Chapter 8 Strengthening and toughening 8.1 Introduction This chapter primarily concerns alloy behaviour, partly because of the inherent versatility of alloy sys- The production of materials tems and partly because the research background to room and eleva much of the current understanding of strength, tough is of great practical importance. We have ness and fracture is essentially metallurgical. However ow alloying, solute-dislocation interaction, grain size it is often possible to extend the basic principles to non- control and cold-working can give rise to an increased metallic materials, particularly in the case of fracture ield stress. Of these methods, refining the grain size is processes. This will be apparent later, in Chapter 10, of universal application to materials in which the yield when we describe how the unique transformation char- stress has a significant dependence upon grain size. acteristics of zirconia can be used to inhibit crack In certain alloy systems, it is possible to produce an propagation in a brittle ceramic such as aluminaMeth ods for toughening glasses are described in the same treatment alone. Such a method has many advantages, chapter. In Chapter 11 we consider the strengthening since the required strength can be induced at the most and toughening effects produced when plastics, met convenient stage of production or fabrication; more- als and ceramics are reinforced with filaments to form over, the component is not sent into service in a highly stressed, plastically deformed state. The basic require composite materials ment for such a special alloy is that it should undergo alloy satisfying this requirement, already considered, 8.2 Strengthening of non-ferrous that which can undergo an order-disorder reac- alloys by heat-treatment in many ways to precipitation-hardening)is termed 8.2.1 Precipitation-hardening of Al-Cu alloys order-hardening. However, conditions for this form of 8.2.1.1 Precipitation from supersaturated solid cipal hardening methods, commonly used for alloys,solution are based upon(1)precipitation from a supersaturated The basic requirements of a precipitation-hardening solid solution and (2)eutectoid decomposition alloy system is that the solid solubility limit should In engineering applications, strength is doubt, an important parameter. However, it I for the Al-Cu system. During the means the only important one and usually a 1 precipitation-hardening heat-treatment procedure the must provide a combination of properties. Some duc- alloy is first solution heat-treated at tility is generally essential, enabling the material to perature and then rapidly cooled by quenching relieve stress concentrations by plastic deformation and into water or some other cooling medium. The rapid to resist fracture. The ability of materials to resist crack cooling suppresses the separation of the e-phase propagation and fracture, known generally as tough- so that the alloy exists at the low temperature in ness, will be discussed in this chapter. Fracture can an unstable supersaturated state. If,however, after take many forms; some special forms, such as brit- quenching, the alloy is allowed to age for a sufficient tle fracture by cleavage, ductile fracture by microvoid length of time, the second phase precipitates out coalescence, creep fracture by triple-point cracking and This precipitation occurs by a nucleation and growth fatigue cracking, will be e process, fluctuations in solute concentration providing
Chapter 8 Strengthening and toughening 8.1 Introduction The production of materials which possess considerable strength at both room and elevated temperatures is of great practical importance. We have already seen how alloying, solute-dislocation interaction, grain size control and cold-working can give rise to an increased yield stress. Of these methods, refining the grain size is of universal application to materials in which the yield stress has a significant dependence upon grain size. In certain alloy systems, it is possible to produce an additional increase in strength and hardness by heattreatment alone. Such a method has many advantages, since the required strength can be induced at the most convenient stage of production or fabrication; moreover, the component is not sent into service in a highly stressed, plastically deformed state. The basic requirement for such a special alloy is that it should undergo a phase transformation in the solid state. One type of alloy satisfying this requirement, already considered, is that which can undergo an order-disorder reaction; the hardening accompanying this process (similar in many ways to precipitation-hardening) is termed order-hardening. However, conditions for this form of hardening are quite stringent, so that the two principal hardening methods, commonly used for alloys, are based upon (1) precipitation from a supersaturated solid solution and (2) eutectoid decomposition. In engineering applications, strength is, without doubt, an important parameter. However, it is by no means the only important one and usually a material must provide a combination of properties. Some ductility is generally essential, enabling the material to relieve stress concentrations by plastic deformation and to resist fracture. The ability of materials to resist crack propagation and fracture, known generally as toughness, will be discussed in this chapter. Fracture can take many forms; some special forms, such as brittle fracture by cleavage, ductile fracture by microvoid coalescence, creep fracture by triple-point cracking and fatigue cracking, will be examined. This chapter primarily concerns alloy behaviour, partly because of the inherent versatility of alloy systems and partly because the research background to much of the current understanding of strength, toughness and fracture is essentially metallurgical. However, it is often possible to extend the basic principles to nonmetallic materials, particularly in the case of fracture processes. This will be apparent later, in Chapter 10, when we describe how the unique transformation characteristics of zirconia can be used to inhibit crack propagation in a brittle ceramic such as alumina. Methods for toughening glasses are described in the same chapter. In Chapter 11 we consider the strengthening and toughening effects produced when plastics, metals and ceramics are reinforced with filaments to form composite materials. 8.2 Strengthening of non-ferrous alloys by heat-treatment 8.2.1 Precipitation-hardening of AI-Cu alloys 8.2.1.1 Precipitation from supersaturated solid solution The basic requirements of a precipitation-hardening alloy system is that the solid solubility limit should decrease with decreasing temperature as shown in Figure 8.1 for the AI-Cu system. During the precipitation-hardening heat-treatment procedure the alloy is first solution heat-treated at the high temperature and then rapidly cooled by quenching into water or some other cooling medium. The rapid cooling suppresses the separation of the 0-phase so that the alloy exists at the low temperature in an unstable supersaturated state. If, however, after quenching, the alloy is allowed to 'age' for a sufficient length of time, the second phase precipitates out. This precipitation occurs by a nucleation and growth process, fluctuations in solute concentration providing
260 Modern Physical Metallurgy and Materials Engineering small clusters of atoms in the lattice which act as nuclei 1.23 GN/m2. The structure-sensitive properties such as for the precipitate. However, the size of the precipitate hardness, yield stress, etc. are, of course, extremely becomes finer as the temperature at which precipitation dependent on the structural distribution of the occurs is lowered, and extensive hardening of the phases and, consequently, such alloys usually exhibit alloy is associated with a critical dispersion of the softening as the finely dispersed precipitates coarsen precipitate. If, at any given temperature, ageing is A simple theory of precipitation, involving the allowed to proceed too far, coarsening of the particles nucleation and growth of particles of the expecte the large ones to grow still larger as discussed in the alloy would show a single hardening peak, m at phase, leads one to Section 8.2.6) and the numerous electrical resistivity a decrease, and the lattice paaa number of more widely dispersed than the solvent atom) as the solute is removed from In this state the alloy becomes softe solution. Such prop said to be in the over-aged condition(see Figure 8.2). but only at low supersaturations and high ageing tem- peratures. At higher supersaturations and lower ageing 8.2.1.2 Changes in properties accompanying temperatures the various property changes are not ce precipitation sistent with such a simple picture of precipitation; the alloy may show two or more age-hardening peaks, and The actual quenching treatment gives rise to small the electrical resistivity and lattice parameter may not changes in many of the mechanical and physical prop- change in the anticipated manner. A hardening pro defects in excess of the equilibrium concentration are minium-copper alloys(Figure 8.2a)where the initial retained during the process, and because the quench hardening occurs without any attendant precipitation itself often produces lattice strains. Perhaps the prop- being visible in the light microscope and, moreover erty most markedly affected is the electrical resistance is accompanied by a decrease in conductivity and no and this is usually considerably increased. In con- change in lattice parameter. Such behaviour may be trast, the mechanical properties are affected relatively accounted for if precipitation is a process involving muc On ageing, the change in properties in a at the lower ageing temperatures, involves a cluster- ing of solute atoms on the solvent lattice sites to form the mechanical properties often show striking zones or clusters, coherent with the matrix: the zones modifications. For example, the tensile strength of cannot be seen in the light microscope and for this Duralumin (i.e. an aluminium% copper alloy son this stage was at one time termed pre-precipitation containing magnesium, silicon and manganese)may At a later stage of the ageing process these clusters a Cu-2Be alloy may be increased from 0. 46 to particles with their own crystal structure and a definite interface. These hypotheses were confirmed originall by structural studies using X-ray diffraction techniques but nowadays the so-called pre-precipitation effects n be observed directly in the electron microscop Even though clustering occurs, the general kinetic behaviour of the precipitation process is in agreement with that expected on thermodynamic grounds. From markedly with increasing temperature while the peak hardness decreases. Two-stage hardening takes place at low g temperature iated with high maximum hardness, while single-stage hardening GP[2] or 8 occurs at higher ageing temperatures, or at lower ageing temperatures for lower solute contents. Another phenomenon commonly observed in orecipitation-hardening alloys is reversion or retrogre GP[ 11 If an is subsequently heated to a higher ageing temperature it softens temporarily, but becomes harder again on more prolonged heating. This temporary softening, or wt %C eversion of the hardening process, occurs because the ery small nuclei or zones precipitated at the low tem- Figure 8.1 Al-rich Al-Cu binary diagram showing GP /1 rature are unstable when raised to the higher ageing perature, and consequently they redissolve
260 Modem Physical Metallurgy and Materials Engineering small clusters of atoms in the lattice which act as nuclei for the precipitate. However, the size of the precipitate becomes finer as the temperature at which precipitation occurs is lowered, and extensive hardening of the alloy is associated with a critical dispersion of the precipitate. If, at any given temperature, ageing is allowed to proceed too far, coarsening of the particles occurs (i.e. the small ones tend to redissolve, and the large ones to grow still larger as discussed in Section 8.2.6) and the numerous finely dispersed, small particles are gradually replaced by a smaller number of more widely dispersed, coarser particles. In this state the alloy becomes softer, and it is then said to be in the over-aged condition (see Figure 8.2). 8.2.1.2 Changes in properties accompanying precipitation The actual quenching treatment gives rise to small changes in many of the mechanical and physical properties of alloys because both solute atoms and point defects in excess of the equilibrium concentration are retained during the process, and because the quench itself often produces lattice strains. Perhaps the property most markedly affected is the electrical resistance and this is usually considerably increased. In contrast, the mechanical properties are affected relatively much less. On ageing, the change in properties in a quenched material is more marked and, in particular, the mechanical properties often show striking modifications. For example, the tensile strength of Duralumin (i.e. an aluminium-4% copper alloy containing magnesium, silicon and manganese) may be raised from 0.21 to 0.41 GN/m 2 while that of a Cu-2Be alloy may be increased from 0.46 to 6001" ~~ a + liquid o ,~ 400 e,l E 200 /• GP[2] or O" GP[~! a+O 0 1 2 3 4 5 wt % Cu Figure 8.1 Al-rich AI-Cu binary diagram showing GP [1], 0" and 0' solvus lines (dotted). 1.23 GN/m 2. The structure-sensitive properties such as hardness, yield stress, etc. are, of course, extremely dependent on the structural distribution of the phases and, consequently, such alloys usually exhibit softening as the finely dispersed precipitates coarsen. A simple theory of precipitation, involving the nucleation and growth of particles of the expected new equilibrium phase, leads one to anticipate that the alloy would show a single hardening peak, the electrical resistivity a decrease, and the lattice parameter an increase (assuming the solute atom is smaller than the solvent atom) as the solute is removed from solution. Such property changes are found in practice, but only at low supersaturations and high ageing temperatures. At higher supersaturations and lower ageing temperatures the various property changes are not consistent with such a simple picture of precipitation; the alloy may show two or more age-hardening peaks, and the electrical resistivity and lattice parameter may not change in the anticipated manner. A hardening process which takes place in two stages is shown in aluminium-copper alloys (Figure 8.2a) where the initial hardening occurs without any attendant precipitation being visible in the light microscope and, moreover, is accompanied by a decrease in conductivity and no change in lattice parameter. Such behaviour may be accounted for if precipitation is a process involving more than one stage. The initial stage of precipitation, at the lower ageing temperatures, involves a clustering of solute atoms on the solvent lattice sites to form zones or clusters, coherent with the matrix; the zones cannot be seen in the light microscope and for this reason this stage was at one time termed pre-precipitation. At a later stage of the ageing process these clusters break away from the matrix lattice to form distinct particles with their own crystal structure and a definite interface. These hypotheses were confirmed originally by structural studies using X-ray diffraction techniques but nowadays the so-called pre-precipitation effects can be observed directly in the electron microscope. Even though clustering occurs, the general kinetic behaviour of the precipitation process is in agreement with that expected on thermodynamic grounds. From Figure 8.2 it is evident that the rate of ageing increases markedly with increasing temperature while the peak hardness decreases. Two-stage hardening takes place at low ageing temperatures and is associated with high maximum hardness, while single-stage hardening occurs at higher ageing temperatures, or at lower ageing temperatures for lower solute contents. Another phenomenon commonly observed in precipitation-hardening alloys is reversion or retrogression. If an alloy hardened by ageing at low temperature is subsequently heated to a higher ageing temperature it softens temporarily, but becomes harder again on more prolonged heating. This temporary softening, or reversion of the hardening process, occurs because the very small nuclei or zones precipitated at the low temperature are unstable when raised to the higher ageing temperature, and consequently they redissolve and the
261 GRI] alloy developed streaks extending from an aluminium lattice reflection along(100)Al direct .5%Cu plate-like shape on 1100) planes of the aluminium matrix (now called Guinier-Preston zones or GP 0%Cu zones). The net effect of the regrouping is to mod- fy the scattering power of, and spacing between, very 3·0%C small groups of (100) planes throughout the crystal 20%c4 However, being only a few atomic planes thick, the zones produce the diffraction effect typical of a two- dimensional lattice, i.e. the diffraction spot becomes a diffraction streak. In recent years the Laue method has Ageing time (days)at130吃c一 been replaced by a single-crystal oscillation technique employing monochromatic radiation, since interpreta- tion is made easier if the wavelength of the X-rays used is known. The second technique makes use of the phe- nomenon of scattering of X-rays at small angles(see 45%cu Chapter 5). Intense small-angle scattering can often be observed from age-hardening alloys(as shown in Figures 8.3 and 8.5) because there is usually a differ ence in electron density between the precipitated zone and the surrounding matrix. However, in alloys such 3.0%Cu s as aluminium-magnesium or aluminium -silicon the technique is of no value because in these alloys the small difference in scattering power between the alu- minium and silicon or magnesium atoms, respectively, Ageing time(days)at 190c insufficient to give rise to appreciable scattering at ° Cand(b)arl90°C( after Silcock, Heal and hardy with the advent of the electron microscope the age ing of aluminium alloys was one of the first subjects to investigated with the thin-foil transmission method ot only can the detailed structural changes whick alloy becomes softer; the temperature above which the ccur during the ageing process be followed, but elec nuclei or zones dissolve is known as the solvus tem- tron diffraction pictures taken from selected areas of perature; Figure 8.1 shows the solvus temperatures for e specimen while it is still in the microscope enable GP zones, 8", e and 0. On prolonged ageing at the further important information on the structure of the ugher temperature larger nuclei, characteristic of that precipita temperature, are formed and the alloy again hardens. some conditions the interaction of moving dislocations Clearly, the reversion process is reversible, provided and precipitates can be observed. This naturally leads re-hardening at the higher ageing temperature is not to a more complete understanding of the hardening allowed to occur Both the X-ray and electron-microscope techniques 8.2.1.3 Structural changes during precipitation show that in virtually all age-hardening systems the initial precipitate is not the same structure as the equi Early metallographic investig microstructural changes which occur during the initial intermediate precipitates equilibrium precipitate is tages of ageing are on too fine a scale to be resolved followed. This sequence occurs because the equilib- by the light microscope, yet it is in these early stages rium precipitate is incoherent with the matrix, whereas that the most profound changes in properties are found. the transition structures are either fully coherent, as in Accordingly, to study the process, it is necessary to the case of zones, or at least partially coherent. Then, employ the more sensitive and refined techniques because of the importance of the surface energy and X-ray diffraction and electron microscopy strain energy of the precipitate to the precipitation pro The two basic X-ray techniques, important in study- cess, the system follows such a sequence in order to ng the regrouping of atoms during the early stages have the lowest free energy in all stages of precipita- of ageing, depend on the detection of radiation scat- tion. The surface energy of the precipitates dominates tered away from the main diffraction lines or spots the process of nucleation when the interfacial energy is (see Chapter 5). In the first technique, developed large (i.e. when there is a discontinuity in atomic struc independently by Guinier and Preston in 1938, the ture, somewhat like a grain boundary, at the interface Laue method is used. They found that the single- between the nucleus and the matrix), so that for the crystal diffraction pattern of an aluminium-copper incoherent type of precipitate the nuclei must exceed a
Strengthening and toughening 261 z I/,O C '0 L,. ff 6o 40 (a) . . C~. 11] .... G.R[2] ... s--,...~ i ~ _..__......~.,." ,,,....,~,~, "... . ~ eOOloo f ~ 30%Cu .. 2.0%C%--~ ~,,~s , , I t loo Ageing time (days) at 130 ~ -"" 100 45'/, Cu-" ~ I r T"~ ~" / // 9 I ll~dl~ll i t 80 ~" 4.0*/,CtJ.. loll ' "" e el i e . ... ... ...... -; ---" ."" ....."'..'.::: .:. :'. 3.0 %Cu,:,'"" . .. 9 "2-0% Cu :I: /.,0 1 *" l l i 0.01 0.1 1 10 100 (b) Ageing time(days) at 190~ ------ Figure 8.2 The ageing of aluminium-copper alloys at (a) 130~ and (b) at 190~ (after Silcock, Heal and Hardy, 1953-4). alloy becomes softer; the temperature above which the nuclei or zones dissolve is known as the solvus temperature; Figure 8.1 shows the solvus temperatures for GP zones, 0", 0' and 0. On prolonged ageing at the higher temperature larger nuclei, characteristic of that temperature, are formed and the alloy again hardens. Clearly, the reversion process is reversible, provided re-hardening at the higher ageing temperature is not allowed to occur. 8.2.1.3 Structural changes during precipitation Early metallographic investigations showed that the microstructural changes which occur during the initial stages of ageing are on too fine a scale to be resolved by the light microscope, yet it is in these early stages that the most profound changes in properties are found. Accordingly, to study the process, it is necessary to employ the more sensitive and refined techniques of X-ray diffraction and electron microscopy. The two basic X-ray techniques, important in studying the regrouping of atoms during the early stages of ageing, depend on the detection of radiation scattered away from the main diffraction lines or spots (see Chapter 5). In the first technique, developed independently by Guinier and Preston in 1938, the Laue method is used. They found that the singlecrystal diffraction pattern of an aluminium-copper alloy developed streaks extending from an aluminium lattice reflection along (100)A! directions. This was attributed to the formation of copper-rich regions of plate-like shape on {100} planes of the aluminium matrix (now called Guinier-Preston zones or GP zones). The net effect of the regrouping is to modify the scattering power of, and spacing between, very small groups of { 100} planes throughout the crystal. However, being only a few atomic planes thick, the zones produce the diffraction effect typical of a twodimensional lattice, i.e. the diffraction spot becomes a diffraction streak. In recent years the Laue method has been replaced by a single-crystal oscillation technique employing monochromatic radiation, since interpretation is made easier if the wavelength of the X-rays used is known. The second technique makes use of the phenomenon of scattering of X-rays at small angles (see Chapter 5). Intense small-angle scattering can often be observed from age-hardening alloys (as shown in Figures 8.3 and 8.5) because there is usually a difference in electron density between the precipitated zone and the surrounding matrix. However, in alloys such as aluminium-magnesium or aluminium-silicon the technique is of no value because in these alloys the small difference in scattering power between the aluminium and silicon or magnesium atoms, respectively, is insufficient to give rise to appreciable scattering at small angles. With the advent of the electron microscope the ageing of aluminium alloys was one of the first subjects to be investigated with the thin-foil transmission method. Not only can the detailed structural changes which occur during the ageing process be followed, but electron diffraction pictures taken from selected areas of the specimen while it is still in the microscope enable further important information on the structure of the precipitated phase to be obtained. Moreover, under some conditions the interaction of moving dislocations and precipitates can be observed. This naturally leads to a more complete understanding of the hardening mechanism. Both the X-ray and electron-microscope techniques show that in virtually all age-hardening systems the initial precipitate is not the same structure as the equilibrium phase. Instead, an ageing sequence: zones intermediate precipitates ~ equilibrium precipitate is followed. This sequence occurs because the equilibrium precipitate is incoherent with the matrix, whereas the transition structures are either fully coherent, as in the case of zones, or at least partially coherent. Then, because of the importance of the surface energy and strain energy of the precipitate to the precipitation process, the system follows such a sequence in order to have the lowest free energy in all stages of precipitation. The surface energy of the precipitates dominates the process of nucleation when the interfacial energy is large (i.e. when there is a discontinuity in atomic structure, somewhat like a grain boundary, at the interface between the nucleus and the matrix), so that for the incoherent type of precipitate the nuclei must exceed a
262 Modern Physical Metallurgy and Materials Engineering Figure 8.3 (a)Small-angle X-ray pattern from aluminium-4% copper single cry radiation at a nple to film distance of 4 cm(after Guinier and Fournet, 1955: courtesy of Jc of aluminium-4% copper aged 16 hours at 130C, showing GP/1) zones(after on, Thomas and Nutting 1958-9) certain minimum size before they can nucleate a new tion n a wide variet phase. To avoid such a slow mode of precipitation of alloy systems as in table 8.1 The coherent type of precipitate is formed instead, for aluminium-copper alloy exhibits the greates which the size effect is relatively unimportant. The number of intermediate stages in its precipitation condition for coherence usually requires the precipi- pr tate to strain its equilibrium lattice to fit that of the widely studied. When the copper content is high and matrix, or to adopt a metastable lattice. However, in the ageing temperature low, the sequence of stage spite of both a higher volume free energy and a higher followed is GP [ll, GP [2]. 0 and 0( CuAl2). Or strain energy, the transition structure is more stable in ageing at higher temperatures, however, one or more the early stages of precipitation because of its lower of these intermediate stages may be omitted and interfacial energy as shown in Figure 8.2, corresponding differences When the precipitate does become incoherent the in the hardness curves can be detected. The early loy will, nevertheless, tend to reduce its surface stages of ageing are due to GP [1] zones, which nergy as much as possible, by arranging the orienta- are interpreted as plate-like clusters of copper atoms ion relationship between the matrix and the precipitate segregated onto(100 planes of the aluminium matri that the crystal planes which are parallel to, and sep- A typical small-angle X-ray scattering pattern and arated by, the bounding surface have similar atomic thin-foil transmission electron micrograph from GP [ll spacings. Clearly, for these habit planes, as they are zones are shown in Figure 8.3, The plates are only called, the better the crystallographic match, the less a few atomic planes thick (giving rise to the (100) will be the distortion at the interface and the lower streaks in the X-ray pattern), but are about 10 nm long, energy. This principle governs the precip- and hence appear as bright or dark lines on the electron own by the fre quent occurrence of the Widmanstatten structure, i.e GP [2] is best described as a coherent intermediate plate-shaped precipitates lying along prominent crys- precipitate rather than a zone, since it has a defi- tallographic planes of the matrix. Most precipitates are nite crystal structure; for this reason the symbol A is often preferred. These precipitates, usually of max for this form imum thickness 10 nm and up to 150 nm diameter The existence of a precipitation sequence is reflected have a tetragonal structure which fits perfectly with in the ageing curves and, as we have seen in the aluminium unit cell in the a and b directions but Figure 8. 2, often leads to two stages of hardening. not in the c. The structure postulated has a central The zones, by definition, are coherent with the plane which consists of 100% copper atoms, the next matrix, and as they form the alloy becomes harder vo planes a mixture of copper and aluminium and The intermediate precipitate may be coherent with the other two basal planes of pure aluminium, giv the matrix, in which case a further increase of g an overall composition of CuAl2. Because of their hardness occurs, or only partially coherent, when either size, 0 precipitates are easily observed in the elec hardening or softening may result. The equilibrium tron microscope, and because of the ordered arrange precipitate is incoherent and its formation always leads ments of copper and aluminium atoms within the to softening. These features are best illustrated by a structure, their presence gives rise to intensity max ideration of some actual age-hardening systems ima on the diffraction streaks in an X-ray photograph
262 Modern Physical Metallurgy and Materials Engineering Figure 8.3 (a) Small-angle X-ray pattern from aluminium-4% copper single crystal taken with molybdenum Kot radiation at a sample to film distance of 4 cm (after Guinier and Fournet, 1955; courtesy of John Wiley and Sons). (b) Electron micrograph of aluminium-4% copper aged 16 hours at 130~ showing GP [1] zones (after Nicholson, Thomas and Nutting, 1958-9). certain minimum size before they can nucleate a new phase. To avoid such a slow mode of precipitation a coherent type of precipitate is formed instead, for which the size effect is relatively unimportant. The condition for coherence usually requires the precipitate to strain its equilibrium lattice to fit that of the matrix, or to adopt a metastable lattice. However, in spite of both a higher volume free energy and a higher strain energy, the transition structure is more stable in the early stages of precipitation because of its lower interfacial energy. When the precipitate does become incoherent the alloy will, nevertheless, tend to reduce its surface energy as much as possible, by arranging the orientation relationship between the matrix and the precipitate so that the crystal planes which are parallel to, and separated by, the bounding surface have similar atomic spacings. Clearly, for these habit planes, as they are called, the better the crystallographic match, the less will be the distortion at the interface and the lower the surface energy. This principle governs the precipitation of many alloy phases, as shown by the frequent occurrence of the Widmanst~itten structure, i.e. plate-shaped precipitates lying along prominent crystallographic planes of the matrix. Most precipitates are plate-shaped because the strain energy factor is least for this form. The existence of a precipitation sequence is reflected in the ageing curves and, as we have seen in Figure 8.2, often leads to two stages of hardening. The zones, by definition, are coherent with the matrix, and as they form the alloy becomes harder. The intermediate precipitate may be coherent with the matrix, in which case a further increase of hardness occurs, or only partially coherent, when either hardening or softening may result. The equilibrium precipitate is incoherent and its formation always leads to softening. These features are best illustrated by a consideration of some actual age-hardening systems. Precipitation reactions occur in a wide variety of alloy systems as shown in Table 8.1. The aluminium-copper alloy system exhibits the greatest number of intermediate stages in its precipitation process, and consequently is probably the most widely studied. When the copper content is high and the ageing temperature low, the sequence of stages followed is GP [1], GP [2], 0' and 0 (CuA12). On ageing at higher temperatures, however, one or more of these intermediate stages may be omitted and, as shown in Figure 8.2, corresponding differences in the hardness curves can be detected. The early stages of ageing are due to GP [1] zones, which are interpreted as plate-like clusters of copper atoms segregated onto { 1 0 0} planes of the aluminium matrix. A typical small-angle X-ray scattering pattern and thin-foil transmission electron micrograph from GP [ 1] zones are shown in Figure 8.3. The plates are only a few atomic planes thick (giving rise to the (1 00) streaks in the X-ray pattern), but are about 10 nm long, and hence appear as bright or dark lines on the electron micrograph. GP [2] is best described as a coherent intermediate precipitate rather than a zone, since it has a definite crystal structure; for this reason the symbol 0" is often preferred. These precipitates, usually of maximum thickness 10 nm and up to 150 nm diameter, have a tetragonal structure which fits perfectly with the aluminium unit cell in the a and b directions but not in the c. The structure postulated has a central plane which consists of 100% copper atoms, the next two planes a mixture of copper and aluminium and the other two basal planes of pure aluminium, giving an overall composition of CuAI2. Because of their size, 0" precipitates are easily observed in the electron microscope, and because of the ordered arrangements of copper and aluminium atoms within the structure, their presence gives rise to intensity maxima on the diffraction streaks in an X-ray photograph
Strengthening and toughening 263 Table 8. 1 Some common precipitation-hardening systems Base Solute Transition structure equilibriu metal precipitate () Plate-like solute rich GP 8-cuAl2 g-phase(plates) Spherical solute-rich zones;(ii) platelets y-Ag2AI 1 y on (1111 ()GP zones rich in Mg and Si atoms on [100AI planes; (ii) ordered zones of B g, Cu (i) GP zones rich in Mg and Cu atoms on 100 Al planes; (i)s platelets on Mg, Zn h in Mg and Zn; (ii)platelet MgZ of nm' phase on(11 1)Al Be (i) Be-rich regions on [100Jcu planes; (ii)y GP ccN B-Co plates (i Martensite(); (ii)martensite(); Fe3C plates cementite (a) discsen martensite(a);(i)martensite N AL. TI y cubes y-Ni3(AlTl) Since the c parameter 0 78 nm differs from that of hexagonal y- equilibrium hexagonal y. The hard- ium planes parallel to ening is associated with the first two stages in which the plate are distorted by elastic coherency strain the precipitate is coherent and partially coherent with Moreover, the precipitate grows with the c direction the matrix, respectively ormal to the plane of the plate, so that the strain During the quench and in the early stages of ageing, fields become larger as it grows and at peak hard- silver atoms cluster into small spherical aggregates and ness extend from one precipitate particle to the next a typical small-angle X-ray picture of this stage, shown see Figure 8.4a). The direct observation of coherency in Figure 8.5a, has a diffuse ring surrounding the trace strains confirms the theories of hardening based on the of the direct beam. The absence of intensity in the development of an elastically strained matrix(see next entre of the ring(i.e. at(000)) is attributed to the section) fact that clustering takes place so rapidly that there is The transition structure e is tetragonal; the true left a shell-like region surrounding each cluster which nd the axes are parallel to(100)Al directions. The size and decrease in number, and this is characterized strains around the e plates can be relieved, however, by the X-ray pattern showing a gradual decrease in ring by the formation of a stable dislocation loop around ameter. The concentration and size of clusters can be he precipitate and such a loop has been observed followed very accurately by measuring the intensity around small 6 plates in the electron microscope distribution across the ring as a function of ageing shown in Figure 8.4b, The long-range strain fields time. This intensity may be represented(see Chapter 5) of the precipitate and its dislocation largely cancel. by an equation of the form Consequently, it is easier for glide dislocations to move through the lattice of the alloy containing an incoherent I(e)=Mn[exp(-27x2R22/32) ecipitate such as e than a coherent precipitate such as 8, and the hardness falls -exp(-22R?2/3x2)2 The 0 structure is als so tetragona and c=0.487 nm. This equilibrium precipitate is and for values of e greater than that corresponding ent with the matrix and its formation always leads to softening, since coherency strains disap second term, which represents the denuded region surrounding the cluster, can be neglected. Figure 8.5b shows the variation in the Xray intensity, scattered at small angles(SAS) with cluster growth, on ageing an 8.2.2 Precipitation hardening of Al-Ag alloys aluminium-silver alloy at 120C. An analysis of this Investigations using X-ray diffraction and electron intensity distribution, using equation(8.1), indicates microscopy have shown the existence of three di that the size of the zones increases from 2 to 5 tinct stages in the age-hardening process, which may just a few hours at 120 C. These zones may, of be summarized: silver-rich clusters intermediate be seen in the electron microscope and Figu
Table 8.1 Some common precipitation-hardening systems Strengthening and toughening 263 Base Solute Transition structure metal Equilibrium precipitate AI Cu Ag Mg, Si Mg, Cu Mg, Zn Cu Be Co Fe C Ni AI, Ti (i) Plate-like solute rich GP [1] zones on {l 00}Al; (ii) ordered zones of GP [2]; (iii) if-phase (plates). (i) Spherical solute-rich zones; (ii) platelets of hexagonal y' on { 111}Al. (i) GP zones rich in Mg and Si atoms on {100}A! planes; (ii) ordered zones of ft. (i) GP zones rich in Mg and Cu atoms on {1 00}gl planes; (ii) S' platelets on {0 21 }gl planes. (i) Spherical zones rich in Mg and Zn; (ii) platelets of rf phase on {11 l}Al. (i) Be-rich regions on {100}Cu planes; (ii) y'. Spherical GP zones. (i) Martensite (or'); (ii) martensite (a"); (iii) e-carbide. (i) Nitrogen martensite (c~'); (ii) martensite (c~") discs. y' cubes 0-CuAI2 y-Ag2AI fl-Mg2Si (plates) S-AI2CuMg (laths) r/-MgZn 2 (plates) y-CuBe t-Co plates Fe3C plates cementite Fe4N y-Ni3(AITi) Since the c parameter 0.78 nm differs from that of aluminium 0.404 nm the aluminium planes parallel to the plate are distorted by elastic coherency strains. Moreover, the precipitate grows with the c direction normal to the plane of the plate, so that the strain fields become larger as it grows and at peak hardness extend from one precipitate particle to the next (see Figure 8.4a). The direct observation of coherency strains confirms the theories of hardening based on the development of an elastically strained matrix (see next section). The transition structure 0' is tetragonal; the true unit cell dimensions are a = 0.404 and c = 0.58 nm and the axes are parallel to (100)gl directions. The strains around the O' plates can be relieved, however, by the formation of a stable dislocation loop around the precipitate and such a loop has been observed around small O' plates in the electron microscope as shown in Figure 8.4b. The long-range strain fields of the precipitate and its dislocation largely cancel. Consequently, it is easier for glide dislocations to move through the lattice of the alloy containing an incoherent precipitate such as O' than a coherent precipitate such as 0", and the hardness falls. The 0 structure is also tetragonal, with a = 0.606 and c--0.487 nm. This equilibrium precipitate is incoherent with the matrix and its formation always leads to softening, since coherency strains disappear. 8.2.2 Precipitation-hardening of AI-Ag alloys Investigations using X-ray diffraction and electron microscopy have shown the existence of three distinct stages in the age-hardening process, which may be summarized: silver-rich clusters ~ intermediate hexagonal y' -~ equilibrium hexagonal y. The hardening is associated with the first two stages in which the precipitate is coherent and partially coherent with the matrix, respectively. During the quench and in the early stages of ageing, silver atoms cluster into small spherical aggregates and a typical small-angle X-ray picture of this stage, shown in Figure 8.5a, has a diffuse ring surrounding the trace of the direct beam. The absence of intensity in the centre of the ring (i.e. at (000)) is attributed to the fact that clustering takes place so rapidly that there is left a shell-like region surrounding each cluster which is low in silver content. On ageing, the clusters grow in size and decrease in number, and this is characterized by the X-ray pattern showing a gradual decrease in ring diameter. The concentration and size of clusters can be followed very accurately by measuring the intensity distribution across the ring as a function of ageing time. This intensity may be represented (see Chapter 5) by an equation of the form l(e) = MnE[exp (-27rEREe2/3~ z) - exp (--2rt2RI2E2/3X2)] 2 (8.1) and for values of e greater than that corresponding to the maximum intensity, the contribution of the second term, which represents the denuded region surrounding the cluster, can be neglected. Figure 8.5b shows the variation in the X-ray intensity, scattered at small angles (SAS) with cluster growth, on ageing an aluminium-silver alloy at 120~ An analysis of this intensity distribution, using equation (8.1), indicates that the size of the zones increases from 2 to 5 nm in just a few hours at 120~ These zones may, of course, be seen in the electron microscope and Figure 8.6a