than the buckled ones. This behavior is put to use by the following techniques: 1. Permeability measurements are made by introducing a magnetic field, scanning across the width of the tension-loaded strip. The permeability varies with the local tensile stress. This method is advocated for thin strip The strip under tension may traverse over a flat table. The strip is forced vertically away from the table by a magnetic field (method introduced by Mitsubishi) or by air under pressure (Sendzimir), or by water jets (Kawasaki Steel Corp.) Most mill producers are active in developing methods to measure waviness of the outgoing strip, and many principles have been employed. T. Sendzimir, Inc., has developed the following technique. The outgoing strip is maintained under tension by a tension device described in Fig a. The length of the strip that is stretched is made to float over a thin layer of air under moderate pressure. The band of strip which was reduced to a higher degree is under lower tension than the rest of the strip and therefore floats further from the base, where proximity gauges are lined up at intervals across the width of the 77

15 FIGURE (a) The Sendzimir method to measure waviness. (b) ASEA stressometer flatness control system. strip. Signals are transferred from the proximity gauges to the cams that control roll bending on the Sendzimir cluster rolling mill. The water-jet technique 28 is used in hot strip rolling, at the exit from the last stand. The hot environment, filled with vapor and water, makes other methods unsuitable. In the water-jet method the electric resistance of the line between the nozzle and the strip is proportional to the gap. This resistance is measured to indicate strip flatness. 78

16 The Mitsubishi unit forces vertical displacement by a magnetic field and is good for steel strip. The vertical displacement reflects the tension at spots across the width. This vertical displacement is measured by proximity gauges placed across the width of the strip. Continuous readings are obtained while the strip is advancing. The above method is advocated for thicker strip. Another method to measure the relative tension on bands across the width is described in Ref. 29. There, as shown in Fig b, an instrumented roller is set at the exit from the mill, before the strip is picked up by the payoff reel. By the description of Ref. 29, The measuring roll is divided into a number of zones. Each measuring zone measures the radial force from the strip with the aid of magnetoelastic force transducers. The force is translated to thickness through a minicomputer, and a signal is produced to create the required roll-bending moment to counter the effect of the roll separation force. The list of recent technological developments which have been utilized in flatness-measurement devices include lasers and computer technology. 30 Here, a laser beam and a camera measure, by triangulation, the distance from a moving strip as it emerges from the last hot mill stand. The height over a reference plane, the roller plane, is calculated by an on-line computer. Measurements of the height are made on a longitudinal line at the center of the strip and along lines on the two edges of the strip. Along each line the height is measured at constant intervals so that the lengths of short fibers along the path can be calculated. [The length is the square root of the sum of squares of the height difference ( h) and length of travel 2 2 ( l) of the strip between two readings: l = ( l) + ( h).] An on-line computer compares the total length on the center line with the lengths of the edges and determines the waviness of the strip. Signals from the abovementioned measurement units (and others) can be utilized to control continuously the mill stand (roll bending variable-crown control) or leveler through a closed-loop feedback system Spread and Barreling. When a rectangular bar or a strip is rolled, the side surfaces bulge and the width increases. Let the original width of the strip be w 0 ; then its final width, emerging from the rolls, is w f, where w f > w 0. This phenomenon is called spread or lateral flow. Furthermore, the original flat surface bulges or barrels. (See Fig ) Both the amount of bulge (b) and the measure of spread (s) are dependent on the independent process parameters. In Section the power of deformation (J ) was computed as a function of the independent process parameters under the assumption of plane-strain deformation. The assumption of plane strain presupposes that bulge and spread are both zero. When bulge (b) and spread (s) are assumed, the analysis becomes more complex and no analytical solution is derivable. However, numerical solutions are available. Symbolically the power computed becomes * t0 t0 w0 J = f m b s 1,,, σ,,, (a) t f R0 t0 79

17 FIGURE Flow and flaws. For every specific combination of the independent parameters t 0 /t f, t 0 /R 0, m, σ, and w 0 /t 0 some combination of b and s minimizes the function J *. The values of b and s that minimize J * are the expected bulge and spread respectively. Through numerical computations both bulge and spread can be presented as functions of the independent process parameters as follows: b = t f t t 0 0 2,, f R0 w 0, m, σ 0 (b) t 0 80

18 s = t f t t 0 0 3,, f R0 w 0, m, σ 0 (c) t 0 The functional relations of Eq. (b) are available through computer programs, 31 formulae [Eq. (9) of Ref. 32], experimental data, 33,34 and graphical presentations, including nomograms. 35 The available information on spread is partial and does not cover all combinations of the independent process parameters. The information on bulge is scarcer yet Edge Cracking. Edge cracking as described in Fig is a progressive defect starting as microcracks at the middle of the bulge along the strip. The cracks grow deeper into the strip and wider while passing between the rolls and from one pass to the next. To make the strip usable the edges are sheared off, removing the damaged ends and making the strip narrower. The sheared-off portions end up as scrap. Edge cracking alone is responsible for more scrap strip material than all other faults put together. All strip rolling operations are plagued with the phenomenon to one degree or another. The depth of the crack depends on the five independent process parameters (t 0 /t f, t 0 /R 0, m, σ, w 0 /t 0 ) and on factors such as the temperature drop at the edges and material properties, especially impurities and inclusions. The width of the strip is not under direct control by tooling (rolls), and therefore it fluctuates somewhat. It is therefore a common practice to shear the edges to establish the precise desired width, even in the absence of edge cracking Other Defects. Besides edge cracking, only a few of the many forms of defects that may occur during strip rolling are mentioned here. Defects can be classified into these categories: 1. Shape distortions. 2. Internal defects. 3. Surface defects. To the shape distortions already mentioned, such as variations in thickness, nonflatness, bulge, and uneven width, one may add the alligatoring of the front and back ends of slap, plate, rod and strip (see Fig ). Alligatoring starts during slab rolling as a small dimple, which gets deeper and deeper during subsequent rolling passes. Even when the overlap is pressed together by subsequent rolling, the ends must be sheared as scrap. Internal defects caused by rolling include voids, cracks, strings of broken hard particles, and even chevrons (central-burst defect) have been observed. (See Fig ). Chevrons as observed in rod drawing and extrusion (Sec ) rarely occur, and if that happens, it is during rolling of heavy gauge strip with smalldiameter rolls. The chevron shape is observed when the strip is cut longitudinally 81

19 across the thickness, or on the side surface. It will extend widthwise. When the strip is rolled down to thin strip, especially during hot rolling, the defect collapses and goes unnoticed. Its lasting effects on the product may vary from intolerable to nil. A study of the closure of internal pores, conducted through the upper-bound approach, is provided in Ref. 61. The main causes of chevrons, as in drawing and extrusion, are poor processing with wrong choices of the reduction, ratio of strip thickness to roll diameter, front and back tension, etc. The defect may initiate and fully develop during a single pass through one mill station. Hard inclusions are a major source of internal progressive damage. The harder particles do not deform, or deform to a lesser degree than the matrix, and the uneven flow produces voids on one or two sides of the inclusions, in the direction of rolling. As rolling proceeds to thinner and thinner strip, the harder particles, especially if they are brittle, may break, and the fragments will string in the direction of rolling with voids and hard particles alternating. The size of the inclusion relative to the size of the ingot may be very small indeed. However, as rolling proceeds and the thickness of the strip decreases, the hard particles that do not deform in unison with the matrix (Ref. 62) retain a substantial ratio of size to the thickness of the strip. The material becomes nonuniform on the macroscale, with all the associated ill effects. Some of the hard particles, which might have started as small inclusions in the interior of the ingot, may emerge as relatively large inclusions on the surface, causing gouging as shown in Fig Other surface defects include stringers, which appear as lines of obscure origin aligned in the rolling direction. Herringbone marks over the rolled surface are caused by processing parameters which have not yet been identified. Many other flow patterns and defects, as well a metallurgical considerations, which are of great concern for the practicing rolling engineer have been omitted here because of space limitations or the defined scope of this more mechanically oriented text. Directionality, however, as a characteristic property of rolled strip, should be mentioned. Because the strip is continuously reduced in thickness while elongating, fibering is produced, with consequent directionality of the strength properties. Microscopic examinations reveal mechanical fibering with the long axis in the rolling direction. Preferred crystallographic orientation is produced as well. The behavior during subsequent forming operations like deep drawing is highly affected by this directionality. For example, see the earing effect in Ref. 36. Rolling practices to develop desired directionality and avoid ill effects have been continually improved. One simple practice to impose equal properties in the length and width directions is to roll plates rather than strip. Here a square plate is rolled alternately in perpendicular directions to minimize fibering. BACK NEXT 82