Revealing the difference of precipitation kinetics between TiC and VC in low-carbon tempered martensitic steels

Abstract

The precipitation kinetics of TiC and VC during high-temperature tempering of low-carbon martensitic steels was studied by means of hardness measurement and theoretical analysis. The precipitation–temperature–time diagram, which was determined through the hardness versus tempering time curves, shows that the precipitation rate of TiC is more rapid than that of VC at 600 °C or above, while they are almost the same at 550 °C. The number density of TiC precipitates is larger than that of VC precipitates, thus leading to a larger secondary hardening effect. An analytical model to describe the precipitation kinetics of microalloying carbides during tempering of martensitic steel was presented. Using this model, the difference of precipitation kinetics between TiC and VC can be well explained, in terms of the shape and relative position of kinetics curves and the nose temperature.

Appendices

Appendix 1: Analysis of dissolution and precipitation of TiN, Ti₄C₂S₂ and MnS during 1250 °C soaking for the Ti steel

The equilibrium precipitation temperatures of TiN, Ti₄C₂S₂ and MnS in austenite for the Ti steel are calculated as 1962, 1470 and 1350 °C according to their solubility product formulas:

$$\log \left[ {{\text{Ti}}} \right] \cdot \left[ {\text{N}} \right] = 0.32 - 8000/T\;\;\;\;[3]$$

(20)

$$\log \left[ {{\text{Ti}}} \right] \cdot \left[ {\text{C}} \right]^{0.5} \cdot \left[ {\text{S}} \right]^{0.5} = 6.32 - 15350/T \;\;\;\;[3]$$

(21)

$$\log \left[ {{\text{Mn}}} \right] \cdot \left[ {\text{S}} \right] = 5.02 - 11625/T\;\;\;\;[2]$$

(22)

where [Ti],[N], [C], [Mn] and [S] are the equilibrium solid solubility of Ti, N, C, Mn and S in austenite, respectively, and T is the absolute temperature. It can be seen that Ti₄C₂S₂ precipitates preferentially over MnS. Moreover, most TiN actually precipitates from liquid steel before solidification, forming micron-sized TiN particles [3].

The dissolved N content at 1250 °C is calculated as 0.000065% according to Eq. (20) and the stoichiometric ratio of Ti to N for the undissolved TiN:

$$\frac{{{\text{Ti}} - \left[ {{\text{Ti}}} \right]}}{{{\text{N}} - \left[ {\text{N}} \right]}} = \frac{{A_{{{\text{Ti}}}} }}{{A_{{\text{N}}} }} = 3.42$$

(23)

Likewise, the dissolved S content is calculated as 0.0000162% according to Eq. (21) and the stoichiometric ratios of Ti to S and Ti to C for the undissolved Ti₄C₂S₂:

$$\frac{{{\text{Ti}} - \left[ {{\text{Ti}}} \right]}}{{{\text{S}} - \left[ {\text{S}} \right]}} = \frac{{2A_{{{\text{Ti}}}} }}{{A_{{\text{S}}} }} = 2.99$$

(24)

$$\frac{{{\text{Ti}} - \left[ {{\text{Ti}}} \right]}}{{{\text{C}} - \left[ {\text{C}} \right]}} = \frac{{2A_{{{\text{Ti}}}} }}{{A_{{\text{C}}} }} = 7.97$$

(25)

where Ti, N, C and S are the contents of Ti, N, C and S, respectively, A_Ti, A_N, A_S and A_C denote the atomic weights of Ti, N, S and C, respectively. It can be seen that almost all N and S precipitate in the form of TiN and Ti₄C₂S₂ in the Ti steel during soaking at 1250 °C; thus, the dissolved Ti content can be obtained by subtracting the Ti content that precipitates in the form of TiN and Ti₄C₂S₂ from the total Ti content, i.e., $w_{{\left[ {{\text{Ti}}} \right]}} = w_{{{\text{Ti}}}} - {3}.{42}w_{{\text{N}}} - {2}.{99}w_{{\text{S}}} = 0.{166}$ wt.%.

Appendix 2: Estimation of dislocation density before precipitation

The dislocation density of as-quenched martensite of the studied steels is estimated as 5 × 10¹⁴ m⁻² according to the carbon content of the tested steel [43], and it is assumed that the dislocation density could decrease to about 2 × 10¹⁴ m⁻² after the first stage tempering at 600 °C for the Ti steel according to the kinetics of dislocation recovery for a Ti-microalloyed steel proposed in the literature [25].

It is observed that the Ti and V steels have the similar average prior austenite grain size of about 218 μm, as shown in Fig. 

Figure 8

Micrographs of prior austenite grains of Ti steel a and V steel b

8, leading to the similar packet and block sizes, and thus, both steels should have the similar grain boundary strengthening effects. On the other hand, the solid solution strengthening effects of both steels are considered to comparable since their chemical compositions are very similar except for Ti and V contents. Therefore, the dislocation density of the V steel before precipitation can be estimated from the difference of yield strength between the Ti and V steels. According to the Bailey–Hirsch relationship [28],$\sigma_{dis} = \alpha MGb\sqrt \rho$, the difference of yield strength before precipitation is expressed as

$$\sigma_{{y\left( {{\text{Ti}}} \right)}} - \sigma_{y\left( V \right)} = \alpha MGb\left( {\sqrt {\rho_{{{\text{Ti}}}} } - \sqrt {\rho_{{\text{V}}} } } \right)$$

(26)

where σ_dis is the dislocation strengthening, M is the Taylor factor (2.75 for bcc metals [28]), α is a constant (= 0.25 in bcc iron [28]), G is the shear modulus (= 81.6 GPa [28]), b is the Burgers vector (0.248 nm) and ρ is the dislocation density. The difference of yield strength can be estimated according to the correlation of strength with hardness proposed in the literature [44] as:

$$\sigma_{{\text{y}}} = {2}.{5}0{7}HV + {11}0.{9 }\left( {{\text{MPa}}} \right)$$

(27)

In the case of tempering at 600 °C, the difference of hardness between the Ti and V steels before precipitation was measured to be 36.4HV (see also Fig. 1); thus, the difference of yield strength, $\sigma_{{y\left( {{\text{Ti}}} \right)}} - \sigma_{{y\left( {\text{V}} \right)}}$, is calculated as 91.3 MPa. Substituting it and other parameters into Eq. (20), we can obtain the following equation:

$$\sqrt {\rho_{{{\text{Ti}}}} } - \sqrt {\rho_{{\text{V}}} } = 6.01 \times 10^{6}$$

(28)

Substituting the estimated ρ_Ti (2 × 10¹⁴ m⁻²) into the above equation, the dislocation density of V steel before precipitation is calculated as 6.61 × 10¹³ m⁻².

In the present study, the dislocation density before precipitation at other temperatures is assumed to be comparable to the dislocation density at 600 °C. This seems reasonable for temperatures below 700 °C, since it is found that the precipitation start time is shorter at higher tempering temperature, which suggests a shorter time available for dislocation recovery at higher temperature, thus possibly leading to a similar effect of dislocation recovery at different temperatures. Nevertheless, this is only a rough estimation. More accurate estimation of dislocation density requires XRD measurement or other advanced characterization methods, which will be carried out in future work.