Effect of Strain-Induced Precipitation on the Recrystallization Kinetics in a Model Alloy

Nb is often added to steels to retard recrystallization during thermomechanical processing, through effects such as solute drag and precipitate pinning.[1,2] Solute drag effect refers to the retarding force caused by the alloying elements segregating to the migrating boundaries. Precipitate pinning effect is caused by strain-induced precipitates (SIPs) forming during annealing, which pin the migrating boundaries. The spatial distribution of SIPs and their sizes are influenced by the dislocation structures.[3] Though the effect of Nb on retarding recrystallization in steels after hot deformation has been well studied in the past three decades, the available data of Nb precipitation kinetics and austenite recrystallization kinetics are rather limited. Model austenitic alloys allow cold deformation data to be garnered to establish a predictive model for recrystallization and precipitation in Nb-containing alloys. Wang and Zurob measured the precipitation kinetics in a cold-deformed Ni-30Fe alloy with 0.85 wt pct Nb, where the strain level was 0.1 to 0.36, and the annealing temperature was 700 °C (heating rate was not specified). It was found that the time for precipitation of 10 pct of the equilibrium precipitate volume fraction occurred at between 20 and 100 seconds, which decreased with increasing strain.[4]

The effect of Nb (C, N) strain-induced precipitation on the recrystallization kinetics has been reported to retard or even halt the recrystallization process. The Zener pinning equation has been widely applied to describe the recrystallization and precipitation interaction for both cold deformation and annealing and hot deformation processes.[5‐8] Different recrystallization Avrami exponents have been observed in both cold- and hot-deformed steels, although very few studies have been carried out on SIP and recrystallization interaction after cold deformation. Literature data have been summarized in Table I. It can be seen that the reported recrystallization Avrami exponents vary significantly. More importantly, the effect of SIP on recrystallization mechanism is not consistent: there have been three categories reported in Table I, i.e., recrystallization Avrami exponent did not change compared to Nb-free condition, it decreased, or the recrystallization curve shows a plateau. Zurob et al. pointed out that the shape of a recrystallization curve is determined by both recrystallization and precipitation kinetics.[3] Nevertheless, there is still a lack of any predictive approach for describing the effect of SIP on the recrystallization Avrami exponent. Little information was found on the effect of Nb addition and SIPs on recrystallization grain size distribution evolution, particularly any comparison of recrystallized grain size between Nb-free and Nb-containing steels.

To further understand the effect of Nb and SIPs on the recrystallization kinetics (Avrami exponent) and grain size distribution, precipitation kinetics and the precipitate size distributions have been determined for Fe-30Ni steels (cold deformed and annealed over a range of conditions). Fe-30Ni steel has been used as a model alloy for recrystallization and precipitation studies after hot deformation. Cizek et al. observed microband substructure in Fe-30Ni steel at 950 °C, 0.2 to 0.8 strain.[9,10] Nagarajan et al. pointed out that the SIPs nucleate and grow on the dislocations and microband structures, and coarsening occurs in seconds after deformation between 0.45 and 1 strain and holding at 850 °C to 950 °C, for Fe-30Ni steel with a Nb range of 0.1 to 0.38 wt pct. Typical SIP size is 2 to 15 nm after holding at 850 °C to 950 °C for 100 seconds.[11‐13] Black mentioned that recrystallization was halted by SIPs in Fe-30Ni-0.1 wt pct Nb steels below 1000 °C.[14] Abdollah-Zadeh claimed that the recrystallization kinetics was retarded by SIPS at 850 °C, 0.25 strain in of Fe-30Ni-0.02 wt pct Nb steel.[15] Poddar et al. observed that SIPs below 10 nm in diameter could pin the microband structure effectively after hot deformation up to strain of 1 at 925 °C for Fe-30Ni-0.1 wt pct Nb steel.[16] However, no quantitative effect of precipitation kinetics in Fe-Ni-Nb steels on the recrystallization kinetics and grain size distribution has been reported. Additionally, it has been shown that the dislocation structures produced after cold deformation are comparable with those seen after hot deformation in this material, although it is worth noting that the stored energy from room temperature deformation will not be the same as for the same strain at high temperature.[17,18] Additionally, differences in recovery can arise between cold-deformed and annealed (recovery occurring on heating to the annealing temperature) and hot-deformed (dynamic recovery prior to recrystallization) samples; however, it has been reported that recovery does not affect the recrystallization Avrami exponent, which is being considered in this paper, although it will affect the recrystallization start and finish times.[19]

The materials used in this work are laboratory cast Fe-30Ni ingots with and without a Nb addition (Table II). Other alloying elements, such as Al and N, were below the detectable levels. Thermo-Calc (TCFE9 database) has been used to calculate the dissolution temperature for precipitates under equilibrium conditions in the Fe-30Ni-0.044 wt pct Nb model alloy. The dissolution temperature for NbC in this Fe-30Ni-0.044 wt pct Nb model alloy is 1010 °C. The Nb-containing steel was homogenized at 1150 °C for 4 hours to remove any segregation from solidification. The Nb-free steel was reheated to 1300 °C for 5 minutes to provide comparable starting grain size distributions for the deformation trials. Cylindrical specimens of 10 mm in diameter and 15 mm in height were machined from the heat-treated slabs. The specimens were deformed to 0.3 strain at room temperature by uniaxial compression, using an Instron 3300 series static testing machine, lubricated by PTFE film with a strain rate of 2/min, before being reheated, at a heating rate of 30 °C/s, to 950 °C, 900 °C, or 850 °C for various times to give partial and full recrystallization (Table III), followed by quenching into water. Samples were immediately quenched after heating to the holding temperature (0 second hold time) to assess the extent of any microstructural/stored energy changes during heating. No barreling was observed for the cold-deformed samples. The deformed and heat-treated specimens were sectioned, mounted in Bakelite and ground, polished, and etched with Kalling's reagent to reveal the austenite grain structures. The recrystallization fraction was determined by point counting from optical images.

TEM thin foil examination has been performed to investigate the NbC precipitation behavior after cold deformation to 0.3 strain and the recrystallization heat treatments. TEM was performed using both JEOL 2000FX and JEOL 2100 transmission electron microscopes operated at 200 kV; STEM was carried out using a FEI Talos at 200 kV. The sample was firstly cut from the bulk specimen as a 1-mm-thick plate using a silicon carbide blade and cooling lubricant. Then, the thin plate was glued onto a Gatan disc grinder to minimize specimen bending or damage. After that, the plate was ground by silicon carbide paper to a thickness of 150 μm. Then, a Gatan disc punch was used to cut the plate into several disc specimens with a diameter of 3 mm. Electropolishing was carried out by Struers Tenupol-5 twin-jet electropolisher. For each sample, more than 250 precipitates over 3 areas were measured with local foil thickness being determined using convergent beam electron diffraction (CBED) techniques. The average sizes of the strain-induced precipitates were between 3 and 10 nm. Due to the limitation of TEM measurement, an approximate area of 7 μm² was characterized for each condition.

To account for both the effect of precipitate pinning and solute drag on recrystallization kinetics, the pinning force and reduced boundary mobility have been calculated using the data from Table VI. The pinning force is given by Zurob,where \(\gamma \) is the interfacial energy, f is the volume fraction of SIP, and r is the radius of the SIP.

Zurob mentioned that the boundary mobility is affected by the Nb content level in solution,[30] which is given as

where

In Eq. [7], \(\beta \) is the grain boundary width (taken to be 1 nm), k is the Boltzmann constant, E_b is the solute boundary binding energy (25 kJ/mol), D is the bulk diffusivity of Nb in austenite (1.4 × 10⁻⁴exp(−270,000/RT)) m²/s, and T is the temperature. These values are summarized by Dutta and Zurob.[31]

The estimated local pinning force and mobility are shown in Table VII for the samples after 0.3 strain. It can be seen that the local pinning force at 950 °C is 0.18 MPa compared to 0.12 MPa at 850 °C at the onset of recrystallization, and the pinning force increases gradually at 950 °C, 120 seconds to 0.28 MPa. The pinning force at 950 °C was insufficient to stop recrystallization completely but was high enough to retard the onset of recrystallization and slow the rate. At 900 °C, the strain-induced precipitates are also expected to be already present at the onset of recrystallization, e.g., they were observed after 120 seconds at 20 pct of recrystallization where the SIPs are already 5.9 nm in size, leading to a sluggish onset of recrystallization. The pinning force increases from 0.17 to 0.27 MPa during annealing at 900 °C. However, at 850 °C, the pinning force increased significantly with time, attributed to the slow precipitation growth rate at 850 °C up to 3000 seconds and increasing number density of SIPs (to 1200 seconds) indicating additional precipitation is occurring. The boundary mobility is affected by the Nb content, which increases with decreasing Nb solute atoms in the matrix as precipitation proceeds.

However, the mobility values calculated for annealing at 850 °C are still considerably lower than those at 900 °C and 950 °C indicating that a markedly greater slowing of the recrystallization process will occur from solute drag at the lowest temperature. The boundary mobility increases as a result of Nb depletion during precipitation, and the trade-off between solute drag and precipitation pinning leads to a change in the recrystallization kinetics and Avrami exponent. The Avrami exponents in both Nb-free and Nb-containing steels are below those expected theoretically. Previous work has identified strain inhomogeneity[32,33] and grain size distributions[19] as contributing factors to reductions in Avrami exponent. These both need to be considered for their potential effects on the Avrami exponent in the Nb-free steel. In this study, as noted above, there is no barreling and so macroscopic strain distribution can be considered uniform. The initial grain size distributions in the two steels in this study are also relatively coarse (see above) with 95 pct of the grains being above 60 to 80 μm. Although there is uniform macrostrain, microscopic strain variations could still be present due to grain size and texture differences. Both steels have been processed in a similar manner and have a recrystallized austenitic grain structure so that texture differences are minimal. In terms of stored energy differences due to grain size, this has been extensively studied for fcc materials.[34‐37] These studies indicate that the change in stored energy with increasing grain size for grain sizes of > 80 μm is small (~ 10 pct). Thus, it is reasonable to assume that the average stored energy applies across the grain size distribution in these samples after 0.3 cold strain without barreling. This is the situation for the Nb-free steel (as in Reference [19]) but to account for the effects of Nb solute drag and SIPs on recrystallization kinetics, a modified JMAK model has been proposed as follows.

The addition of Nb has been shown above to retard the onset of recrystallization, which is accompanied by the formation of strain-induced precipitates. Table VII also shows that the change in Avrami exponent (at 0.5 recrystallization fraction at 850 °C) correlates with a large increase in the pinning force exerted by these SIPs.

The growth rate is given by Zurob et al.,[38]where M is boundary mobility, \({F}_{\mathrm{rex}}\) is the macroscopic recrystallization driving force, and P is the estimated pinning force at time “t”; F_rex is assumed constant (as discussed above), while M and P for the various conditions come from Table VII. Assuming site-saturated nucleation and Nb have negligible effect on the number of recrystallization nucleation site, a proposed estimation of the effect of precipitation and solute drag on the overall recrystallization Avrami exponent is given as

The overall recrystallization Avrami exponent, n₀, for Fe-30Ni Nb-free steel, has been measured to be 1.3, which can also be predicted by the individual grain size class approach.[19] The effect of changing growth rate on Avrami exponent at 950 °C to 850 °C is shown in Figure 11. It can be seen in Table VIII that the predicted recrystallization Avrami exponents agree well with the measured data. The combined effect of solute drag and precipitation pinning caused a decrease in recrystallization Avrami exponent at 850 °C due to the slow coarsening rate, i.e., high pinning force. This approach thus could link quantitatively the precipitation kinetics and recrystallization behavior for large enough starting grain size distributions where stored energy variation are secondary.

The effect of Nb on the recrystallization Avrami exponent is dependent on the growth and coarsening rate of precipitates and the amount of solute left in solution. At a lower temperature, i.e., 850 °C, 0.3 strain, the slower precipitate formation and coarsening rate leads to a prolonged pinning effect on recrystallization, which, combined with reduced boundary mobility, leads to a lower Avrami exponent, i.e., a single Avrami exponent does not cover the entire recrystallization fraction. When full precipitation and coarsening occurs during recrystallization, the pinning forces (Zener and solute drag) decrease as does the recrystallization rate, but the Avrami exponent is not affected.