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 characterized 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 parameters very close to that of aluminium. However, the structure is hexagonal and, consequently, the precipitates 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 partially 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 constitutionally more complex ternary and quaternary alloys as to the binary alloys. Spherical zones are found in aluminium-magnesium-zinc alloys as in aluminium-zinc, although the magnesium atom is some 12% larger than the aluminium atom. The intermediate 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 similar lattice parameters ((<0.25%), depending on composition) 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 nondeformable 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 themselves which are important, it will be necessary for the moving dislocations either to cut through them or go round them. Thus, merely from elementary reasoning, 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 dislocation 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 spacings, 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 movement 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 particles. 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 simple 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 clustering 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 interaction 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 precipitates do not deform with the matrix and that the yield stress is the stress necessary to expand a loop of dislocation 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 discussed above, this process will be important in the later stages of precipitation when the precipitate becomes incoherent and the misfit strains disappear. A moving 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 obstacles 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 dislocation 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 strengthening 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 magnitude 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, copperberyllium 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 hardening due to dislocations cutting the particles is again predominant. To illustrate that more than one mechanism 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 twoor 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 similarity 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 system 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 consistent 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 electronmicroscope 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 curvature 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 dislocations 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 electronmicroscope 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 surfaces of crystals containing GP [1] zones also support this interpretation. If the zones possess no strain field, as in aluminium-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 temperature profoundly affects the flow stress if the barrier which the dislocations have to overcome is of a shortrange 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 temperatures (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 dispersionhardening. 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 containing 0 precipitates at room temperature and, consequently, 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 somewhat 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