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Dynamic recrystallization: plasticity enhancing structural development
Journal of Alloys and Compounds 378 (2004) 35–43
Dynamic recrystallization: plasticity enhancing structural development H.J. McQueen a,∗ , C.A.C. Imbert b a
Mechanical and Industrial Engineering, Concordia University, Montreal, Canada H3G 1M8 b The University of the West Indies, St. Augustine, Trinidad and Tobago Received 1 September 2003; accepted 20 October 2003
Abstract Dislocation mobility upsurge usually causes significant improvement in the plasticity of crystalline solids, partly through its ability to deter crack formation. Dynamic recrystallization (DRX) that proceeds during deformation reduces the flow stress and markedly raises the ductility, characterizing the hot working range. While it facilitates straining, it’s nucleation rate and equilibrium grain size are defined by the deformation temperature and strain rate. The flow stress in steady state is not directly determined by the grain size but rather by the average dislocation density, which is tied to both dynamic recovery (DRV) and DRX in so far as the migration of grain boundaries reduces the dislocation density below that attained by DRV annihilation and polygonization of substructure. Dynamic recrystallization does not, in its operation, produce any strain. It is a restoration or softening process, which facilitates straining with respect to ease and extent. In contrast to its static counterpart, its progress and effects are intimately associated with the plastic deformation in real time. © 2004 Elsevier B.V. All rights reserved. Keywords: Dynamic recrystallization; Plastic strain enhancement; Hot ductility; Flow softening
1. Introduction In processes having dislocation motion as the preponderant deformation mechanism, the interaction of the dislocations with crystal defects has a strong effect on deformation behavior. As a simple example, vacancies make possible dislocation climb at high temperature, T, but their condensation at low T can create dislocation loops, which hinder flow. Clearly raising T (or lowering strain rate, ε˙ ) through its good effects on lattice vibration and vacancies, facilitates the motion of dislocations (cross slip and climb), which in turn alters their interactions. Strain hardening combinations are outweighed by the opportunities for annihilation and array polygonization in the restorative mechanism of dynamic recovery (DRV) [1–11]. The T and ε˙ effects can be combined as the number of thermally activated events per unit strain, which can be expressed in the Zener–Hollomon parameter, Z [12]: ∗ Corresponding author. Tel.: +1-514-848-3145; fax: +1-514-848-3175. E-mail address: [email protected] (H.J. McQueen).
0925-8388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2003.10.067
1 Q = ε˙ −1 exp − = (A sinh (ασ)n )−1 Z RT
(1)
where Q is the activation energy R the gas constant (Arrhenius kinetics), σ the stress and A, α and n are materials constants. The imperfection and mechanism to be examined arise from the passage of grain boundaries (GB) through the metal which alters the progress of deformation lowering stress σ by replacing regions of high dislocation density from strain hardening reactions, with soft regions ripe for the operation of dislocation sources. This process called discontinuous dynamic recrystallization (dDRX) is dependent on nucleation; it is found primarily in low stacking fault energy (SFE) metals, such as Cu, Ni and ␥-Fe alloys above 0.5TM (melting K) due to the low level of DRV [7–10,12–17]. The other types of DRX have been previously described [11,18–20]. DRX is here examined in so far as it enables operation of the principal deformation mechanism of dislocation motion that is also affected simultaneously by DRV. However, the effects of DRX on some minor mechanisms such as GB sliding will also be considered. With emphasis on the effect on the
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deformation mechanisms, the presentation will depart from the traditional focus on initiation and grain size, which can be found elsewhere [13,17–21].
2. Influence of DRX on deformation In common hot deformation at 10−2 to 10 s−1 of specimens with grains 50–200 m, the nucleation of small strain-free regions lead to a decrease in the rate of strain hardening θ(= dσ/dε) and progress towards it balancing with the softening as seen in the peak σ p of the σ–ε curve (Figs. 1 and 2) [13–17,22–24]. Beyond the peak where it has reached about 35%, DRX proceeds rapidly, causing softening to σ ss , (εss ), where steady-state straining begins
(Fig. 3). Several discrete cycles of DRX cause a wavy flow curve (Section 3). Eq. (1) can be applied to different characteristic points such as σ p or σ ss ; for each there are separate values of A, n, Q and Z. In θ–σ plots, the downward slope that is greater for higher T (or lower ε˙ ) due to DRV, becomes less steep as subgrains form but later abruptly deflects downwards upon nucleation; θ reaches zero at the peak [13,14,22–27]. The progress of DRX in tool steels is shown from initiation at εCD (from θ–σ curves) to the effective onset of steady state at 99% DRX in Fig. 4 [28–30]. Fig. 5 shows recrystallized grains of torsion specimens of an A2 and M2 tool steels. The amount of dynamic recrystallization XDRX , as indicated along the flow curves, has been found to follow the Avrami behavior established for static recrystallization (SRX) (mechanism independent of
Fig. 1. Plots of θ–σ, for several as-cast (C) and worked (W) austenitic stainless steels, juxtaposed with σ–ε plots, showing commencement of subgrain formation, DRX initiation, peak stress and as derived through extrapolation, the saturation stress σs∗ as would be developed by DRV alone [22].
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Fig. 2. Micrographs of austenitic stainless steels in torsion: (a) homogenized 304, 23 s−1 , 1000 ◦ C, at ε = 1, showing original grains, serrated boundaries (twins) and DRX nuclei (optical 100×); (b) same as (a) but at ε = 2, with fine DRX grains (optical 100×); (c) as-cast 317, 1 s−1 , at 1000 ◦ C, DRX grains and substructure exhibited by SEM-EBS (170×); (d) same as (c) but illustrating decrease in subgrain size and more regular array at lower temperature (TEM, 4000×); and (e) same as (d) but at 1100 ◦ C, showing large subgrains (TEM, 4000×) [22,25,26].
stress); such an Avrami relationship has also been confirmed for stainless steels [14,22,25–27]. When the rate of DRX is corrected for the variation in driving force with σp2 , the activation energy is very close to that for grain boundary migration [22]. The repeated nucleation and growth maintain an average dislocation density lower than would DRV
alone, as estimated from σs∗ the stress at θ = 0, obtained from extrapolation of the second linear portion of the θ–σ curve (before nucleation) in Fig. 1 [13,14,22,25,26]. The steady-state microstructural behavior is specified by the grain size DS and subgrain size dS that are determined by Z and in turn control the flow stress:
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H.J. McQueen, C.A.C. Imbert / Journal of Alloys and Compounds 378 (2004) 35–43 −p
σs = Kg Ds
−q
σs = Ksg ds
Fig. 3. The drop in flow stress from σ p to σ SS increases as Z increases indicating that DRX more aggressively reduces dislocation density due to the higher rate. Curves with data points are tool steels [28,29]; lines without data are for austenitic stainless steels [22,25,26].
(2a) (2b)
where Kg , Ksg , p (≈0.8) and q (≈1) are material constants [14,22,25–27]. The dependence of σ s on ds is the same as that before initiation of DRX [31]. The dependence on Ds is not a Petch effect, since each related σ s –Ds are at a different T and GB are dislocation sinks rather than barriers. A smaller Ds indicates a higher rate of DRX that rapidly eliminates dislocations, thus producing a greater softening from σs∗ or from σ p (Fig. 3). The nucleation and growth of new grains are attained by the migration of high angle GB that absorb existing dislocations leaving behind a region with low dislocation density suitable for source operation. As a new grain grows, multiple sources in the initially formed part can send dislocations into the region behind the advancing GB creating a gradient (Fig. 7). This gradient sharpens quite rapidly so that the increased strain energy behind the advancing GB stops the growth, thus determining the grain size [14,21]. In the necklace mechanism of the first wave of DRX, new grains form along the initial boundaries, but stop at the characteristic size, allowing new necklaces of same-size grains to form [7,13–16]. For later necklaces and during steady state, the nucleation process then proceeds possibly by bulging of a short segment of the halted boundary into regions of notably higher strain energy [21,32,33]. While DRV is operating during all high T metal shaping processes, DRX is somewhat limited by the need to surpass the critical strain. It is found
Fig. 4. Flow curves at selected Z values of tool steels illustrating volume fraction of dynamic recrystallization as derived from the Avrami function and confirmed by microscopy [28,29].
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velop during high ε (∼4 or 5) to a very high degree so that on recrystallization, a different texture results from the preferential nucleation and growth of minor components in the plastic strain texture [5,8,38,39].
3. Dependence of DRX on deformation The DRX grain size is smaller as the Z of straining becomes higher (T lower, ε˙ higher) (Fig. 6), as a result of the lower level of DRV and smaller subgrain size that actually determines the higher σ [13–16,28,29,40]. Fig. 6b shows the relationship for austenitic stainless steels between σ SS , subgrain size dS and grain sizes DS for DRX (and from
Fig. 5. Optical micrographs of torsion specimens: (a) A2 tool steel deformed at 900 ◦ C, 4 s−1 (200×), transverse section showing recrystallized grain in surface layers strained beyond εCD ; and (b) M2 tool steel, deformed at 1000 ◦ C, 1 s−1 (500×), showing DRX grains after the first wave (volume fraction of carbides 18%) [28,29].
in high strain processes such as extrusion of austenitic steel and alloys of Cu and of Ni and in rotary piercing. In planetary mill rolling of stainless steel [25,26] with 93% reduction in one pass near 1200–1350 ◦ C, DRX considerably reduces the flow stress, provides ductility and refines the grain size [34]. In most multistage rolling schedules, its role is limited as explained below. Before inception of DRX, the texture in torsion develops similarly in Cu as it does in Al, that does not undergo DRX [33–36]. While there may be some randomization during the rapid DRX expansion in the work softening stage, the texture becomes stable during steady state, whereas for Al it undergoes a change towards a component with a lower Taylor factor [4,35,37]. It must be realized that DRX commences at relatively low critical strain, εCD , before an intense strain texture can develop with strongly differentiated components. The DRX grains nucleate from GB bulging, so have orientation similar to the old grains and deform to strengthen those orientations. Texture development with concurrent DRX and strain thus differs considerably from that in cold work, where the deformation texture can de-
Fig. 6. Dynamically recrystallized grain sizes (a) of M2, D2, A2 and W1 tool steels as a function of the deformation conditions Z and the steady-state flow stress [28,29] and (b) for austenitic stainless steels along with subgrain sizes in relationship with the steady-state flow stress [14,22,25,26].
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Fig. 7. Interaction of nucleation and growth of DRX grains with preceding and succeeding dislocation substructures: with rising ε˙ 1 , ε˙ 2 , ε˙ 3 , the matrix density rises ρM1 , ρM2 , ρM3 so the critical size decreases DN1 , DN2 , DN3 ; in growth, the boundary proceeds leftward to successive positions (very heavy solid lines) the dislocation density (curved medium solid lines) that catches up with the GB slowing it down at final sizes Ds1 , Ds2 , Ds3 [21].
metadynamic recrystallization (MRX), the latter occurring immediately after deformation by growth of dynamically formed nuclei); the ratio of sizes shows that only one subgrain in ten develops into a DRX nucleus [14,22,25–27]. For greater ε˙ (Figs. 1 and 4) the strains for initiation of DRX, for the peak and for steady state are all higher, yet when divided by ε˙ result in times that are shorter. Under the higher driving force of differential strain energy at higher ε˙ , DRX is faster. However, the grain size is not determined by impingement, but by the more rapid development of substructure behind the moving GB (Fig. 7) [13–16,21,40]. At constant T, the increasing critical strain with rising ε˙ indicates that the concurrent deformation hinders the formation of nuclei. This is the opposite of ε˙ influence on static recrystallization (SRX) to which comparisons are made in the next section [16,17]. In single crystals with no possibility of GB nucleation, a very high strain is required to initiate DRX. Nucleation occurs at a critical stress, which increases as ε˙ rises and T falls and is followed by a burst of very rapid growth with much growth twinning [13,14,41,42]. The stress drops and growth stops due to build up of substructure in the new grains. As a result of nucleation around their periphery, almost steady-state straining proceeds as in polycrystals. The operation of DRX depends very strongly on the current straining conditions in distinction from SRX where the accumulated dislocation structure is more significant. Change in T or ε˙ to increase Z cause a rapid transient to a higher stress level with a single peak before reaching the new characteristic stress and grain size [15,43]. When the initial grain size is smaller than twice the projected grain size, it requires several cycles of partial DRX with increasing grain size to reach the final one; this is accompanied by cyclic variation in the stress. When Z is decreased the transient flow curve exhibits this cyclic character related to the
increase in grain size, though several waves [43,44]. Continuous deformation during gradual decline in T delays DRX due to an initially slow rate of substructure formation and rising εCD , so that there is a long stress rise to one peak followed by a little softening before further gradual stress rise [45]. In multistage straining, as in rolling schedules, SRX during intervals between large passes at a high T produces grain refinement, but very short intervals, between small rapid passes during finishing in (high speed) continuous mills, inhibit SRX so that strain energy accumulates and may lead to DRX to give beneficial stress reduction and grain refinement [23,46–48]. If a hot working test is stopped before (but relatively close to) εCD without unloading, then during relaxation DRX may occur giving a very rapid decline in stress compared to static recovery (SRV) [49,50]. There is no evidence that the simultaneous deformation alters the atomistic mechanism of GB migration. It is dependent on thermally activated jumping of atoms from the existing grain to the new grain, because of the difference in lattice energies associated with the presence and absence of dislocation substructures. The activation energies are about the same [22,25,53] and the effects of solute and fine particles are similar in both DRX and SRX. DRX is not observed in 99.99% Al, but is in ≥99.999% Al, because the mobility of the GB is so much enhanced by absence of impurities that it undergoes SRX at 20◦ C after cold working [52,54]. (T , ε Application to Al deformed to σss D ˙ ) of a low stress σ σSS causes enhanced recovery due to DRV at ε˙ ss ε˙ = σ ) [55]. However, (or setting ε˙ ε˙ leads to σSS recrystallization may ensue that would be DRX nucleated [56]. There is no by the dense substructure related to σSS steady-state grain size determined by current ε˙ and T by the prior deformation. Moreover, such transient DRX retards nucleation and completion compared to SRX due to insertion
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of substructure in the new grains and growth of matrix subgrains. Particle stimulated nucleation (PSN) has been found to initiate SRX after cold working in Al alloys in which there are hard particles larger than 1 m, because of surrounding formation of dense substructure due to strain compensating for the rigid particle. These are generally compounds with Si and transition metals that form during solidification. After hot working [57] or during it [58–60], PSN has been found only in Al–Mg alloys where the solute notably reduces the rate of DRV, preventing it from eliminating the fine cells that serve as nucleation sites [57]. PSN nucleation has been noted in as-cast 300 series austenitic stainless steels where the ␣-phase, segregated at the GB, increases the rate of strain hardening and causes nucleation (at a lower εCD than when homogeneous) in its proximity, but presumably at ␥–␥ GB [24,26]. In duplex stainless steels, ␥-phase is present as stringers, so that DRX has great difficulty nucleating until substructures are very dense and T is higher than that in 300 series [61,62]. There is no evidence that PSN–DRX is induced in the ferritic phase [61,63] either in duplex steels or in as-cast ferritic ones with austenite along GB, or as side plates. The alloy carbide particles in tool steels stimulate nucleation, thus reducing εp as do ␣-segregates in as-cast 300 series [28,29,64,65]. In Fig. 3 it is seen that for the same Z (1 s−1 , 1000 ◦ C), the D2 steel has a sharper decline and so recrystallizes much earlier than the A2 steel for almost the same peak. This is related to the enhancement of DRX by the carbide particles of which the D2 has a total volume fraction of 13.7% at 1000 ◦ C as opposed to 7.4% for A2 [28,29].
4. DRX and hot ductility DRX is extremely important in extending ductility in addition to refining grain size and lowering flow stress. Above about 0.4TM , GB sliding becomes significant and may create angular W-cracks at triple junctions, as a result of differential sliding on the arms having different orientation relative to the stress state [66–69]. The problem is relieved, to some degree, by DRV, which softens the lattice so that it can flow plastically in response to local stresses; in Al and ␣-Fe this effect provides for very high ductility (εf > 50 in torsion) [20,40,68,69]. In low SFE metals with limited DRV (Cu, Ni and ␥-Fe), there is a minimum in ductility with rising T, because GB sliding becomes significant about 0.4TM and then DRX causes a marked rise above 0.5TM [40,69]. In Mg alloys only grain and twin boundary regions develop an equiaxed substructure that leads to DRX leaving the grain cores unaltered [77–80]. The mantle of fine grains are able to deform easily and repeatedly undergo DRX, providing suitable ductility that rises with T as the mantle becomes wider to engulf the entire grains above about 350 ◦ C. In alloys where hot ductility depends on DRX, solute and particles reduce ductility much more strongly than in those where DRV is the significant factor
41
[25,26,30]. In the two phase steels described in the previous section, hot ductility is severely reduced by interphase stress concentrations and cracking [30,70–72]. Since DRX starts from the GB, it relieves the stresses from sliding of the original large grains; the new small grains tend to diffuse the sliding. The W-cracks, the voids opened near inclusions, or the pores created at GB irregularities at very high T can only extend along the GB (in the absence of net tensile stresses). The migration of the GB in DRX isolates the fissures and stops their growth, except when they capture GB. During steady-state straining in torsion there is usually a gradual accumulation of voids, they increase in size and finally link up to cause failure [40,68–70,73]. In pure Cu, Ni, ␥-Fe and C steels, DRX confers true fracture strains εf > 10 in torsion. This is equivalent to an elongation of 4000%, which far exceeds superplastic strains in fine-grained materials; the actual tensile elongations seldom exceed 120% because the strain rate sensitivity is near 0.25 [20,69,74]. For conditions where superplasticity would proceed in a material with 10 m grains, a large grained specimen would undergo DRX to grains several times that size and exhibit a flow stress similarly higher [75]. Under conditions where DRX provides 10 m grains, the grain size remains constant during steady state, whereas grains would grow substantially during superplastic deformation at suitable conditions with much lower ε˙ [74,76]. The situation where SRX comes closest to DRX in both operation and in effects is in multistage rolling. The metal is preheated sufficiently (Al ∼ 520 ◦ C, steel ∼ 1200 ◦ C), so that it can proceed through the sequence of 11–17 passes without lowering temperature beyond that for good ductility [51,81–84]. The individual passes are limited to reductions of ∼30% to maintain good shape control. Notably in the steels, there is sufficient time between the initial 5–7 passes that SRX takes place replacing the as-cast structure with refined grains. The SRX also fills the same role as DRX in improving ductility through relieving stresses or isolating small fissures, but only if individual pass strains are not so large as to induce much cracking [40,51].
5. Conclusions Discontinuous dynamic recrystallization (dDRX) makes available during straining, regions low in dislocation density, as nuclei and as zones behind the advancing GB. Dislocations are easily generated in these regions or flow into them from the older central regions of growing grains; the distributed nature of this lowers the flow stress below that from dynamic recovery alone. DRX provides grain refinement and enhances ductility by moving the sliding grain boundaries, thus relaxing stress concentrations or isolating fissures. In hot working after its initiation, DRX predominates over the constantly operating DRV. The commencement of subgrain formation and subsequent nuclei can be tracked on
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θ–σ curves. Through particle stimulated nucleation, DRX relieves the stress concentrations at the particles. DRX kinetics depends strongly on Z and the volume fraction has been found to follow an Avrami function. DRX facilitates processes such as planetary rolling, rotary piercing and extrusion of certain alloys, as well as some multistage deformation processes, due to strain accumulation over several passes. References [1] H.J. McQueen, E. Evangelista, Czech. J. Phys. B38 (1988) 359– 372. [2] H.J. McQueen, in: M. Tiryakioglu (Ed.), Advances in Metallurgy of Aluminum Alloys (J.T. Staley Symposium), ASM International, Materials Park, OH, 2001, pp. 351–360. [3] H.J. McQueen, in: T.G. Langdon, H.D. Merchant (Eds.), Hot Deformaton of Aluminum Alloys, TMS-AIME, Warrendale, PA, 1991, pp. 31–54. [4] H.J. McQueen, W. Blum, in: T.R. McNelley (Ed.), Recrystallization and Related Topics (Rex ’96), Monterey Inst. Advanced Studies, CA, USA, 1997, pp. 123–136. [5] H.J. McQueen, W. Blum, Mater. Sci. Eng. A290 (2000) 95–107. [6] H.J. McQueen, Metal. Mater. Trans. 33A (2002) 345–362. [7] H.J. McQueen, D.L. Bourell, J. Met. 39 (7) (1987) 28–35. [8] R.D. Doherty, D.A. Hughes, F.J. Humphreys, J.J. Jonas, D. Juul-Jensen, M.E. Kassner, W.E. King, T.R. McNelley, H.J. McQueen, A.D. Rollett, Mater. Sci. Eng. 238 (1998) 219–274. [9] H.J. McQueen, N.D. Ryan, R. Zaripova, K. Farkhutdinov, in: Proc. 37 Mech. Working and Steel Processing Conf. Iron Steel Soc., AIME, Warrendale, PA, 1996, pp. 883–894. [10] H.J. McQueen, in: S. Yue, E. Essadiqi (Eds.), Thermomechanical Processing of Steel (Jonas Symposium), Met. Soc. CIM, Montreal, 2000, pp. 323–333. [11] H.J. McQueen, in: J. Kazadi, et al. (Eds.), Light Metals 2000, Met. Soc. CIM, Montreal, 2000, pp. 287–296. [12] H.J. McQueen, N.D. Ryan, in: S.V. Raj (Ed.), Rate Processes in Plastic Deformation II, TMS-AIME, 2000, Mater. Sci. Eng. A322 (2002) 43–63. [13] H.J. McQueen, Mater. Sci. Eng. A101 (1987) 149–160. [14] H.J. McQueen, E. Evangelista, N.D. Ryan, in: T. Chandra (Ed.), Recrystallization (’90) in Metals and Materials, AIME, Warrendale, PA, USA, 1990, pp. 89–100. [15] T. Sakai, J.J. Jonas, Acta Metall. 32 (1984) 189–209. [16] C.M. Sellars, Phil. Trans. Royal Soc. A288 (1978) 147–158. [17] H.J. McQueen, E. Evangelista, N. Jin, M.E. Kassner, in: J.J. Jonas, T.R. Bieler, KJ. Bowman (Eds.), Advances in Hot Deformation Textures and Microstructures, TMS-AIME, Warrendale, PA, USA, 1993, pp. 251–266. [18] S.J. Hales, T.R. McNelley, H.J. McQueen, Metall. Trans. A22 (1991) 1037–1047. [19] H.J. McQueen, E. Evangelista, M.E. Kassner, Z. Metallkde 82 (1991) 336–345. [20] M.E. Kassner, M.M. Myshlyaev, H.J. McQueen, Mater. Sci. Eng. A108 (1989) 45–61. [21] H.J. McQueen, in: M. Fuentes, J. Gil Sevillano (Eds.), Recrystallization ’92, TransTech Pub., Switzerland (Mater. Sci. Forum 113–115, 1993), 1992, pp. 429–434. [22] N.D. Ryan, H.J. McQueen, High Temp. Technol. 8 (1990) 185–200. [23] H.J. McQueen, N.D. Ryan, in: N.D. Ryan, A. Brown, H.J. McQueen (Eds.), Strip Casting, Hot and Cold Working of Stainless Steels, Met. Soc. CIMM, Montreal, 1993, pp. 91–106. [24] H.J. McQueen, Y. Cui, B. Li, Q. Meng, N.D. Ryan, ibid., pp. 181–192.
[25] N.D. Ryan, H.J. McQueen, J. Mater. Proc. Technol. 21 (1990) 177– 199. [26] E. Evangelista, N.D. Ryan, H.J. McQueen, Metall. Sci. Technol. 5 (2) (1987) 50–58. [27] N.D. Ryan, H.J. McQueen, Can. Met. Q. 29 (1990) 147–162. [28] C.A.C. Imbert, H.J. McQueen, Mater. Sci. Eng. A313 (2001) 88–103, 104–116. [29] C.A.C. Imbert, H.J. McQueen, Mater. Sci. Technol. 16 (2000) 524–531, 532–538. [30] C.A.C. Imbert, H.J. McQueen, Can. Metall. Quart. 40 (2001) 235– 244. [31] L. Fritzmeier, M. Luton, H.J. McQueen, in: P. Haasen, et al. (Eds.), Strength of Metals and Alloys (ICSMA 5), vol. 1, Pergamon Press, Frankfurt, 1979, pp. 95–100. [32] H.J. McQueen, in: G. Krausz (Ed.), Deformation, Processing and Structure, ASM, Metals Park, OH, USA, 1983, pp. 231–238. [33] L. Gavard, M. Montheillet, H.J. McQueen, in: J.A. Szpunar (Ed.), Proc. ICOTOM 12, NRC Res. Pub., Ottawa, 1999, pp. 878–883. [34] N.D. Ryan, H.J. McQueen, in: Proceedings of the Fourth International Steel Rolling Conference (France), 1987, pp. F.17.1–F.17.9. [35] H.J. McQueen, in: J.A. Szpunar (Ed.), Proc. ICOTOM 12, NRC Res. Pub., Ottawa, 1999, pp. 836–841. [36] F. Montheillet, M. Cohen, J.J. Jonas, Acta Metall. 32 (1984) 2077– 2089. [37] J.K. Solberg, H.J. McQueen, N. Ryum, E. Nes, Phil. Mag. 60 (1989) 447–471, 473–485. [38] B. Bay, N. Hansen, D.A. Hughes, D. Kuhlmann-Wilsdorf, Acta Metall. Mater. 40 (1992) 205–219. [39] D.A. Hughes, N. Hansen, in: J.J. Jonas, et al. (Eds.), Advances in Hot Deformation Textures and Microstructures, TMS-AIME, Warrendale, PA, USA, 1995, pp. 427–444. [40] H.J. McQueen, J.J. Jonas, J. Appl. Metall. Working 3 (1984) 233–241, 410–420. [41] P. Karduck, G. Gottstein, H. Mecking, Acta Metall. 31 (1983) 1525– 1536. [42] G. Gottstein, U.F. Kocks, Acta Metall. 31 (1983) 175–188. [43] T. Sakai, M.G. Akben, J.J. Jonas, in: A.J. DeArdo, et al. (Eds.), Thermomechanical Processing of Microalloyed Austenite, TMS-AIME, Warrendale, PA, USA, 1982, pp. 237–252. [44] L. Blaz, T. Sakai, J.J. Jonas, Met. Sci. 17 (1983) 609–616. [45] A.H. Ucisik, I. Weiss, H.J. McQueen, J.J. Jonas, Can. Met. Q. 20 (1981) 351–358. [46] J.J. Jonas, in: T. Chandra (Ed.), Recrystallization ’90 in Metals and Materials, TMS-AIME, Warrendale, PA, USA, 1990, pp. 27–36. [47] J.J. Jonas, C.M. Sellars, in: J.A. Charles, et al. (Eds.), Future Developments of Metals and Ceramics, Inst. Materials, London, 1992, pp. 147–177. [48] J.J. Jonas, E.I. Poliak, Mater. Sci. Forum 426–432 (2003) 57–66. [49] L. Vazquez, H.J. McQueen, J.J. Jonas, Acta Met. 35 (1987) 1951– 1962. [50] P.J. Wray, Metall. Trans. 6A (1975) 1197–1205. [51] N.D. Ryan, H.J. McQueen, Mater. Sci. Technol. 7 (1991) 815–828. [52] H. Yamagata, Scripta Metall. Mater. 30 (1994) 411–416. [53] D. Ponge, M. Bredehoft, G. Gottstein, Scripta Mater. 37 (1997) 1769–1775. [54] M.E. Kassner, H.J. McQueen, J. Pollard, E. Evangelista, E. Cerri, Scripta Metall. Mater. 31 (1994) 1331–1336. [55] P.H. Thornton, R.W. Cahn, J. Inst. Met. 89 (1960–1961) 455. [56] Y. Huang, F.J. Humphreys, Acta Mater. 45 (1997) 4491–4503. [57] F.J. Humphreys, P. Kalu, Acta Metall. 35 (1987) 2815–2829. [58] H.J. McQueen, E. Evangelista, J. Bowles, G. Crawford, Met. Sci. 18 (1984) 395–402. [59] T. Sheppard, M.G. Tutcher, Met. Technol. 8 (1981) 319–327. [60] F.R. Castro-Fernandez, C.M. Sellars, Mater. Sci. Technol. 4 (1988) 621–627.
H.J. McQueen, C.A.C. Imbert / Journal of Alloys and Compounds 378 (2004) 35–43 [61] E. Evangelista, H.J. McQueen, B. Verlinden, M. Barteri, in: G. DiCaprio, et al. (Eds.), Stainless Steel ’99 Science and Market, Assoc. Ital. Metall., Milan, 1999, pp. 253–264. [62] E. Evangelista, H.J. McQueen, M. Niewczas, M. Cabibbo, Can. Met. Quart. 43 (2004) in press. [63] P. Cizek, B.P. Wynne, Mater. Sci. Eng. A230 (1997) 88–94. [64] E. Evangelista, P. Mengucci, J. Bowles, H.J. McQueen, High Temp. Mater. Proc. 12 (1993) 57–66. [65] N.D. Ryan, H.J. McQueen, C. Imbert, in: N.D. Ryan, et al. (Eds.), Strip Casting, Hot and Cold Working of Stainless Steels, Met. Soc. CIM, Montreal, 1993, pp. 165–180. [66] H. Conrad, in: J.E. Dorn (Ed.), Mechanical Behavior of Materials at High Temperature, McGraw-Hill, New York, 1961, pp. 149–217. [67] F. Garofalo, Fundamentals of Creep, Creep Rupture in Metals, Macmillan, New York, 1965. [68] M.E. Kassner, N.Q. Nguyen, G.A. Henshall, H.J. McQueen, Mater. Sci. Eng. A132 (1991) 97–105. [69] H.J. McQueen, Defects, Fracture and Fatigue, Marinus Nijhoff Pub., The Hague, 1983, pp. 459–471 (Mont. Gabriel, May 1982). [70] H.J. McQueen, J. Bowles, N.D. Ryan, Microstruct. Sci. 17 (1989) 357–373. [71] H.J. McQueen, C.A.C. Imbert, in: E.M. Taleff, et al. (Eds.), Deformation, Processing and Properties of Structural Materials (Honoring Prof. O.D. Sherby), TMS-AIME, Warrendale, PA, USA, 2000, pp. 79–92. [72] H.J. McQueen, E. Evangelista, N.D. Ryan, in: E.J. Palmiere, et al. (Eds.), Thermomechanical Processing: Mechanics, Microstructure, & Control, University of Sheffield, England, 2003, pp. 359–367.
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[73] A. Gittins, C.M. Sellars, Met. Sci. 6 (1972) 118. [74] H.J. McQueen, M.E. Kassner, in: T.T McNelley, H.C. Herkkenen (Eds.), Superplasticity in Aerospace II, TMS-AIME, Warrendale, PA, USA, 1991, pp. 189–206. [75] H.J. McQueen, B. Baudelet, in: P. Haasen, et al. (Eds.), Strength of Metals and Alloys (Proc. ICSMA 5, Aachen), vol. 1, Pergamon Press, Frankfurt, 1979, pp. 329–336. [76] H.J. McQueen, in: D.G. Sanders, D.C. Dunand (Eds.), Superplasticity and Superplastic Forming, ASM International, Metals Park, OH, 2002, pp. 154–163. [77] S.E. Ion, F.J. Humphreys, S.H. White, Acta Metall. 30 (1982) 1909– 1919. [78] F.J. Humphreys, in: N. Hansen, et al. (Eds.), Deformation of Polycrystals, RISO Natl. Lab., Denmark, 1981, pp. 305–310. [79] A. Mwembela, E.V. Konopleva, H.J. McQueen, Scripta Metall. Mater. 37 (1997) 1789–1795. [80] M.M. Myshlyaev, H.J. McQueen, A. Mwembela, E.V. Konopleva, Mater. Sci. Eng. A337 (2002) 121–133. [81] N.D. Ryan, H.J. McQueen, Mater. Forum (Australia) 14 (1990) 283– 295. [82] N.D. Ryan, H.J. McQueen, Can. Met. Quart. 30 (1991) 113– 124. [83] N.D. Ryan, H.J. McQueen, J. Mater. Proc. Technol. 36 (1993) 103– 123. [84] E. Evangelista, H.J. McQueen, N.D. Ryan, J. Bowles, in: Stainless Steels, 1991 (Chiba), Iron Steel Institute, Japan, Tokyo, 1991, pp. 842–849.
Dynamic recrystallization: plasticity enhancing structural development H.J. McQueen a,∗ , C.A.C. Imbert b a
Mechanical and Industrial Engineering, Concordia University, Montreal, Canada H3G 1M8 b The University of the West Indies, St. Augustine, Trinidad and Tobago Received 1 September 2003; accepted 20 October 2003
Abstract Dislocation mobility upsurge usually causes significant improvement in the plasticity of crystalline solids, partly through its ability to deter crack formation. Dynamic recrystallization (DRX) that proceeds during deformation reduces the flow stress and markedly raises the ductility, characterizing the hot working range. While it facilitates straining, it’s nucleation rate and equilibrium grain size are defined by the deformation temperature and strain rate. The flow stress in steady state is not directly determined by the grain size but rather by the average dislocation density, which is tied to both dynamic recovery (DRV) and DRX in so far as the migration of grain boundaries reduces the dislocation density below that attained by DRV annihilation and polygonization of substructure. Dynamic recrystallization does not, in its operation, produce any strain. It is a restoration or softening process, which facilitates straining with respect to ease and extent. In contrast to its static counterpart, its progress and effects are intimately associated with the plastic deformation in real time. © 2004 Elsevier B.V. All rights reserved. Keywords: Dynamic recrystallization; Plastic strain enhancement; Hot ductility; Flow softening
1. Introduction In processes having dislocation motion as the preponderant deformation mechanism, the interaction of the dislocations with crystal defects has a strong effect on deformation behavior. As a simple example, vacancies make possible dislocation climb at high temperature, T, but their condensation at low T can create dislocation loops, which hinder flow. Clearly raising T (or lowering strain rate, ε˙ ) through its good effects on lattice vibration and vacancies, facilitates the motion of dislocations (cross slip and climb), which in turn alters their interactions. Strain hardening combinations are outweighed by the opportunities for annihilation and array polygonization in the restorative mechanism of dynamic recovery (DRV) [1–11]. The T and ε˙ effects can be combined as the number of thermally activated events per unit strain, which can be expressed in the Zener–Hollomon parameter, Z [12]: ∗ Corresponding author. Tel.: +1-514-848-3145; fax: +1-514-848-3175. E-mail address: [email protected] (H.J. McQueen).
0925-8388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2003.10.067
1 Q = ε˙ −1 exp − = (A sinh (ασ)n )−1 Z RT
(1)
where Q is the activation energy R the gas constant (Arrhenius kinetics), σ the stress and A, α and n are materials constants. The imperfection and mechanism to be examined arise from the passage of grain boundaries (GB) through the metal which alters the progress of deformation lowering stress σ by replacing regions of high dislocation density from strain hardening reactions, with soft regions ripe for the operation of dislocation sources. This process called discontinuous dynamic recrystallization (dDRX) is dependent on nucleation; it is found primarily in low stacking fault energy (SFE) metals, such as Cu, Ni and ␥-Fe alloys above 0.5TM (melting K) due to the low level of DRV [7–10,12–17]. The other types of DRX have been previously described [11,18–20]. DRX is here examined in so far as it enables operation of the principal deformation mechanism of dislocation motion that is also affected simultaneously by DRV. However, the effects of DRX on some minor mechanisms such as GB sliding will also be considered. With emphasis on the effect on the
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deformation mechanisms, the presentation will depart from the traditional focus on initiation and grain size, which can be found elsewhere [13,17–21].
2. Influence of DRX on deformation In common hot deformation at 10−2 to 10 s−1 of specimens with grains 50–200 m, the nucleation of small strain-free regions lead to a decrease in the rate of strain hardening θ(= dσ/dε) and progress towards it balancing with the softening as seen in the peak σ p of the σ–ε curve (Figs. 1 and 2) [13–17,22–24]. Beyond the peak where it has reached about 35%, DRX proceeds rapidly, causing softening to σ ss , (εss ), where steady-state straining begins
(Fig. 3). Several discrete cycles of DRX cause a wavy flow curve (Section 3). Eq. (1) can be applied to different characteristic points such as σ p or σ ss ; for each there are separate values of A, n, Q and Z. In θ–σ plots, the downward slope that is greater for higher T (or lower ε˙ ) due to DRV, becomes less steep as subgrains form but later abruptly deflects downwards upon nucleation; θ reaches zero at the peak [13,14,22–27]. The progress of DRX in tool steels is shown from initiation at εCD (from θ–σ curves) to the effective onset of steady state at 99% DRX in Fig. 4 [28–30]. Fig. 5 shows recrystallized grains of torsion specimens of an A2 and M2 tool steels. The amount of dynamic recrystallization XDRX , as indicated along the flow curves, has been found to follow the Avrami behavior established for static recrystallization (SRX) (mechanism independent of
Fig. 1. Plots of θ–σ, for several as-cast (C) and worked (W) austenitic stainless steels, juxtaposed with σ–ε plots, showing commencement of subgrain formation, DRX initiation, peak stress and as derived through extrapolation, the saturation stress σs∗ as would be developed by DRV alone [22].
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Fig. 2. Micrographs of austenitic stainless steels in torsion: (a) homogenized 304, 23 s−1 , 1000 ◦ C, at ε = 1, showing original grains, serrated boundaries (twins) and DRX nuclei (optical 100×); (b) same as (a) but at ε = 2, with fine DRX grains (optical 100×); (c) as-cast 317, 1 s−1 , at 1000 ◦ C, DRX grains and substructure exhibited by SEM-EBS (170×); (d) same as (c) but illustrating decrease in subgrain size and more regular array at lower temperature (TEM, 4000×); and (e) same as (d) but at 1100 ◦ C, showing large subgrains (TEM, 4000×) [22,25,26].
stress); such an Avrami relationship has also been confirmed for stainless steels [14,22,25–27]. When the rate of DRX is corrected for the variation in driving force with σp2 , the activation energy is very close to that for grain boundary migration [22]. The repeated nucleation and growth maintain an average dislocation density lower than would DRV
alone, as estimated from σs∗ the stress at θ = 0, obtained from extrapolation of the second linear portion of the θ–σ curve (before nucleation) in Fig. 1 [13,14,22,25,26]. The steady-state microstructural behavior is specified by the grain size DS and subgrain size dS that are determined by Z and in turn control the flow stress:
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H.J. McQueen, C.A.C. Imbert / Journal of Alloys and Compounds 378 (2004) 35–43 −p
σs = Kg Ds
−q
σs = Ksg ds
Fig. 3. The drop in flow stress from σ p to σ SS increases as Z increases indicating that DRX more aggressively reduces dislocation density due to the higher rate. Curves with data points are tool steels [28,29]; lines without data are for austenitic stainless steels [22,25,26].
(2a) (2b)
where Kg , Ksg , p (≈0.8) and q (≈1) are material constants [14,22,25–27]. The dependence of σ s on ds is the same as that before initiation of DRX [31]. The dependence on Ds is not a Petch effect, since each related σ s –Ds are at a different T and GB are dislocation sinks rather than barriers. A smaller Ds indicates a higher rate of DRX that rapidly eliminates dislocations, thus producing a greater softening from σs∗ or from σ p (Fig. 3). The nucleation and growth of new grains are attained by the migration of high angle GB that absorb existing dislocations leaving behind a region with low dislocation density suitable for source operation. As a new grain grows, multiple sources in the initially formed part can send dislocations into the region behind the advancing GB creating a gradient (Fig. 7). This gradient sharpens quite rapidly so that the increased strain energy behind the advancing GB stops the growth, thus determining the grain size [14,21]. In the necklace mechanism of the first wave of DRX, new grains form along the initial boundaries, but stop at the characteristic size, allowing new necklaces of same-size grains to form [7,13–16]. For later necklaces and during steady state, the nucleation process then proceeds possibly by bulging of a short segment of the halted boundary into regions of notably higher strain energy [21,32,33]. While DRV is operating during all high T metal shaping processes, DRX is somewhat limited by the need to surpass the critical strain. It is found
Fig. 4. Flow curves at selected Z values of tool steels illustrating volume fraction of dynamic recrystallization as derived from the Avrami function and confirmed by microscopy [28,29].
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velop during high ε (∼4 or 5) to a very high degree so that on recrystallization, a different texture results from the preferential nucleation and growth of minor components in the plastic strain texture [5,8,38,39].
3. Dependence of DRX on deformation The DRX grain size is smaller as the Z of straining becomes higher (T lower, ε˙ higher) (Fig. 6), as a result of the lower level of DRV and smaller subgrain size that actually determines the higher σ [13–16,28,29,40]. Fig. 6b shows the relationship for austenitic stainless steels between σ SS , subgrain size dS and grain sizes DS for DRX (and from
Fig. 5. Optical micrographs of torsion specimens: (a) A2 tool steel deformed at 900 ◦ C, 4 s−1 (200×), transverse section showing recrystallized grain in surface layers strained beyond εCD ; and (b) M2 tool steel, deformed at 1000 ◦ C, 1 s−1 (500×), showing DRX grains after the first wave (volume fraction of carbides 18%) [28,29].
in high strain processes such as extrusion of austenitic steel and alloys of Cu and of Ni and in rotary piercing. In planetary mill rolling of stainless steel [25,26] with 93% reduction in one pass near 1200–1350 ◦ C, DRX considerably reduces the flow stress, provides ductility and refines the grain size [34]. In most multistage rolling schedules, its role is limited as explained below. Before inception of DRX, the texture in torsion develops similarly in Cu as it does in Al, that does not undergo DRX [33–36]. While there may be some randomization during the rapid DRX expansion in the work softening stage, the texture becomes stable during steady state, whereas for Al it undergoes a change towards a component with a lower Taylor factor [4,35,37]. It must be realized that DRX commences at relatively low critical strain, εCD , before an intense strain texture can develop with strongly differentiated components. The DRX grains nucleate from GB bulging, so have orientation similar to the old grains and deform to strengthen those orientations. Texture development with concurrent DRX and strain thus differs considerably from that in cold work, where the deformation texture can de-
Fig. 6. Dynamically recrystallized grain sizes (a) of M2, D2, A2 and W1 tool steels as a function of the deformation conditions Z and the steady-state flow stress [28,29] and (b) for austenitic stainless steels along with subgrain sizes in relationship with the steady-state flow stress [14,22,25,26].
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Fig. 7. Interaction of nucleation and growth of DRX grains with preceding and succeeding dislocation substructures: with rising ε˙ 1 , ε˙ 2 , ε˙ 3 , the matrix density rises ρM1 , ρM2 , ρM3 so the critical size decreases DN1 , DN2 , DN3 ; in growth, the boundary proceeds leftward to successive positions (very heavy solid lines) the dislocation density (curved medium solid lines) that catches up with the GB slowing it down at final sizes Ds1 , Ds2 , Ds3 [21].
metadynamic recrystallization (MRX), the latter occurring immediately after deformation by growth of dynamically formed nuclei); the ratio of sizes shows that only one subgrain in ten develops into a DRX nucleus [14,22,25–27]. For greater ε˙ (Figs. 1 and 4) the strains for initiation of DRX, for the peak and for steady state are all higher, yet when divided by ε˙ result in times that are shorter. Under the higher driving force of differential strain energy at higher ε˙ , DRX is faster. However, the grain size is not determined by impingement, but by the more rapid development of substructure behind the moving GB (Fig. 7) [13–16,21,40]. At constant T, the increasing critical strain with rising ε˙ indicates that the concurrent deformation hinders the formation of nuclei. This is the opposite of ε˙ influence on static recrystallization (SRX) to which comparisons are made in the next section [16,17]. In single crystals with no possibility of GB nucleation, a very high strain is required to initiate DRX. Nucleation occurs at a critical stress, which increases as ε˙ rises and T falls and is followed by a burst of very rapid growth with much growth twinning [13,14,41,42]. The stress drops and growth stops due to build up of substructure in the new grains. As a result of nucleation around their periphery, almost steady-state straining proceeds as in polycrystals. The operation of DRX depends very strongly on the current straining conditions in distinction from SRX where the accumulated dislocation structure is more significant. Change in T or ε˙ to increase Z cause a rapid transient to a higher stress level with a single peak before reaching the new characteristic stress and grain size [15,43]. When the initial grain size is smaller than twice the projected grain size, it requires several cycles of partial DRX with increasing grain size to reach the final one; this is accompanied by cyclic variation in the stress. When Z is decreased the transient flow curve exhibits this cyclic character related to the
increase in grain size, though several waves [43,44]. Continuous deformation during gradual decline in T delays DRX due to an initially slow rate of substructure formation and rising εCD , so that there is a long stress rise to one peak followed by a little softening before further gradual stress rise [45]. In multistage straining, as in rolling schedules, SRX during intervals between large passes at a high T produces grain refinement, but very short intervals, between small rapid passes during finishing in (high speed) continuous mills, inhibit SRX so that strain energy accumulates and may lead to DRX to give beneficial stress reduction and grain refinement [23,46–48]. If a hot working test is stopped before (but relatively close to) εCD without unloading, then during relaxation DRX may occur giving a very rapid decline in stress compared to static recovery (SRV) [49,50]. There is no evidence that the simultaneous deformation alters the atomistic mechanism of GB migration. It is dependent on thermally activated jumping of atoms from the existing grain to the new grain, because of the difference in lattice energies associated with the presence and absence of dislocation substructures. The activation energies are about the same [22,25,53] and the effects of solute and fine particles are similar in both DRX and SRX. DRX is not observed in 99.99% Al, but is in ≥99.999% Al, because the mobility of the GB is so much enhanced by absence of impurities that it undergoes SRX at 20◦ C after cold working [52,54]. (T , ε Application to Al deformed to σss D ˙ ) of a low stress σ σSS causes enhanced recovery due to DRV at ε˙ ss ε˙ = σ ) [55]. However, (or setting ε˙ ε˙ leads to σSS recrystallization may ensue that would be DRX nucleated [56]. There is no by the dense substructure related to σSS steady-state grain size determined by current ε˙ and T by the prior deformation. Moreover, such transient DRX retards nucleation and completion compared to SRX due to insertion
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of substructure in the new grains and growth of matrix subgrains. Particle stimulated nucleation (PSN) has been found to initiate SRX after cold working in Al alloys in which there are hard particles larger than 1 m, because of surrounding formation of dense substructure due to strain compensating for the rigid particle. These are generally compounds with Si and transition metals that form during solidification. After hot working [57] or during it [58–60], PSN has been found only in Al–Mg alloys where the solute notably reduces the rate of DRV, preventing it from eliminating the fine cells that serve as nucleation sites [57]. PSN nucleation has been noted in as-cast 300 series austenitic stainless steels where the ␣-phase, segregated at the GB, increases the rate of strain hardening and causes nucleation (at a lower εCD than when homogeneous) in its proximity, but presumably at ␥–␥ GB [24,26]. In duplex stainless steels, ␥-phase is present as stringers, so that DRX has great difficulty nucleating until substructures are very dense and T is higher than that in 300 series [61,62]. There is no evidence that PSN–DRX is induced in the ferritic phase [61,63] either in duplex steels or in as-cast ferritic ones with austenite along GB, or as side plates. The alloy carbide particles in tool steels stimulate nucleation, thus reducing εp as do ␣-segregates in as-cast 300 series [28,29,64,65]. In Fig. 3 it is seen that for the same Z (1 s−1 , 1000 ◦ C), the D2 steel has a sharper decline and so recrystallizes much earlier than the A2 steel for almost the same peak. This is related to the enhancement of DRX by the carbide particles of which the D2 has a total volume fraction of 13.7% at 1000 ◦ C as opposed to 7.4% for A2 [28,29].
4. DRX and hot ductility DRX is extremely important in extending ductility in addition to refining grain size and lowering flow stress. Above about 0.4TM , GB sliding becomes significant and may create angular W-cracks at triple junctions, as a result of differential sliding on the arms having different orientation relative to the stress state [66–69]. The problem is relieved, to some degree, by DRV, which softens the lattice so that it can flow plastically in response to local stresses; in Al and ␣-Fe this effect provides for very high ductility (εf > 50 in torsion) [20,40,68,69]. In low SFE metals with limited DRV (Cu, Ni and ␥-Fe), there is a minimum in ductility with rising T, because GB sliding becomes significant about 0.4TM and then DRX causes a marked rise above 0.5TM [40,69]. In Mg alloys only grain and twin boundary regions develop an equiaxed substructure that leads to DRX leaving the grain cores unaltered [77–80]. The mantle of fine grains are able to deform easily and repeatedly undergo DRX, providing suitable ductility that rises with T as the mantle becomes wider to engulf the entire grains above about 350 ◦ C. In alloys where hot ductility depends on DRX, solute and particles reduce ductility much more strongly than in those where DRV is the significant factor
41
[25,26,30]. In the two phase steels described in the previous section, hot ductility is severely reduced by interphase stress concentrations and cracking [30,70–72]. Since DRX starts from the GB, it relieves the stresses from sliding of the original large grains; the new small grains tend to diffuse the sliding. The W-cracks, the voids opened near inclusions, or the pores created at GB irregularities at very high T can only extend along the GB (in the absence of net tensile stresses). The migration of the GB in DRX isolates the fissures and stops their growth, except when they capture GB. During steady-state straining in torsion there is usually a gradual accumulation of voids, they increase in size and finally link up to cause failure [40,68–70,73]. In pure Cu, Ni, ␥-Fe and C steels, DRX confers true fracture strains εf > 10 in torsion. This is equivalent to an elongation of 4000%, which far exceeds superplastic strains in fine-grained materials; the actual tensile elongations seldom exceed 120% because the strain rate sensitivity is near 0.25 [20,69,74]. For conditions where superplasticity would proceed in a material with 10 m grains, a large grained specimen would undergo DRX to grains several times that size and exhibit a flow stress similarly higher [75]. Under conditions where DRX provides 10 m grains, the grain size remains constant during steady state, whereas grains would grow substantially during superplastic deformation at suitable conditions with much lower ε˙ [74,76]. The situation where SRX comes closest to DRX in both operation and in effects is in multistage rolling. The metal is preheated sufficiently (Al ∼ 520 ◦ C, steel ∼ 1200 ◦ C), so that it can proceed through the sequence of 11–17 passes without lowering temperature beyond that for good ductility [51,81–84]. The individual passes are limited to reductions of ∼30% to maintain good shape control. Notably in the steels, there is sufficient time between the initial 5–7 passes that SRX takes place replacing the as-cast structure with refined grains. The SRX also fills the same role as DRX in improving ductility through relieving stresses or isolating small fissures, but only if individual pass strains are not so large as to induce much cracking [40,51].
5. Conclusions Discontinuous dynamic recrystallization (dDRX) makes available during straining, regions low in dislocation density, as nuclei and as zones behind the advancing GB. Dislocations are easily generated in these regions or flow into them from the older central regions of growing grains; the distributed nature of this lowers the flow stress below that from dynamic recovery alone. DRX provides grain refinement and enhances ductility by moving the sliding grain boundaries, thus relaxing stress concentrations or isolating fissures. In hot working after its initiation, DRX predominates over the constantly operating DRV. The commencement of subgrain formation and subsequent nuclei can be tracked on
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θ–σ curves. Through particle stimulated nucleation, DRX relieves the stress concentrations at the particles. DRX kinetics depends strongly on Z and the volume fraction has been found to follow an Avrami function. DRX facilitates processes such as planetary rolling, rotary piercing and extrusion of certain alloys, as well as some multistage deformation processes, due to strain accumulation over several passes. References [1] H.J. McQueen, E. Evangelista, Czech. J. Phys. B38 (1988) 359– 372. [2] H.J. McQueen, in: M. Tiryakioglu (Ed.), Advances in Metallurgy of Aluminum Alloys (J.T. Staley Symposium), ASM International, Materials Park, OH, 2001, pp. 351–360. [3] H.J. McQueen, in: T.G. Langdon, H.D. Merchant (Eds.), Hot Deformaton of Aluminum Alloys, TMS-AIME, Warrendale, PA, 1991, pp. 31–54. [4] H.J. McQueen, W. Blum, in: T.R. McNelley (Ed.), Recrystallization and Related Topics (Rex ’96), Monterey Inst. Advanced Studies, CA, USA, 1997, pp. 123–136. [5] H.J. McQueen, W. Blum, Mater. Sci. Eng. A290 (2000) 95–107. [6] H.J. McQueen, Metal. Mater. Trans. 33A (2002) 345–362. [7] H.J. McQueen, D.L. Bourell, J. Met. 39 (7) (1987) 28–35. [8] R.D. Doherty, D.A. Hughes, F.J. Humphreys, J.J. Jonas, D. Juul-Jensen, M.E. Kassner, W.E. King, T.R. McNelley, H.J. McQueen, A.D. Rollett, Mater. Sci. Eng. 238 (1998) 219–274. [9] H.J. McQueen, N.D. Ryan, R. Zaripova, K. Farkhutdinov, in: Proc. 37 Mech. Working and Steel Processing Conf. Iron Steel Soc., AIME, Warrendale, PA, 1996, pp. 883–894. [10] H.J. McQueen, in: S. Yue, E. Essadiqi (Eds.), Thermomechanical Processing of Steel (Jonas Symposium), Met. Soc. CIM, Montreal, 2000, pp. 323–333. [11] H.J. McQueen, in: J. Kazadi, et al. (Eds.), Light Metals 2000, Met. Soc. CIM, Montreal, 2000, pp. 287–296. [12] H.J. McQueen, N.D. Ryan, in: S.V. Raj (Ed.), Rate Processes in Plastic Deformation II, TMS-AIME, 2000, Mater. Sci. Eng. A322 (2002) 43–63. [13] H.J. McQueen, Mater. Sci. Eng. A101 (1987) 149–160. [14] H.J. McQueen, E. Evangelista, N.D. Ryan, in: T. Chandra (Ed.), Recrystallization (’90) in Metals and Materials, AIME, Warrendale, PA, USA, 1990, pp. 89–100. [15] T. Sakai, J.J. Jonas, Acta Metall. 32 (1984) 189–209. [16] C.M. Sellars, Phil. Trans. Royal Soc. A288 (1978) 147–158. [17] H.J. McQueen, E. Evangelista, N. Jin, M.E. Kassner, in: J.J. Jonas, T.R. Bieler, KJ. Bowman (Eds.), Advances in Hot Deformation Textures and Microstructures, TMS-AIME, Warrendale, PA, USA, 1993, pp. 251–266. [18] S.J. Hales, T.R. McNelley, H.J. McQueen, Metall. Trans. A22 (1991) 1037–1047. [19] H.J. McQueen, E. Evangelista, M.E. Kassner, Z. Metallkde 82 (1991) 336–345. [20] M.E. Kassner, M.M. Myshlyaev, H.J. McQueen, Mater. Sci. Eng. A108 (1989) 45–61. [21] H.J. McQueen, in: M. Fuentes, J. Gil Sevillano (Eds.), Recrystallization ’92, TransTech Pub., Switzerland (Mater. Sci. Forum 113–115, 1993), 1992, pp. 429–434. [22] N.D. Ryan, H.J. McQueen, High Temp. Technol. 8 (1990) 185–200. [23] H.J. McQueen, N.D. Ryan, in: N.D. Ryan, A. Brown, H.J. McQueen (Eds.), Strip Casting, Hot and Cold Working of Stainless Steels, Met. Soc. CIMM, Montreal, 1993, pp. 91–106. [24] H.J. McQueen, Y. Cui, B. Li, Q. Meng, N.D. Ryan, ibid., pp. 181–192.
[25] N.D. Ryan, H.J. McQueen, J. Mater. Proc. Technol. 21 (1990) 177– 199. [26] E. Evangelista, N.D. Ryan, H.J. McQueen, Metall. Sci. Technol. 5 (2) (1987) 50–58. [27] N.D. Ryan, H.J. McQueen, Can. Met. Q. 29 (1990) 147–162. [28] C.A.C. Imbert, H.J. McQueen, Mater. Sci. Eng. A313 (2001) 88–103, 104–116. [29] C.A.C. Imbert, H.J. McQueen, Mater. Sci. Technol. 16 (2000) 524–531, 532–538. [30] C.A.C. Imbert, H.J. McQueen, Can. Metall. Quart. 40 (2001) 235– 244. [31] L. Fritzmeier, M. Luton, H.J. McQueen, in: P. Haasen, et al. (Eds.), Strength of Metals and Alloys (ICSMA 5), vol. 1, Pergamon Press, Frankfurt, 1979, pp. 95–100. [32] H.J. McQueen, in: G. Krausz (Ed.), Deformation, Processing and Structure, ASM, Metals Park, OH, USA, 1983, pp. 231–238. [33] L. Gavard, M. Montheillet, H.J. McQueen, in: J.A. Szpunar (Ed.), Proc. ICOTOM 12, NRC Res. Pub., Ottawa, 1999, pp. 878–883. [34] N.D. Ryan, H.J. McQueen, in: Proceedings of the Fourth International Steel Rolling Conference (France), 1987, pp. F.17.1–F.17.9. [35] H.J. McQueen, in: J.A. Szpunar (Ed.), Proc. ICOTOM 12, NRC Res. Pub., Ottawa, 1999, pp. 836–841. [36] F. Montheillet, M. Cohen, J.J. Jonas, Acta Metall. 32 (1984) 2077– 2089. [37] J.K. Solberg, H.J. McQueen, N. Ryum, E. Nes, Phil. Mag. 60 (1989) 447–471, 473–485. [38] B. Bay, N. Hansen, D.A. Hughes, D. Kuhlmann-Wilsdorf, Acta Metall. Mater. 40 (1992) 205–219. [39] D.A. Hughes, N. Hansen, in: J.J. Jonas, et al. (Eds.), Advances in Hot Deformation Textures and Microstructures, TMS-AIME, Warrendale, PA, USA, 1995, pp. 427–444. [40] H.J. McQueen, J.J. Jonas, J. Appl. Metall. Working 3 (1984) 233–241, 410–420. [41] P. Karduck, G. Gottstein, H. Mecking, Acta Metall. 31 (1983) 1525– 1536. [42] G. Gottstein, U.F. Kocks, Acta Metall. 31 (1983) 175–188. [43] T. Sakai, M.G. Akben, J.J. Jonas, in: A.J. DeArdo, et al. (Eds.), Thermomechanical Processing of Microalloyed Austenite, TMS-AIME, Warrendale, PA, USA, 1982, pp. 237–252. [44] L. Blaz, T. Sakai, J.J. Jonas, Met. Sci. 17 (1983) 609–616. [45] A.H. Ucisik, I. Weiss, H.J. McQueen, J.J. Jonas, Can. Met. Q. 20 (1981) 351–358. [46] J.J. Jonas, in: T. Chandra (Ed.), Recrystallization ’90 in Metals and Materials, TMS-AIME, Warrendale, PA, USA, 1990, pp. 27–36. [47] J.J. Jonas, C.M. Sellars, in: J.A. Charles, et al. (Eds.), Future Developments of Metals and Ceramics, Inst. Materials, London, 1992, pp. 147–177. [48] J.J. Jonas, E.I. Poliak, Mater. Sci. Forum 426–432 (2003) 57–66. [49] L. Vazquez, H.J. McQueen, J.J. Jonas, Acta Met. 35 (1987) 1951– 1962. [50] P.J. Wray, Metall. Trans. 6A (1975) 1197–1205. [51] N.D. Ryan, H.J. McQueen, Mater. Sci. Technol. 7 (1991) 815–828. [52] H. Yamagata, Scripta Metall. Mater. 30 (1994) 411–416. [53] D. Ponge, M. Bredehoft, G. Gottstein, Scripta Mater. 37 (1997) 1769–1775. [54] M.E. Kassner, H.J. McQueen, J. Pollard, E. Evangelista, E. Cerri, Scripta Metall. Mater. 31 (1994) 1331–1336. [55] P.H. Thornton, R.W. Cahn, J. Inst. Met. 89 (1960–1961) 455. [56] Y. Huang, F.J. Humphreys, Acta Mater. 45 (1997) 4491–4503. [57] F.J. Humphreys, P. Kalu, Acta Metall. 35 (1987) 2815–2829. [58] H.J. McQueen, E. Evangelista, J. Bowles, G. Crawford, Met. Sci. 18 (1984) 395–402. [59] T. Sheppard, M.G. Tutcher, Met. Technol. 8 (1981) 319–327. [60] F.R. Castro-Fernandez, C.M. Sellars, Mater. Sci. Technol. 4 (1988) 621–627.
H.J. McQueen, C.A.C. Imbert / Journal of Alloys and Compounds 378 (2004) 35–43 [61] E. Evangelista, H.J. McQueen, B. Verlinden, M. Barteri, in: G. DiCaprio, et al. (Eds.), Stainless Steel ’99 Science and Market, Assoc. Ital. Metall., Milan, 1999, pp. 253–264. [62] E. Evangelista, H.J. McQueen, M. Niewczas, M. Cabibbo, Can. Met. Quart. 43 (2004) in press. [63] P. Cizek, B.P. Wynne, Mater. Sci. Eng. A230 (1997) 88–94. [64] E. Evangelista, P. Mengucci, J. Bowles, H.J. McQueen, High Temp. Mater. Proc. 12 (1993) 57–66. [65] N.D. Ryan, H.J. McQueen, C. Imbert, in: N.D. Ryan, et al. (Eds.), Strip Casting, Hot and Cold Working of Stainless Steels, Met. Soc. CIM, Montreal, 1993, pp. 165–180. [66] H. Conrad, in: J.E. Dorn (Ed.), Mechanical Behavior of Materials at High Temperature, McGraw-Hill, New York, 1961, pp. 149–217. [67] F. Garofalo, Fundamentals of Creep, Creep Rupture in Metals, Macmillan, New York, 1965. [68] M.E. Kassner, N.Q. Nguyen, G.A. Henshall, H.J. McQueen, Mater. Sci. Eng. A132 (1991) 97–105. [69] H.J. McQueen, Defects, Fracture and Fatigue, Marinus Nijhoff Pub., The Hague, 1983, pp. 459–471 (Mont. Gabriel, May 1982). [70] H.J. McQueen, J. Bowles, N.D. Ryan, Microstruct. Sci. 17 (1989) 357–373. [71] H.J. McQueen, C.A.C. Imbert, in: E.M. Taleff, et al. (Eds.), Deformation, Processing and Properties of Structural Materials (Honoring Prof. O.D. Sherby), TMS-AIME, Warrendale, PA, USA, 2000, pp. 79–92. [72] H.J. McQueen, E. Evangelista, N.D. Ryan, in: E.J. Palmiere, et al. (Eds.), Thermomechanical Processing: Mechanics, Microstructure, & Control, University of Sheffield, England, 2003, pp. 359–367.
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[73] A. Gittins, C.M. Sellars, Met. Sci. 6 (1972) 118. [74] H.J. McQueen, M.E. Kassner, in: T.T McNelley, H.C. Herkkenen (Eds.), Superplasticity in Aerospace II, TMS-AIME, Warrendale, PA, USA, 1991, pp. 189–206. [75] H.J. McQueen, B. Baudelet, in: P. Haasen, et al. (Eds.), Strength of Metals and Alloys (Proc. ICSMA 5, Aachen), vol. 1, Pergamon Press, Frankfurt, 1979, pp. 329–336. [76] H.J. McQueen, in: D.G. Sanders, D.C. Dunand (Eds.), Superplasticity and Superplastic Forming, ASM International, Metals Park, OH, 2002, pp. 154–163. [77] S.E. Ion, F.J. Humphreys, S.H. White, Acta Metall. 30 (1982) 1909– 1919. [78] F.J. Humphreys, in: N. Hansen, et al. (Eds.), Deformation of Polycrystals, RISO Natl. Lab., Denmark, 1981, pp. 305–310. [79] A. Mwembela, E.V. Konopleva, H.J. McQueen, Scripta Metall. Mater. 37 (1997) 1789–1795. [80] M.M. Myshlyaev, H.J. McQueen, A. Mwembela, E.V. Konopleva, Mater. Sci. Eng. A337 (2002) 121–133. [81] N.D. Ryan, H.J. McQueen, Mater. Forum (Australia) 14 (1990) 283– 295. [82] N.D. Ryan, H.J. McQueen, Can. Met. Quart. 30 (1991) 113– 124. [83] N.D. Ryan, H.J. McQueen, J. Mater. Proc. Technol. 36 (1993) 103– 123. [84] E. Evangelista, H.J. McQueen, N.D. Ryan, J. Bowles, in: Stainless Steels, 1991 (Chiba), Iron Steel Institute, Japan, Tokyo, 1991, pp. 842–849.