Q&P Response of a Medium Carbon Low Alloy Steel

Abstract

An Fe-0.44%C-1.8%Si-1.3%Mn-0.82%Cr-0.28%Mo steel was subjected to quenching followed by low-temperature tempering (Q&T) and quenching and partitioning (Q&P) processing after full austenitization. The Q&P treatment led to an increase in the volume fraction of retained austenite (RA) by factors ranging from 30 to 40 depending on the quenching temperature, T_q, and an additional precipitation of transition η-carbides in the martensitic matrix. The Q&P processing provided a decrease in the yield stress (YS) from 1730 to 1350 MPa and an increase in the ductility by a factor of 3; the product of strength and elongation (PSE) increased from 13.7 to 32 GPa·%. The novelty of the work lies in establishing the origin of the good ductility and high YS of Q&P steel. Blocky-type RA plays a vital role in the effect of Q&P processing on mechanical properties. The main feature of RA is a very high dislocation density proving the strength of ~1000 MPa of this structural component. The strength of RA controls the YS of the steel if its volume fraction is ≥25%. Ductility is provided by the almost full transformation of RA into strain-induced martensite under tension. The localization of plastic deformation in the form of deformation bands is associated with the γ→α′ transformation. Medium carbon Q&P steel with a high volume fraction of RA meets the requirements for advanced high-strength steel (AHSS) belonging to the third generation of AHSS due to the combination of the YS > 1050 MPa with the PSE > 30 GPa·%.

1. Introduction

The strength and ductility are the key properties of advanced high-strength steels (AHSS) [1]. Materials may be strong or ductile, but the combination of high strength with good ductility is rare. A widely adopted criterion describing the combination of strength and ductility having opposing characteristics is the product of strength and elongation (PSE), σ_B·δ (MPa·%) [2,3,4,5,6,7]. The first generation of AHSS exhibits elongation-to-failure ≥30% and σ_B·δ ~1.5 ÷ 2 × 10⁴ (MPa·%), corresponding to relatively lower ultimate tensile strength (UTS) and yield stress (YS). High-Mn steels belonging to the second generation of AHSS [1,7] exhibit σ_B·δ ≥ 3 × 10⁴ (MPa·%) due to δ ≥ 30% and UTS ≥ 1100 MPa, while the YS of these materials ranges from 230 to 350 MPa that is even smaller than YS of low-alloy steels belonging to the first generation of AHSS [1,7,8]. The main requirement for the third generation of AHSS is the combination of YS ≥ 1000 MPa with the PSE ranging from 2 × 10⁴ to 4 × 10⁴ MPa·% [1]. This attractive relationship between YS, UTS, and ductility, achieved through the development of Q&P (quenching and partitioning) processing, is the result of the complex behavior of the different constituent phases present in these steels [1,2,3,4,5,6,9,10,11].

The microstructural design of Q&P steels consists of the combination of carbon-depleted martensite with carbon-enriched retained austenite (RA) [1,9,10,12]. Q&P processing is a complex heat treatment consisting of at least four steps [1,9,10,12,13,14]. The first step involves full austenitization followed by rapid cooling in a salt bath to a quenching temperature, T_q, lying between the martensite-start (M_s) and martensite- finish (M_f) temperatures (Figure 1) [1,2,3,4,5,6,9,10,12,13,14]. The second step is quenching in a heated salt bath, which produces primary martensite and a considerable amount of RA. The carbon partitioning from martensite to austenite to enrich RA with carbon occurs during isothermal annealing at a temperature, T_p, that is usually above the T_q and M_s temperatures. This third step of Q&P processing is termed as “partitioning” [1,9,10,11]. The final fourth step is air cooling or water quenching from T_p to ambient temperature that leads to the partial transformation of RA into secondary martensite distinguished by morphology, higher dislocation density, and carbon content from primary martensite [12]. In addition, transition carbides are rarely observed in secondary martensite compared to primary martensite [12]. Typically, the temperature of partitioning, T_p, is higher than M_s, but there are Q&P routes in which T_p lies below M_s or even M_s = T_p [1,2,3,4,10,14].

The combination of high YS > 1000 MPa and PSE ≤ 2 × 10⁴ MPa·% can normally be achieved in low alloy Q&P steels with a carbon content ranging from 0.2 to 0.3% [1,9,15]. In contrast, a PSE ≥ 3 × 10⁴ MPa·% and YS > 1000 MPa were reported for Q&P steels with a carbon content ranging from 0.4 to 0.56% [2,3,4,5,6]. These mechanical properties are associated with a volume fraction of RA ranging from 12 to 30% and a carbon content of ~1.3 wt.% in RA [5]. A major portion of RA belongs to the blocky-type [2,3,4,5,6]. A relatively high elongation is attributed to the transformation-induced plasticity (TRIP) effect associated with the almost complete transformation of RA into → strain-induced martensite under tension [2,9,10]. These data support the work of Xiong et al. [16], which reported on the easy transformation of blocky RA into martensite at low strains. Recently, X.X. Dong et al. [6] showed that blocky RA with a high volume fraction of 26 wt.% and a carbon content of 1.14 wt.% is responsible for the high PSE value in a Q&P steel with 0.5 wt.% C. These data for Q&P steels are in contrast with the effect of carbon content and the morphology of RA on the mechanical properties of TRIP steels with a bainitic matrix [17,18]. In Q&P steels with a carbon content of ~0.2 wt.%, the volume fraction of RA is ≤10% [6,19,20]. Film-like RA is dominant and the blocky type of RA is rarely observed in these steels [6,20,21]. The volume fraction of RA decreases under tension insignificantly [6], confirming the high stability of film-like RA under plastic deformation [21]. These Q&P steels are characterized by a PSE value ranging from 2 × 10⁴ to 2.72 × 10⁴ MPa·% and a YS ranging from 1050 to 1238 MPa [6,20,21] and, therefore, Q&P steels with a low carbon content may meet the requirements for AHSS belonging to the third generation [1]. It is worth noting that the carbon content in RA is nearly the same as in low carbon and medium carbon Q&P steels [2,3,4,5,6,20,21].

Thus, there exist two different types of low alloy Q&P steels exhibiting a PSE ≥ 2 × 10⁴ MPa·% and a YS > 1000 MPa. The first type is medium carbon steels with a dominance of blocky RA. The second type is low carbon steels with a dominance of film-like RA. It is apparent that the mechanisms responsible for the mechanical behavior of these two types of Q&P steels are different. The origin and nature of the tensile behavior of Q&P steels with a multiphase structure is a difficult task as it requires information on the strength and plasticity of the constituent phases and the mechanism of the interaction between the constituents under tension [12]. At present, the mechanical behavior of Q&P steels with medium carbon levels is clearer than that of low carbon Q&P steels. Obviously, the ductility of medium carbon Q&P steels is attributed to the TRIP effect. However, there is no unambiguous interpretation of the origin and nature of high YS of advanced high-strength steels. The multi-phase mixture rule is commonly used to describe the YS of Q&P steels with a martensitic matrix and RA [1,11,12,22,23]:

$$\mathrm{YS}={\displaystyle \sum _{i=1}^N({\sigma }_{0.2}^i}\cdot f^i)$$

(1)

where ${\sigma }_{0.2}^i$ and fⁱ are the YS and volume fraction of primary martensite, secondary martensite, and RA, respectively. However, RA was considered as a soft phase with a low dislocation density [12,22], and the dislocation strengthening of RA was discarded [23], despite the very high dislocation density observed experimentally in this phase [21]. Thus, the question of the significance of retained austenite in achieving high YS remains open.

The aim of the present study is to report on the mechanical behavior of a 0.44% C steel processed with Q&P treatment compared to quenched and tempered (Q&T) steel. The second aim is to consider the origin of the good ductility and high YS of this material. Specific attention is paid to the examination of the role of RA in tension behavior.

2. Materials and Methods

An Fe-0.44%C-1.81%Si-1.33%Mn-0.82%Cr-0.28%Mo (in mass pct.) steel was produced by means of air induction melting followed by electro-slag remelting. Next, the steel was subjected to solution treatment at 1150 °C for 4 h followed by forging at temperatures from 1150 to 950 °C into a billet with dimensions of 60 × 150 × 450 mm³ with subsequent air cooling. Samples with 3 mm thickness were machined from the billet and subjected to austenitization at 900 °C for 5 min followed by quenching in a salt bath heated to different temperatures, T_q, ranging from 140 to 300 °C for 15 s and subsequent partitioning at a temperature, T_p, of 400 °C for 60 s in a salt bath (Q&P processing). In addition, the samples after austenitization were water quenched and tempered at 200 and 280 °C for 1 h (Q&T treatment). The Q&T and Q&P processes are shown in Figure 1.

Hardness was measured using an Wolpert Wilson 600 MRD (Illinois ToolWorks Inc., Norwood, MA, USA) tester in accordance with the ASTM E18 standard at room temperature. The flat specimens with a gauge length of 35 mm and a cross-section of 7 × 3 mm² were cut from the Q&T and Q&P samples and then tensioned using an Instron 5882 testing machine (Illinois ToolWorks Inc., Norwood, MA, USA) at room temperature and an initial loading rate of 1 mm/min in accordance with the ASTM E08M-04 standard. The Portevin–Le Chatelier (PLC) bands were observed using the digital image correlation (DIC) method described in [24] on Q&P samples only. This method made it possible to record the change in the distribution of local strain fields on the surface of the sample during testing by correlating successive images of the speckle pattern. The calculations were performed using the Vic-2D correlation program (Correlated Solutions, Inc., Irmo, SC, USA). Local strain rate values were determined by numerically differentiating strain data with respect to time.

Structural characterization was carried out using a Quanta 600 FEG scanning electron microscope (SEM) (FEI Corporation, Hillsboro, OR, USA) equipped with an electron backscatter diffraction (EBSD) pattern analyzer incorporating an orientation imaging microscopy (OIM) system and a JEOL JEM-2100 (JEOL Ltd., Tokyo, Japan) transmission electron microscope (TEM). The study of the structure was carried out in the central part (depth) of the sample. Foils for TEM studies were prepared by means of double-jet electro-polishing using a solution of 10% perchloric acid in glacial acetic acid under a voltage of 21.0 V at an ambient temperature. Surfaces of the specimens for SEM observation were mechanically polished and then electropolished using the same electrolyte. These specimens were examined using the EBSD technique. The OIM images were subjected to a clean-up procedure, setting the minimal confidence index to 0.1. The low- (LAB) and high-angle (HAB) boundaries were defined with misorientations of 2° ≤ θ < 15° and ≥15°, respectively, and depicted in the OIM images using white and black lines, respectively. The density of lattice dislocation on TEM micrographs, ρ_TEM, was estimated by counting individual dislocations within martensite and RA per unit area [25]. In addition, densities of lattice dislocations were calculated from misorientation maps obtained by means of the EBSD technique using Kernel misorientation [26]:

$${\rho }_{\mathrm{KAM}=\frac{8{\theta }_{\mathrm{KAM}}}{3\sqrt{3}b·h}}$$

(2)

where b is the Burgers vector, and the distance h corresponds to the step size of the scanning. The ${\rho }_{\mathrm{K}\mathrm{A}\mathrm{M}}$ value characterizes the elastic bending of the crystal lattice and, therefore, the internal elastic stress-field originated from lattice dislocations since it is assumed that all dislocations have the same Burgers vector. The data processing and application of parent austenite grains reconstruction algorithms were performed in the open-source crystallographic toolbox MTEX 5.8 with the software suite ORTools [27]. A threshold of 3° was used to separate the grains. A graph clustering method was applied to reconstruct prior austenite grains (PAG) on misorientation maps [27,28]. The different packets (variant selection) were determined as the closest {111} plane in austenite to a {011} plane in martensite [27,28] using the technique of parent grain reconstruction described by Niessen et al. [27].

The volume fraction of RA was determined by means of magnetic saturation measurements using a Fischer Feritscope FMP30 (Helmut Fischer Gmbh, Sindelfingen, Germany) and X-ray analysis using a Rigaku Ultima IV diffractometer (Rigaku Co., Tokyo, Japan) with a step size of 0.02 deg, 40 kV and 40 mA and a 2θ Bragg angle range from 30 to 135°. X’pert High Score Plus software was used to calculate the volume fraction of RA according to the peaks intensities for an fcc lattice: (200)_γ, (220)_γ, (311)_γ and bcc lattice: (200)_α′, (211)_α′, (220)_α′ [29]. The volume fraction of RA, V_γ, was calculated from the integrated intensity of the austenite and martensite peaks in the manner explained in work [30] in detail. The austenite lattice parameter a_γ was obtained by means of the Nelson–Riley extrapolation method [29]. The average concentration of carbon in RA was calculated using the well-known equation proposed by Dyson and Holmes [30,31]:

$${\alpha }_{\mathsf{\gamma }}(\stackrel{•}{\mathrm{A}})=3.578+0.33{\mathrm{C}}_{\mathrm{RA}}+0.00095{\mathrm{Mn}}_{\mathrm{RA}}+0.0031{\mathrm{Mo}}_{\mathrm{RA}}$$

(3)

where C_RA, Mn_RA, and Mo_RA are the concentration of carbon, manganese, and molybdenum in RA in wt.%, respectively. The C_RA value was calculated from the lattice parameter obtained experimentally, while Mn_RA and Mo_RA values were taken as the Mn and Mo content in the steel, taking into account the fact that no partitioning of substitutional atoms occurs during the Q&P process [12].

The A_c3 and A_c1 critical temperatures were calculated by means of the Thermo-Calc software (Ver. 5, Thermo-Calc Software, Stockholm, Sweden) using the TCFE7 database. The dilatometry curve obtained during cooling from 900 °C to room temperature at a cooling rate of 100 °C/s using a DIL 805 dilatometer (TA Instruments Inc., New Castle, DE, USA) was used to determine the M_S and M_F temperatures on cylindrical samples with a 10 mm length and a 3 mm diameter.

3. Results

3.1. Critical Temperatures and Q&T/Q&P Route

Before the development of the Q&P route, the A_c1, A_c3, M_S, and M_F critical points were defined, and these are summarized in

Table 1. Critical points of the Fe-0.44C steel.

Method	Ac1, °C	Ac3, °C	MS, °C	MF, °C
Thermo-Calc	729	798	–	–
Dilatometry curve	760	857	270	51

. It is seen that the A_c1 and A_c3 temperatures determined by the dilatometry curve (Figure 2a) are 31 and 59 K higher than those calculated by means of Thermo-Calc software. According to the results of dilatometry analysis, it was revealed that the temperature A_c1 for the studied steel is about 760 °C and the A_c3 temperature is 857 °C. Therefore, the optimal austenitization temperature to obtain fully austenitic structure and to hinder the growth of prior austenite grains for new Fe-0.44C steel is T = 900 °C. Figure 2b shows the dilatometry curve obtained during cooling from 900 °C to room temperature. The martensite-start (M_S) and martensite-finish (M_F) temperatures were determined as 270 and 51 °C, respectively, with a high accuracy. Therefore, water quenching provides a low fraction of RA, and quenching in a salt bath with a temperature ranging from ~100 to 250 °C leads to the formation of a multiphase structure consisting of primary martensite and RA. At T > 270 °C, no martensitic transformation may occur under isothermal conditions.

Four quenching temperatures, T_q, of 140, 160, 200, and 250 °C, were chosen for Q&P processing, lying between the M_S and M_F temperatures, in order to produce structures with different volume fractions of RA. Quenching at a T_q of 300 °C was also carried out for comparison. A partitioning temperature of 400 °C above M_S was used. Therefore, the multiphase structure that evolved after Q&P processing may consist of primary martensite, RA, and secondary martensite. Q&T treatment with tempering temperatures of 200 and 280 °C was also performed to compare structures and constitutive phases that evolved after Q&P and Q&T processing.

3.2. Microstructure

3.2.1. Q&T

The typical microstructure after water quenching is presented in Figure 3a–c. Relatively coarse PAGs with an average size of ~28 μm could be distinguished (Figure 3a,b). At the same time, the average distance between HABs of 1.3 μm is small. This is attributed to the fact that packets which are aggregations of the blocks with the same {111}_γ plane [31] and strongly distinguished by dimension and shape [32] evolve within a PAG (Figure 3c). First-order packets (indicated as B and C in Figure 3c) with dimensions ≥ 10 μm and an irregular shape contain a number of blocks (>3) and are located at the boundaries of PAGs. Second-order packets with an elongated shape and an average longitudinal dimension of ~10 μm and an average transverse direction of ~3 μm (D in Figure 3c) are located on the boundaries of first-order packets or PAGs. Third-order packets consisting of one block usually appear within the matrix of first-order packets (Figure 3b,c). The other distinct feature of the lath martensite structure evolving in the present steel is a high dislocation density of ${\rho }_{\mathrm{K}\mathrm{A}\mathrm{M}}=$ 5.4 × 10¹⁴ m⁻². The volume fraction of RA is negligible (~0.7).

Tempering results in insignificant changes in the microstructure (not shown here). The average distance between HABs decreases down to 0.9 and 0.7 μm after tempering at temperatures of 200 and 280 °C, respectively. Precipitation of η-Fe₂C transition carbides with a plate-like shape within laths takes place. These carbides have a longitudinal dimension of ~40 nm and a transverse dimension of ~14 μm after tempering at 280 °C (Figure 3d).

3.2.2. Q&P

The multiphase structure that evolved after Q&P processing (Figure 4, Figure 5, Figure 6 and Figure 7) differs from the microstructure that evolved after Q&T treatment. SEM observations (Figure 4a–c) revealed two structural components. First, there is primary martensite with dense transition carbides located parallel to habit planes within the martensite blocks [33,34]. Carbides of this type were not observed after water quenching. However, η-Fe₂C transition carbides precipitated under Q&T treatment with tempering at T ≥ 200 °C, and therefore, these carbides precipitate in the matrix of primary martensite at T_q and/or T_p due to auto-tempering [33,35,36] (Figure 7). The density of η-Fe₂C transition carbides is significantly higher than that after Q&T and the precipitation of these carbides along three mutually perpendicular habit planes (Figure 7c) produces a 3D array of these particles in the primary martensite plates. It is worth noting that the black matrix of primary martensite is heavily etched and looks like smooth and dark ferrite after quenching from intercritical temperature, which is indicative of carbon-depleted constituents [20,34,35,36,37]. Primary martensite exhibits plate-like shape with a high aspect ratio (AR). The volume fraction of primary martensite decreases with increasing T_q.

The second constituent is islands of secondary martensite/RA with an irregular shape (Figure 4a–c) [20,33,34,35,36,37]. These islands are gray regions of a featureless surface [20,37] and are distinctly distinguished from primary martensite by less etching and color [33,34,35]. TEM observations (Figure 7) revealed that the density of free lattice dislocations ρ_TEM~2 × 10¹⁵ m⁻² in RA and secondary martensite is essentially the same (

Table 2. Effect of quenching temperature on the KAM value of RA/martensite and the average size of RA.

Tq, °C	KAM Value of RA, °	KAM Value of Martensite, °	Average Grain Size of RA, μm
140	0.56	0.53	1.84
160	0.59	0.52	2.35
180	0.60	0.51	2.4
200	0.59	0.57	2.65
220	0.6	0.59	2.4
250	0.59	0.57	2.36

). It is worth noting that the very high dislocation density observed in RA by TEM and EBSD studies is in contrast with the earlier presumption [12] and could be attributed to intense plastic straining of this phase during γ→α′ transformation. In SEM micrographs (Figure 4), the secondary martensite could not be distinguished from RA by etching, which is indicative of the same carbon content in these two structural components. The secondary martensite/RA islands, characterized by high AR, are located between the plates of primary martensite. The volume fraction of this structural component increases with increasing T_q.

Isothermal holding at T_q = 300 °C resulted in the formation of martensite with nearly the same carbon content and a small fraction of lower bainite, which is typical for partitioning at a temperature above M_S [38] (Figure 4d). Transition η-Fe₂C carbides could be found in some blocks (Figure 4d).

EBSD and TEM studies (Figure 5, Figure 6 and Figure 7) revealed that only PAGs and thin laths are distinctly distinguished in the lath martensite structure [32,39]. Packets could be occasionally found in primary martensite at T_q ≤ 160 °C (Figure 6) if the volume fraction of this structural component is high. The average size of PAGs is ~35 μm and the thickness of thin laths is ~300 nm (Figure 5 and Figure 7a,b). These parameters are nearly independent of T_q. The average distance between HABs decreases from 0.82 to 0.6 μm with increasing T_q from 140 to 250 °C, which is attributed to the increased portion of secondary martensite/RA constituents. Boundaries between the secondary constituent and primary martensite are HABs, and these boundaries replace packet and block boundaries in the hierarchy of lath martensite structure [39]. It is worth noting that well-defined blocks are observed in primary martensite. The average thickness of blocks is ~2 μm, and these blocks could be distinguished in the coarse plates of primary martensite. There is no distinct difference between the lath thickness in primary and secondary martensite, while the lath length in primary martensite is significantly larger. The internal distortion is predominantly localized in secondary martensite, whereas the plates of primary martensite are nearly strain-free (Figure 5 column 4). At low T_q, the internal elastic strains are the lowest in the coarse blocks of primary martensite. As a result, increasing T_q leads to increased internal distortions (Table 2).

Quenching temperature, T_q, affects the parameters of RA (Figure 5 column 2, where RA is shown in red, and Figure 8). The RA grains exhibit an irregular blocky shape and are distributed in the martensitic matrix almost uniformly. No definite correlation between T_q and the dimension of RA blocks (Table 2)/carbon content in RA (Table 3) was found, while the volume fraction of RA increases with increasing T_q up to M_S (Figure 8).

The Fe-0.44C steel is characterized by the irregular distribution of RA over the cross section of the sample (Figure 9). In addition, the size of RA blocks also varies with depth; therefore, all dimensions in Table 2 are based on the dimensioning in Figure 5. It is important to note that the investigated steel is characterized by good hardenability.

Therefore, such local methods as EBSD and SEM do not allow one to reliably determine the volume fraction of RA. So, the volume fraction of RA was determined using two methods: the X-ray technique and the magnetic induction method, which demonstrated a good correlation (Figure 8a). The volume fraction of RA increases from 16 to 25% with increasing T_q from 140 to 250 °C. The following increase in the quenching temperature from 250 to 300 °C leads to a drop in the volume fraction of RA to 5% since no primary martensite may evolve above M_S. Isothermal holding at 300 °C leads to the formation of low bainite along the boundaries of PAGs and the precipitation of transition carbides in bainitic ferrite (Figure 4d). The temperature dependence of the volume fraction of RA is typical for Q&P steels [12] and ΔT = M_S − T_q = 30 K provides the maximum value of RA (Figure 8a).

The phase fractions during Q&P processing could be calculated using Koistinen-Marburger (K-M) dependence [12,40]:

$$f_{\mathrm{M}1}=1-\exp (a\cdot (M_s-T_{\mathrm{q}}))$$

(4)

where f_M1 is the volume fraction of primary martensite, a = −0.011. The f_M values were calculated and are presented in Table 4 and Figure 8c. It is seen that increasing T_q strongly decreases the volume fraction of primary martensite, which correlates with experimental observations (Figure 4). The fraction of secondary martensite, f_M2, could be evaluated from the balance of structural components:

$$f_{\mathrm{M}1}+f_{\mathrm{M}2}+f_{\mathrm{RA}}=1$$

(5)

The volume fraction of RA, f_RA, was taken from experimental data presented in Figure 8a. It is seen (Table 4) that increasing T_q from 140 to 250 °C increases the f_M2 value by a factor of ~10. The volume fractions of primary and secondary martensite become nearly the same, if ΔT = M_S − T_q < 50 K. Therefore, increasing T_q to M_S leads to a relatively lower increase in f_RA, which is accompanied by a strong increase in the volume fraction of untempered secondary martensite.

3.3. Mechanical Properties

3.3.1. Q&T

Engineering stress–strain curves are presented in Figure 10. After water quenching, the failure occurs immediately after yielding; the elongation-to-failure is 0.5%, and the YS and UTS are 1500 and 1730 MPa, respectively. Therefore, the quenched specimen exhibits intense work hardening after yielding. Tempering at 200 and 280 °C provides a strong increase in the ductility and strength, concurrently, due to work hardening after continuous yielding. After tempering at 200 °C, the YS, UTS and elongation-to-failure are 1640 MPa, 2120 MPa, and 7.3%, respectively. After tempering at 280 °C, the YS, UTS, and elongation-to-failure are 1730 MPa, 2100 Mpa, and 6.5%, respectively. Thus, the precipitation of η-Fe₂C transition carbides provides a 15% increase in the YS, and the ductility increases by a factor of ~13. As a result, the PSE of ~1.5 × 10⁴ MPa·% is relatively high after tempering. The hardness of 55 HRC is nearly independent of tempering.

3.3.2. Q&P

Engineering stress–strain curves are presented in Figure 11a, and the effects of T_q on the YS, UTS, and elongation-to-failure are shown in Figure 11b. Continuous yielding followed by work hardening is observed for all T_q. At T_q ≤ 200 °C, the PLC effect appears as the rise in the flow stress, followed by a drop to or below the general stress level [41]. Increasing T_q from 140 to 250 °C leads to the increase in the elongation-to-failure from 17.5 to 21.4% and the decrease in the UTS from 1780 to 1580 MPa. The PSE > 3 × 10⁴ MPa·% is observed in the T_q range 140–250 °C (Figure 11c). The highest PSE value of 3.5 × 10⁴ MPa·% was achieved at T_q = 220 °C and correlates with f_RA = 24% and f_M1 > f_M2. Thus, Q&P may increase the PSE value by a factor of more than 2 in comparison with low temperature tempering in Q&T treatment. An increase in the T_q from 260 to 300 °C leads to a drop in the ductility and PSE and an increase in the UTS. The fracturing of the specimen quenched at 300 °C occurs immediately after yielding (Figure 11a). Therefore, embrittlement occurs if the quenching temperature is >270 °C, and is associated with a high volume fraction of untempered martensite. A relatively high volume fraction of RA could not provide ductility if low-temperature martensite containing η-Fe₂C transition carbides is lacking. Therefore, high ductility and PSE are achieved due to a balance between primary martensite, secondary martensite, and RA structural components. Solely f_RA ≥ 5% is not sufficient for increased ductility. The steel with untempered martensite produced by Q&T treatment or Q&P processing with T_q > M_S is brittle and the brittleness is independent of the presence of RA containing relatively low carbon, since at T_p = 400 °C no partitioning occurred due to the lack of primary martensite after quenching at T_q = 300 °C.

Hardness is nearly independent of T_q and increases remarkably at T_q > M_S up to 58 HRC (Figure 11d). Thus, hardness values after Q&T and Q&P with T_q > M_S are essentially the same.

3.4. PLC Band Behavior

An EBSD study and X-ray data of the tensioned specimen in the neck area after failure showed that the volume fraction of RA does not exceed 3% (Figure 12a) and therefore, the volume fraction of RA decreases by a factor of ~12 under tension. These data support the statement about the easy (blocky RA → α′) transformation under tension [6,16]; the TRIP effect [10,18] provides good ductility and high PSE. The DIC method makes it possible to monitor the local strain distribution on the specimen’s surface during tension by correlating successive images of the speckle pattern. The local strain rate map (Figure 12c) and the corresponding sections of the deformation curve (Figure 12b) for the specimen after quenching at 160 °C show the localization of plastic deformation in the PLC bands [41], as indicated by the distribution of the local strain rate in the tensile direction. The first deformation band appears in the central region of the tensile specimen after attaining a critical strain of ~6% and propagates to the edge of the gauge section. The formation of a PLC band correlates with a flow stress jump of ~7 MPa, and the termination of the band propagation at the specimen edge correlates with a flow stress drop of ~6 MPa. A new PLC band nucleates at the bottom part of the tension specimen and this process is repeated until the Considère criterion dσ/dε = σ is met. Therefore, type A oscillation takes place at the work-hardening stage and uniform elongation is attributed to the propagation of PLC bands [41]. It is worth noting that a weak strain/strain rate localization takes place in the mobile PLC bands.

The onset of necking is attributed to the immobility of the PLC band and a strong increase in the degree of strain/strain rate localization after reaching the Considère strain (ε~0.13) [42]. Thus, the Considère criterion effectively describes the transition from a stable plastic flow to an unstable one. The localization of plastic deformation leads to the fracture. Similar mechanical behavior was reported for TRIP steels [42,43,44]. Thus, a high PSE value is achieved due to the TRIP effect during the tension and mobility of PLC bands lacking deformation localization up to achieving the Considère criterion.

4. Discussion

Inspection of the experimental data shows that Q&P processing provides a combination of the strength, ductility, and PSE of the present steel in accordance with the requirements for third-generation AHSS [1]. The role of RA in enhancing ductility and PSE after Q&T and Q&P processing is ambiguous. The steel exhibits high strength and sufficient ductility after low-temperature tempering almost without RA and is brittle after Q&P at T_q = 300 °C (see Section 3.3.2). Structural observation shows that the dislocation densities in martensite and RA are almost the same (see Section 3.2.2). It is apparent that RA may provide high elongation and PSE if its strength is close to the YS.

In order to calculate the overall YS of RA, we can use a linear combination of the strengthening mechanisms written as follows [12,45,46]:

YS = σ₀ + σ_SS + σ_HP + σ_disl,

(6)

where σ₀ is the lattice friction stress of about 63.5 MPa in high purity austenite [46], σ_SS is the solid solution strengthening, σ_HP is the grain boundary strengthening, and σ_disl is the dislocation strengthening. The solid solution strengthening (σ_SS) can be expressed using the following relationship [46]:

σ_SS = 356.5 × (wt.%C) + 20.1 × (wt.%Si) + 3.7 × (wt.%Cr) + 14.6 × (wt.%Mo)

(7)

The average concentrations of carbon in RA and σ_SS values are summarized in Table 3. It is seen that partitioning provides σ_SS ~ 600 MPa in the RA, and their strong strengthening takes place under the partitioning pass. Isothermal quenching provides a high volume fraction of RA in the present steel, and partitioning makes this phase “strong”.

The grain boundary strengthening (σ_HP) can be evaluated by the Hall–Petch type relationship [47,48,49,50,51,52]:

σ_HP = K_HPD^−0.5

(8)

where K_HP is the Hall–Petch coefficient. K_HP = 160 MPa × μm^0.5 reported for austenitic steel [49] was taken for the present calculations. The size of the RA grain, determined from the misorientation map (Table 2), for different states averages D ~ 2.3 μm. Changing the grain size does not lead to significant changes in strengthening relative to the overall value. The contribution of σ_HP varies within 100 MPa, which is approximately 10% of the total strength.

Table 3. Effect of quenching temperature on the contributions of different strengthening mechanisms to the yield strength.

Tq, °C	CRA	ρKAM, ×1014 m−2	σSS	σHP	σdisl	σ0.2 of RA $\left({\mathit{\sigma }}_{0.2}^{\mathit{R}\mathit{A}}\right)$, MPa	YS, MPa	ΔYS, MPa
140	1.315	5.81	575.8	118.0	331.9	1025.7	1350	324.3
160	1.313	6.18	575.1	104.4	342.3	1021.8	1350	328.2
180	1.4	6.30	606.1	103.3	345.7	1055.1	1220	164.9
200	1.383	6.22	600.0	98.3	343.4	1041.7	1120	78.3
220	1.393	6.26	603.6	103.3	344.5	1051.4	1080	28.6
250	1.572	6.15	667.4	104.2	341.4	1113	1060	−53

Table 3. Effect of quenching temperature on the contributions of different strengthening mechanisms to the yield strength.

Tq, °C	CRA	ρKAM, ×1014 m−2	σSS	σHP	σdisl	σ0.2 of RA $\left({\mathit{\sigma }}_{0.2}^{\mathit{R}\mathit{A}}\right)$, MPa	YS, MPa	ΔYS, MPa
140	1.315	5.81	575.8	118.0	331.9	1025.7	1350	324.3
160	1.313	6.18	575.1	104.4	342.3	1021.8	1350	328.2
180	1.4	6.30	606.1	103.3	345.7	1055.1	1220	164.9
200	1.383	6.22	600.0	98.3	343.4	1041.7	1120	78.3
220	1.393	6.26	603.6	103.3	344.5	1051.4	1080	28.6
250	1.572	6.15	667.4	104.2	341.4	1113	1060	−53

The dislocation strengthening (σ_disl) due to the high dislocation density (ρ) can be expressed by the Taylor-type relationship [12,49,50,51,52]:

σ_disl = αMGbρ^0.5,

(9)

where α is the dislocation strengthening factor of about 0.24 for materials with an fcc lattice [49,50,52], M denotes the Taylor factor, taken as 3.06 from misorientation maps, G is the shear modulus (=75 GPa [51]), b is the magnitude of the Burgers vector (=0.25 nm) [12,49,51,52], and ρ is the dislocation density. Despite the fact that the dislocation density determined by TEM shows higher values for the austenitic phase (ρ ~ 2 × 10¹⁵ m⁻²), since it takes into account dislocations of different signs, the ${\rho }_{\mathrm{K}\mathrm{A}\mathrm{M}}$ ~ 6 × 10¹⁴ m⁻² value, associated with internal stress fields, was used for the calculations. The dislocation strengthening calculated from the ${\rho }_{\mathrm{K}\mathrm{A}\mathrm{M}}$ values provides the best fit to the experimental YS (Table 3). The contributions of different strengthening mechanisms to the overall strength of RA and YS of steel are summarized in Figure 13. It is seen that the superposition of high dislocation strengthening, originating from the intense plastic straining of RA during γ→α′ phase transformation under quenching, and the solid solution strengthening, enhanced by partitioning treatment, provides the high strength of the RA (Table 3). The role of grain boundary strengthening is minor for the blocky RA, but could give a significant contribution to the overall strength of RA for the film-like RA due to the fact that dimensions of this type of RA are ~20 times smaller than those of the blocky RA.

Table 4. Volume fractions of the primary martensite, secondary martensite, and RA calculated by Equation (4).

Tq, °C	Volume Fraction of M1, %	Volume Fraction of RA, %	Volume Fraction of M2, %	Contribution of M1 to YS, 1730·fM1 (MPa)	Contribution of M2 to YS, 1500·fM2 (MPa)	Contribution of RA to YS, ${\mathit{\sigma }}_{0.2}^{\mathit{R}\mathit{A}}$	YS Calculated by Equation (1)
140	77	17	6	1332	90	174	1596
160	72	17	11	1246	165	172	1583
180	65	22	13	1125	195	232	1552
200	56	23	21	969	315	239	1523
220	45	24	31	778	465	252	1495
250	24	25	51	415	765	278	1458

Table 4. Volume fractions of the primary martensite, secondary martensite, and RA calculated by Equation (4).

Tq, °C	Volume Fraction of M1, %	Volume Fraction of RA, %	Volume Fraction of M2, %	Contribution of M1 to YS, 1730·fM1 (MPa)	Contribution of M2 to YS, 1500·fM2 (MPa)	Contribution of RA to YS, ${\mathit{\sigma }}_{0.2}^{\mathit{R}\mathit{A}}$	YS Calculated by Equation (1)
140	77	17	6	1332	90	174	1596
160	72	17	11	1246	165	172	1583
180	65	22	13	1125	195	232	1552
200	56	23	21	969	315	239	1523
220	45	24	31	778	465	252	1495
250	24	25	51	415	765	278	1458

In the present steel, the YS and strength of RA are nearly the same at T_q ≥ 220 °C, when f_RA ≥ 24%, and the volume fraction of primary martensite is <50%. Obviously, the strength of RA controls the YS of the present steel with such a structure. At T_q ≤ 160 °C, the difference between the σ_0.2 of RA and YS of the steel is higher than 300 MPa (Table 3). In order to evaluate the validity of Equation (1), we can take the strength of secondary martensite as equal to 1500 MPa, i.e., the YS of the steel after water quenching, and the strength of primary martensite equal to 1730 MPa, i.e., the YS of the steel after water quenching followed by tempering at 280 °C. It is worth noting that this approach is simplified due to the fact that the carbon content in the secondary martensite will be higher than 0.44 wt.% C in martensite after water quenching due to partitioning at 400 °C. The carbon content in primary martensite after Q&P processing is significantly smaller than that in martensite after tempering at 280 °C followed by water quenching due to partitioning at 400 °C and a significantly higher density of η-Fe₂C transition carbides after Q&P processing. The values of strength of the primary martensite, secondary martensite, and RA and the overall YS calculated by Equation (1) are shown in Table 4. It is seen that the composite law (Equation (1)) gives a strong overestimation of YS at T_q ≥ 180 °C and, therefore, the use of this law to predict YS in Q&P with multiphase structure is ambiguous. At the same time, at T_q ≤ 160 °C, the difference between the calculated YS and experimental YS is relatively small and could be attributed to the low carbon content in the primary martensite as compared to the low-temperature-tempered martensite. It is apparent that the composite law (Equation (1)) could be valid if there is a dominant phase, and the strengths of other phases are close to the strength of this dominant phase.

5. Conclusions

Q&T treatment with tempering temperatures of 200 and 280 °C ensures the formation of a martensite structure with high dislocation density and η-Fe₂C transition carbides. The volume fraction of retained austenite is negligible (~0.7). After water quenching, the failure occurs immediately after yielding. Tempering at 200 and 280 °C provides a strong increase in ductility (~7%). The PSE is ~15 GPa·%.

The Fe-0.44C steel processed by Q&P shows the striking PSE > 30 GPa·% and yield stress > 1000 MPa. The superior combination of strength and plasticity is attributed to the high volume fraction of retained austenite with a blocky shape and its strength of ~1000 MPa. The origin of the high yield stress of retained austenite is associated with carbon enrichment (~1.3wt.%) and the high density of lattice dislocations (~6 × 10¹⁴ m⁻²) in this phase. Almost full transformation of retained austenite into martensite under tension at room temperature leads to the significant work hardening and relatively high ductility. The onset of the necking is associated with immobility of the Portevin–Le Chatelier bands and described by the Considère criterion, dσ/dε = σ.

The strength of retained austenite controls the YS of the present steel when f_RA ≥ 24%. Superposition of high dislocation strengthening, originating from the intense plastic straining of retained austenite during the γ→α′ phase transformation under quenching, the solid solution strengthening, enhanced by partitioning treatment, and grain boundary strengthening provides the high strength of the retained austenite > 1000 MPa.