Lecture notes on Metal forming

lecture notes on heavy metals, what metals are magnetic and what metals are not magnetic and what makes metals good conductors of heat pdf free download
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Metals 3 Chapter 1 Metals Introduction This first group of chapters looks at metals. There are so many different metals – literally hundreds of them – that it is impossible to remember them all. It isn’t necessary – nearly all have evolved from a few “generic” metals and are simply tuned- up modifications of the basic recipes. If you know about the generic metals, you know most of what you need. This chapter introduces the generic metals. But rather than bore you with a cata- logue we introduce them through three real engineering examples. They allow us not only to find examples of the uses of the main generic metals but also to introduce the all-important business of how the characteristics of each metal determine how it is used in practice. Metals for a model traction engine Model-making has become big business. The testing of scale models provides a cheap way of getting critical design information for things from Olympic yacht hulls to tidal barrages. Architects sell their newest creations with the help of miniature versions correct to the nearest door-handle and garden shrub. And in an age of increasing leisure time, many people find an outlet for their energies in making models – perhaps putting together a miniature aircraft from a kit of plastic parts or, at the other extreme, building a fully working model of a steam engine from the basic raw materials in their own “garden-shed” machine shop. Figure 1.1 shows a model of a nineteenth-century steam traction engine built in a home workshop from plans published in a well-known modellers’ magazine. Every- thing works just as it did in the original – the boiler even burns the same type of coal to raise steam – and the model is capable of towing an automobile But what interests us here is the large range of metals that were used in its construction, and the way in which their selection was dictated by the requirements of design. We begin by looking at metals based on iron ( ferrous metals). Table 1.1 lists the generic iron-based metals. How are these metals used in the traction engine? The design loads in components like the wheels and frames are sufficiently low that mild steel, with a yield strength σ y of around 220 MPa, is more than strong enough. It is also easy to cut, bend or machine to shape. And last, but not least, it is cheap.4 Engineering Materials 2 Fig. 1.1. A fully working model, one-sixth full size, of a steam traction engine of the type used on many farms a hundred years ago. The model can pull an automobile on a few litres of water and a handful of coal. But it is also a nice example of materials selection and design. Table 1.1 Generic iron-based metals Metal Typical composition Typical uses (wt%) Low-carbon (“mild”) steel Fe + 0.04 to 0.3 C Low-stress uses. General constructional steel, suitable (+ ≈ 0.8 Mn) for welding. Medium-carbon steel Fe + 0.3 to 0.7 C Medium-stress uses: machinery parts – nuts and bolts, (+ ≈ 0.8 Mn) shafts, gears. High-carbon steel Fe + 0.7 to 1.7 C High-stress uses: springs, cutting tools, dies. (+ ≈ 0.8 Mn) Low-alloy steel Fe + 0.2 C 0.8 Mn High-stress uses: pressure vessels, aircraft parts. 1 Cr 2 Ni High-alloy (“stainless”) Fe + 0.1 C 0.5 Mn High-temperature or anti-corrosion uses: chemical or steel 18 Cr 8 Ni steam plants. Cast iron Fe + 1.8 to 4 C Low-stress uses: cylinder blocks, drain pipes. (+ ≈ 0.8 Mn 2 Si)Metals 5 Fig. 1.2. A close-up of the mechanical lubricator on the traction engine. Unless the bore of the steam cylinder is kept oiled it will become worn and scored. The lubricator pumps small metered quantities of steam oil into the cylinder to stop this happening. The drive is taken from the piston rod by the ratchet and pawl arrangement. The stresses in the machinery – like the gear-wheel teeth or the drive shafts – are a good deal higher, and these parts are made from either medium-carbon, high-carbon or low-alloy steels to give extra strength. However, there are a few components where even the strength of high-carbon steels as delivered “off the shelf” (σ ≈ 400 MPa) y is not enough. We can see a good example in the mechanical lubricator, shown in Fig. 1.2, which is essentially a high-pressure oil metering pump. This is driven by a ratchet and pawl. These have sharp teeth which would quickly wear if they were made of a soft alloy. But how do we raise the hardness above that of ordinary high- carbon steel? Well, medium- and high-carbon steels can be hardened to give a yield strength of up to 1000 MPa by heating them to bright red heat and then quenching them into cold water. Although the quench makes the hardened steel brittle, we can make it tough again (though still hard) by tempering it – a process that involves heating the steel again, but to a much lower temperature. And so the ratchet and pawls are made from a quenched and tempered high-carbon steel. Stainless steel is used in several places. Figure 1.3 shows the fire grate – the metal bars which carry the burning coals inside the firebox. When the engine is working hard the coal is white hot; then, both oxidation and creep are problems. Mild steel bars can burn out in a season, but stainless steel bars last indefinitely.6 Engineering Materials 2 Fig. 1.3. The fire grate, which carries the white-hot fire inside the firebox, must resist oxidation and creep. Stainless steel is best for this application. Note also the threaded monel stays which hold the firebox sides together against the internal pressure of the steam. Finally, what about cast iron? Although this is rather brittle, it is fine for low-stressed components like the cylinder block. In fact, because cast iron has a lot of carbon it has several advantages over mild steel. Complicated components like the cylinder block are best produced by casting. Now cast iron melts much more easily than steel (adding carbon reduces the melting point in just the way that adding anti-freeze works with water) and this makes the pouring of the castings much easier. During casting, the carbon can be made to separate out as tiny particles of graphite, distributed through- out the iron, which make an ideal boundary lubricant. Cylinders and pistons made from cast iron wear very well; look inside the cylinders of your car engine next time the head has to come off, and you will be amazed by the polished, almost glazed look 8 of the bores – and this after perhaps 10 piston strokes. These, then, are the basic classes of ferrous alloys. Their compositions and uses are summarised in Table 1.1, and you will learn more about them in Chapters 11 and 12, but let us now look at the other generic alloy groups. An important group of alloys are those based on copper (Table 1.2). The most notable part of the traction engine made from copper is the boiler and its firetubes (see Fig. 1.1). In full size this would have been made from mild steel, and the use of copper in the model is a nice example of how the choice of material can depend on the scale of the structure. The boiler plates of the full-size engine are about 10 mm thick, of which perhaps only 6 mm is needed to stand the load from the pressurisedMetals 7 Table 1.2 Generic copper-based metals Metal Typical composition (wt%) Typical uses Copper 100 Cu Ductile, corrosion resistant and a good electrical conductor: water pipes, electrical wiring. Brass Zn Stronger than copper, machinable, reasonable corrosion resistance: water fittings, screws, electrical components. Bronze Cu + 10–30 Sn Good corrosion resistance: bearings, ships’ propellers, bells. Cupronickel Cu + 30 Ni Good corrosion resistance, coinage. steam safely – the other 4 mm is an allowance for corrosion. Although a model steel boiler would stand the pressure with plates only 1 mm thick, it would still need the same corrosion allowance of 4 mm, totalling 5 mm altogether. This would mean a very heavy boiler, and a lot of water space would be taken up by thick plates and firetubes. Because copper hardly corrodes in clean water, this is the obvious material to use. Although weaker than steel, copper plates 2.5 mm thick are strong enough to resist the working pressure, and there is no need for a separate corrosion allowance. Of course, copper is expensive – it would be prohibitive in full size – but this is balanced by its ductility (it is very easy to bend and flange to shape) and by its high thermal conduct- ivity (which means that the boiler steams very freely). Brass is stronger than copper, is much easier to machine, and is fairly corrosion- proof (although it can “dezincify” in water after a long time). A good example of its use in the engine is for steam valves and other boiler fittings (see Fig. 1.4). These are intricate, and must be easy to machine; dezincification is a long-term possibility, so occasional inspection is needed. Alternatively, corrosion can be avoided altogether by using the more expensive bronzes, although some are hard to machine. Nickel and its alloys form another important class of non-ferrous metals (Table 1.3). The superb creep resistance of the nickel-based superalloys is a key factor in designing the modern gas-turbine aero-engine. But nickel alloys even appear in a model steam engine. The flat plates in the firebox must be stayed together to resist the internal steam pressure (see Fig. 1.3). Some model-builders make these stays from pieces of monel rod because it is much stronger than copper, takes threads much better and is very corrosion resistant. Metals for drinks cans Few people would think that the humble drink can (Fig. 1.5) was anything special. But to a materials engineer it is high technology. Look at the requirements. As far as possible we want to avoid seams. The can must not leak, should use as little metal as possible and be recyclable. We have to choose a metal that is ductile to the point that it can be drawn into a single-piece can body from one small slug of metal. It must not corrode in beer or coke and, of course, it must be non-toxic. And it must be light and must cost almost nothing.8 Engineering Materials 2 Fig. 1.4. Miniature boiler fittings made from brass: a water-level gauge, a steam valve, a pressure gauge, and a feed-water injector. Brass is so easy to machine that it is good for intricate parts like these. Table 1.3 Generic nickel-based metals Metals Typical composition (wt%) Typical uses Monels Ni + 30 Cu 1 Fe 1 Mn Strong, corrosion resistant: heat-exchanger tubes. Superalloys Ni + 30 Cr 30 Fe 0.5 Ti 0.5 Al Creep and oxidation resistant: furnace parts. Ni + 10 Co 10 W 9 Cr 5 A12 Ti Highly creep resistant: turbine blades and discs. Aluminium-based metals are the obvious choice (Table 1.4) – they are light, corro- sion resistant and non-toxic. But it took several years to develop the process for form- ing the can and the alloy to go with it. The end product is a big advance from the days when drinks only came in glass bottles, and has created a new market for aluminium (now threatened, as we shall see in Chapter 21, by polymers). Because aluminium is One thinks of aluminium as a cheap material – aluminium spoons are so cheap that they are thrown away. It was not always so. Napoleon had a set of cutlery specially made from the then-new material. It cost him more than a set of solid silver.Metals 9 Fig. 1.5. The aluminium drink can is an innovative product. The body is made from a single slug of a 3000 series aluminium alloy. The can top is a separate pressing which is fastened to the body by a rolled seam once the can has been filled. There are limits to one-piece construction. Table 1.4 Generic aluminium-based metals Metal Typical composition (wt%) Typical uses 1000 Series 99 Al Weak but ductile and a good electrical unalloyed Al conductor: power transmission lines, cooking foil. 2000 Series Al + 4 Cu + Mg, Si, Mn Strong age-hardening alloy: aircraft skins, spars, major additive Cu forgings, rivets. 3000 Series Al + 1 Mn Moderate strength, ductile, excellent corrosion resistance: major additive Mn roofing sheet, cooking pans, drinks can bodies. 5000 Series Al + 3 Mg 0.5 Mn Strong work-hardening weldable plate: pressure major additive Mg vessels, ship superstructures. 6000 Series Al + 0.5 Mg 0.5 Si Moderate-strength age-hardening alloy: anodised major additives extruded sections, e.g. window frames. Mg + Si 7000 Series Al + 6 Zn + Mg, Cu, Mn Strong age-hardening alloy: aircraft forgings, major additives sparts, lightweight railway carriage shells. Zn + Mg Casting alloys Al + 11 Si Sand and die castings. Aluminium– Al + 3 Li Low density and good strength: aircraft skins lithium alloys and spars.10 Engineering Materials 2 lighter than most other metals it is also the obvious choice for transportation: aircraft, high-speed trains, cars, even. Most of the alloys listed in Table 1.4 are designed with these uses in mind. We will discuss the origin of their strength, and their uses, in more detail in Chapter 10. Metals for artificial hip joints As a last example we turn to the world of medicine. Osteo-arthritis is an illness that affects many people as they get older. The disease affects the joints between different bones in the body and makes it hard – and painful – to move them. The problem is caused by small lumps of bone which grow on the rubbing surfaces of the joints and which prevent them sliding properly. The problem can only be cured by removing the bad joints and putting artificial joints in their place. The first recorded hip-joint re- placement was done as far back as 1897 – when it must have been a pretty hazardous business – but the operation is now a routine piece of orthopaedic surgery. In fact 30,000 hip joints are replaced in the UK every year; world-wide the number must approach half a million. Figure 1.6 shows the implant for a replacement hip joint. In the operation, the head of the femur is cut off and the soft marrow is taken out to make a hole down the centre of the bone. Into the hole is glued a long metal shank which carries the artificial head. Fig. 1.6. The titanium alloy implant for a replacement hip joint. The long shank is glued into the top of the femur. The spherical head engages in a high-density polythene socket which is glued into the pelvic socket.Metals 11 Table 1.5 Generic titanium-based metals Metal Typical composition (wt%) Typical uses a–b titanium alloy Ti–6 A14 V Light, very strong, excellent corrosion resistance, high melting point, good creep resistance. The alloy workhorse: turbofans, airframes, chemical plant, surgical implants. This fits into a high-density polythene socket which in turn is glued into the old bone socket. The requirements of the implant are stringent. It has to take large loads with- 6 out bending. Every time the joint is used (≈10 times a year) the load on it fluctuates, giving us a high-cycle fatigue problem as well. Body fluids are as corrosive as sea water, so we must design against corrosion, stress corrosion and corrosion fatigue. The metal must be bio-compatible. And, ideally, it should be light as well. The materials that best meet these tough requirements are based on titanium. The α–β alloy shown in Table 1.5 is as strong as a hardened and tempered high-carbon steel, is more corrosion resistant in body fluids than stainless steel, but is only half the weight. A disadvantage is that its modulus is only half that of steels, so that it tends to be “whippy” under load. But this can be overcome by using slightly stiffer sections. The same alloy is used in aircraft, both in the airframes and in the compressor stages of the gas turbines which drive them. Data for metals When you select a metal for any design application you need data for the properties. Table 1.6 gives you approximate property data for the main generic metals, useful for the first phase of a design project. When you have narrowed down your choice you should turn to the more exhaustive data compilations given under Further Reading. Finally, before making final design decisions you should get detailed material specifica- tions from the supplier who will provide the materials you intend to use. And if the component is a critical one (meaning that its failure could precipitate a catastrophe) you should arrange to test it yourself. There are, of course, many more metals available than those listed here. It is use- ful to know that some properties depend very little on microstructure: the density, modulus, thermal expansion and specific heat of any steel are pretty close to those listed in the table. (Look at the table and you will see that the variations in these properties are seldom more than ±5%.) These are the “structure-insensitive” properties. Other proper- ties, though, vary greatly with the heat treatment and mechanical treatment, and the detailed alloy composition. These are the “structure-sensitive” properties: yield and tensile strength, ductility, fracture toughness, and creep and fatigue strength. They cannot be guessed from data for other alloys, even when the composition is almost the same. For these it is essential to consult manufacturers’ data sheets listing the proper- ties of the alloy you intend to use, with the same mechanical and heat treatment.12 Engineering Materials 2 Table 1.6 Properties of the generic metals Metal Cost Density Young’s Yield Tensile −3 (UK£ (US) (Mg m ) modulus strength strength −1 tonne ) (GPa) (MPa) (MPa) Iron 100 (140) 7.9 211 50 200 Mild steel 200–230 (260–300) 7.9 210 220 430 High-carbon steel 150 (200) 7.8 210 350–1600 650–2000 Low-alloy steels 180–250 (230–330) 7.8 203 290–1600 420–2000 High-alloy steels 1100–1400 (1400–1800) 7.8 215 170–1600 460–1700 Cast irons 120 (160) 7.4 152 50–400 10–800 Copper 1020 (1330) 8.9 130 75 220 Brasses 750–1060 (980–1380) 8.4 105 200 350 Bronzes 1500 (2000) 8.4 120 200 350 Nickel 3200 (4200) 8.9 214 60 300 Monels 3000 (3900) 8.9 185 340 680 Superalloys 5000 (6500) 7.9 214 800 1300 Aluminium 910 (1180) 2.7 71 25–125 70–135 1000 Series 910 (1180) 2.7 71 28–165 70–180 2000 Series 1100 (1430) 2.8 71 200–500 300–600 5000 Series 1000 (1300) 2.7 71 40–300 120–430 7000 Series 1100 (1430) 2.8 71 350–600 500–670 Casting alloys 1100 (1430) 2.7 71 65–350 130–400 Titanium 4630 (6020) 4.5 120 170 240 Ti–6 A14 V 5780 (7510) 4.4 115 800–900 900–1000 Zinc 330 (430) 7.1 105 120 Lead–tin solder 2000 (2600) 9.4 40 Diecasting alloy 800 (1040) 6.7 105 280–330 Further reading Smithells’ Metals Reference Book, 7th edition, Butterworth-Heinemann, 1992 (for data). ASM Metals Handbook, 10th edition, ASM International, 1990 (for data). Problems 1.1 Explain what is meant by the following terms: (a) structure-sensitive property; (b) structure-insensitive property. List five different structure-sensitive properties. List four different structure-insensitive properties. Answers: Structure-sensitive properties: yield strength, hardness, tensile strength, ductility, fracture toughness, fatigue strength, creep strength, corrosion resistance,Metals 13 Ductility Fracture Melting Specific Thermal Thermal toughness temperature heat conductivity expansion 1/2 −1 −1 −1 −1 (MPa m ) (K) (J kg K ) (W m K ) coefficient −1 (MK ) 0.3 80 1809 456 78 12 0.21 140 1765 482 60 12 0.1–0.2 20–50 1570 460 40 12 0.1–0.2 50–170 1750 460 40 12 0.1–0.5 50–170 1680 500 12–30 10–18 0–0.18 6–20 1403 0.5–0.9 100 1356 385 397 17 0.5 30–100 1190 121 20 0.5 30–100 1120 85 19 0.4 100 1728 450 89 13 0.5 100 1600 420 22 14 0.2 100 1550 450 11 12 0.1–0.5 45 933 917 240 24 0.1–0.45 45 915 24 0.1–0.25 10–50 860 180 24 0.1–0.35 30–40 890 130 22 0.1–0.17 20–70 890 150 24 0.01–0.15 5–30 860 140 20 0.25 1940 530 22 9 0.1–0.2 50–80 1920 610 6 8 0.4 693 390 120 31 456 0.07–0.15 650 420 110 27 wear resistance, thermal conductivity, electrical conductivity. Structure-insensitive properties: elastic moduli, Poisson’s ratio, density, thermal expansion coefficient, specific heat. 1.2 What are the five main generic classes of metals? For each generic class: (a) give one example of a specific component made from that class; (b) indicate why that class was selected for the component.14 Engineering Materials 2 Chapter 2 Metal structures Introduction At the end of Chapter 1 we noted that structure-sensitive properties like strength, ductility or toughness depend critically on things like the composition of the metal and on whether it has been heated, quenched or cold formed. Alloying or heat treating work by controlling the structure of the metal. Table 2.1 shows the large range over which a material has structure. The bracketed subset in the table can be controlled to give a wide choice of structure-sensitive properties. Table 2.1 Structural feature Typical scale (m) −15 Nuclear structure 10 −10 Structure of atom 10 −9 Crystal or glass structure 10 5 −9 Structures of solutions and compounds 10 4 −8 Structures of grain and phase boundaries 10 6 Range that can be controlled to alter properties −7 −3 Shapes of grains and phases 10 to 10 4 −5 −2 Aggregates of grains 10 to 10 7 −3 3 Engineering structures 10 to 10 Crystal and glass structures We begin by looking at the smallest scale of controllable structural feature – the way in which the atoms in the metals are packed together to give either a crystalline or a glassy (amorphous) structure. Table 2.2 lists the crystal structures of the pure metals at room temperature. In nearly every case the metal atoms pack into the simple crystal structures of face-centred cubic (f.c.c.), body-centred cubic (b.c.c.) or close-packed hexagonal (c.p.h.). Metal atoms tend to behave like miniature ball-bearings and tend to pack together as tightly as possible. F.c.c. and c.p.h. give the highest possible packing density, with 74% of the volume of the metal taken up by the atomic spheres. However, in some metals, like iron or chromium, the metallic bond has some directionality and this makes the atoms pack into the more open b.c.c. structure with a packing density of 68%. Some metals have more than one crystal structure. The most important examples are iron and titanium. As Fig. 2.1 shows, iron changes from b.c.c. to f.c.c. at 914°C but goesMetal structures 15 Table 2.2 Crystal structures of pure metals at room temperature Pure metal Structure Unit cell dimensions (nm) ac Aluminium f.c.c. 0.405 Beryllium c.p.h. 0.229 0.358 Cadmium c.p.h. 0.298 0.562 Chromium b.c.c. 0.289 Cobalt c.p.h. 0.251 0.409 Copper f.c.c. 0.362 Gold f.c.c. 0.408 Hafnium c.p.h. 0.320 0.506 Indium Face-centred tetragonal Iridium f.c.c. 0.384 Iron b.c.c. 0.287 Lanthanum c.p.h. 0.376 0.606 Lead f.c.c. 0.495 Magnesium c.p.h. 0.321 0.521 Manganese Cubic 0.891 Molybdenum b.c.c. 0.315 Nickel f.c.c. 0.352 Niobium b.c.c. 0.330 Palladium f.c.c. 0.389 Platinum f.c.c. 0.392 Rhodium f.c.c. 0.380 Silver f.c.c. 0.409 Tantalum b.c.c. 0.331 Thallium c.p.h. 0.346 0.553 Tin Body-centred tetragonal Titanium c.p.h. 0.295 0.468 Tungsten b.c.c. 0.317 Vanadium b.c.c. 0.303 Yttrium c.p.h. 0.365 0.573 Zinc c.p.h. 0.267 0.495 Zirconium c.p.h. 0.323 0.515 Fig. 2.1. Some metals have more than one crystal structure. The most important examples of this polymorphism are in iron and titanium.16 Engineering Materials 2 back to b.c.c. at 1391°C; and titanium changes from c.p.h. to b.c.c. at 882°C. This multiplicity of crystal structures is called polymorphism. But it is obviously out of the question to try to control crystal structure simply by changing the temperature (iron is useless as a structural material well below 914°C). Polymorphism can, however, be brought about at room temperature by alloying. Indeed, many stainless steels are f.c.c. rather than b.c.c. and, especially at low temperatures, have much better ductility and toughness than ordinary carbon steels. This is why stainless steel is so good for cryogenic work: the fast fracture of a steel vacuum flask containing liquid nitrogen would be embarrassing, to say the least, but stainless steel is essential for the vacuum jackets needed to cool the latest supercon- ducting magnets down to liquid helium temperatures, or for storing liquid hydrogen or oxygen. If molten metals (or, more usually, alloys) are cooled very fast – faster than about 6 −1 10 K s – there is no time for the randomly arranged atoms in the liquid to switch into the orderly arrangement of a solid crystal. Instead, a glassy or amorphous solid is pro- duced which has essentially a “frozen-in” liquid structure. This structure – which is termed dense random packing (drp) – can be modelled very well by pouring ball-bearings into a glass jar and shaking them down to maximise the packing density. It is interest- ing to see that, although this structure is disordered, it has well-defined characteristics. For example, the packing density is always 64%, which is why corn was always sold in bushels (1 bushel = 8 UK gallons): provided the corn was always shaken down well in the sack a bushel always gave 0.64 × 8 = 5.12 gallons of corn material It has only recently become practicable to make glassy metals in quantity but, because their struc- ture is so different from that of “normal” metals, they have some very unusual and exciting properties. Structures of solutions and compounds As you can see from the tables in Chapter 1, few metals are used in their pure state – they nearly always have other elements added to them which turn them into alloys and give them better mechanical properties. The alloying elements will always dissolve in the basic metal to form solid solutions, although the solubility can vary between 0.01% and 100% depending on the combinations of elements we choose. As examples, the iron in a carbon steel can only dissolve 0.007% carbon at room temperature; the copper in brass can dissolve more than 30% zinc; and the copper–nickel system – the basis of the monels and the cupronickels – has complete solid solubility. There are two basic classes of solid solution. In the first, small atoms (like carbon, boron and most gases) fit between the larger metal atoms to give interstitial solid solutions (Fig. 2.2a). Although this interstitial solubility is usually limited to a few per cent it can have a large effect on properties. Indeed, as we shall see later, interstitial solutions of carbon in iron are largely responsible for the enormous range of strengths that we can get from carbon steels. It is much more common, though, for the dissolved atoms to have a similar size to those of the host metal. Then the dissolved atomsMetal structures 17 Fig. 2.2. Solid-solution structures. In interstitial solutions small atoms fit into the spaces between large atoms. In substitutional solutions similarly sized atoms replace one another. If A–A, A–B and B–B bonds have the same strength then this replacement is random. But unequal bond strengths can give clustering or ordering. simply replace some of the host atoms to give a substitutional solid solution (Fig. 2.2b). Brass and cupronickel are good examples of the large solubilities that this atomic substitution can give. Solutions normally tend to be random so that one cannot predict which of the sites will be occupied by which atoms (Fig. 2.2c). But if A atoms prefer to have A neigh- bours, or B atoms prefer B neighbours, the solution can cluster (Fig. 2.2d); and when A atoms prefer B neighbours the solution can order (Fig. 2.2e). Many alloys contain more of the alloying elements than the host metal can dissolve. Then the surplus must separate out to give regions that have a high concentration of the alloying element. In a few alloys these regions consist of a solid solution based on the alloying element. (The lead–tin alloy system, on which most soft solders are based, Table 1.6, is a nice example of this – the lead can only dissolve 2% tin at room temper- ature and any surplus tin will separate out as regions of tin containing 0.3% dissolved lead.) In most alloy systems, however, the surplus atoms of the alloying element separate out as chemical compounds. An important example of this is in the aluminium– copper system (the basis of the 2000 series alloys, Table 1.4) where surplus copper separates out as the compound CuAl . CuAl is hard and is not easily cut by disloca- 2 2 tions. And when it is finely dispersed throughout the alloy it can give very big increases in strength. Other important compounds are Ni Al, Ni Ti, Mo C and TaC (in 3 3 2 super-alloys) and Fe C (in carbon steels). Figure 2.3 shows the crystal structure of 3 CuAl . As with most compounds, it is quite complicated. 218 Engineering Materials 2 Fig. 2.3. The crystal structure of the “intermetallic” compound CuAl . The structures of compounds are usually 2 more complicated than those of pure metals. Phases The things that we have been talking about so far – metal crystals, amorphous metals, solid solutions, and solid compounds – are all phases. A phase is a region of material that has uniform physical and chemical properties. Water is a phase – any one drop of water is the same as the next. Ice is another phase – one splinter of ice is the same as any other. But the mixture of ice and water in your glass at dinner is not a single phase because its properties vary as you move from water to ice. Ice + water is a two-phase mixture. Grain and phase boundaries A pure metal, or a solid solution, is single-phase. It is certainly possible to make single crystals of metals or alloys but it is difficult and the expense is only worth it for high- technology applications such as single-crystal turbine blades or single-crystal silicon for microchips. Normally, any single-phase metal is polycrystalline – it is made up of millions of small crystals, or grains, “stuck” together by grain boundaries (Fig. 2.4). Fig. 2.4. The structure of a typical grain boundary. In order to “bridge the gap” between two crystals of different orientation the atoms in the grain boundary have to be packed in a less ordered way. The packing density in the boundary is then as low as 50%.Metal structures 19 Fig. 2.5. Structures of interphase boundaries. Because of their unusual structure, grain boundaries have special properties of their own. First, the lower bond density in the boundary is associated with a boundary −2 surface-energy: typically 0.5 Joules per square metre of boundary area (0.5 J m ). Secondly, the more open structure of the boundary can give much faster diffusion in the boundary plane than in the crystal on either side. And finally, the extra space makes it easier for outsized impurity atoms to dissolve in the boundary. These atoms tend to segregate to the boundaries, sometimes very strongly. Then an average impurity concentration of a few parts per million can give a local concentration of 10% in the boundary with very damaging effects on the fracture toughness. As we have already seen, when an alloy contains more of the alloying element than the host metal can dissolve, it will split up into two phases. The two phases are “stuck” together by interphase boundaries which, again, have special properties of their own. We look first at two phases which have different chemical compositions but the same crystal structure (Fig. 2.5a). Provided they are oriented in the right way, the crystals can be made to match up at the boundary. Then, although there is a sharp change in Henry Bessemer, the great Victorian ironmaster and the first person to mass-produce mild steel, was nearly bankrupted by this. When he changed his suppliers of iron ore, his steel began to crack in service. The new ore contained phosphorus, which we now know segregates badly to grain boundaries. Modern steels must contain less than ≈0.05% phosphorus as a result.20 Engineering Materials 2 chemical composition, there is no structural change, and the energy of this coherent −2 boundary is low (typically 0.05 J m ). If the two crystals have slightly different lattice spacings, the boundary is still coherent but has some strain (and more energy) associ- ated with it (Fig. 2.5b). The strain obviously gets bigger as the boundary grows side- ways: full coherency is usually possible only with small second-phase particles. As the particle grows, the strain builds up until it is relieved by the injection of dislocations to give a semi-coherent boundary (Fig. 2.5c). Often the two phases which meet at the boundary are large, and differ in both chemical composition and crystal structure. Then the boundary between them is incoherent; it is like a grain boundary across which there is also a change in chemical composition (Fig. 2.5d). Such a phase boundary has −2 a high energy – comparable with that of a grain boundary – and around 0.5 J m . Shapes of grains and phases Grains come in all shapes and sizes, and both shape and size can have a big effect on the properties of the polycrystalline metal (a good example is mild steel – its strength can be doubled by a ten-times decrease in grain size). Grain shape is strongly affected by the way in which the metal is processed. Rolling or forging, for instance, can give stretched-out (or “textured”) grains; and in casting the solidifying grains are often elongated in the direction of the easiest heat loss. But if there are no external effects like these, then the energy of the grain boundaries is the important thing. This can be illustrated very nicely by looking at a “two-dimensional” array of soap bubbles in a thin glass cell. The soap film minimises its overall energy by straightening out; and at the corners of the bubbles the films meet at angles of 120° to balance the surface tensions (Fig. 2.6a). Of course a polycrystalline metal is three-dimensional, but the same principles apply: the grain boundaries try to form themselves into flat planes, and these planes always try to meet at 120°. A grain shape does indeed exist which not only satisfies these conditions but also packs together to fill space. It has 14 faces, and is therefore called a tetrakaidecahedron (Fig. 2.6b). This shape is remarkable, not only for the properties just given, but because it appears in almost every physical science (the shape of cells in plants, of bubbles in foams, of grains in metals and of Dirichlet cells in solid-state physics). If the metal consists of two phases then we can get more shapes. The simplest is when a single-crystal particle of one phase forms inside a grain of another phase. Then, if the energy of the interphase boundary is isotropic (the same for all orientations), the second-phase particle will try to be spherical in order to minimise the interphase boundary energy (Fig. 2.7a). Naturally, if coherency is possible along some planes, but not along others, the particle will tend to grow as a plate, extensive along the low- energy planes but narrow along the high-energy ones (Fig. 2.7b). Phase shapes get more complicated when interphase boundaries and grain boundaries meet. Figure 2.7(c) shows the shape of a second-phase particle that has formed at a grain boundary. The particle is shaped by two spherical caps which meet the grain boundary at an angle θ. This angle is set by the balance of boundary tensions For a long time it was thought that soap foams, grains in metals and so on were icosahedra. It took Lord Kelvin (of the degree K) to get it right.Metal structures 21 Fig. 2.6. (a) The surface energy of a “two-dimensional” array of soap bubbles is minimised if the soap films straighten out. Where films meet the forces of surface tension must balance. This can only happen if films meet in “120° three-somes”. Fig. 2.6. (b) In a three-dimensional polycrystal the grain boundary energy is minimised if the boundaries flatten out. These flats must meet in 120° three-somes to balance the grain boundary tensions. If we fill space with equally sized tetrakaidecahedra we will satisfy these conditions. Grains in polycrystals therefore tend to be shaped like tetrakaidecahedra when the grain-boundary energy is the dominating influence.22 Engineering Materials 2 Fig. 2.7. Many metals are made up of two phases. This figure shows some of the shapes that they can have when boundary energies dominate. To keep things simple we have sectioned the tetrakaidecahedral grains in the way that we did in Fig. 2.6(b). Note that Greek letters are often used to indicate phases. We have called the major phase a and the second phase b. But g is the symbol for the energy (or tension) of grain boundaries (g ) and interphase interfaces (g ). gb ab 2γ cos θ = γ (2.1) αβ gb where γ is the tension (or energy) of the interphase boundary and γ is the grain αβ gb boundary tension (or energy). In some alloys, γ can be  γ /2 in which case θ = 0. The second phase will then αβ gb spread along the boundary as a thin layer of β. This “wetting” of the grain boundary can be a great nuisance – if the phase is brittle then cracks can spread along the grain boundaries until the metal falls apart completely. A favourite scientific party trick is to put some aluminium sheet in a dish of molten gallium and watch the individual grains of aluminium come apart as the gallium whizzes down the boundary. The second phase can, of course, form complete grains (Fig. 2.7d). But only if γ αβ and γ are similar will the phases have tetrakaidecahedral shapes where they come gb together. In general, γ and γ may be quite different and the grains then have more αβ gb complicated shapes. Summary: constitution and structure The structure of a metal is defined by two things. The first is the constitution: (a) The overall composition – the elements (or components) that the metal contains and the relative weights of each of them.

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