**1. Introduction**

Tire cord steel is a kind of high-carbon steel and thus possesses high strength and toughness. Therefore, it is widely used in the production of tires for cars and airplanes [1]. With the development of lightweight materials, the strength level of tire cord steel has become a significant factor to be considered. The main types of tire cord steel were SWRH 62A and SWRH 67A (about 1750 MPa) before the 1990s, and then after that SWRH 72A (about 1870 MPa). In the 21st century, the hypereutectoid tire cord steel (SWRH 82A) dominated the market due to its higher strength level [2,3]. Nowadays, the research on ultra-high strength level steel, such as SWRH 92A tire cord steel, has been drawing the increasing attention of manufacturing engineers.

Non-metallic inclusions, such as oxide-or Ti-bearing inclusions, existing in tire cord steel have serious detrimental effects on the drawing performance and fatigue properties. Furthermore, the properties of inclusions, such as size, composition, amount, and morphology, play a key role on the quality of steel [4,5]. At present, the damage problems of brittle oxide inclusions for steel can be better controlled by morphology-controlling technology. Nevertheless, for Ti-bearing inclusions, due to their non-deformable characteristic, they could cause a serious detrimental effect on the drawing performance, which would reduce the life of high-carbon steels, especially for the SWRH 82A and SWRH 92A tire cord steels. Titanium nitride (TiN), with high hardness and melting point, would cause filament breaks during wire drawing and rope stranding or deteriorate the fatigue properties of steels. Furthermore, TiN inclusion has more harmful effects on the material processing than those of oxide inclusions. For example, a TiN inclusion of 6 μm would cause a similar fatigue performance to an oxide inclusion of 25 μm [6]. Titanium carbonitride (TiC*x*N1-*x*, *x* represents the molar ratio of TiC in TiC*x*N1-*x*), a continuous solid solution formed via replacing partial moles of N in TiN crystal with C has similar properties to those of TiN. It also has a detrimental effect on the fatigue performance and, as a result, leads to wire breaking during the drawing and stranding processes [7]. It has been reported [8] that the molar ratio of TiC increases with increasing strength of tire core steel, which would cause a more seriously destructive effect. However, the value of *x* in TiC*x*N1-*<sup>x</sup>* is still very small [8]. In other words, the main composition of Ti-bearing inclusion precipitated in tire cord steel is still TiN. Thus, it is important to control TiN inclusion to improve the performance of SWRH 92A tire cord steel.

Many researchers [2–4,9–14] have reported the precipitation behaviors of TiN inclusion in different types of steels over the decades. Jiang et al. [4] found that the solidification segregation ratio of Ti was far greater than that of N, and reported that TiN inclusion would not precipitate until the solid fraction reached 0.9 when using SWRH 82A tire cord steel. Cai et al. [9] showed that the precipitation of TiN could only occur in the solid–liquid two-phase region where the solid fraction was greater than 0.95, and the particle size of TiN decreased with increasing cooling rate. Similar results were also reported in other references [11–13]. However, Liu et al. [14] demonstrated that TiN would not precipitate in the liquid phase or mushy zone, but in austenite (γ-Fe). The precipitation temperature of 1598 K (below the solidus temperature in this reference) was calculated. Nowadays, in the industrial production of SWRH 92A tire cord steel, TiN inclusion always appears in samples even though the concentration of N and Ti are controlled at extremely low levels (0.0043 mass% and 0.0005 mass% for N and Ti, respectively). Therefore, the precipitation behavior of TiN in SWRH 92A tire cord steel remains a hard problem to be solved. In order to make the mechanism of TiN precipitation clearer, a series of relevant studies were initiated in this paper, to show guidance for the development of ultra-high strength grade steels.

#### **2. Material and Equilibrium Solubility Product**

The chemical composition of SWRH 92A tire cord steel studied (from a Chinese steel mill) is shown in Table 1. Elements O and N were analyzed by the ONH analyzer (TC500C, LECO Corporation, St. Joseph, MI, American), elements C and S were analyzed by the CS Analyzer (Model EMIA-820V), and the contents of other elements were analyzed by ICP technology (IRIS Advantage ER/S, Thermo Elemental Corporation, Waltham, MA, American). Content of C was about 0.9203 mass%.

**Table 1.** Chemical composition of studied SWRH 92A tire cord steel (mass%).


To evaluate the stage (liquid phase, mushy zone, or solid phase) at which the TiN inclusion would precipitate in the steel, the liquidus temperature (*T*L) and solidus temperature (*T*S) as well as the equilibrium solubility product of N and Ti were first calculated.

Equations (1) and (2) were employed to estimate *T*<sup>L</sup> and *T*<sup>S</sup> [15], respectively,

$$T\_{\rm L} = T\_{\rm Fe} - \sum \Delta t\_{\rm L} \cdot w\_{[i]} \tag{1}$$

$$T\_{\rm S} = T\_{\rm Fe} - \sum \Delta t\_{\rm S} \cdot w\_{[i]} \tag{2}$$

where *T*Fe was the melting point of pure Fe, 1811 K; Δ*t*<sup>L</sup> and Δ*t*<sup>S</sup> were the reduced temperature values for element *i* when the mass fraction was 1 mass%, K, the corresponding values can be acquired from Table 2 [15]; *w*[*i*] represented the mass fraction of element *i*, 1 mass% was considered as the unit. Combining Table 1, Table 2, Equations (1) and (2), the values of *T*<sup>L</sup> and *T*<sup>S</sup> can be calculated, i.e., *T*<sup>L</sup> = 1748 K, *T*<sup>S</sup> = 1636 K.

**Table 2.** Values of Δ*t*<sup>L</sup> and Δ*t*<sup>S</sup> in Equations (1) and (2) [15], respectively.


The chemical reaction for the formation of TiN in molten steel can be expressed by Equation (3),

$$\text{[Ti]} + \text{[N]} = \text{TiN}\_{\text{(s)}} \tag{3}$$

Standard Gibbs free energy change Δ*G*<sup>θ</sup> <sup>3</sup> for Equation (3) can be derived from Equations (4)–(7) [8,16],

$$\text{Ti}(\text{s}) = \text{Ti}(l) \cdot \Delta G\_4^0 = 15500 - 8T \text{ (J/mol)} \tag{4}$$

$$\text{Ti}(l) = \text{ [Ti]} \quad \Delta G\_5^0 = -69500 - 27.28T \text{ (J/mol)} \tag{5}$$

$$\frac{1}{2}\text{N}\_2(\text{g}) = [\text{N}]\ \Delta G\_6^0 = 10500 + 20.37T \text{ (J/mol)}\tag{6}$$

$$\text{Ti(s)} + \frac{1}{2}\text{N}\_2(\text{g}) = \text{TiN(s)} \cdot \text{A} \\ \text{G}\_7^0 = -334500 + 93T \text{ (J/mol)} \tag{7}$$

Therefore, the expression of Δ*G*<sup>θ</sup> <sup>3</sup> can be obtained,

$$\begin{array}{rcl} \Delta G\_3^0 &=& -\Delta G\_4^0 - \Delta G\_5^0 - \Delta G\_6^0 + \Delta G\_7^0 \\ &=& -291000 + 107.91T \text{ (J/mol)} \end{array} \tag{8}$$

The reaction equilibrium constant *K*<sup>θ</sup> <sup>3</sup> for Equation (3) is shown as follows:

$$K\_3^0 = \frac{a\_{\rm TIN}}{a\_{\rm [Tl]} \cdot a\_{\rm [N]}} = \frac{1}{w\_{\rm [Tl]} \cdot w\_{\rm [N]} \cdot f\_{\rm [Tl]} \cdot f\_{\rm [N]}} \tag{9}$$

where *a*TiN, *a*[Ti], and *a*[N] denote the activities of TiN, Ti, and N in molten steel, respectively, herein, *a*TiN = 1; *w*[Ti] and *w*[N] denote the mass fractions of Ti and N in molten steel, respectively; *f*[Ti] and *f*[N] denote the activity coefficients of Ti and N, which can be estimated by Equations (10) and (11) [13], respectively.

$$\log f\_{\text{[Ti]}} = \lg f\_{\text{[Ti]}}^{1873 \text{ K}} \cdot (\frac{2557}{T} - 0.365) \tag{10}$$

$$\log f\_{\rm{[N]}} = \lg f\_{\rm{[N]}}^{1873 \text{ K}} \cdot (\frac{3280}{T} - 0.75) \tag{11}$$

where lg *f* 1873 K [Ti] and lg *<sup>f</sup>* 1873 K [N] are the interaction coefficients of Ti and N at 1873 K, which can be calculated by Equations (12) and (13) [7–9], respectively:

$$\log f\_{\text{[T]}}^{1873 \text{ K}} = \sum \epsilon\_{\text{Ti}}^{i} \cdot w\_{[i]} \tag{12}$$

$$\log f\_{[\mathbf{N}]}^{1873 \text{ K}} = \sum \mathbf{e}\_{\mathbf{N}}^{i} \cdot w\_{[i]} \tag{13}$$

Due to the fact that the mass fraction of Fe is more than 90 mass% in molten steel, then the impact of second-order interaction coefficients can be ignored. Thus, the first-order interaction coefficients (as shown in Table 3) are used only during the calculation process [15,17].

**Table 3.** First-order interaction coefficients *e<sup>i</sup> <sup>j</sup>* of solute elements in molten steel at 1873 K [15,17].


According to Equations (10)–(13), one can obtain,

$$
\lg f\_{[\text{Ti}]} + \lg f\_{[\text{N}]} = \frac{24.3832}{T} - 0.0395 \tag{14}
$$

For Equation (9), take the logarithm of 10 on both sides at the same time,

$$\log \mathsf{K}\_3^0 = - (\log f\_{\text{[Ti]}} + \log f\_{\text{[N]}}) - (\log w\_{\text{[Ti]}} + \log w\_{\text{[N]}}) \tag{15}$$

$$
\log K\_3^0 = \frac{\ln K\_3^0}{2.303} = -\frac{\Delta G\_3^0}{2.303RT} = \frac{15204.6}{T} - 5.6383\tag{16}
$$

Taking the equilibrium solubility product of Ti and N as *K*equ <sup>3</sup> (*K*equ <sup>3</sup> = *w*[Ti] · *w*[N]), and combining Equations (14)–(16), one can obtain,

$$\text{lgK}\_3^{\text{equ}} = -\frac{15229}{T} + 5.6778 \tag{17}$$

By substituting *T* = 1636 K and *T* = 1748 K into Equation (17), respectively, the relationship between *w*[Ti] and *w*[N] can be obtained, as shown in Figure 1. Figure 1 shows that concentrations of N and Ti in the sample, see Point A in this figure, are much lower than those at the liquidus phase and solidus phase temperatures, which indicates that TiN will not precipitate in the liquid phase or mushy zone.

**Figure 1.** Required solubility product of N and Ti for the precipitation of TiN inclusion in SWRH 92A tire cord steel.
