Engineering Materials Vol II (microstructures processing design) 2nd ed. - M. Ashby_ D. Jones (1999) Episode 13 pptx

Teaching yourself phase diagrams 351 Questions 3.2 Check, using the phase rule, that three phases can coexist only at a point (the eutectic point) in the lead–tin system at constant pressure. If you have trouble, revise the phase rule on p. 327. 3.3 Not all alloys in the lead–tin system show a eutectic: pure lead, for example, does not. Examine the Pb–Sn phase diagram and list the composition range for which a eutectic reaction is possible. 3.4 We defined a eutectic reaction (e.g. that of the lead–tin system) as a three-phase reaction by which, on cooling, a liquid transforms into two solids. In general: L → α + β 5 or, for the lead–tin system 6 on cooling Liquid (Pb–Sn) → (Pb) + (Sn) 7 What happens on heating? Eutectic structure The aluminium casting alloys are mostly based on the Al–Si system (phase diagram Fig. A1.31). It is a classic eutectic system, with a eutectic point at about 11% Si and Fig. A1.31. 352 Engineering Materials 2 577°C. Consider the cooling of an Al–6% Si casting alloy. The liquidus is reached at about 635°C, when solid (Al) starts to separate out (top of Fig. A1.32). As the temper- ature falls further the liquid composition moves along the liquidus line, and the amount of solid (Al) increases. When the eutectic temperature (577°C) is reached, about half the liquid has solidified (middle of Fig. A1.32). The solid that appears in this way is called primary solid, primary (Al) in this case. At 577°C the eutectic reaction takes place: the liquid decomposes into solid (Al) mixed with solid Si, but on a finer scale than before (bottom of Fig. A1.32). This intimate mixture of secondary (Al) with secondary Si is the eutectic structure. On further cooling to room temperature the composition of the (Al) changes – it dissolves less silicon at the lower temperature. So silicon must diffuse out of the (Al), and the amount of Si must increase a little. But the final structure still looks like the bottom of Fig. A1.32. Dendrites When a metal is cast, heat is conducted out of it through the walls of the mould. The mould walls are the coldest part of the system, so solidification starts there. In the Al–Si casting alloy, for example, primary (Al) crystals form on the mould wall and grow inwards. Their composition differs from that of the liquid: it is purer, and contains less silicon. This means that silicon is rejected at the surface of the growing crystals, and the liquid grows richer in silicon: that is why the liquid composition moves along the liquidus line. Fig. A1.32. Teaching yourself phase diagrams 353 Fig. A1.33. Fig. A1.34. Dendrites of silver in a copper–silver eutectic matrix, ×330. (After G. A. Chadwick, Metallography of Phase Transformations , Butterworth, 1972.) The rejected silicon accumulates in a layer just ahead of the growing crystals, and lowers the melting point of the liquid there. That slows down the solidification, because more heat has to be removed to get the liquid in this layer to freeze. But suppose a protrusion or bump on the solid (Al) pokes through the layer (Fig. A1.33). It finds itself in liquid which is not enriched with silicon, and can solidify. So the bump, if it forms, is unstable and grows rapidly. Then the (Al) will grow, not as a sphere, but in a branched shape called a dendrite. Many alloys show primary dendrites (Fig. A1.34); and the eutectic, if it forms, fills in the gaps between the branches. 354 Engineering Materials 2 Segregation If an 80 at% Pb alloy is cooled, the first solid appears at 305°C, and is primary (Pb) with a composition of about 90% Pb (see Fig. A1.35). From 305 to 255°C the amount of primary (Pb) increases, and its composition, which (at equilibrium) follows the solidus line, changes: it becomes richer in tin. This means that lead must diffuse out of the solid (Pb), and tin must diffuse in. This diffusion takes time. If cooling is slow, time is available and equilibrium is maintained. But if cooling is rapid, there is insufficient time for diffusion, and, al- though the new primary (Pb), on the outside of the solid, has the proper composition, the inside (which solidified first) does not. The inside is purer than the outside; there is a composition gradient in each (Pb) grain, from the middle to the outside. This gradient is called segregation, and is found in almost all alloys (see Fig. A1.36). The phase diagram describes the equilibrium constitution of the alloy – the one given by very slow cooling. In the last example all the liquid should have solidified at the point marked 2 on Fig. A1.35, when all the solid has moved to the composition X Pb = 80% and the temperature is 255°C. Rapid cooling prevents this; the solid has not had time to move to a composition X Pb = 80%. Instead, it has an average composition about half-way between that of the first solid to appear (X Pb = 90%) and the last (X Pb = 80%), that is, an average composition of about X Pb = 85%. This “rapid cooling” solidus lies to Fig. A1.35. Fig. A1.36. Teaching yourself phase diagrams 355 the right of the “equilibrium” solidus; it is shown as a broken line on Fig. A1.35. If this is so, the alloy is not all solid at 260°C. The rule for calculating the amounts of each phase still applies, using the “rapid cooling” solidus as one end of the tie line: it shows that the alloy is completely solid only when point 3 is reached. Because of this, the liquid composition overshoots the point marked X, and may even reach the eutectic point – so eutectic may appear in a rapidly cooled alloy even though the equilibrium phase diagram says it shouldn’t. Eutectoids Figure A1.37 shows the iron–carbon phase diagram up to 6.7 wt% carbon (to the first intermetallic compound, Fe 3 C). Of all the phase diagrams you, as an engineer, will encounter, this is the most important. So much so that you simply have to learn the names of the phases, and the approximate regimes of composition and temperature they occupy. The phases are: Ferrite: α (b.c.c.) iron with up to 0.035 wt% C dissolved in solid solution. Austenite: γ (f.c.c.) iron with up to 1.7 wt% C dissolved in solid solution. δ -iron: δ (b.c.c.) with up to 0.08 wt% C dissolved in solid solution. Cementite:Fe 3 C, a compound, at the right of the diagram. Ferrite (or α ) is the low-temperature form of iron. On heating, it changes to austenite (or γ ) at 914°C when it is pure, and this form remains stable until it reaches 1391°C when it changes to δ -iron (if you have forgotten this, check back to p. 319). The phase Fig. A1.37. 356 Engineering Materials 2 diagram shows that carbon changes the temperatures of these transitions, stabilising γ over a wider temperature interval. The iron–carbon system has a eutectic: find it and mark it on the diagram (Fig. A1.37). At the eutectic point the phase reaction, on cooling, is Liquid → austenite + cementite. But the diagram shows another feature which looks like a eutectic: it is the V at the bottom of the austenite field. The transformation which occurs there is very like the eutectic transformation, but this time it is a solid, austenite, which transforms on cool- ing to two other solids. The point at the base of the V is called a eutectoid point. DEF.A eutectoid reaction is a three-phase reaction by which, on cooling, a solid transforms into two other solid phases at the same time. If the bottom of a single-phase solid field closes (and provided the adjacent two-phase fields are solid also), it does so with a eutectoid point. The compositions of the two new phases are given by the ends of the tie line through the eutectoid point. Questions 3.5 The copper–zinc system (which includes brasses) has one eutectoid reaction. Mark the eutectoid point on the phase diagram (Fig. A1.38). 3.6 The copper–tin system (which includes bronzes) has four eutectoids (Fig. A1.39). One is obvious; the other three take a little hunting for. Remember that, if the Fig. A1.38. Teaching yourself phase diagrams 357 Fig. A1.39. bottom of the single-phase field for a solid closes, then it does so with a eutectoid. Try to locate (and ring carefully) the four eutectoid points on the copper–tin phase diagram. Eutectoid structures Eutectoid structures are like eutectic structures, but much finer in scale. The ori- ginal solid decomposes into two others, both with compositions which differ from the original, and in the form (usually) of fine, parallel plates. To allow this, atoms of B must diffuse away from the A-rich plates and A atoms must diffuse in the opposite direction, as shown in Fig. A1.40. Taking the eutectoid decomposition of iron as an example, carbon must diffuse to the carbon-rich Fe 3 C plates, and away from the (carbon-poor) α -plates, just ahead of the interface. The colony of plates then grows to the right, consuming the austenite ( γ ). The eutectoid structure in iron has a special name: it is called pearlite (because it has a pearly look). The micrograph (Fig. A1.41) shows pearlite. 358 Engineering Materials 2 Fig. A1.41. Pearlite in a eutectoid-composition plain-carbon steel, ×500. (After K. J. Pascoe, An Introduction to the Properties of Engineering Materials , Van Nostrand Reinhold, London, 1978.) Fig. A1.40. Peritectics Eutectics and eutectoids are common features of engineering alloys. At their simplest, they look like a V resting on a horizontal line (see Fig. A1.42). The phase reactions, on cooling, are Liquid L → α + β (eutectic) Solid β → α + γ (eutectoid). Teaching yourself phase diagrams 359 Fig. A1.43. Fig. A1.42. Many phase diagrams show another feature. It looks like an upside-down V (i.e. a ٙ) touching a horizontal line. It is a peritectic reaction, and the tip of the ٙ is a peritectic point (see Fig. A1.43). DEF.A peritectic reaction is a three-phase reaction by which, on cooling, two phases (one of them liquid) react to give a single new solid phase. On Fig. A1.43, the peritectic reaction is Liquid + solid α → solid β . The composition of the β which forms (in this example) is 50 at% B. Questions 3.7 The iron–carbon diagram (Fig. A1.37) has a peritectic point. Ring it on the diagram. 3.8 The copper–zinc system shown in Fig. A1.38 has no fewer than five peritectic reactions. Locate them and ring the peritectic points. (Remember that when a single-phase field closes above at a point, the point is a peritectic point.) 360 Engineering Materials 2 Peritectoids DEF. A peritectoid is a three-phase reaction by which, on cooling, two solid phases react to give a single new solid phase. On Fig. A1.44 the peritectoid reaction is A + B → δ . Fig. A1.44. Answers to questions: part 3 3.1 (See Fig. A1.45.) 550°C, 67%; 580°C, 11%; 1350°C, 49%. 3.2 The reduced (constant pressure) phase rule is F = C − P + 1. There are two components; the three phases (two solids and one liquid) coexist. So F = 0, that is, the three phases can coexist only at a point (the eutectic point). 3.3 From X Pb = 1.45% to X Pb = 71%. 3.4 Remember that this is an equilibrium diagram. Any point on the diagram corres- ponds to a unique constitution. So, on heating, the reaction simply goes in reverse. The two solids “react” to give a single liquid. In general: α + β → Liquid 5 or, for the lead–tin system 6 on heating (Pb) + (Sn) → Liquid (Pb–Sn) 7 3.5 (Also 3.8) (See Fig. A1.46.) 3.6 Eutectoids ringed with solid circles (see Fig. A1.47). 3.7 (See Fig. A1.48.) [...]... 2×1+ 3×2 given in Fig A1.56 On cooling 30% B mixture from 1600°C: at 139 7°C, solidifica22 tion commences by separation of γ crystals Just above 130 0°C 27 (= 81.5%) liquid 5 (35% B) + 27 (= 18.5%) γ (8% B) At 130 0°C, all γ + some liquid form β in peritectic 5 reaction Just below 130 0°C 15 (= 75%) liquid (35% B) + 20 (= 25%) β (15% B) 20 5 130 0°C → 1000°C, more β separates Just above 1000°C 30 (= 17%) liquid... Glazes 202 GP zones 106 Grain boundaries 18 growth 55, 137 shape 20, 64 size 93 strengthening 153 Grains 20 Granite 164, 175 Graphite 121 Habit plane 83 Hammer design 139 Hardenability 125 Heat 48 Heat-affected zone 137 Heat flow 62 Heterogeneous nucleation 69, 90 Homogeneous nucleation 69 Hot isostatic pressing 196 Hot pressing 196 Hydrogen cracking 138 Hydroplastic forming 194, 201 Ice 41, 51, 89, 164,... and of having had an outer shell of γ -iron, an inner shell of ε-iron and a core of α-iron Use the p–T phase diagram for iron to deduce the approximate magnitude of the pressure wave Express the result in atmospheres (see Fig A1.49) Fig A1.49 4.2 Your ancient granny dies and leaves you her most prized possession: an Urn of Pure Gold One afternoon, while mixing paint-remover in the urn, you are disturbed... 0°C, amount of α decreases and δ 37 5 increases At 0°C 30 (= 86%) δ (35% B) + 35 (= 14%) α (0% B) 35 370 Engineering Materials 2 Appendix 2 Symbols and formulae List of principal symbols Symbol Meaning(units) Note: Multiples or sub-multiples of basic units indicate the unit suffixes normally used in materials data a a A A1 A3 Acm b c C CCR DP E f F g G G Gc H ∆H I k k k KIC L lattice parameter (nm) crack... interface Chapter 10: The light alloys Solid solution hardening σy ∝ ε 3/2 C 1/2 s C = solute concentration; εs = mismatch parameter Work-hardening σy ∝ ε n ε = true strain; n = constant Chapter 14: Metal processing Forming pressure No friction pf = σy 374 Engineering Materials 2 Sticking friction (w/2) − x   pf = σ y 1 +  d   σy = yield strength; w = width of forging die; x = distance from centre... component; V = volume of component; σ = tensile stress on component; V0 = volume of test sample; σ0 = stress that, when applied to test sample, gives Ps = 1/e (= 0.37); m = Weibull modulus Failure probability Pf = 1 − Ps Slow crack-growth n  σ  t(test)  =  t  σ TS  σ = strength of component after time t; σ TS = strength of component measured over time t(test); n = slow crack-growth exponent... hardening Alexander Keilland oil platform 136 Alloy 15, 25, 321 Alumina 163, 164, 167 Aluminium-based alloys 8, 12, 100 et seq., 347, 351 Amorphous metals 96 polymers 236 structure 16 Anisotropy 266, 280, 316 Annealing 151 Atactic polymers 231 Austenite 114, 130 , 355 Availability 50 Bain strain 84 Bakelite 221 Beryllium 100 Binary alloy 25, 327, 336 Boiler design 133 Bone 164, 165 Borosilicate glass 162,... distressing result: 364 Engineering Materials 2 Fig A1.50 Copper Zinc Gold 60 at%; 40 at%; . When the temperature or pressure is decreased very rapidly, high temperature or high pressure phases can be “trapped”, and are observed at atmospheric temper- ature and pressure (diamond, for instance,. the last example all the liquid should have solidi ed at the point marked 2 on Fig. A1.35, when all the solid has moved to the composition X Pb = 80% and the temperature is 255°C. Rapid cooling. 1150°C and melts at 1980°C. These form solid solutions α , β and γ containing B, α being the low-temperature one. An intermediate compound A 2 B 3 melts at 1230°C. It has a limited solid solubility for