Effect of annealing process on the abnormal grain growth behavior during carburizing of 20CrMnTi steel

Abnormal grain growth (AGG) as an important physical metallurgical behavior is to be avoided during carburizing due to its adverse effect on properties such as fatigue, impact toughness and the quenching distortion. In this work, two types of annealing process which produce different morphology of precipitated particles were conducted to investigate its effect on the subsequent austenite grain growth behavior during carburizing of 20CrMnTi steel. Calculation from Humphreys’ model exhibited a good agreement with experimental observations, which indicates the large sized particle from high temperature annealing led to the locally insufficient pinning force for the blockage of grain boundary migration and is therefore responsible for the AGG. The isothermal precipitation kinetics for TiC particles is able to be described by the diffusional growth and LSW coarsening models with reasonable accuracy provided with the transition time from growth to coarsening stage. Design of microalloying and pre-treatment processing to suppress AGG can be assisted with the combinatory application of Humphrey’s model and precipitation kinetics model.


Introduction
Abnormal grain growth (AGG) leads to coarse grains which pose adverse effects on properties of manufactured parts such as fatigue, impact toughness and at the same time, increase the quenching distortion. Besides, currently in-use technological measures aimed at the inhibition of AGG give rise to the manufacturing cycle and costs. For example, normalizing or annealing subsequent to cold working is often required to prevent AGG during carburizing. High temperature carburizing, where the processing time can be shortened, is avoided because of the high grain coarsening tendency induced by AGG.
Considering its technological importance, AGG behavior and the counter measures in alloy chemistry and processing design have been investigated in large amount. The theoretical basis for most of the studies is the Gladman equation [1], i.e.: where r crit is the critical radius of precipitate particle,R is the average radius of matrix grain, f is the volume fraction the precipitates, and X is the size ratio defined as the radius of growing grain divided byR. Using Gladman equation, Kubota and Ochi [2] developed anti-coarsening steels for carburizing with different levels of Al and Nb addition. The optimal alloy design is correlated with manufacturing process in such a way that small initial grain size, large degree of grain size mix and small pinning effect by second phase particles should be avoided. Tanaka et al [3] investigated the grain coarsening behavior of SCM420, 'SCM420+Nb' and 'SCM420+Ti' steel. Smaller particle size and larger volume fraction of TiC in 'SCM420+Ti' steel facilitated the maintained fine grain size even at the simulated carburizing temperature of 1050°C. Imanami et al [4] redesigned SCM420 steel which allows the removal of annealing prior to cold forging and normalizing before carburizing. The easy grain coarsening of cold forged parts during carburizing was suppressed by sufficient Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. amount of refined NbC precipitates. Kubota et al [5] investigated the effect of spheroidizing annealing prior to cold forging on AGG and found the coarsening of precipitated particles during annealing was the reason for AGG. In a similar study by Tominaga et al [6], the austenite grain refinement at the initial stage of carburizing was held to be responsible for AGG.
Despite the wide application, attentions should be paid to two aspects when using Gladman equation and other similar model for alloy or processing design. Firstly, the employed parameters in Gladman equation are time-dependent. Using parameters which characterize the precipitates and matrix prior to or at the initial stage of carburizing cannot accurately predict the subsequent possible AGG. For example, Okamoto et al [7] presented a classical example for the application of 'critical grain size' model regarding to specific morphology of secondary particle in terms of volume fraction and size. On the carburized surface, the distribution of TiC can be assumed to be unchanged and therefore, the model prediction agreed well with the measured grain size. On the other hand, the unstable smaller TiC precipitates dissolved into the matrix at the sample interior part, leading to the decreasing number density of TiC precipitates and ultimately the AGG. Secondly, AGG is essentially induced by the imbalance between driving force for grain growth and pinning force from precipitates. The usage of parameters, such as the average radius of precipitate particles and average diameter of matrix grains, cannot predict a local AGG behavior. For instance, Murakami et al [8] pre-formed 3 different size distributions of Nb(CN) particles and supplied for quasi-carburization. The one with the average particle size smaller than the critical particle size calculated by Gladman equation, however, also led to the AGG. It was concluded that the fast decrease in number density of Nb(CN) particle brought about the locally insufficient pinning force. Recently, Imanami et al [9] revealed that spheroidized cementite particles which exhibit different dissolution kinetics owing to the varied Cr content and particle size result in the local and non-uniform decrease in pinning force and thus the AGG.
In this work, two types of precipitation morphology as represented by volume fraction and size were obtained in 20CrMnTi steel by isothermal annealing at 650°C alone or further annealing at 1025°C. Subsequent quasi-carburizing experiments were carried out to investigate the austenite grain growth behavior. The Humphreys' model for AGG and the diffusional growth and LSW coarsening models for precipitated TiC particles were used to interpret the experimental results.

Materials and experiments
A commercial steel i.e. 20CrMnTi supplied in Φ38mm hot-rolled bar was employed in the present work. The chemical composition is shown in table 1. Considering free N is fixed by Ti due to the formation of TiN, the remaining Ti content of 0.05 wt% was employed for thermodynamic calculation by using ThermoCalc with Tcfe9 database. With the major elements including the C, Mn, Cr and Ti, the variation of equilibrium weight fraction of phases with respect to temperature was calculated and presented in figure 1.
Samples with a dimension of Φ38 mm×12 mm was sliced from hot-rolled bar and heat treated following experimental procedure illustrated in figure 2. In order to dissolve the pre-existing TiC precipitates, the steel was first homogenized at 1200°C for 2 h and water quenched. Then, two types of annealing treatment were carried out, i.e. holding at 650°C for 1 or 3 h and holding at 1025°C for 3 or 5 h subsequent to 1 h-holding at 650°C. Correspondingly, they are designated as ①, ②, ③ and ④ sample, respectively. Finally, quasi-carburizing was conducted at 930°C for 8 h. Heating rate for every stage of treatment was 2°C-5°C s −1 .

Microstructure characterization
Samples for optical metallography (LEICA-DMIRM) were prepared by conventional method, including grinding, polishing. Observation of prior austenite grain boundaries was made by etching with saturated aqueous solution of picric acid containing a wetting agent i.e. sodium dodecyl benzene sulfonate. And at least 1000 grains were counted for each sample to determine the distribution of prior austenite grain size. For TEM (TECNAI G2 20 F) analysis, 400 μm thick slices were cut from the samples followed by mechanical grinding to 50 μm. Next, twin-jet electrolytic thinning was carried out in a mixture of 9% perchloric acid and 91% absolute ethyl alcohol at 248 K and potential of 25 V. More than 150 precipitated particles per sample were collected for sample ① and ② to determine the size distribution, while the threshold decreased to 50 for sample ③ and ④ due to the substantial low particle density. Measurements for prior austenite size and precipitated particles were both done by using Image-Pro Plus software.

Modeling calculation
Modeling efforts were made to interpret the results obtained from experimental studies. The Humphrey's model for AGG and the growth and coarsening model for TiC particles employed in this work are described as follows.
(1) Humphrey's model for AGG [10] Considering the pinning pressure P z =3fγ/d exerted by a volume fraction ( f ) of particles with diameter (d), the growth rate of the grain assemblydR dt and a particular grain dR/dt is determined as whereḡ andM, γ and M are the boundary energy and mobility for grain assembly and a particular grain, respectively. Then, the condition for AGG of a particular grain is given as where j is the dimensionless pinning parameter which equalsfR d 3 .
Using the size ratio X i.e.R R and other two normalized parameters¯ḡ g = = Q M M G , ,the instability condition becomes Then the bounds for normal/abnormal grain growth are defined by two roots Equation (6) can be simplified by considering an ideal grain assembly where all boundary energies and mobilities are equal i.e.¯ḡ g .Then, the effect of precipitated particles on austenite grain growth behavior can be formulated as follows.
• For j<0.25, the two roots from equation (6) corresponds to the minimum size ratio for the initiation of AGG and the maximum size ratio to which the grains may eventually grow, respectively.
• For 0.25<j<1, becausedR dt is always zero, AGG will always occur provided that dR/dt is positive.
• For j>1, the growth of even the largest abnormally growing grain becomes impossible as indicated by equation (3).
(1) Diffusional growth and LSW coarsening model for TiC particles According to diffusional growth theory, the evolution of average diameter d of TiC particles with time t follows the parabolic law [11,12], i.e. where X Ti 0 is the mole fraction of pre-dissolved Ti at solution temperature; X Ti eq is the equilibrium mole fraction of Ti in matrix that can be calculated from solubility product; X Ti TiC is mole fraction of Ti in TiC particle which equals 0.5.
For the coarsening of TiC particles, based on LSW (Lifshitz-Slyozov-Wagner) theory [13], the average size d t after isothermal holding time t is where d 0 is the original average size of TiC particle; V TiC and V m is the molar volume of TiC and matrix, respectively; σ is the interface energy of TiC with matrix. For simplicity, V m can be substituted by the molar volume of BCC Fe. R and T have their usual meaning. It should be mentioned that since the molar volume varies negligibly with temperature, the known molar volume of TiC at 1100°C are employed in the present calculation as a first approximation. Physical parameters involved in calculation were listed in table 2.

Results and discussion
Microstructure of prior austenite grains after quasi-carburizing and the corresponding distribution of grain size is shown in figures 3 and 4, respectively. It is suggested that the distribution similar to lognormal type is seen from both sample ① and ②. While, some extremely large prior austenite grains with size 75 μm can be found in sample ③ and ④ which are delineated by red lines in figures 3(c), (d), and their number fraction is over 10%, Table 2. Physical parameters [14] involved in calculation of growth and coarsening kinetics. indicating an apparent AGG behavior. The resultant size ratio is calculated to be 2.8, 3, 14.9 and 12.7 for sample ①, ②, ③ and ④, respectively. In order to find the cause for AGG behavior in sample ③ and ④, TEM analysis was conducted to reveal the morphology of precipitated particles after annealing. In samples ① and ② (see figure 5), both small sized (<15 nm) and large sized particles (>30 nm) are observed. Figures 5(c) and (d) shows the bright-field and darkfiled image of the large sized particles in sample ②, respectively. Corresponding selected area diffraction pattern in inset of figure 5(d) indicates that the large sized particles are cementite. The M 7 C 3 carbide, which was calculated to be the equilibrium constituent phase at 650°C in figure 1, is not present. Figure 6 shows the TEM micrographs for sample ③ and ④. As identified by EDS, the precipitated particles in figure 6(b) are TiC i.e. the only second phase at 1025°C according to figure 1.   Figure 7 shows the statistics on the size of precipitated particles, where the particle with size larger than 30 nm was excluded in sample ① and ②. Lognormal distribution for sample ① and ② can also be seen. However, due to the limited number of particles as revealed by TEM, no characteristics can be found in the size distribution of sample ③ and ④. The average size of precipitated particles for sample ①, ②, ③ and ④ is 6.1, 8.6, 45.7 and 60.2 nm, respectively.

Parameters Expression or value
Considering the successful application of Humphreys' model in describing the AGG behavior in aluminum alloys [15][16][17][18][19], it was also used in this work to quantify the effect of annealing, in other words, precipitated particles on austenite grain growth behavior at the beginning of quasi-carburizing. In addition to the above known parameters, the size ratio at the time when AGG takes place is to be determined. As a first approximation, by excluding the abnormally grown ones, the austenite grain assembly in figure 3 was employed to calculate the size ratio, which is 2.8, 3, 2.86 and 2.9 for sample ①, ②, ③ and ④ respectively. Figure 8 presents the calculation results in the classical size ratio versus pinning parameter diagram. Sample ① and ② locate in the 'no grain growth region', while sample ③ and ④ enter into the 'AGG region'. A fairly good agreement has been obtained between the calculation by Humphreys' model and experimental observations.
As suggested in figure 8, pinning parameter is more critical in determining the austenite grain growth behavior. If one can accurately predict the evolution of diameter and volume fraction of precipitated particles, and therefore the pinning parameter, the design of microalloying and pre-treatment processing to suppress the AGG can be assisted. Therefore, efforts have been made to fit the measured size of TiC particles with the simple and straightforward mean-field diffusional growth and LSW coarsening models.
In figures 5(a), (b), it can be noticed that the number density of precipitated TiC particles decreased when annealing time at 650°C extended from 1 h to 3 h. Therefore, besides the physical parameters listed in table 2, the transition time from growth to coarsening i.e. t tr , which was defined as the time when the mean diameter and the critical nucleus diameter become equal [20], is also required and set as the only fitting parameter in this work. In figure 9, as presented by the red curve, a reasonable good agreement between the model calculation and experimental results was achieved when t tr =0.5 h. In comparison, the black curve suggests an overestimation when continuous growth of precipitated TiC particles is assumed i.e. t tr >3 h. Further studies are required to incorporate the nucleation model and then facilitate the calculation of t tr .
Following the 1 h annealing at 650°C, annealing at 1025°C would result in an overall dissolution of precipitated TiC particles due to the increased solubility of Ti and C. However, complex evolution of average size of precipitated particles during dissolution has been observed by researchers. Lee et al [21] studied the dissolution behavior of NbC during simulated slab reheating process and found the particle coarsening phenomenon at relatively low heating rate of 0.0013°C/s. Similar to present annealing treatment, Jones and Ralph [22] investigated the dissolution of NbC in an austenitic stainless steel by annealing at 1100°C-1300°C subsequent to isothermal precipitation of NbC at 930°C. Incomplete solution treatment annealing i.e. at temperatures below solvus resulted in an initial sharp increase of average size of precipitated NbC particles from <10 nm to 70-100 nm. More recently, Gong et al [23] also confirmed the initial coarsening phenomenon during dissolution in Nb steel and even revealed a continuous coarsening behavior in Nb-Ti steel as a result of stabilizing effect from Ti. Apparently, the simple growth and coarsening models would not be able to capture  this complex size evolution of precipitated particles. Besides, the two-step annealing in this work was only designed for the investigation of AGG and is not a common practice in carburizing heat treatment, the prediction of size evolution of precipitated TiC particles therein will be left for further investigation.

Conclusions
(1) Annealing at 650°C created finely dispersed TiC which effectively pinned the migration of austenite grain boundary, while the sparse and large sized TiC for further annealing at 1025°C led to the abnormal austenite grain growth.
(2) Humphreys' model which describes the austenite grain growth behavior agrees well with the experimental observations, i.e. annealing at 650°C and further at 1025°C respectively corresponds to the no growth region and AGG region.  (3) Provided with the transition time from growth to coarsening stage, the evolution of average size of precipitated TiC particles during annealing at 650°C can be described by the diffusional growth and LSW coarsening models with reasonable accuracy.