Mechanical behaviour of materials 207 iA Figure 7. 15 Diagram showing structure of edge dislocation during gliding from (a)equilibrium to (b) metastable position 7.4 Dislocation behaviour during Direct measurements of dislocation velocity v have plastic deformation now been made in some crystals by means of the etch pitting technique; the results of such an experiment are 7.4.1 Dislocation mobility shown in Figure 7.16. Edge dislocations move faster The ease with which crystals can than screws, because of the frictional drag of jogs on deformed at stresses many orders of magnitude less lastically screws, and the velocity of both varies rapidly with than the theoretical strength(t= ub/2ra)is quite remarkable, and due to the mobility of dislocations Figure 7. 15a shows that as a dislocation glides througl of (110)[IO] the lattice it moves from one symmetrical lattice 105 waves=3.6 x 105cm/s position to another and at each position the dislocation s in neutral equilibrium, because the atomic forces acting on it from each side are balanced. As the dislocation moves from these symmetrical lattice ositions some imbalance of atomic forces does exist, and an applied stress is required to overcome As shown in Figure 7. 15b, ntermediate displacement of the dislocation also leads to an approximately balanced force syster The lattice friction depends rather sensitively on the dislocation width w and has been shown by Peierls and Nabarro to be given by Screw components τ≈pexp[-2nw/b (75) for the shear of a rectangular lattice The friction stress is therefore often referred to as he Peierls -Nabarro stress. The two affecting w are (1)the elastic energy of the crystal which is reduced by spreading out the elastic strains nd(2)the misfit ber of misaligned atoms across the slip plane metals with close-packed structures have extended disloc- tions and hence w is large. Moreover, the close-packed anes are widely between them (i.e. have a small b/a factor) These metals have highly mobile dislocations and are intrin- sically soft. In contrast, directional bonding in crystals tc. s Stress tends to produce narrow dislocations, which leads to LL intrinsic hardness and brittleness. Extreme examples are ionic and ceramic crystals and the covalent mate- Applied shear stress, kg. rials such as diamond and silicon. The bcc transition Figure 7. 16 Stress dependence of the velocity of edge and metals display intermediate behaviour (i.e. intrinsically screw dislocations in lithium fluoride(from ctile above room temperatures but brittle belo Gilman, 1959: courtesy of the American Institute of Physics
Mechanical behaviour of materials 207 ( ( ( ( _! ---- ~ slip plane ------~--- --- - } (a) (b) Figure 7.15 Diagram showing structure of edge dislocation during gliding from (a) equilibrium to (b) metastable position. 7.4 Dislocation behaviour during plastic deformation 7.4.1 Dislocation mobility The ease with which crystals can be plastically deformed at stresses many orders of magnitude less than the theoretical strength (rt = lzb/2rca) is quite remarkable, and due to the mobility of dislocations. 107 Figure 7.15a shows that as a dislocation glides through the lattice it moves from one symmetrical lattice 106 position to another and at each position the dislocation is in neutral equilibrium, because the atomic forces acting on it from each side are balanced. As the 105 dislocation moves from these symmetrical lattice positions some imbalance of atomic forces does 10 ~ exist, and an applied stress is required to overcome this lattice friction. As shown in Figure 7.15b, an 103 intermediate displacement of the dislocation also leads to an approximately balanced force system. = 102 The lattice friction depends rather sensitively on the E dislocation width w and has been shown by Peierls and u . 10 Nabarro to be given by ~, r ~/x exp [-27rw/b] (7.5) _g 1"0 U ) for the shear of a rectangular lattice of interpla- ~ 10-1 nar spacing a with w = ~b/2rr(l - v)rt = a(1 - v). -,= o The friction stress is therefore often referred to as u o 10 -2 the Peierls-Nabarro stress. The two opposing factors affecting w are (1)the elastic energy of the crystal, i5 which is reduced by spreading out the elastic strains, 10-3 and (2) the misfit energy, which depends on the number of misaligned atoms across the slip plane. Metals 10 -~ with close-packed structures have extended dislocations and hence w is large. Moreover, the close-packed 10-5 planes are widely spaced with weak alignment forces between them (i.e. have a small b/a factor). These 30-6 metals have highly mobile dislocations and are intrinsically soft. In contrast, directional bonding in crystals 10.? tends to produce narrow dislocations, which leads to 0.1 intrinsic hardness and brittleness. Extreme examples are ionic and ceramic crystals and the covalent materials such as diamond and silicon. The bcc transition metals display intermediate behaviour (i.e. intrinsically ductile above room temperatures but brittle below). Direct measurements of dislocation velocity v have now been made in some crystals by means of the etch pitting technique; the results of such an experiment are shown in Figure 7.16. Edge dislocations move faster than screws, because of the frictional drag of jogs on screws, and the velocity of both varies rapidly with 0-5 1-0 5 10 50 100 Apptied sheor stress, kg/mm 2 Figure 7.16 Stress dependence of the velocity of edge and screw dislocations in lithium fluoride (from Johnston and Gilman, 1959; courtesy of the American Institute of Physics)
208 Modern Physical Metallurgy and Materials Eng Lithium fluoride Tensin Macroscopic shear yield stress 10 Figure 7. 17 (a) Correlation between stress to cause dislocation motion and the macro-yield stresses of edge dislocation motions in Fe-3% Si crystals (after Stein and Low, 1960: courtesy of the American Institute applied stress t according to an em he form v=(t/To), where to is t strengthening mechanisms ase the stress neces- peed and n is an index which varies for t sary to produce a given finite dislocation velocity in a materials. At high stresses the velocity may approach similar way to that found by lowering the temperature he speed of elastic waves 10m/s. The index n is sually low(<10)for intrinsically hard, covalent crys- 7.4.2 Variation of yield stress with als such as ge, a40 for bcc crysta high(≈200) for intrinsically soft fcc crystals. It is observed that a temperature and strain rate critical applied stress is required to start the disloc- The high Peierls-Nabarro stress, which is associated tions moving and denotes the onset of microplasticity with materials with narrow dislocations, gives rise to a A macroscopic tensile test is a relatively insensitive short-range barrier to dislocation motion. Such barriers neasure of the onset of plastic deformation and the are effective only over an atomic spacing or so, hence yield or flow stress measured in such a test is related thermal activation is able to aid the applied stress in not to the initial motion of an individual dislocation but overcoming them. Thermal activation helps a portion to the motion of a number of dislocations at some finite of the dislocation to cross the barrier after which glide elocity, e.g. 10 nm/s as shown in Figure 17 17 hen proceeds by the sideways movement of kinks Decreasing the temperature of the test or increasing the (This process is shown in Figure 7.29, Section 7. 4.8. strain-rate increases the stress level required to produce Materials with narrow dislocations therefore exhibit the same finite velocity(see Figure 7. 17b),i.e a significant temperature-sensitivity; intrinsically hard placing the velocity-stress curve to the right. Indeed, materials rapidly lose their strength with increasi same effect on the dislocation dynamics. This obser- In this diagram the(yield stress/modulus) ratio is plot vation is consistent with the increase in yield stress ted against T/Tm to remove the effect of modulus perature or increasing strain-rate, which decreases with temperature. Figure 7. 18b shows Most metals and alloys are hardened by cold working that materials which exhibit a strong temperature or by placing obstacles (e.g. precipitates) in the path dependent yield stress also exhibit a high strain-rate
208 Modern Physical Metallurgy and Materials Engineering C 3~ ............... ~ .. 121 o ~ Iron-sdlcon O "~.,_O-'O ,.. o 2-E (units of~~j~ul0' d/cmy~ "6 m fluoride ~ , ~~"j (units of 10' d/cm 2) ~o /~~,.,,.ds - 1-- / co ~ -- - Tension J I .1 . I "~1 Bending 0 1 2 3 4 (a) Macroscopic shear yield stress 10-2 -- 10-3 _ 10-4 .~ 10 -s 0 > 10-6 10-r 10-8 0.5 (b) 1 l I 1 1 i i 1 f 1 2 3 4 5 [10 8 N/m 2] Stress Figure 7.17 (a) Correlation between stress to cause dislocation motion and the macro-yield stresses of cr3,stals. (b) Edge dislocation motions in Fe-3% Si crystals (after Stein and Low, 1960; courtesy of the American Institute of Physics). applied stress r according to an empirical relation of the form v = (r/r0Y', where r0 is the stress for unit speed and n is an index which varies for different materials. At high stresses the velocity may approach the speed of elastic waves ~103 m]s. The index n is usually low (< 10) for intrinsically hard, covalent crystals such as Ge, ~40 for bcc crystals, and high (~200) for intrinsically soft fcc crystals. It is observed that a critical applied stress is required to start the dislocations moving and denotes the onset of microplasticity. A macroscopic tensile test is a relatively insensitive measure of the onset of plastic deformation and the yield or flow stress measured in such a test is related not to the initial motion of an individual dislocation but to the motion of a number of dislocations at some finite velocity, e.g. ~10 nm/s as shown in Figure 17.17a. Decreasing the temperature of the test or increasing the strain-rate increases the stress level required to produce the same finite velocity (see Figure 7.17b), i.e. displacing the velocity-stress curve to the right. Indeed, hardening the material by any mechanism has the same effect on the dislocation dynamics. This observation is consistent with the increase in yield stress with decreasing temperature or increasing strain-rate. Most metals and alloys are hardened by cold working or by placing obstacles (e.g. precipitates) in the path of moving dislocations to hinder their motion. Such strengthening mechanisms increase the stress necessary to produce a given finite dislocation velocity in a similar way to that found by lowering the temperature. 7.4.2 Variation of yield stress with temperature and strain rate The high Peierls-Nabarro stress, which is associated with materials with narrow dislocations, gives rise to a short-range barrier to dislocation motion. Such barriers are effective only over an atomic spacing or so, hence thermal activation is able to aid the applied stress in overcoming them. Thermal activation helps a portion of the dislocation to cross the barrier after which glide then proceeds by the sideways movement of kinks. (This process is shown in Figure 7.29, Section 7.4.8.) Materials with narrow dislocations therefore exhibit a significant temperature-sensitivity; intrinsically hard materials rapidly lose their strength with increasing temperature, as shown schematically in Figure 7.18a. In this diagram the (yield stress/modulus) ratio is plotted against T/Tm to remove the effect of modulus which decreases with temperature. Figure 7.18b shows that materials which exhibit a strong temperaturedependent yield stress also exhibit a high strain-rate
Mechanical behaviour of materials 209 T/Tm strain-rate Figure 7.18 Variation of yield stress with(a)temperature,(b) strain-rate for crystals with(i)fcc,(ii)bcc.(iii)ionic b liv) covalent-bonded structure sensitivity, i.e. the higher the imposed strain rate, the Dislocation loop activation is less effective at the faster rate of defor. In bcc metals a high lattice friction to the move- ment of a dislocation may arise from the dissocia- tion of a dislocation on several planes. As discussed in Chapter 4, when a screw dislocation with Burgers vector a/2[11 11 lies along a symmetry direction it n the basal an dissociate on three crystallographically equivalent planes. If such a dissociation occurs, it will be nec- essary to constrict the dislocation before it can glide in any one of the slip planes. This constriction will be more difficult to make as the temperature is low Stacking fault ered so that the large temperature dependence of the yield stress in bcc metals, shown in Figure 7. 18a and also Figure 7. 30, may be due partly to this effect. In fcc metals the dislocations lie on (11 1) planes, and although a dislocation will dissociate in any given (11 1)plane, there is no direction in the ship plar Figure 7.19 Dissociation in the basal plane of a screw along which the dislocation could also dissociate on dislocation moving on a non basal glide plane other planes; the temperature-dependence of the yield tress is small as shown in Figure 7. 18a. In cph metals he dissociated dislocations moving in the basal plane will also have a small Peierls force and be glissile with low temperature-dependence. However, screw dislo- oving on non-basal plane and pyramidal planes) may have a high Peierls force because they are able to extend in the basal plane as shown in Figure 7. 19. Hence, constrictions will once gain have to be made before the screw dislocations an advance on non-basal planes. This effect con- ributes to the high critical shear stress and strong emperature-dependence of non-basal glide observed in this crystal system, as mentioned in Chapter 4 7.4.3 Dislocation source operation When a stress is applied to a material the specimen Figure 7.20 Shear produced by gliding dislocations plastically deforms at a rate governed by the strain rate of the deformation process(e.g. tensile testing, rolling, dimensions L, x L2x 1 cm shown in Figure 7. 20 a etc. )and the strain rate imposes a particular velocity dislocation with velocity v moves through the crystal on the mobile dislocation population. In a crystal of in time t= Li/v and produces a shear strain b/L2, i.e
Mechanical behaviour of materials 209 -g (iv) ii) "o >, ''iii, ...... - (i) -- _-- ,,, i , ,,, T/Tm strain-rate (a) (b) Figure 7.18 Variation of yield stress with (a) temperature, (b) strain-rate for crystals with (i) fcc, (ii) bcc, (iii) ionic-bonded, (iv) covalent-bonded structure. sensitivity, i.e. the higher the imposed strain rate, the higher the yield stress. This arises because thermal activation is less effective at the faster rate of deformation. In bcc metals a high lattice friction to the movement of a dislocation may arise from the dissociation of a dislocation on several planes. As discussed in Chapter 4, when a screw dislocation with Burgers vector a/2[1 1 1] lies along a symmetry direction it can dissociate on three crystallographically equivalent planes. If such a dissociation occurs, it will be necessary to constrict the dislocation before it can glide in any one of the slip planes. This constriction will be more difficult to make as the temperature is lowered so that the large temperature dependence of the yield stress in bcc metals, shown in Figure 7.18a and also Figure 7.30, may be due partly to this effect. In fcc metals the dislocations lie on {1 1 1 } planes, and although a dislocation will dissociate in any given (1 1 1) plane, there is no direction in the slip plane along which the dislocation could also dissociate on other planes; the temperature-dependence of the yield stress is small as shown in Figure 7.18a. In cph metals the dissociated dislocations moving in the basal plane will also have a small Peierls force and be glissile with low temperature-dependence. However, screw dislocations moving on non-basal planes (i.e. prismatic and pyramidal planes) may have a high Peierls force because they are able to extend in the basal plane as shown in Figure 7.19. Hence, constrictions will once again have to be made before the screw dislocations can advance on non-basal planes. This effect contributes to the high critical shear stress and strong temperature-dependence of non-basal glide observed in this crystal system, as mentioned in Chapter 4. 7.4.3 Dislocation source operation When a stress is applied to a material the specimen plastically deforms at a rate governed by the strain rate of the deformation process (e.g. tensile testing, rolling, etc.) and the strain rate imposes a particular velocity on the mobile dislocation population. In a crystal of Dts tocat ion loop expanding wn a non-basal plane Stacking fault ~nPart~al d~slocat ~on/~/ Figure 7.19 Dissociation in the basal plane of a screw dislocation moving on a non-basal glide plane. -r- __ _L I L2 .... L I ....... Figure 7.20 Shear produced by gliding dislocations. dimensions Lj • L2 • 1 cm shown in Figure 7.20 a dislocation with velocity v moves through the crystal in time t = Ll/v and produces a shear strain b/~, i.e
210 Modern Physical Metallurgy and Materials Engineerin Figure 7. 21 Successive stages in the operation of a Frank-Read source. The plane of the paper is assumed to be the slip plan the strain rate is bv/L, L2. If the density of glissible line to decrease its radius of curvature further until it dislocations is p, the total number of dislocations becomes semi-circular(position 2). Beyond this point hich become mobile in the crystal is pL, L2 and the it has no equilibrium position so it will expand rapidly, overall strain rate is thus given by rotating about the nodes and taking up the succession of tween stag Y LOL,L2=pbv (7.6) and 5 the two parts of the loop below AB meet and annihilate each other to form a complete dislocation At conventional strain rates(e.g. 1 s-l)the disloc loop, which expands into the slip plane and a new tions would be moving at quite moderate speeds of ine source between A and B. The sequence is then a few cm/s if the mobile density <107/cm2. During thar ated and one unit of slip is produced by each loop high-speed deformation the velocity approaches the limiting velocity. The shear strain produced by these must be sufficient to overcome the restoring force on dislocations is given by the dislocation line due to its line tension. Referring to y= pbx (7.7) Figure 7.22 this would be 2Tde/2> told/2, and if T- ub/2 the stress to do this is about ub/l, where where x is the average distance a dislocation moves. u and b have their usual meaning and I is the length If the distance x 2 10-4cm( the size of an average of the Frank-Read source; the substitution of typical sub-grain) the maximum strain produced by p a 10 values(u=4 x 100 N m"2, b=2.5 x 10-10 m, and is about (10x 3 x 10-8 x 10-)which is only a I=10-6m)into this estimate shows that a critical fraction of 1%. In practice, shear strains >100% can shear stress of about 100 gf mm" is required. This be achieved, and hence to produce these large strains value is somewhat less than but of the same order as re dislocations than the origina dislocations are required. To account for the increase single crystals. Another source mechanism i metal in number of mobile dislocations during straining the multiple cross-slip as shown in Figure 7. 23. It depend The pt of a dislocation source has been introduced molest type of source is that due to Frank and Read and accounts for the regenerative multiplication of dislocations. A modified form of the frank-Read source is the multiple cross-glide source, first proposed by Koehler, which, as the name implies, depends on the cross-slip of screw dislocations and is there more common in metals of intermediate and stacking fault energy Figure 7.21 shows a Frank-Read source consisting of a dislocation line fixed at the nodes a and fixed, for example, because the other dislocations that join the nodes do not lie in slip planes). Because of its high elastic energy (4 ev per atom plane Figure 7.22 Geometry of frank-Read source used to threaded by a dislocation) the dislocation possesses calculate the stress to operate ne tension tending to make it shorten its length as much as possible(position 1, Figure 7. 21). This line tension T is roughly equal to aub, where u is the shear modulus, b the Burgers vector and a a constant usually taken to be about i. Under an applied stress the dislocation line will bow out, decreasing its radius planes of curvature until it reaches an equilibrium position in which the line tension balances the force due to the applied stress. Increasing the applied stress causes the Figure 7. 23 Cross-slip multiplication source
Node_t_ Node A~ B A.,"- l-'" B (1) (2) (3) (z,) (5) 210 Modern Physical Metallurgy and Materials Engineering Figure 7.21 Successive stages in the operation of a Frank-Read source. The plane of the paper is assumed to be the slip plane. the strain rate is bv/L1L2. If the density of glissible dislocations is p, the total number of dislocations which become mobile in the crystal is pL~L2 and the overall strain rate is thus given by b v Y = ~ -~l pLl L2 = pbv (7.6) At conventional strain rates (e.g. 1 s -~) the dislocations would be moving at quite moderate speeds of a few cm/s if the mobile density ~107/cm 2. During high-speed deformation the velocity approaches the limiting velocity. The shear strain produced by these dislocations is given by y = pbE (7.7) where 2 is the average distance a dislocation moves. If the distance x ~ 10 -4 cm (the size of an average sub-grain) the maximum strain produced by p ~ 107 is about (107x3x 10 -Sx 10 -4) which is only a fraction of 1%. In practice, shear strains > 100% can be achieved, and hence to produce these large strains many more dislocations than the original ingrown dislocations are required. To account for the increase in number of mobile dislocations during straining the concept of a dislocation source has been introduced. The simplest type of source is that due to Frank and Read and accounts for the regenerative multiplication of dislocations. A modified form of the Frank-Read source is the multiple cross-glide source, first proposed by Koehler, which, as the name implies, depends on the cross-slip of screw dislocations and is therefore more common in metals of intermediate and high stacking fault energy. Figure 7.21 shows a Frank-Read source consisting of a dislocation line fixed at the nodes A and B (fixed, for example, because the other dislocations that join the nodes do not lie in slip planes). Because of its high elastic energy (~4 eV per atom plane threaded by a dislocation) the dislocation possesses a line tension tending to make it shorten its length as much as possible (position 1, Figure 7.21). This line tension T is roughly equal to cq.tb 2, where /z is the shear modulus, b the Burgers vector and c~ a constant l usually taken to be about ~. Under an applied stress the dislocation line will bow out, decreasing its radius of curvature until it reaches an equilibrium position in which the line tension balances the force due to the applied stress. Increasing the applied stress causes the line to decrease its radius of curvature further until it becomes semi-circular (position 2). Beyond this point it has no equilibrium position so it will expand rapidly, rotating about the nodes and taking up the succession of forms indicated by 3, 4 and 5. Between stages 4 and 5 the two parts of the loop below AB meet and annihilate each other to form a complete dislocation loop, which expands into the slip plane and a new line source between A and B. The sequence is then repeated and one unit of slip is produced by each loop that is generated. To operate the Frank-Read source the force applied must be sufficient to overcome the restoring force on the dislocation line due to its line tension. Referring to Figure 7.22 this would be 2TdO/2 > rbldO/2, and if T ".~ lzb2/2 the stress to do this is about lzb/l, where /z and b have their usual meaning and l is the length of the Frank-Read source; the substitution of typical values (/z = 4 x 101~ N m -2, b = 2.5 x 10 -1~ m, and l = 10 -6 m) into this estimate shows that a critical shear stress of about 100 gf mm -2 is required. This value is somewhat less than but of the same order as that observed for the yield stress of virgin pure metal single crystals. Another source mechanism involves multiple cross-slip as shown in Figure 7.23. It depends rb Figure 7.22 Geometry of Frank-Read source used to calculate the stress to operate. ~Primary ~ -- ptanes Figure 7.23 Cross-slip mldtiplication source
Mechanical behaviour of materials 211 on the Frank-Read principle but does not 二 a to a certain high load A, known as the upper yield dislocation segment to be anchored by nodes if point, and then it suddenly yields plastically. The part of a moving screw dislocation undergoes double important feature to note from this curve is that the cross-slip the two pieces of edge dislocation on the stress required to maintain plastic flow immediately ross-slip plane effectively act as anchoring points after yielding has started is lower than that required to for a plane parallel to the original plane may operate as lower yield point). A yield point elongation to C then a Frank-Read source and any loops produced may occurs after which the specimen work hardens and the n turn cross slip and become a source. This process therefore not only increases the number of dislocations curve rises steadily and smoothly on the original slip plane but also causes the slip band Overstraining the yield point can be removed tem- to widen orarily by applying a small preliminary plastic strain The concept of the dislocation source accounts to the specimen Thus, if after reaching the point D,for for the observation of slip bands on the surface of example, the specimen is unloaded and a second test is ade fairly soon afterwards, a stress-strain curve of ne passage of a single dislocation is too small to be type 2 wili be obtained. The specimen deforms elasti cr. bservable as a slip line or band under the light micr cally up to the unloading point, D, and the absence of scope. To be resolved it must be at least 300 nm a yield point at the beginning of plastic flow is char sht and hence 1000 dislocations must have oper- acteristic of a specimen in an overstrained condition ted in a given slip band. Moreover, in general, the sli the operation of the cross.glide source as the predom- overstrained to remove the yield point is allowed straining hown in Figure 7. 24a, curve 3. This process, which is 7.4. 4 Discontinuous yielding ccompanied by hardening(as shown by the increased ress. ielding) is know eing or, low begins in an abrupt manner wi on, strain-ageing is slow at room temperature but is in which the applied stress falls, durin an upper to a lower yield point. Such y iour ture. Thus, a strong yield point returns after an ageing commonly found in iron containing small amounts treatment of only a few seconds at 200'C, but the same f carbon or nitrogen as impurity. The main char eld point will take many hours to develop if ageing cteristics of the yield phenomenon in iron may be is carried out at room temperature summarized as follows Guiders band formation Closely related to the yiel Yield point A specimen of iron during tensile defor- point is the formation of Liders bands. These bands mation( Figure 7.24a, curve 1)behaves elastically up are markings on the surface of the specimen which No uppe B C B Strain -e (b) Figure 7.24 Schematic representation of (a)strain ageing and (b) Liiders band formation
Mechanical behaviour of materials 211 on the Frank-Read principle but does not require a dislocation segment to be anchored by nodes. Thus, if part of a moving screw dislocation undergoes double cross-slip the two pieces of edge dislocation on the cross-slip plane effectively act as anchoring points for a new source. The loop expanding on the slip plane parallel to the original plane may operate as a Frank-Read source and any loops produced may in turn cross slip and become a source. This process therefore not only increases the number of dislocations on the original slip plane but also causes the slip band to widen. The concept of the dislocation source accounts for the observation of slip bands on the surface of deformed metals. The amount of slip produced by the passage of a single dislocation is too small to be observable as a slip line or band under the light microscope. To be resolved it must be at least 300 nm in height and hence ~ 1000 dislocations must have operated in a given slip band. Moreover, in general, the slip band has considerable width, which tends to support the operation of the cross-glide source as the predominant mechanism of dislocation multiplication during straining. 7.4.4 Discontinuous yielding In some materials the onset of macroscopic plastic flow begins in an abrupt manner with a yield drop in which the applied stress falls, during yielding, from an upper to a lower yield point. Such yield behaviour is commonly found in iron containing small amounts of carbon or nitrogen as impurity. The main characteristics of the yield phenomenon in iron may be summarized as follows. Yield point A specimen of iron during tensile deformation (Figure 7.24a, curve 1) behaves elastically up to a certain high load A, known as the upper yield point, and then it suddenly yields plastically. The important feature to note from this curve is that the stress required to maintain plastic flow immediately after yielding has started is lower than that required to start it, as shown by the fall in load from A to B (the lower yield point). A yield point elongation to C then occurs after which the specimen work hardens and the curve rises steadily and smoothly. Overstraining The yield point can be removed temporarily by applying a small preliminary plastic strain to the specimen. Thus, if after reaching the point D, for example, the specimen is unloaded and a second test is made fairly soon afterwards, a stress-strain curve of type 2 will be obtained. The specimen deforms elastically up to the unloading point, D, and the absence of a yield point at the beginning of plastic flow is characteristic of a specimen in an overstrained condition. Strain-age hardening If a specimen which has been overstrained to remove the yield point is allowed to rest, or age, before retesting, the yield point returns as shown in Figure 7.24a, curve 3. This process, which is accompanied by hardening (as shown by the increased stress, EF, to initiate yielding) is known as strainageing or, more specifically, strain-age hardening. In iron, strain-ageing is slow at room temperature but is greatly speeded up by annealing at a higher temperature. Thus, a strong yield point returns after an ageing treatment of only a few seconds at 200~ but the same yield point will take many hours to develop if ageing is carried out at room temperature. Liiders band formation Closely related to the yield point is the formation of Ltiders bands. These bands are markings on the surface of the specimen which O" I lNO upper jF~...,..,,~ I ,ll e c I-,, "o .~- ~, I II 9 -o~ I -6 il Strain ~ t ........ -.--.- "' ...._-.-- ~.-" .~.C ----C (a) (b) Figure 7.24 Schematic representation of (a) strain ageing and (b) Liiders band formation