Manufacturing Methods for Composite Parts
The key to manufacturing methods for composites is control of the direction, overlap, and other placement parameters of the fiber reinforcements as well as ensuring that the fibers are fully wetted by the resin. In some manufacturing methods this control is very precise, whereas in others the control is more relaxed and, as a result, the fiber directions are more random. Some methods are best suited to parts having a particular shape characteristic (such as a constant cross section); other methods are used because they have great flexibility in the way the fibers can be arranged.
The nature of the molds used for shaping composites depends on the pressure and temperatures involved in the process. In all cases, however, some provisions must be made to ensure proper wet-out, to shape properly, to effect good solidification, and to assist in removing the part from the mold. Generally, this involves applying a mold release to the mold prior to any material being placed into it.
19.5.1. Molds for Composite Manufacturing Processes
Manufacturing Processes
The molds for composite manufacturing processes must give shape to the composite part during the molding operation. In some composite manufacturing methods, the molding is done with high pressure and typically the molds are metal. These are called hard molds. In other processes, the pressure is much less and other materials can be used. Some processes have variable pressure and so various mold types are possible, depending on the particular methods employed by the molder. These are called soft molds even though they may occasionally be quite hard to the touch. Another consideration for selecting the mold material is the volume of parts that are expected from the mold. When volumes are large, the molds are usually metal.
In parts where dimensional tolerances are very tight, metal molds are preferred. However, when a thermal cure is used, the metal mold often has a different coefficient of thermal expansion (CTE) compared to the composite part being molded. This can be a problem when dimensional tolerances are close. A metal material, Invar, has been developed that has a CTE very close to that of epoxy/carbon fiber composites. The use of this metal as a mold material solves the CTE problem, although the high cost of Invar has restricted its use to only high-performance parts such as those for the aerospace industry.
Using composites as the mold material would, of course, also solve the CTE problem since both the mold and the part could be made of the same material. The use of composites for molds has the additional advantages of ease of making the mold (which might be molded rather than machined) and lighter weight. Composites are rarely used when pressures are very high. However, to withstand the intermediate pressures of many composite manufacturing methods, some way must be found to prevent deflection of the mold during the molding process. One way to do this is simply to make the composite mold thicker or fill the resin with a heavy filler (usually metal powders). These methods work reasonably well, but they add considerable cost and weight to the mold. They also complicate shaping the mold by molding rather than machining. Another way of supporting a composite mold against intermediate pressures is to build a set of fixed supports, somewhat like a scaffolding, that keeps the mold from moving during pressurization steps. This process is called egg-crating because of the similarity of such a support system to those in an egg crate. Egg-crating can also be used to support metal molds where the thickness of the metal has been reduced to improve weight savings and costs. Egg-crating reduces the weight considerably compared to solid metal or even solid composite molds but requires considerable effort to fabricate the support structure. Even so, this method is widely used. A mold supported by an egg-crate construction is shown in Photo 19.8. Some clever methods have been developed recently to support thin mold shells without building egg-crate structures. One uses water pressure as the support medium. Another method uses mechanical pins that can be moved to touch the back side of the mold and prevent it from moving.
If both sides of the part need to be carefully controlled for dimensions and shape, the usual molding arrangement is two hard mold halves. These are sometimes called matched-die molds. However, if only one side of the part needs precise definition, an open mold can be used. If pressure needs to be exerted against the open side, a vacuum bag can be employed, which allows for vacuum pressure on that side. This method is most often used in open molding and is described in more detail in that section.
Another important consideration with all molds is the ability to withstand the molding temperatures. Metals are the material of choice when temperatures are high, as they usually are for advanced composite molding. When temperatures are only slightly above room temperature, composite molds can be employed but usually only with resins that have a high glass transition temperature. Special molding resins are widely available that have higher thermal resistance than general-purpose resins.
19.5.2. Thermoplastic Processes Using Very Short Fibers
When the standard thermoplastic processes such as injection molding and extrusion are used to make composite parts with very short fibers, only minor changes need to be made in the way they are performed. The most important change is that all gaps in the flow path of the resin and fibers should be large enough to allow the fibers to pass. In injection molding, the critical points in the path are the gate at the entry to the mold cavities, the runners, and the orifice at the end of the injection nozzle. Similar close tolerances could exist in an extrusion die. When these gaps are opened or enlarged to ensure good fiber passage, some decrease in back pressure can occur. This lowered back pressure may change the way the plastic material flows in the mold or die and can require some adjustments in temperature or pressure.
Another change besides enlarging the gaps can be in the viscosity of the resin. The resin manufacturer may have intentionally changed the viscosity to give more uniform flow of the resin with the fibers. Therefore, the temperatures of the molding system may need to be adjusted to get optimum molding conditions.
The close tolerances between the screw and the barrel in the melting portion of an injection molding machine or an extruder can cause fiber damage. Whenever possible, the amount of melting from mechanical action should be minimized, usually by increasing the temperatures in the extruder.
The use of very short fibers in thermoplastic resins limits the use of these composite materials to engineering composite applications. These composite materials should be considered for the same applications as their non-reinforced analogues.
19.5.3. Matched-Die or Compression Molding
Two of the major advantages of compression molding over injection molding are the short flow path of the resin and the ability to load compression molds while they are open. In compression molding, the resin has to travel only the distance needed to fill the mold. This short path means that much longer fibers can be molded into composite parts by compression molding than can be molded by injection molding. Also, compression molding largely eliminates the problem of plugging the system with fibers too long to go through narrow openings. Maximum fiber length is that length that allows free movement of both resins and fiber within the mold. Fibers from 0.4 to 4 inches (10 to 100 mm) work well.
If, however, the fibers are not to move at all, as would be the case if a preform of an entire part were placed in the compression mold, continuous fibers and mats can be used effectively. When the preform method is used, the preform is placed in the mold and the resin is poured on top of it. The pressure from the mold closing then distributes the resin. Some fiber redistribution also occurs during this process but is usually minor.
Compression molding with chopped fibers is much more important than molding with preforms. In the standard compression molding method, the fibers have been previously combined with resin (usually crosslinkable polyester) and a filler (such as calcium carbonate) into a molding compound, as was previously described in Chapter 9. This molding compound is then used as the charge material in compression molding, by weighing the molding compound just prior to placing it into the open compression mold. Weighing and charging can be done either automatically or manually.
Matched-die (compression) molding has the advantage over some other composite manufacturing methods in that it produces parts with both sides defined by the mold. Reasonably complex shapes (such as ribs and bosses) are possible in compression molding provided that the shapes are not so sharp or narrow that the fibers do not move easily to fill them. Little trimming is required in matched-die molding. The products usually have low void contents, and the reject rate is usually low. A matched-die mold is shown in Photo 19.9.
Compression molding does have disadvantages. The molding compounds require refrigeration for storage, molds are usually metal so they cost more than molds used in lower-pressure processes, and the molding of large parts often requires large and costly presses.
Molding compounds (especially sheet molding compound) can be used to make large parts, such as the body of the Corvette automobile and bodies for truck cabs, as seen in Photo 19.10. It is also used to make parts that have high strength requirements (within the scope of engineering composites).
19.5.4. Resin Transfer Molding (RTM or Resin Infusion Molding
Although resin transfer molding (RTM) is similar to both traditional transfer molding and reaction in-jection molding (RIM), which were discussed in Chapter 18, RTM differs from them in that a reinforcement is molded with the resin. The physical arrangement and type of equipment used in RTM are like RIM; in fact, the same equipment can be used for both processes. RTM equipment is diagrammed in Figure 19.7. An RTM machine is pictured in Photo 19.11.
In RTM a fiber preform is placed in the mold and then the mold is closed. A fiber preform is made by forming noncoated fibers into the shape of the final part and then spraying them with a small amount of binders to hold them together. The fiber preforms used in RTM can be made from either chopped fibers, mat, or continuous fibers that are knitted or woven into the desired shape. Sometimes, the preform is stitched with reinforcing fiber to allow for transport and loading in the mold without significant preform damage. The resin is injected into the closed mold and wets out the fibers in the preform as the resin fills the mold.
Although polyurethane or other reactive resins can be used to make RTM parts, the more likely materials are polyesters and epoxies. The two pumping chambers contain polyester resin and initiator or epoxy resin and hardener. Resin injection is similar to that in RIM except that care must be taken to inject slowly enough that the fibers in the preform are not moved significantly as the resin fills the mold. Proper wetout of the fibers is a major concern. A vacuum is often applied to the part of the mold farthest from the inlet to assist in resin movement inside the mold.
The viscosity of the resin is an important feature of the RTM process. It must be low enough that it will easily flow and wet the fibers. However, if the resin viscosity is too low, the resin might flow around the outside of the mold and not wet the fibers properly (a problem called racetracking). Experience has shown that the best viscosity for RTM resins is from 10 to 300 centipoise, or about the viscosity of 10W30 motor oil. The best formed RTM parts are usually made using a combination of moderate pressure and vacuum when injecting the resin. The vacuum facilitates entry of the resin and the pressure forces the resin throughout the preform, helps push out the trapped air, and squeezes out the voids. The relatively moderate pressures involved allow RTM molds to be made of light metals, such as aluminum, or composites that are appropriately supported. The mold halves might be held together by placing the mold assembly inside a press (like a compression press), but when pres-sures are not too high, mechanical clamps can be used on the sides of the mold. The mechanical clamps are obviously much less expensive than the large press and make the entire system much more portable.
Because the fibers are loaded into an open mold (although the mold is subsequently closed before injection), layup of the fibers is quite easy and parts of high complexity with continuous fibers are possible. Inserts are also easy to place.
The ability to use both long and short fibers of any of the three major types and to use polyester or epoxy resins means that RTM can be used to make both engineering and advanced composites. This process is rapidly gaining popularity and seems to solve many of the problems inherent in other composite-making processes, such as how to make a composite part in an automated or semiautomated fashion, how to use fiber weaving and knitting technology to allow for more flexibility in the lay-up of fibers, and how to reduce pollution by confining the molding operation to a closed mold.
Photo 19.11 Resin transfer molding equipment. (Courtesy of BYU)
19.5.5. Spray-up
This method of manufacturing composite parts involves using a spray gun to which a fiber-chopping apparatus has been attached. As the resin and initiator are mixed in the gun and then sprayed out of the nozzle, the stream picks up fibers that have been chopped so that they drop into the resin stream. These fibers are then wetted by the resin and, simultaneously, blown forward. The operator directs the stream onto the surface of a mold. This process is depicted in Figure 19.8. Because of incomplete wetting of the fibers during the spray process, the fibers and resin mixture is often manually rolled after it has been sprayed into the mold. The spray-up process is shown in Photo 19.12.
The need to transport the chopped fibers through the air in a spray limits the length of the fibers to about 3 inches (80 mm). The spray-up method depends on the skill of the operator to achieve an even coating of resin and fiber over the entire surface of the part. These two factors combine to dictate that the spray-up method be used only for engineering composites. Therefore, the most common materials used are polyester resin and fiberglass. Cures are done at room temperature, although modest heating is also common.
The spray-up method is well suited to making large parts such as boats and spas. No pressure is used and so the molds can be made of almost any rigid material able to withstand the temperature of the particular cure. Materials such as wood, aluminum, and polyester or epoxy with fiberglass are common.
The spray-up method creates a rough and uneven surface. Therefore, a thin coat of resin is sprayed into the mold and allowed to partially cure (to a gel state) before the resin and fiberglass are sprayed on top. This precoat, called the gel coat, gives the part a smooth outer surface. It can be colored to give permanent color to the part and to assist in hiding the fiber pattern underneath. Furthermore, the gel coat serves as a physical (cured resin) barrier to prevent fibers from working their way to the surface of the part and thereby causing surface blemishes (a process called fiber blooming). Where the part is used in a wet environment, the gel coat also prevents wicking of the moisture along fibers that bloom to the surface. Wicking can cause weakness in the part. A very thin sheet of fiberglass (called a surface veil) can be placed against the gel coat to further prevent fibers from blooming. The veil also hides the fiber pattern and improves surface appearance. Typical practice is to spray a relatively thin (about 1/8-inch, 3 mm) layer on top of the veil. If additional thickness is needed for strength or stiffness, other layers can be sprayed on top of the first. These are each kept thin so that the exotherm is not excessive.
19.5.6. Hand Lay-up (Wet and Prepreg)
The hand lay-up method for wet fibers is used for engineering composites. Polyester and fiberglass are the dominant materials. In this method a layer of fiber mat or fabric is placed in the mold, usually after a gel coat has been applied, and then the resin is poured on top of the fibers. The resin is then distributed over the entire fiber surface and into the fibers by using hand rollers. These rollers also compress the fibers to remove any air that might be trapped. If additional thickness is desired, another layer of fiber mat or cloth is placed in the mold and more resin is added and distributed. Sometimes, the layers of resin and fiber are allowed to partially cure before additional layers are applied to avoid excessive exotherms. The hand lay-up method is shown in Figure 19.9. As with spray-up, the molds used can be very large. Because no pressure is applied, mold materials can be almost anything able to withstand the curing temperatures
Hand lay-up with pre-preg materials is used for advanced composites. (Pre-pregs, fibers which have been precoated with resin, were discussed previously.) The pre-preg materials are carefully placed in the mold so that the fiber orientation meets the design requirement and is smoothed flat so that no wrinkles occur in the prepreg sheet. Additional layers can be placed directly onto the previous layers. Pre-pregs are generally slightly tacky, so the layers stick to each other. After the required number of layers have been properly placed, the pre-pregs are subjected to a vacuum process called debulking, which removes any trapped air. The stack of pre-preg materials on the mold can then be heated to cure the resin. Debulking and curing can be done simultaneously using a vacuum bag assembly like that diagrammed in Figure 19.10. The vacuum bag assembly also removes excess resin so that the fiber-to-resin ratio is high, thus maximizing the strength and stiffness to weight of the composite part.
In the vacuum bag assembly, a layer of release cloth is placed on top of the pre-preg layers. This cloth allows all the other materials in the vacuum bag assembly to be removed from the part after the part is cured. The release cloth is usually a fiberglass cloth coated with a release material, like a fluorocarbon plastic and hole-punched so as to be porous.
The next layer is an absorbent material called a bleeder cloth. The amount of bleeder cloth determines the amount of resin that is removed. Some experience is required in determining the amount of bleeder to ensure that just the right amount of resin is removed to give the optimal weight, but not so much that the fibers are undercoated with resin. Almost any absorbent material will work as a bleeder although the most common are padding materials such as fiberfill or cotton. Additional layers of material can be placed on top of the bleeder to ensure that the resin stays within the bleeder layer. These layers are called the barrier. Finally, the entire assembly is covered with a vacuum bag (usually made from nylon film or silicone elastomer). The vacuum bag is adhered to the mold face using a sealant tape and has a vacuum valve attached so that the entire assembly can be placed under a vacuum and compacted against the face of the mold. A vacuum is applied and the excess air is removed from the entire assembly. A vacuum bag assembly is shown in Photo 19.13.
After applying the vacuum, the mold and vacuum bag assembly can be placed in an oven or autoclave to cure. The autoclave, which applies both heat and pressure, is used if very low void contents are required. Typical cure temperatures are 250°F (120°C) and 350°F (175°C) for 3 to 4 hours. An autoclave is pictured in Photo 19.14. After the required time at the proper temperature, the mold and assembly are removed and the vacuum bag assembly is taken off the part. The part is removed from the mold and, if required, finished by machining or other finishing methods.
A composite manufacturing technique related to hand lay-up is roll wrapping. This technique is used for making generally cylindrical composite parts from pre-preg materials. In roll wrapping a mandrel is used instead of a mold. A mandrel is a core (usually metal) on which the composite material is placed and then cured. In roll wrapping, the pre-preg materials are cut so that they wrap around the mandrel an even number of times. The composite strips are then wrapped around the mandrel until the proper number of layers have been placed. (This wrapping can be semi-automated if desired.) The entire assembly is then overwrapped with a layer of cellophane tape that shrinks when heated to give the compaction necessary to bond the layers together and squeeze out the air. The assembly is then cured in an oven. After curing, the cellophane is removed and the mandrel is extracted from the composite part, which is then finished by machining.
19.5.7. Sandwich Composites
Sometimes a very thick composite part is desired but weight constraints do not allow a solid composite to be made. If the compressive forces are not too high, a rigid, lightweight material can be placed between composite laminate plates (called faces or skins) to give the thickness required without the weight. This layered construction is called a sandwich composite. The material in the middle of the sandwich is called the sandwich core material. The most commonly used sandwich core materials are rigid plastic foam, honeycomb, and balsa wood. The composite face plates are attached to the core material with adhesives. The sandwich construction is depicted in Figure 19.11 and in Photo 19.15. In addition to thickness with little increase in weight, sandwich construction gives increased stiffness to bending forces applied against the face of the composite. The stiffness depends on the thickness of the core and increases geometrically with the thickness.
Photo 19.15 Sandwich panel. (a) Sandwich construction using rigid foam. (b) Sandwich construction using honeycomb. (Courtesy of BYU)
19.5.8. Filament Winding and Fiber Placement
These two processes both use mandrels as the method of shaping the fibers and resins prior to curing, but they differ in how the fibers are placed against the mandrel. In one case (filament winding), the fibers are placed against the mandrel under tension. In the other case (fiber placement), the fibers are pressed against the mandrel by a compaction head. Both are highly automated processes as compared to roll wrapping, which is mostly manual.
Filament winding is more widely used than fiber placement. In filament winding the fibers are attached to the mandrel and then the mandrel is turned to draw the fibers off the spools. The fibers are gathered together into a ring or some other guide called the payoff. The payoff acts as a guide for the fibers and is mounted on a carriage or some other transport system that moves laterally along the long axis of the mandrel as the fibers are being drawn off. This payoff motion is synchronized with the turning of the mandrel to produce a pattern of fibers on the mandrel. The angles of the fiber pattern are determined by the relative motion and speeds of the mandrel and the payoff system.
Between the spools and the mandrel, the fibers pass through a resin bath so that they are soaked with resin when placed on the mandrel. The most common resins used are polyester (when glass is the fiber) and epoxy (when carbon or aramid is the fiber). In both cases the resin in the bath is fully activated with initiator or hardener so that the only heat required is to cure the resin. The filament winding system is depicted in Figure 19.12. Photo 19.16 is an actual filament winding machine.
Photo 19.16 Filament winding machine. (Courtesy: EnTec Corp.)
The use of a mandrel to shape the fibers and resin dictates that the general shape of parts made by filament winding is cylindrical. Pipes, pressure vessels, and similar products are most commonly made by filament winding. However, by allowing the payoff head to move vertically or to twist and rotate, quite complicated shapes can be made. All, however, must have an axis of rotation. Photo 19.17 shows a mandrel and a typical winding pattern.
Photo 19.17 Filament winding showing the mandrel and the winding pattern. (Courtesy of Entec Composite Machines Inc., Salt Lake City, Utah)
After winding is complete, the mandrel with the fibers and resin is placed into an oven or autoclave for curing. The curing is done at the temperatures appropriate for the particular resin used. The autoclave is used when high compaction (low void content) is required. Other innovative systems to obtain compaction include winding on an inflatable mandrel that is pressurized during cure to press the fibers and resin against a clamshell mold that has been placed over the mandrel assembly. (A clam-shell mold is made in two halves that can be clamped together for molding and then separated for part removal afterwards.) Continuous filament winding on a moving mandrel with in-line curing is used to make pipe and other continuous products. Filament winding is used extensively for both engineering and advanced composites, with appropriate resins and fibers. Large parts made by filament winding are shown in Photo 19.18.
Photo 19.18 Various large filament wound parts. (a) Filament wound pipes on collapsible mandrel. (b) Filament wound pipe. (c) Filament wound propeller blades. ((a) Courtesy of Entec Composite Machines, Inc.; (b), (c) Courtesy of Scott W. Beckwith)
Fiber placement compresses the fibers against the mandrel by using a compaction head to payoff the fibers rather than using the turning of the mandrel to draw the fibers off the spools under tension. Normally, the fibers used are thin strips of pre-preg rather than dry fibers tows wetted during the wind-ing process. When these pre-preg fiber strips are pressed against a turning mandrel, greater precision in locating the fibers is achieved. Furthermore, compaction against the mandrel allows shapes to be made using fiber placement that cannot be made with filament winding. For instance, with fiber placement the mandrel can be concave, whereas with filament winding a concave mandrel results in fibers bridging across the face of the mandrel rather than touching it.
The major drawbacks of fiber placement are the high cost of the machine and the relatively slow production rate. The high cost arises in part because of the complexity of the compaction/payoff head. The payoff head must be able to rotate and move in several directions to accommodate the varied shapes of the mandrels that might be used. The high cost of making parts with fiber placement usually dictates that only advanced composite parts be made by this method.
19.5.9. Pultrusion
The pultrusion process makes parts that have a constant cross section. In this process, the fibers are drawn off the spools, through a resin bath, and then through a curing die. The force for drawing is supplied by a puller placed after the die. Therefore, as shown in Figure 19.13, the process continuously makes composite parts that are shaped by the die. A cutoff system after the puller cuts the parts to the desired length. An actual pultruder is shown in Photo 19.19.
Photo 19.19 Commercial pultrusion machine and die -- pultrusion process for reinforced plastic wrap. (Courtesy of Entec Machines, Inc.)
Parts made in pultrusion can be reinforced in directions other than the machine direction by pulling strips of mat or cloth into the die with the fibers. These can be pulled through the resin bath, but normally the fibers carry sufficient excess resin that wet-out of the mat or fabric occurs within the die. Compaction of these materials with the fibers is also accomplished within the die.
Pultrusion is a low-cost production method best suited to engineering composites because of the difficulty in precisely controlling the fiber placement. The pultrusion process is used principally with fiberglass and polyester. Some common composite parts made by pultrusion are moldings, sides of ladders, and tubes. Several pultruded parts are shown in Photo 19.20.
Photo 19.20 Standard pultruded structural and custom composite parts. (Courtesy: Creative Pultrusions, Inc., Alum Bank, PA)
19.5.10. Processes for Long and Continuous Fibers Using Thermoplastics
Some high-performance thermoplastic resins can be used as matrix materials for very long and continuous-fiber composites. These resins are usually high molecular weight, highly crystalline thermoplastics that have a high degree of aromatic character. This combination of characteristics results in thermoplastics that have high stiffness, high strength, high toughness, and can withstand high temperatures and most solvents. The properties are comparable to high-performance epoxies with the added advantage of improved toughness. The costs of these high-performance thermosplastics are higher than those of epoxies so the value of the thermoplastics is in applications where the toughness property or some other property is critical. With the development of new manufacturing methods particularly suited to the advanced thermoplastics, manufacturing cost advantages may also be realized over epoxy composites.
The major drawback in the processing of these high-performance thermoplastics to make advanced composites is the difficulty encountered in wetting-out the fibers. The ability to wet-out fibers is complicated by the very high molecular weight of the thermoplastics, which is required to achieve the physical and mechanical properties. Some innovative methods do accomplish this wet-out, however. One method is to melt the resin and then apply the melt to the fibers while the resin is subjected to shear forces. The non-Newtonian nature of the resins means that resin viscosity is lowered by shearing. This property is called shear thinning and is used to make the resins thin enough to coat the fibers. Another technique is to powder the resin and then coat the fibers with the powder. During cure, the powder melts and covers the fibers. Still another method is to make fibers out of the thermoplastic resins and then coweave or comingle the thermoplastic fibers with the reinforcing fibers. Then, when the fibers are heated, the thermoplastic fibers melt and coat the reinforcements. One other method is to place a thin sheet of thermoplastic resin over a mat or fabric of dry fibers and then heat the thermoplastic until it is soft and press the resin onto the fibers. Some success has been achieved with each of these methods, but all continue to have significant problems.
By using the wet-out methods discussed, a significant number of composites using high-performance thermoplastic resins and continuous or very long fibers have been made. The most common manufacturing methods are those that are used for thermoset resins: hand lay-up, filament winding, and pultrusion. One unique method for making thermoplastic composites have proven to be very economical and viable. Called press thermoforming, this method is similar to matched-die thermoforming. In this method, the thermoplastic pre-preg materials are stacked in the sequence, orientation, and thicknesses needed to meet the design. The materials are then heated to the point where the thermoplastic resins begin to sag, placed into a matched-die mold (which is cold), and pressed to give them the shape of the mold. The pressing cycle is very short (often less than 10 seconds) because the only thermal requirement during the pressing cycle is that the materials cool enough to solidify. This method holds great promise for making advanced composites out of thermoplastic resins. The method is illustrated in Figure 19.14, where both the open and closed modes of the press are shown.
19.5.11. Troubleshooting
The problems in composite manufacturing depend upon the process being used. The diversity of these processes complicates the design of a single troubleshooting guide, but, nevertheless, some common problems exist. These are summarized in a troubleshooting guide, which is given in Table 19.4.
Table 19.4 Troubleshooting Guide for Composite Materials Manufacturing
Table 19.4 Continued
 made.png)