MATERIAL BEHAVIOR IN METAL FORMING

Transcription

1 MATERIAL BEHAVIOR IN METAL FORMING Considerable insight about the behavior o metals during orming can be obtained rom the stressstrain curve. The typical stress-strain curve or most metals is divided into an elastic region and a plastic region. In metal orming, the plastic region is o primary interest because the material is plastically and permanently deormed in these processes. The typical stress-strain relationship or a metal exhibits elasticity below the yield point and strain hardening above it. Figures [true-stress-strain and true-stress-strain on log-log-scale] indicate this behavior in linear and logarithmic axes. In the plastic region, the metal's behavior is expressed by the low curve: n K Where K = the strength coeicient, MPa; and n is the strain-hardening exponent. The stress and strain in the low curve are true stress and true strain. The low curve is generally valid as a relationship that deines a metal's plastic behavior in cold working. Flow Stress The low curve describes the stress-strain relationship in the region in which metal orming takes place. It indicates the low stress o the metal-the strength property that determines orces and power required to accomplish a particular orming operation. For most metals at room temperature, the stress-strain plot indicates that as the metal is deormed, its strength increases due to strain hardening. The stress required to continue deormation must be increased to match this increase in strength. Flow stress is deined as the instantaneous value o stress required to continue deorming the material-to keep the metal "lowing". It is the yield strength o the metal as a unction o strain, which can be expressed in this way: n K Where = low stress, MPa. Average Flow Stress The average low stress (also called the mean low stress) is the average value o stress over the stress-strain curve rom the beginning o strain to the inal (maximum) value that occurs during deormation. The value is illustrated in the stress-strain plot o Figure [shown below]. The average low stress is determined by integrating the low curve equation, Eq. between zero and the inal strain value deining the range o interest. This yields the equation: n K n K 1 n 1

2 Where = average low stress, MPa; and = maximum strain value during the deormation process. FIGURE: Stress-strain curve indicating location o average low stress strength and inal low stress. in relation to yield TEMPERATURE IN METAL FORMING The low curve is a valid representation o stress-strain behavior o a metal during plastic deormation, particularly or cold working operations. For any metal, the values o K and n depend on temperature. Both strength and strain hardening are reduced at higher temperatures. In addition ductility is increased at higher temperatures. These changes are important because any deormation operation can be accomplished with lower orces and power at elevated temperature. There are three temperature ranges: cold, warm, and hot working. Cold Working Cold working (also known as cold orming) is metal orming perormed at room temperature or slightly above. Signiicant advantages o cold orming compared to hot working are (1) better accuracy, meaning closer tolerances; (2) better surace inish; (3) strain hardening increases strength and hardness o the part; (4) grain low during deormation provides the opportunity or desirable directional properties to be obtained in the resulting product; and (5) no heating o the work is required, which saves on urnace and uel costs and permits higher production rates to be achieved. Owing to this combination o advantages, many cold orming processes have developed into important mass-production operations. They provide close tolerances and good suraces, minimizing the amount o machining required and permitting these operations to be classiied as net shape or near net shape processes. 2

3 There are certain disadvantages or limitations associated with cold-orming operations: (1) higher orces and power are required to perorm the operation; (2) care must be taken to ensure that the suraces o the starting work piece are ree o scale and dirt; and (3) ductility and strain hardening o the work metal limit the amount o orming that can be done to the part. In some operations, the metal must be annealed in order to allow urther deormation to be accomplished. In other cases, the metal is simply not ductile enough to be cold worked. To overcome the strain hardening problem and reduce orce and power requirements, many orming operations are perormed at elevated temperatures. There are two elevated temperature ranges involved, giving rise to the terms warm working and hot working. Warm Working Because plastic deormation properties are normally enhanced by increasing work piece temperature, orming operations are sometimes perormed at temperatures somewhat above room temperature but below the recrystallization temperature. The term warm working is applied to this second temperature range. The dividing line between cold working and warm working is oten expressed in terms o the melting point or the metal. The dividing line is usually taken to be 0.3 T m, where T m is the melting point (absolute temperature) or the particular metal. The lower strength and strain hardening, as well as higher ductility o the metal at the intermediate temperatures, provide warm working with the ollowing advantages over cold working: (1) lower orces and power, (2) more intricate work geometries possible, and (3) need or annealing may be reduced or eliminated. Hot Working Hot working (also called hot orming) involves deormation at temperatures above the recrystallization temperature. The recrystallization temperature or a given metal is about one-hal o its melting point on the absolute scale. In practice, hot working is usually carried out at temperatures somewhat above 0.5T m. The work metal continues to soten as temperature is increased beyond 0.5 T m, thus enhancing the advantage o hot working above this level. However, the deormation process itsel generates heat which increases work temperatures in localized regions o the part. This can cause melting in these regions, which is highly undesirable. Also, scale on the work surace is accelerated at higher temperatures. Accordingly, hot working temperatures are usually maintained within the range 0.5T m to 0.75T m. The most signiicant advantage o hot working is the capability to produce substantial 3

4 plastic deormation o the metal-ar more than is possible with cold working or warm working. The principal reason or this is that the low curve o the hotworked metal has a strength coeicient that is substantially less than at room temperature, the strain hardening exponent is zero (at least theoretically), and the ductility o the metal is signiicantly increased. All o this results in the ollowing advantages relative to cold working: (1) the shape o the work part can be signiicantly altered; (2) lower orces and power are required to deorm the metal; (3) metals that usually racture in cold working can be hot ormed; (4) strength properties are generally isotropic because o the absence o the oriented grain structure typically created in cold working; and (5) no strengthening o the part occurs rom work hardening. This last advantage may seem inconsistent, since strengthening o the metal is oten considered an advantage or cold working. However, there are applications in which it is undesirable or the metal to be work hardened because it reduces ductility; or example, i the part is to be subsequently processed by cold orming. Disadvantages o hot working include lower dimensional accuracy, higher total energy required (due to the thermal energy to heat the work piece), work surace oxidation (scale), poorer surace inish, and shorter tool lie. Recrystallization o the metal in hot working involves atomic diusion, which is a time-dependent process. Metal-orming operations are oten perormed at high speeds that do not allow suicient time or complete recrystallization o the grain structure during the deormation cycle itsel. However, because o the high temperatures, recrystallization eventually does occur. It may occur immediately ollowing the orming process or later, as the work piece cools. Even i recrystallization occurs ater the actual deormation, its eventual occurrence-together with the substantial sotening o the metal at high temperatures-distinguishes hot working rom warm working or cold working. STRAIN RATE SENSITIVIT Theoretically, a metal in hot working behaves like a perectly plastic material, with strain hardening exponent n = 0. This means that the metal should continue to low under the same level o low stress, once that stress level is reached. However, there is an additional phenomenon that characterizes the behavior o metals during deormation, especially at the elevated temperatures o hot working. That phenomenon is strain-rate sensitivity. Let us begin our discussion o this topic by deining strain rate. 4

5 The rate at which the metal is strained in a orming process is directly related to the speed o deormation v. In many orming operations, deormation speed is equal to the velocity o the ram or other moving element o the equipment. It is most easily visualized in a tensile test as the velocity o the testing machine head relative to its ixed base. Given the deormation speed, strain rate is deined:. v h Where. = true strain rate, m/s/m, or simply s -1 and h = instantaneous height o the work piece being deormed, m. I deormation speed v is constant during the operation, strain rate will change as h changes. In most practical orming operations, valuation o strain rate is complicated by the geometry o the work part and variations in strain rate in dierent regions o the part. Strain rate can reach 1000 s -1 or more or some metal orming processes such as high speed rolling and orging. We have already observed that the low stress o a metal is a unction o temperature. At the temperatures o hot working, low stress depends on strain rate. The eect o strain rate on strength properties is known as strain-rate sensitivity. The eect can be seen in Figure. As strain rate is increased, resistance to deormation increases. This usually plots approximately as a straight line on a log-log graph, thus leading to the relationship: = C. m [4] Where C is the strength constant (similar but not equal to the strength coeicient in the low curve equation), and m is the strain-rate sensitivity exponent. The value o C is determined at a strain rate o 1.0 and m is the slope o the curve in Figure (b). 5

6 (a) Eect o strain rate on low stress at in elevated work temperature. (b) Same relationship plotted on log-log coordinates The eect o temperature on the parameters o Eq. (4) is pronounced. Increasing temperature decreases the value o C (consistent with its eect on K in the low curve equation) and increases the value o m. The general result can be seen in Figure [shown below]. At room temperature, the eect o strain rate is almost negligible; indicating that the low curve is a good representation o the material behavior. As temperature is increased, strain rate plays a more important role in determining low stress, as indicated by the steeper slopes o the strain rate relationships. This is important in hot working because deormation resistance o the material increases so dramatically as strain rate is increased. FIGURE: Eect o temperature on low stress or a typical metal. The constant C in Eq.(4), indicated by the intersection o each plot with the vertical dashed line at strain rate = 1.0, decreases, and m (slope o each plot) increases with increasing temperature. 6

7 Rolling is the process o reducing the thickness or changing the cross-section o a long workpiece by compressive orces applied through a set o rolls (Fig.), similar to rolling dough with a rolling pin to reduce its thickness. Rolling, which accounts or about 90 percent o all metals produced by metalworking processes, was irst developed in the late 1500s. The basic operation is lat rolling, or simply rolling, where the rolled products are lat plate and sheet. Figure: Schematic outline o various lat- and shape-rolling processes. Source: American Iron and Steel Institute. Plates, which are generally regarded as having a thickness greater than 6 mm, are used or structural applications such as ship hulls, boilers, bridges, girders, machine structures, and 7

8 nuclear vessels. Plates can be as much as 0.3 m thick or the supports or large boilers, 150 mm or reactor vessels, and mm or battleships and tanks. Sheets are generally less than 6 mm thick and are used or automobile bodies, appliances, containers or ood and beverages, and kitchen and oice equipment. Commercial aircrat uselages are usually made o a minimum o 1 mm thick aluminum-alloy sheet. For example, skin thickness o a Boeing 747 is 1.8 mm and or the Lockheed Ll0ll it is 1.9 mm. Aluminum beverage cans are now made rom sheets 0.28 mm in thickness, reduced to a inal can wall thickness o 0.1 mm. Aluminum oil used to wrap candy has a thickness o mm. Sheets are provided to manuacturing acilities as lat pieces or as strip in coils or urther processing into products. Flat Rolling A schematic illustration o the lat rolling process is shown in Fig. a. A strip o thickness h o enters the roll gap and is reduced to h by a pair o rotating rolls, each roll being powered through its own shat by electric motors. The surace speed o the roll is V r. The velocity o the strip increases rom its initial value o V o as it moves through the roll gap, just as luid lows aster as it moves through a converging channel. The velocity o the strip is highest at the exit o the roll gap and is denoted as V. Since the surace speed o the roll is constant, there is relative sliding between the roll and the strip along the arc o contact in the roll gap L. At one point along the contact length, the velocity o the strip is the same as that o the roll. This is called the neutral, or no slip, point. To the let o this point, the roll moves aster than the strip, and to the right o this point, the strip moves aster than the roll. Hence the rictional orces, which oppose motion, act on the strip as shown in Fig. b. Frictional orces The rolls pull the material into the roll gap through a net rictional orce on the material. ou can see that this net rictional orce must be to the right in Fig. b, and consequently the rictional orce on the let o the neutral point must be higher than the orce on the right. 8

9 As you can see, riction is needed to roll materials. However, energy is dissipated in overcoming riction, so increasing riction means increasing orces and power consumption. Furthermore, high riction could damage the surace o the rolled product. Flat Rolling and Its Analysis Flat rolling is illustrated in Figures. It involves the rolling o slabs, strips, sheets, and plates-work parts o rectangular cross-section in which the width is greater than the thickness. In lat rolling, the work is squeezed between two rolls so that its thickness is reduced by an amount called the drat: d = h o - h (1) Where d = drat, mm; h o = starting thickness, mm; and h = inal thickness, mm. Drat is sometimes expressed as a raction o the starting stock thickness, called the reduction: r = d/h o (2) Where r = reduction. When a series o rolling operations are used, reduction is taken as the sum o the drats divided by the original thickness. In addition to thickness reduction, rolling usually increases work width. This is called spreading, and it tends to be most pronounced with low width-to-thickness ratios and low coeicients o riction. Conservation o material is preserved, so the volume o metal exiting the rolls equals the volume entering: h o w o L o = h w L (3) Where w o and w are the beore and ater work widths, mm; and L o and L are the beore and ater work lengths, mm. Similarly, beore and ater volume rates o material low must be the same, so the beore and ater velocities can be related: h o w o v o = h w v (4) Where v o and v are the entering and exiting velocities o the work. The rolls contact the work along a contact arc deined by the angle α. Each roll has radius R, and its rotational speed gives it a surace velocity v r. This velocity is greater than the entering speed o the work v o and less than its exiting speed v. Since the metal low is continuous, there is a gradual change in velocity o the work between the rolls. However, there is one point along the arc where work velocity equals roll velocity. This is called the no-slip point, also known as the neutral point. On either side o this point, slipping and 9

10 riction occur between roll and work. The amount o slip between the rolls and the work can be measured by means o the orward slip, a term used in rolling that is deined: s = v - v r / v r (5) Where s = orward slip; v = inal (exiting) work velocity, m/s; and v r = roll speed, m/s. The true strain experienced by the work in rolling is based on beore and ater stock thicknesses. In equation orm, ε = ln h o /h (6) The true strain can be used to determine the average low stress lat rolling. Recall rom the previous chapter, Eq., that applied to the work material in = Kε n / 1+n (7) The average low stress will be useul to compute estimates o orce and power in rolling. Friction in rolling occurs with a certain coeicient o riction, and the compression orce o the rolls, multiplied by this coeicient o riction, results in a riction orce between the rolls and the work. On the entrance side o the no-slip point, riction orce is in one direction, and on the other side it is in the opposite direction. However, the two orces are not equal. The riction orce on the entrance side is greater, so that the net orce pulls the work through the rolls. I this were not the case, rolling would not be possible. There is a limit to the maximum possible drat that can be accomplished in lat rolling with a given coeicient o riction, given by: d max = µ 2 R (8) Where d max = maximum drat, mm; µ = coeicient o riction; and R = roll radius mm. The equation indicates that i riction were zero, drat would be zero, and it would be impossible to accomplish the rolling operation. Coeicient o riction in rolling depends on lubrication, work material, and working temperature. In cold rolling, the value is around 0.1; in warm working, a typical value is around 0.2; and in hot rolling, J.L is around 0.4. Hot rolling is oten characterized by a condition called sticking, in which the hot work surace adheres to the rolls over the contact arc. This condition oten occurs in the rolling o steels and high-temperature alloys. When sticking occurs, the coeicient o riction can be as high as 0.7. The consequence o sticking is that the surace layers o the work are restricted to 11

11 move at the same speed as the roll speed Vr; and below the surace, deormation is more severe in order to allow passage o the piece through the roll gap. An approximation can be calculated based on the average low stress experienced by the work material in the roll gap. That is, F = w L (10) Where = average low stress rom Eq. (7), MPa; and the product w L is the roll-work contact area, mm 2. Contact length can be approximated by L R( h o h (11) The torque in rolling can be estimated by assuming that the roll orce is centered on the work as it passes between the rolls, and that it acts with a moment arm o one hal the contact length L. Thus, torque or each roll is T = 0.5FL (12) The power required to drive each roll is the product o torque and angular velocity. Angular velocity is 2N, where N = rotational speed o the roll. Thus, the power or each roll is 2NT. Substituting Eq. (12) or torque in this expression or power, and doubling the value to account or the act that a rolling mill consists o two powered rolls, we get the ollowing expression: P = 2πNFL (13) Where P = power, J/s or W; N = rotational speed, l/s (rev/min); F = rolling orce, N; and L = contact length, m. EXAMPLE A 300-mm-wide strip 25 mm thick is ed through a rolling mill with two powered rolls each o radius = 250 mm. The work thickness is to be reduced to 22 mm in one pass at a roll speed o 50 rev/min. The work material has a low curve deined by K = 275 MPa and n = 0.15, and the coeicient o riction between the rolls and the work is assumed to be Determine i the riction is suicient to permit the rolling operation to be accomplished. I so, calculate the roll orce, torque, and horsepower. 11

12 Solution: The drat attempted in this rolling operation is d=25-22= 3 mm From Eq. (8), the maximum possible drat or the given coeicient o riction is d max = (0.12) 2 (250) = 3.6 mm Since the maximum allowable drat exceeds the attempted reduction, the rolling operation is easible. To compute rolling orce, we need the contact length L and the average low stress. The contact length is given by Eq. (11): L = 250 (25-22) = 27.4 mm is determined rom the true strain: ε = ln 25/22 = = 275(0.128) 0.15 / 1.15 = MPa Rolling orce is determined rom Eq. (10): F = 175.7(300)(27.4) = 1,444,786 N Torque required to drive each roll is given by Eq. (12): T = 0.5 (1,444,786) (27.4) (10-3 ) = 19,786 N-m and the power is obtained rom Eq. (13): P = 2π (50) (1,444,786) (27.4) (10-3 ) = 12,432,086 N-m/min = 207,201 N-m/s (W) It can be seen rom this example that large orces and power are required in rolling. Inspection o Eqs. (10) and (13) indicates that orce and/or power to roll a strip o a given width and work material can be reduced by any o the ollowing: (1) using hot rolling rather than cold rolling to reduce strength and strain hardening (K and n) o the work material; (2) reducing the drat in each pass; (3) using a smaller roll radius R to reduce orce; and (4) using a lower rolling speed N to reduce power. 12