《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_brittleness35

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 consider￾able 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 heat￾treatment alone. Such a method has many advantages, since the required strength can be induced at the most convenient stage of production or fabrication; more￾over, the component is not sent into service in a highly stressed, plastically deformed state. The basic require￾ment 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 reac￾tion; 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 prin￾cipal 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 duc￾tility 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 tough￾ness, will be discussed in this chapter. Fracture can take many forms; some special forms, such as brit￾tle 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 sys￾tems and partly because the research background to much of the current understanding of strength, tough￾ness and fracture is essentially metallurgical. However, it is often possible to extend the basic principles to non￾metallic materials, particularly in the case of fracture processes. This will be apparent later, in Chapter 10, when we describe how the unique transformation char￾acteristics of zirconia can be used to inhibit crack propagation in a brittle ceramic such as alumina. Meth￾ods for toughening glasses are described in the same chapter. In Chapter 11 we consider the strengthening and toughening effects produced when plastics, met￾als 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 prop￾erties 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 prop￾erty most markedly affected is the electrical resistance and this is usually considerably increased. In con￾trast, 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 param￾eter 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 tem￾peratures. At higher supersaturations and lower ageing temperatures the various property changes are not con￾sistent 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 pro￾cess which takes place in two stages is shown in alu￾minium-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 cluster￾ing 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 rea￾son 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 retrogres￾sion. 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 tem￾perature 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 tem￾perature; 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 study￾ing the regrouping of atoms during the early stages of ageing, depend on the detection of radiation scat￾tered 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 single￾crystal 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 mod￾ify 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 two￾dimensional 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 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 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 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, is insufficient to give rise to appreciable scattering at small angles. With the advent of the electron microscope the age￾ing 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 elec￾tron 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 equi￾librium phase. Instead, an ageing sequence: zones intermediate precipitates ~ equilibrium precipitate is followed. This sequence occurs because the equilib￾rium 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 pro￾cess, the system follows such a sequence in order to have the lowest free energy in all stages of precipita￾tion. 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 struc￾ture, 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 precipi￾tate 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 orienta￾tion relationship between the matrix and the precipitate so that the crystal planes which are parallel to, and sep￾arated 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 precip￾itation of many alloy phases, as shown by the fre￾quent occurrence of the Widmanst~itten structure, i.e. plate-shaped precipitates lying along prominent crys￾tallographic 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 defi￾nite crystal structure; for this reason the symbol 0" is often preferred. These precipitates, usually of max￾imum 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, giv￾ing an overall composition of CuAI2. Because of their size, 0" precipitates are easily observed in the elec￾tron microscope, and because of the ordered arrange￾ments of copper and aluminium atoms within the structure, their presence gives rise to intensity max￾ima 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 hard￾ness 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 disap￾pear. 8.2.2 Precipitation-hardening of AI-Ag alloys Investigations using X-ray diffraction and electron microscopy have shown the existence of three dis￾tinct stages in the age-hardening process, which may be summarized: silver-rich clusters ~ intermediate hexagonal y' -~ equilibrium hexagonal y. The hard￾ening 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

264 Modern Physical Metallurgy and Materials Engineering B Hours a) A Figure 8.5 Small-angle scattering of Cu Ka radiation by (a) After quenching from 520C (b) 140C for 10 days (after Guinier and Walker, 1953) structure is hexagonal and, consequently, the precipi- ates are easily recognizable in the electron microscope by the stacking fault contrast within them, as shown in Figure 8.6b. Clearly, these precipitates are never fully coherent with the matrix, but, nevertheless, in this alloy system, where the zones are spherical and have little or no coherency strain associated with them, and where no coherent intermediate precipitate resistance to dislocation movement than zones and a Figure 8. 4 Electron mice from Al-4Cu(a) second stage of hardening results 5 hours at60° C shot ates,(b)aged 12 hours The same principles apply to the constitution 200° C showing a dis ally more complex ternary and quaternary alloys 3 days at I60° C showin cipitated on helical s to the binary alloys. Spherical zones are found dislocations(after Nicholson, Thomas and Nutting. 1958-9). in aluminium-magnesium -zinc alloys as in alu minium-zinc,although the magnesium atom is some 12% larger than the aluminium atom. The intermedi is an electron micrograph showing spherical zones ate precipitate forms on the (1 I 1Al planes, and is in an aluminium-silver alloy aged 5 hours at 160C, partially coherent with the with little or no the diameter of the zones is about 10 nm in good strain field associated with agreement with that deduced by X-ray analysis. The the alloy is due purely to dent of solute and solvent atoms. Thus, solute atoms such In nickel-based alloys the hardening phase is the as silver and zinc which have atomic sizes similar to ordered y-Ni] Al; this y is an equilibrium phase in aluminium give rise to spherical zones, whereas solute the Ni-Al and Ni-Cr-Al systems and a metastable oms such as copper which have a high misfit in the phase in Ni-Ti and Ni-Cr-Ti. These systems form solvent lattice form plate-like zones the basis of the superalloys'(see Chapter 9)which With prolonged annealing, the formation and growth owe their properties to the close matching of the y of platelets of a new phase, y, occur. This is and the fcc matrix. The two phases have very simi terized by the appearance in the X-ray pattern lar lattice parameters((<0. 25%), depending on com streaks passing through the trace of the direc (Figure 8.5c). The y platelet lies parallel to the planes of the matrix and its structure has lattice se timr he coherency(interfacial energy yn confers a very low coarsening rate on so that the alloy overages extremely eters very close to that of aluminium. However, the slowl 0.7T

264 Modern Physical Metallurgy and Materials Engineering Figure g.5 Small-angle scattering of Cu Ku radiation by polycr3'stalline AI-Ag. (a) After quenching from 520~ (after Guinier and Walker, 1953). (b) The change in ring intensi~, and ring radius on ageing at 120~ (after Smalhnan and Westmacott, unpublished). (c) After ageing at 140~ for 10 days (after Guhffer and Walker, 1953). Figure 8.4 Electron micrographs from AI-4Cu (a) aged 5 hours at 160~ showing O" plates, (b) aged 12 hours at 200~ showing a dislocation ring round 0" plates, (c) aged 3 days at 160~ showing O" precipitated on helical dislocations (after Nicholson, Thomas and Nutting, 1958-9). is an electron micrograph showing spherical zones in an aluminium-silver alloy aged 5 hours at 160~ the diameter of the zones is about 10 nm in good agreement with that deduced by X-ray analysis. The zone shape is dependent upon the relative diameters of solute and solvent atoms. Thus, solute atoms such as silver and zinc which have atomic sizes similar to aluminium give rise to spherical zones, whereas solute atoms such as copper which have a high misfit in the solvent lattice form plate-like zones. With prolonged annealing, the formation and growth of platelets of a new phase, Y', occur. This is charac￾terized by the appearance in the X-ray pattern of short streaks passing through the trace of the direct beam (Figure 8.5c). The Y' platelet lies parallel to the { 1 1 1} planes of the matrix and its structure has lattice param￾eters very close to that of aluminium. However, the structure is hexagonal and, consequently, the precipi￾tates are easily recognizable in the electron microscope by the stacking fault contrast within them, as shown in Figure 8.6b. Clearly, these precipitates are never fully coherent with the matrix, but, nevertheless, in this alloy system, where the zones are spherical and have little or no coherency strain associated with them, and where no coherent intermediate precipitate is formed, the par￾tially coherent y' precipitates do provide a greater resistance to dislocation movement than zones and a second stage of hardening results. The same principles apply to the constitution￾ally more complex ternary and quaternary alloys as to the binary alloys. Spherical zones are found in aluminium-magnesium-zinc alloys as in alu￾minium-zinc, although the magnesium atom is some 12% larger than the aluminium atom. The intermedi￾ate precipitate forms on the { 1 1 1 }A! planes, and is partially coherent with the matrix with little or no strain field associated with it. Hence, the strength of the alloy is due purely to dispersion hardening, and the alloy softens as the precipitate becomes coarser. In nickel-based alloys the hardening phase is the ordered y'-Ni3A1; this y' is an equilibrium phase in the Ni-AI and Ni-Cr-AI systems and a metastable phase in Ni-Ti and Ni-Cr-Ti. These systems form the basis of the 'superalloys' (see Chapter 9) which owe their properties to the close matching of the y' and the fcc matrix. The two phases have very simi￾lar lattice parameters ((<0.25%), depending on com￾position) and the coherency (interfacial energy y~ -~ 10-20 mJ/m 2) confers a very low coarsening rate on the precipitate so that the alloy overages extremely slowly even at 0.7Tm

65 particles, when the dislocations bypass the particles, he alloy strength is independent properties but is strongly dependent on particle size and dispersion strength decreasing as particle size or dispersion increases. The transition from deformable non-deformable particle-controlled deformation is Re former contrasts with the turbulent plastic flow for non- b. w deformable particles. The latter leads to the production of a high density of dislocation loops, dipoles and other debris which results in a high rate of work-hardening This high rate of work-hardening is a distinguishing feature of all dispersion-hardened systems 8.2.3. 2 Coherency strain-hardening The precipitation of particles having a slight misfit in the matrix gives rise to stress fields which hinder the movement of gliding dislocations. For the dislocations to pass through the regions of internal stress the applied tress must be at least equal to the average internal stress,and for spherical particles this is given by 5 hours at 60 C showing spherical zones, and b/ap aged [= 2uef where u is the shear modulus, a is the misfit of the particle and f is the volume fraction of precipitate This suggestion alone, however, cannot account for the critical size of disp a precipita 8.2.3 Mechanisms of precipitation-hardening the hardening is a maximum, since equation(8.2)is independent of L, the distance between particles. To 8.2. 3 1 The significance of particle explain this, Mott and Nabarro consider the extent to deformability which a dislocation can bow round a particle under the action of a stress t. Like the bowing stress of a The strength of an age-hardening alloy is governed by Frank-Read source this is given by the interaction of moving dislocations and precipitate The obstacles in precipitation-hardening alloys which hinder the motion of dislocations may be either (i) the strains around GP zones, (2)the zones or precipitates where r is the radius of curvature to which the dislo- themselves, or both. Clearly, if it is the zones them ion is bent which is related to the particle spacing selves which are important, it will be necessary for Hence, in the hardest age-hardened alloys where the the moving dislocations either to cut through them or nem. Thus, merely from elementary ing, it would appear that there are at least three causes of hardening, namely: (1)coherency strain hardening, deformable 2)chemical hardening, i.e. when the dislocation cuts when the dislocation goes round or over the precipitate particular alloy system but, generally, there is a critical reformable ispersion at which the strengthening is a maximum, as shown in Figure 8.7. In the small-particle regime the ecipitates, or particles, are coherent and deformable as the dislocations cut through them, while in the arger-particle regime the particles are incoherent nd non-deformable as the dislocations bypass For deformable particles, when the dislocations pass through the particle, the intrinsic properties of the particle are of importance and alloy strength varies Figure 8.7 Variation of strength with particle size, defining only weakly with particle size. For non-deformable the deformable and non-deformable particle regimes

Strengthening and toughening 265 particles, when the dislocations bypass the particles, the alloy strength is independent of the particle properties but is strongly dependent on particle size and dispersion strength decreasing as particle size or dispersion increases. The transition from deformable to non-deformable particle-controlled deformation is readily recognized by the change in microstructure, since the 'laminar' undisturbed dislocation flow for the former contrasts with the turbulent plastic flow for non￾deformable particles. The latter leads to the production of a high density of dislocation loops, dipoles and other debris which results in a high rate of work-hardening. This high rate of work-hardening is a distinguishing feature of all dispersion-hardened systems. Figure 8.6 Electron micrographs from AI-Ag alloy (a) aged 5 hours at 160~ showing spherical zones, and (b) aged 5 days at 160~ showing y' precipitate (after Nicholson, Thomas and Nutting, 1958-9). 8.2.3 Mechanisms of precipitation-hardening 8.2.3.1 The significance of particle deformability The strength of an age-hardening alloy is governed by the interaction of moving dislocations and precipitates. The obstacles in precipitation-hardening alloys which hinder the motion of dislocations may be either (l) the strains around GP zones, (2) the zones or precipitates themselves, or both. Clearly, if it is the zones them￾selves which are important, it will be necessary for the moving dislocations either to cut through them or go round them. Thus, merely from elementary reason￾ing, it would appear that there are at least three causes of hardening, namely: (1) coherency strain hardening, (2) chemical hardening, i.e. when the dislocation cuts through the precipitate, or (3) dispersion hardening, i.e. when the dislocation goes round or over the precipitate. The relative contributions will depend on the particular alloy system but, generally, there is a critical dispersion at which the strengthening is a maximum, as shown in Figure 8.7. In the small-particle regime the precipitates, or particles, are coherent and deformable as the dislocations cut through them, while in the larger-particle regime the particles are incoherent and non-deformable as the dislocations bypass them. For deformable particles, when the dislocations pass through the particle, the intrinsic properties of the particle are of importance and alloy strength varies only weakly with particle size. For non-deformable 8.2.3.2 Coherency strain-hardening The precipitation of particles having a slight misfit in the matrix gives rise to stress fields which hinder the movement of gliding dislocations. For the dislocations to pass through the regions of internal stress the applied stress must be at least equal to the average internal stress, and for spherical particles this is given by r = 21zef (8.2) where /z is the shear modulus, e is the misfit of the particle and f is the volume fraction of precipitate. This suggestion alone, however, cannot account for the critical size of dispersion of a precipitate at which the hardening is a maximum, since equation (8.2) is independent of L, the distance between particles. To explain this, Mott and Nabarro consider the extent to which a dislocation can bow round a particle under the action of a stress r. Like the bowing stress of a Frank-Read source this is given by r = Otlzb/r (8.3) where r is the radius of curvature to which the dislo￾cation is bent which is related to the particle spacing. Hence, in the hardest age-hardened alloys where the \ i~.. \ I deformable .~~ particles ~~ .~. non-deformable particles e" C: == particle size Figure 8.7 Variation of strength with particle size, defining the deformable and non-deformable particle regimes

266 Modern Physical Metallurgy and Materials Engineering yield strength is about u/100, the dislocation can bend to a radius of curvature of about 100 atomic spac Dislocation ings, and since the distance between particles is of the same order it would appear that the dislocation can avoid the obstacles and take a form like that shown in configuration, in order to produce glide, each section of the dislocation line has to be taken over the adverse region of internal stress without any help from other sections of the line - the alloy is then hard. If the precipitate is dispersed on too fine a scale (e. g. when behind the alloy has been freshly quenched or lightly aged) the dislocation is unable or bend sufficiently to lie entirely in the regions of low internal stress, As result, the internal stresses acting on the dislocation Precipitate line largely cancel and the force resisting its move- ment is small -the alloy then appears soft. When the dispersion is on a coarse scale, the dislocation line is able to move between the particles, as shown in Figure 8.8b, and the hardening is smal For coherency strain hardening depends on the ability of the dislocation to bend and Figure 8. 8 Schematic representation of a dislocation(a) thus experience more regions of adverse stress than of curling round the stress fields front precipitates and (l iding stress. The flow stress therefore depends on the passing between widely spaced precipitates(Orowan treatment of averaging the stress, and recent attempts looping) separate the behaviour of small and large coherent par ticles. For small coherent particles the flow stress is gy the matrix (e.g. Al-A T=4.1ue/2f/(/b) between Ag zones and Al matrix)so that ple arithmetic, average of en gthening than the which predicts a greater stre r≈△YsF/b uation(8. 2). For Usually y1 yap and so y can be ted. but the ordering within the particle requires ocations to r=0.7af/(eb3/r3)y/4 glide in pairs. This given by t=(apb/2b)(4yapbrf/T)-f 8.2.3.3 Chemical hardening where t is the dislocation line tension When a dislocation actually passes through a zone as shown in Figure 8.9 a change in the number of 8.2.3,4 Dispersion-hardening solvent-solute near-neighbours occurs across the slip In dispersion-hardening it is assumed that the precipi plane. This tends to reverse the process of cluster- tates do not deform with the matrix and that the yield ing and, hence, additional work must be done by the stress is the stress ary to expand a loop of dislo applied stress to bring this about. This process, known cation between the precipitates. This will be given by as chemical hardening, provides a short-range interac- the Orowan stress tion between dislocations and precipitates and arises from three possible causes: (1)the energy required b几L to create an additional particle/matrix interface with energy y per unit area which is provided by a stress where L is the separation of the precipitates. As di stages of precipitation when the incoherent and the misfit strains disappear. A mov where a is a numerical constant (2) the additional ing dislocation is then able to bypass the obstacles, as work required to create an antiphase boundary inside shown in Figure 8.8b, by moving in the clean pieces the particle with ordered structure, given by of crystal between the precipitated particles. The yield stress decreases as the distance between the obsta r= Byap(fr)/ub les increases in the over-aged condition even when the dispersion of the precipitate here b is a numerical constant and(3) the change a greater applied stress is necessary to force in width of a dissociated dislocation as it passes cation past the obstacles than would be the case if the

266 Modern Physical Metallurgy and Materials Engineering yield strength is about/z/100, the dislocation can bend to a radius of curvature of about 100 atomic spac￾ings, and since the distance between particles is of the same order it would appear that the dislocation can avoid the obstacles and take a form like that shown in Figure 8.8a. With a dislocation line taking up such a configuration, in order to produce glide, each section of the dislocation line has to be taken over the adverse region of internal stress without any help from other sections of the line- the alloy is then hard. If the precipitate is dispersed on too fine a scale (e.g. when the alloy has been freshly quenched or lightly aged) the dislocation is unable or bend sufficiently to lie entirely in the regions of low internal stress. As a result, the internal stresses acting on the dislocation line largely cancel and the force resisting its move￾ment is small- the alloy then appears soft. When the dispersion is on a coarse scale, the dislocation line is able to move between the particles, as shown in Figure 8.8b, and the hardening is again small. For coherency strain hardening the flow stress depends on the ability of the dislocation to bend and thus experience more regions of adverse stress than of aiding stress. The flow stress therefore depends on the treatment of averaging the stress, and recent attempts separate the behaviour of small and large coherent par￾ticles. For small coherent particles the flow stress is given by r = 4.11ze3/2fl/2(r/b) 1/2 (8.4) which predicts a greater strengthening than the sim￾ple arithmetic average of equation (8.2). For large coherent particles 7: = 0.7#fl/E(eb3/r3)l/4 (8.5) 8.2.3.3 Chemical hardening When a dislocation actually passes through a zone as shown in Figure 8.9 a change in the number of solvent-solute near-neighbours occurs across the slip plane. This tends to reverse the process of cluster￾ing and, hence, additional work must be done by the applied stress to bring this about. This process, known as chemical hardening, provides a short-range interac￾tion between dislocations and precipitates and arises from three possible causes: (1) the energy required to create an additional particle/matrix interface with energy y~ per unit area which is provided by a stress r "~ oty~/2(fr)l/2/#b 2 (8.6) where ot is a numerical constant, (2) the additional work required to create an antiphase boundary inside the particle with ordered structure, given by 3/2 "t" ~ /~gapb (fr)l/2/lzb2 (8.7) where /3 is a numerical constant, and (3) the change in width of a dissociated dislocation as it passes Stress field of .. ..... precipitate Dlstoca lion line (a) Moving Ce 6 (b) F Dtslocatlon -- loop left behind 0 @ Figure 8.8 Schematic representation of a dislocation (a) curling round the stress fields from precipitates and (b) passing between widely spaced precipitates (Orowan looping). through the particle where the stacking fault energy differs from the matrix (e.g. AI-Ag where A?'sv 100 mJ/m 2 between Ag zones and A1 matrix) so that r "~" AYsF/b (8.8) Usually y~ < Yapb and so y~ can be neglected, but the ordering within the particle requires the dislocations to glide in pairs. This leads to a strengthening given by r = (Yapb/2b)[4yapbrf/TrT) 1/2 - f] (8.9) where T is the dislocation line tension. 8.2.3.4 Dispersion-hardening In dispersion-hardening it is assumed that the precipi￾tates do not deform with the matrix and that the yield stress is the stress necessary to expand a loop of dislo￾cation between the precipitates. This will be given by the Orowan stress r =otlzb/L (8.10) where L is the separation of the precipitates. As dis￾cussed above, this process will be important in the later stages of precipitation when the precipitate becomes incoherent and the misfit strains disappear. A mov￾ing dislocation is then able to bypass the obstacles, as shown in Figure 8.8b, by moving in the clean pieces of crystal between the precipitated particles. The yield stress decreases as the distance between the obsta￾cles increases in the over-aged condition. However, even when the dispersion of the precipitate is coarse a greater applied stress is necessary to force a dislo￾cation past the obstacles than would be the case if the

Strengthening and toughener interface o●。● ●● ●o o● Figure 8.9 Ordered particle(a)cut by dislocations in(b) to produce new interface and apb. obstruction were not there. Some particle or precipitate 4%)alloy in various structural states, The curves were lengthening remains but the majority of the strength- obtained by testing crystals of approximately the same ening arises from the dislocation debris left around the orientation, but the stress-strain curves from crystals particles giving rise to high work-hardenin containing GP [I] and GP [2] zones are quite different from those for crystals containing A or 0 precipitates 8.2.3.5 Hardening mechanisms in Al-Cu alloys When the crystals contain either GP [1] or GP [2] ven alloy will depend on several factors, such as of pure aluminium crystals, except that there is a two- he type of particle precipitated(e.g. whether zone, or threefold increase in the yield stress. In contrast, when the crystals contain either 8 or g precipitates the nitude of the strain and the testing temperature. In yield stress is less than for crystals containing zones, he earlier stages of ageing (i.e. before over-ageing but the initial rate of work-hardening is extremely the coherent zones are cut by dislocations mov rapid. In fact, the stress-strain curves bear no sim hrough the matrix and hence both coherency strain larity to those of a pure aluminium crystal. It is also hardening and chemical hardening wiHl be important observed that when e or 6 is e.g. in such alloys as aluminium-copper, copper- deformation does not take place on a single slip sys ryllium and iron-vanadium-carbon In alloys such tem but on several systems; the crystal then defo Tmns aluminium-silver and aluminium-zinc, however, more nearly as a polycrystal does and the x-ray pattern the zones possess no strain field, so that chemical develops extensive asterism. These factors are consis- hardening will be the most important contribution. In tent with the high rate of work-hardening observed in the important high-temperature creep-resistant nickel crystals containing e or 8 precipitates alloys the precipitate is of the Ni3 Al form which has The separation of the precipitates cutting any slip pred due to dislocations cutting the particles / hard. plane can be deduced from both X-ray and electron- chemical mech- Fig microscope observations. For the crystals, relating to Figure 8.10, containing of hard ation 15 nm and for GP [2] zones it is 25 nm. It then follows ystem, let us examine the mechanical behaviour from equation(8.3)that to av precipitates th ninium-copper alloy in more detail. Figure 8.10 shows the deformation characteristics vature of about 10 nm. to of single crystals of an aluminium-copper(nominally several times greater than the flow stress and GP (1 2 e 80 Figure 8.10 Stress-strain curves from single crystals of aluminium-4% copper containing GP [1 zones, GP /2), zones, 6-precipitates and e-precipitates respectively(after Fine, Bryne and Kelly

Strengthening and toughening 267 ordered _ particle .= l m slap plane ~ : - -J apb (a) (b) Figure 8.9 Ordered particle (a) cut by dislocations in (b) to produce new interface and apb. obstruction were not there. Some particle or precipitate strengthening remains but the majority of the strength￾ening arises from the dislocation debris left around the particles giving rise to high work-hardening. 8.2.3.5 Hardening mechanisms in AI-Cu alloys The actual hardening mechanism which operates in a given alloy will depend on several factors, such as the type of particle precipitated (e.g. whether zone, intermediate precipitate or stable phase), the mag￾nitude of the strain and the testing temperature. In the earlier stages of ageing (i.e. before over-ageing) the coherent zones are cut by dislocations moving through the matrix and hence both coherency strain hardening and chemical hardening will be important, e.g. in such alloys as aluminium-copper, copper￾beryllium and iron-vanadium-carbon. In alloys such as aluminium-silver and aluminium-zinc, however, the zones possess no strain field, so that chemical hardening will be the most important contribution. In the important high-temperature creep-resistant nickel alloys the precipitate is of the Ni3A1 form which has a low particle/matrix misfit and hence chemical hard￾ening due to dislocations cutting the particles is again predominant. To illustrate that more than one mech￾anism of hardening is in operation in a given alloy system, let us examine the mechanical behaviour of an aluminium-copper alloy in more detail. Figure 8.10 shows the deformation characteristics of single crystals of an aluminium-copper (nominally 4%) alloy in various structural states. The curves were obtained by testing crystals of approximately the same orientation, but the stress-strain curves from crystals containing GP [1 ] and GP [2] zones are quite different from those for crystals containing 01 or 0 precipitates. When the crystals contain either GP [1] or GP [2] zones, the stress-strain curves are very similar to those of pure aluminium crystals, except that there is a two￾or threefold increase in the yield stress. In contrast, when the crystals contain either 01 or 0 precipitates the yield stress is less than for crystals containing zones, but the initial rate of work-hardening is extremely rapid. In fact, the stress-strain curves bear no simi￾larity to those of a pure aluminium crystal. It is also observed that when 0' or 0 is present as a precipitate, deformation does not take place on a single slip sys￾tem but on several systems; the crystal then deforms, more nearly as a polycrystal does and the X-ray pattern develops extensive asterism. These factors are consis￾tent with the high rate of work-hardening observed in crystals containing 01 or 0 precipitates. The separation of the precipitates cutting any slip plane can be deduced from both X-ray and electron￾microscope observations. For the crystals, relating to Figure 8.10, containing GP [1] zones this value is 15 nm and for GP [2] zones it is 25 nm. It then follows from equation (8.3) that to avoid these precipitates the dislocations would have to bow to a radius of cur￾vature of about 10 nm. To do this requires a stress several times greater than the observed flow stress and, % 160 8O GP 111 GP [2] /" / 1 i 1 1 ! 1 ~ ! ! i 1 1 1 I. 1 1 ! ! !. I ! l I I I _1 0 2 t, 6 0 2 4 6 8 2 4 2 t. Strain % Figure 8.10 Stress-strain curves from single crystals of aluminium-4% copper containing GP [1] zones, GP 12], zones, 01-precipitates and O-precipitates respectively (after Fine, Bryne and Kelly)

268 Modern Physical Metallurgy and Materials Engineering e, it must be assumed that the disloca- over-aged condition and the hardening to dispersion tions are forced through the zones. Furthermore, if we hardening. The separation of the 0 particles is greater substitute the observed values of the flow stress in the than that of the e, being somewhat greater than I um elation ub/t=L, it will be evident that the bowing and the initial flow stress is very low. In both cases, mechanism is unlikely to operate unless the particles however, the subsequent rate of hardening is high re about 60 nm apart This is confirmed by electron- because, as suggested by Fisher, Hart and Pry, the microscope observations which show that dislocations gliding dislocation interacts with the dislocation loops pass through GP zones and coherent precipitates, bu in the vicinity of the particles(see Figure 8.8b). The ypass non-coherent particles. Once a dislocation has stress-strain curves show, however, that the rate of work-hardening falls to a low value after a few per dislocations on the same slip plane will be easier. cent strain, and these authors attribute the maximum zones should be low, as shown in Figure 8. 10. The particles. This process is not observed in crystals con- straight, well-defined slip bands observed on the sur- sequently, it seems more likely that the particles will faces of crystals containing GP [1] zones also support be avoided by cross-slip. If this is so. prismatic loops If the zones possess no strain field, as in alu of dislocation will be formed at the particles, by the minium-silver or aluminium-zinc alloys, the flow mechanism shown in Figure 8.11, and these will give approximately the same mean internal stress as that stress would be entirely governed by the chemical calculated by Fisher, Hart and Pry, but a reduced stress hardening effect. However, the zones in aluminic on the particle, The maximum in the work-hardening copper alloys do possess strain fields, as shown in curve would then ce ond to the Figure 8.4, and, consequently, the stresses around a expand these loops; this stress will be of the order of zone will also affect the flow stress. Each dislocation ub/r where r is the radius of the loop which is some- will be subjected to the stresses due to a zone at a what greater than the particle size. At low temperatures small distance from the zone cross-slip is difficult and the stress may be relieved It will be remembered from Chapter 7 that temper- either by initiating secondary slip or by fracture ature profoundly affects the flow stress if the barrier which the dislocations have to overcome is of a short- 8.2.4 Vacancies and precipitation range nature. For this reason, the flow stress of crystals It is clear that because precipitation is controlled by the containing GP [1] zones will have a larger dependence rate of atomic migration in the alloy, temperature will on temperature than that of those containing GP [2] have a pronounced effect on the process. Moreover, zones. Thus, while it is generally supposed that the since precipitation is a thermally activated process, strengthening effect of GP [2] zones is greater than other variables such as time of annealing, composition that of GP [l, and this is true at normal tem tures(see Figure 8.10), at very low temperatures it However, the basic treatment of age-hardening alloys is solution treatment followed by <stengthening effect due to the short-range interactions introduction of vacancies by the latter process must ween zones and dislocations play an important role in the kinetic behaviour The 0 and 0 precipitates are incoherent and do not It has been recognized that near room temperature, deform with the matrix, so that the critical resolved zone formation in alloys such as aluminium-copper shear stress is the stress necessary to expand a loop and aluminium-silver occurs at a rate many orders of dislocation between them. This corresponds to the of magnitude greater than that calculated from the Figure 8.11 Cross-slip of (a)edge and (b) screw dislocation over a particle producing prismatic loops in the proce

268 Modem Physical Metallurgy and Materials Engineering in consequence, it must be assumed that the disloca￾tions are forced through the zones. Furthermore, if we substitute the observed values of the flow stress in the relation l.tb/r = L, it will be evident that the bowing mechanism is unlikely to operate unless the particles are about 60 nm apart. This is confirmed by electron￾microscope observations which show that dislocations pass through GP zones and coherent precipitates, but bypass non-coherent particles. Once a dislocation has cut through a zone, however, the path for subsequent dislocations on the same slip plane will be easier, so that the work-hardening rate of crystals containing zones should be low, as shown in Figure 8.10. The straight, well-defined slip bands observed on the sur￾faces of crystals containing GP [1] zones also support this interpretation. If the zones possess no strain field, as in alu￾minium-silver or aluminium-zinc alloys, the flow stress would be entirely governed by the chemical hardening effect. However, the zones in aluminium copper alloys do possess strain fields, as shown in Figure 8.4, and, consequently, the stresses around a zone will also affect the flow stress. Each dislocation will be subjected to the stresses due to a zone at a small distance from the zone. It will be remembered from Chapter 7 that temper￾ature profoundly affects the flow stress if the barrier which the dislocations have to overcome is of a short￾range nature. For this reason, the flow stress of crystals containing GP [ 1] zones will have a larger dependence on temperature than that of those containing GP [2] zones. Thus, while it is generally supposed that the strengthening effect of GP [2] zones is greater than that of GP [1], and this is true at normal tempera￾tures (see Figure 8.10), at very low temperatures it is probable that GP [1] zones will have the greater strengthening effect due to the short-range interactions between zones and dislocations. The 0' and 0 precipitates are incoherent and do not deform with the matrix, so that the critical resolved shear stress is the stress necessary to expand a loop of dislocation between them. This corresponds to the b (a) over-aged condition and the hardening to dispersion￾hardening. The separation of the 0 particles is greater than that of the 0', being somewhat greater than 1 pm and the initial flow stress is very low. In both cases, however, the subsequent rate of hardening is high because, as suggested by Fisher, Hart and Pry, the gliding dislocation interacts with the dislocation loops in the vicinity of the particles (see Figure 8.8b). The stress-strain curves show, however, that the rate of work-hardening falls to a low value after a few per cent strain, and these authors attribute the maximum in the strain-hardening curve to the shearing of the particles. This process is not observed in crystals con￾taining 0 precipitates at room temperature and, con￾sequently, it seems more likely that the particles will be avoided by cross-slip. If this is so, prismatic loops of dislocation will be formed at the particles, by the mechanism shown in Figure 8.11, and these will give approximately the same mean internal stress as that calculated by Fisher, Hart and Pry, but a reduced stress on the particle. The maximum in the work-hardening curve would then correspond to the stress necessary to expand these loops; this stress will be of the order of pb/r where r is the radius of the loop which is some￾what greater than the particle size. At low temperatures cross-slip is difficult and the stress may be relieved either by initiating secondary slip or by fracture. 8.2.4 Vacancies and precipitation It is clear that because precipitation is controlled by the rate of atomic migration in the alloy, temperature will have a pronounced effect on the process. Moreover, since precipitation is a thermally activated process, other variables such as time of annealing, composition, grain size and prior cold work are also important. However, the basic treatment of age-hardening alloys is solution treatment followed by quenching, and the introduction of vacancies by the latter process must play an important role in the kinetic behaviour. It has been recognized that near room temperature, zone formation in alloys such as aluminium-copper and aluminium-silver occurs at a rate many orders of magnitude greater than that calculated from the b (b) Figure 8.11 Cross-slip of (a) edge and (b) screw dislocation over a particle producing prismatic loops in the process