Study on the precipitation mechanisms of TiC particles in steel matrix composites fabricated by eutectic solidification

The precipitation mechanisms of TiC eutectic particles in steel matrix composites prepared by eutectic solidification are studied through thermodynamic calculations and experimental analyses. The results indicate that the eutectic TiC particles begin to precipitate when the concentrations of Ti and C in the residual molten steel reach a eutectic point during the solidification process. The mass fractions of Ti and C in SMCs play significant roles in the precipitation time, particle characteristics and precipitation mechanism characteristics of TiC eutectic particles. When the mass fractions of Ti and C in SMC are low, TiC particles precipitate in the form of divorced eutectic solidification, showing strip, block and irregular shapes that are mainly distributed on the grain boundaries. When the mass fractions of Ti and C are high, TiC particles precipitate in the form of eutectic solidification, showing flake and dendritic shapes that are distributed on the grain boundaries and also in the grains. There are orientation relationships between the eutectic particles and the matrix.


Introduction
Metal matrix composites (MMCs) have attracted increasing attention because of their high specific strength, high specific modulus, excellent wear resistance, good high temperature performance and good oxidation resistance characteristics. However, MMCs are mainly used in the aerospace, automobile, and electronics fields, and the manufacturing cost is a key factor limiting their widespread use. The manufacturing processes of MMCs, such as pressure infiltration [1,2], stir casting [3][4][5], electrodeposition [6] and powder metallurgy [7][8][9], are usually complex and expensive. MMCs have not been produced on an industrial scale to date. ArcelorMitta [10] successfully developed new eutectic particle-reinforced steel matrix composites through the eutectic precipitation of ceramic particles during solidification, which are produced by traditional mold casting and continuous casting processes, these composites have great potential for industrial production processes.
Reinforcements and interfaces play major roles in the characteristics of MMCs. TiB 2 , TiC, VC and other particles with eutectic reactions in the phase diagram can be precipitated in the form of eutectic solidification, and the volume fractions of the particles can reach up to 25% [11]. The interfaces between the particles and the matrix obtained by eutectic solidification have neither intermediate phases such as oxides or nonstoichiometric borides, nor strain fields that could weaken the interfaces. These 'clean' interfaces are very favorable for good adhesion and high interfacial strength properties [12]. Huang [13,14] used nanoindentation to study the interface properties of eutectic particles and ferrite matrix. High-density dislocations were generated and stored at the interface during the deformation process, improving the debonding resistance levels of eutectic particles.
The main purpose of ArcelorMitta is to produce a new steel with a high specific modulus for automotive lightweighting. TiB 2 was selected as the reinforcement of high modulus steels because of its large contribution to the elastic modulus relative to TiC, VC and other particles [11]. However, the primary TiB 2 particles obtained by hypereutectic solidification have large sizes and high aspect ratios. During tensile and fatigue deformation processes, stress concentration is likely to occur at the primary TiB 2 particles, forming cracks in the primary TiB 2 ; then, cracks extend to the matrix and accelerate the fracture of the material [15,16]. Hadjem-Hamouche [17] found that the fracture of large-scale primary TiB 2 is a main reason for the failure of high-modulus steel during a three-point bending deformation process. Genée [18] characterized the evolution of the geometrically necessary dislocation density distributions in high modulus steel during tensile deformation by Electron Backscatter Diffraction (EBSD), proving that the generation of local plastic deformation is mainly caused by the tips of slender particles and large-sized particles. These results indicate that the key factors limiting the performance levels of eutectic composites are eutectic particles rather than bonding interfaces.
Eutectic particles are thermodynamically stable solidification products, and the structural characteristics and distributions of particles are mainly determined by the alloy composition and the solidification conditions [19][20][21]. Therefore, the generation of large-sized primary particles should be avoided as much as possible. Huang [22][23][24][25][26] produced TiC-reinforced low alloy abrasion resistant steel through hypoeutectic solidification by conventional melting and casting processes. The primary large-sized particles significantly reduced, the mechanical properties improved, and the wear performance was greatly enhanced. However, the precipitation mechanisms of eutectic TiC particles still need to be further investigated to obtain the optimal morphology and size characteristics of TiC particles. The present work combines thermodynamic calculations and experiments to study the precipitation mechanism, crystallography and orientation of TiC insteel matrix composites (SMCs) during eutectic solidification.

Materials and experiment procedure
The SMCs were prepared by traditional melting and casting method. The micron-sized eutectic TiC particles precipitated during solidification were regarded as reinforcement. The chemical compositions of SMCs are shown in table 1. The ideal chemical ratio of Ti and C required to form TiC is w Ti /w C = 3.99, and excessive Ti element was added in the SMC13 so that all C element was consumed to form TiC particles. The SMCs were smelted in a 50 kg vacuum melting furnace because Ti is easier to combine with oxygen and nitrogen to form titanium oxide and titanium nitride, and then casted into a cylindrical ingot with a diameter of 150 mm. Finally, the ingots were hot rolled into 12 mm plates through two-stage controlling rolling process, and then air cooled to room temperature. The metallographic samples (8 mm × 10 mm × 12 mm) were cut from the ingots and plates to observe the morphologies of TiC particles.
The metallographic samples were mechanically ground and polished, and then to observe the micron-sized TiC particles through Scanning Electron Microscope (SEM, ZEISS ULTRA-55) at 15 kV. The surface scan of elements distribution in a randomly selected area containing micron-sized particles in the SMC13 ingot was carried out by JEOL JXA-8530F field Emission Electron Probe (EPMA) at 20 kV to analyze the types of particles. Besides, EBSD analyses were performed using the EBSD attachment (Oxford Instruments, INCA Crystal) equipped on the SEM to study the orientation relationship between the micron-sized particles and matrix. Previously, an argon ion polishing machine was used to eliminate the residual stress on the surface of the samples.

Results and discussion
3.1. Thermodynamic calculations of micron-sized TiC particles Titanium is a strong carbide-forming element that easily combines with carbon to form TiC. The mass fraction of titanium in microalloyed steels is less than 0.1%, and titanium usually forms nanosized precipitates at low temperatures or after deformation; this phenomenon plays a role in precipitation strengthening. SMCs contain relatively high contents of titanium, and there are many micron-sized TiC particles distributed in the matrix. Micron-sized particles act as reinforcement, in which their size, number, morphology and distribution characteristics significantly affect the performance of the SMCs. In order to investigate the precipitation process of micron-sized TiC and control its size, quantity and shape, thermodynamic calculations are performed on the precipitation behaviors of SMCs according to the Gibbs free energy. The equation (1) can be used to express the chemical reaction for the precipitation of TiC in the molten steel: The Gibbs free energy of the chemical reaction of TiC can be described by equations (2)- (3): where ΔG°T iC donates the standard Gibbs free energy of TiC; R is the gas constant (8.314 J/(mol•K)); a TiC , a Ti and a C denote the activities of TiC, Ti and C in molten steel at the different temperatures, respectively, which can be calculated using equations (4)-(5): where the w([Ti]) and w([C]) is the initial mass fraction of Ti and C in the molten steel at the temperature of 1873 K. The f Ti and f C , the activity coefficient of Ti and C in molten steel at different temperatures, can be obtained through equations (6)- (7): where the f Ti, 1873 K and f C, 1873 K represent the interaction coefficient of Ti and C in the molten steel at 1873 K, which can be estimated via equation (8) [27]. Rounding off the values of second-order interaction coefficients where j represents the Ti and C; i is the other solute elements in the molten steel; e i j donates the first-order interaction coefficients, the values of the interaction coefficients are shown in table 2.
Under equilibrium conditions, the Gibbs free energy of the chemical reaction for forming of TiC is zero, and the a TiC are 1, thus the equations (10)-(11) can be obtained.
denote the equilibrium solubility products of TiC, which is a function of temperature T. The liquidus (T L ) and solidus (T S ) of experimental steels can be estimated using the equations (12) and (13), and the results are shown in table 3. According to the chemical composition, the equilibrium solubility products of TiC particles in different SMCs can be calculated, and the results are shown as equations (14)-(16)  TiC 0 = -( ) / Figure 1 shows that TiC has difficulty precipitating in molten steel under equilibrium conditions. However, as solidification progresses, ferrite (δ) and austenite (γ) are gradually generated, and the solute is usually rejected into the liquid. Due to the segregation and redistribution of the solute, microsegregation of the solute occurs in the retained liquid; this process provides conditions for the precipitation of TiC in the retained liquid in the mushy zone. One of the main causes for this phenomenon is that the equilibrium solubility product of TiC decreases with decreasing temperature. Another contributing factor is that the actual solubility product of TiC quickly improves for microsegregation.
The contents of segregated Ti and C in the mushy zone can be calculated using the following model [30]: where T denotes the liquidus temperature (K) of experimental steels; T m is the melting point of pure iron (1809 K); T l is the liquidus temperature; and T s is the solidus temperature. The actual solubility products and equilibrium solubility products of experimental steels in the mushy zone are calculated through the above formulas, and the results are shown in figure 2. There are some intersections between the equilibrium solubility product curves and the actual solubility product curves of experimental steels with different contents of Ti  within the range of the mushy zone, indicating that the thermodynamic conditions for the precipitation of TiC particles are satisfied; therefore, the TiC particles precipitate in the mushy zone. At the beginning of solidification, the actual solubility products of TiC are lower than the equilibrium solubility product. As solidification progresses, the equilibrium solubility product decreases as the temperature decreases, and the actual solubility product gradually increases as the solidification ratio increases. When the actual solubility products exceed the equilibrium solubility products, TiC begins to precipitate in the mushy zone. The higher the mass fractions of Ti in the experimental SMCs are, the faster the actual solubility products increase; however, the mass fraction of C has a small influence on the equilibrium solubility products. The 0.3Ti steel begins to precipitate TiC when the percentage of solidification reaches 75%; 0.6Ti steel is approximately 60%, and 1.3Ti steel is only 30%. Thermo-Calc software is used to calculate the solidification phase diagrams based on the chemical composition in table 1. Figure 3 shows the phase diagrams of SMCs with 0.3, 0.6 and 1.30 wt.% Ti elements. The red and blue lines are the liquidus and solidus, respectively; the red line is the line where α-ferrite begins to precipitate. The purple line is the starting point of the precipitation or transformation of austenite. The content of Ti increases, the temperature of the liquidus decreases, the region of α-ferrite decreases, and the region of γaustenite increases. The precipitation region of TiC particles is above the solidus, and the brown line is the point where precipitation begins; this point indicates that TiC particles precipitate near the end of solidification. The precipitation of TiC particles is closely related to the contents of Ti and C in the solution, and TiC particles precipitate earlier when the contents of Ti and C increase [31,32]. This phenomenon is consistent with the thermodynamic calculation results.
In order to study the precipitation mechanisms of the micron-sized TiC particles in the SMC, the mass fractions of the alloying elements in each phase of the SMC with 0.6Ti during solidification is calculated using Thermo-Calc software; the results are shown in the figure 4. The alloying elements in the molten steel are evenly distributed. With the gradual progress of solidification, α-ferrite and γ-austenite successively precipitate from the molten steel, and the mass fractions of alloying elements in the residual molten steel gradually increase. The molten steel rich in Ti and C provides good conditions for the precipitation of eutectic particles. As shown in figure 4(d), particles begin to precipitate in the molten steel when the temperature is 1577°C. Additionally, the mass fractions of Ti and N are relatively high and stable; however, almost no C exist, indicating that the particles precipitated in the molten steel are mainly TiN at high temperatures. When the temperature decreases to the two-phase region, the mass fractions of Ti and C in the particles gradually increase, and the phenomenon of N is the opposite; these findings indicate that the types of precipitated particles gradually change from TiN to TiC.

Characteristics of micron-sized TiC particles
Eutectic particles are processed by three methods-plane sectioning, deep etching and extraction-to characterize their distribution state and three-dimensional shape characteristics. The morphologies of eutectic particles in solidified SMCs with different Ti contents is shown in figures 5(a)-(f). The distribution and shape characteristics of eutectic particles in SMC03 and SMC06 are similar. These particles are distributed along grain boundaries or dendrite boundaries and appear in strips, blocks or irregular shapes. The eutectic particles in SMC03 are smaller in size and fewer in number than those in SMC06 and SMC13. These eutectic particles in SMC03 and SMC06 precipitate from the residual molten steel in the form of divorced eutectic at the end of solidification. The distribution and shape characteristics of the eutectic particles in SMC13 are different from those in SMC03 and SMC06. The shapes of the eutectic particles of SMC13 are mainly flake and dendritic; the   particles are distributed on the grain boundaries and also in the grain. The particles in SMC13 are mainly coprecipitated with γ-austenite by eutectic solidification; the solidification path can be expressed as L → L+δ→L + γ→L + γ + (γ + TiC) eutectic →γ + (γ + TiC) eutectic [33]. Figures 5(g), (h) show characteriztions of the 3D morphologies of the eutectic particles in SMC13 after deep etching and extraction, indicating that the eutectic particles have no specific regular shape; these particles mainly show flake shapes. There are some cubic particles, and flake particles continue to grow on the corners of the cubic particles. The same phenomenon is observed in figures 5(a)-(b). In general, with the increase in Ti content in the SMC, the size, number, and precipitation time characteristics of eutectic particles increase; additionally, the precipitation mechanisms of eutectic particles change.
The compositions of the eutectic particles are determined through surface scans using EPMA. The alloy element distributions of eutectic particles with different shapes in SMC13 are shown in figure 6. The brighter the color is, the higher the content of the element. The flake eutectic particles mainly contain C, Ti and some Mo. Mo atoms replace some Ti atoms in TiC to form (Ti,Mo)C. Some large-sized bulk particles contain a small amount of N. Previous studies have shown that these primary particles may be composite particles with TiN as the core and TiC as the outer shell [22].
The phase and crystal orientation of the SMC microstructure are investigated by EBSD. The phase and IPF maps of the SMC are shown in figures 7(a), (b). The regions with different colors in figure 7(a) represent eutectic TiC particles with FCC structures. Different colored particles have different crystal orientations. There are three grains in figure 7(b), which have different crystal orientations. By comparing figures 7(a) and (b), it is seen that there are particles on the grain boundaries, and inside the grains. Different orientation relationships exist between particle groups and the matrix, as shown in figures 7(c)-(d). The (100) crystal plane of group I is parallel to the (111) crystal plane of matrix 2. The (111) plane of group II is parallel to the (100) plane of matrix 2. Group III is located on the grain boundary between matrix 2 and matrix 3, in which the (111) crystal plane is parallel to the (100) crystal plane of matrix 2; however, there is no orientation relationship with matrix 3. The (100) crystal plane of group IV and the (111) crystal plane of group V are parallel to the (100) and (111) crystal planes of matrix 3, respectively. There is an uncertain orientation relationship between the particles obtained by solidification and the matrix, indicating that these particles precipitate in a eutectic manner. The two phases of eutectic growth generally have a crystallographic orientation relationship.

Precipitation mechanisms of micron-sized TiC particles
The precipitation mechanisms of SMCs with different mass fractions of Ti are analyzed based on the results of thermodynamic calculations and experimental analyses. A schematic diagram of the solidification process of SMCs and the precipitation of eutectic particles is shown in figure 8. When the temperature is above the liquidus of the SMC, if the mass fraction of N in the molten SMC reaches 30 ppm, the TiN particles precipitate from the molten SMC since the molten SMC contains many Ti elements and the equilibrium solubility product of TiN is low. However, the equilibrium solubility product of TiC is much higher than that of TiN, and TiC cannot precipitate in molten SMC, as shown in figure 8(a). SMCs are hypoeutectoid steels, and the δ-phase begins to precipitate when the temperature is lower than the liquidus temperature ( figure 8(b)); this phenomenon causes the mass fractions of alloying elements in the molten SMC to increase continuously. Then the γ-phase precipitates through the peritectic reaction (δ + L → γ) when the temperature decreases to the peritectic reaction temperature ( figure 8(c)). There is still some residual liquid after the peritectic reaction, and the mass fractions of alloying elements in the first precipitation phase are all lower than those in molten SMC; thus, the mass fractions of alloying elements in the residual molten SMC continues to increase. In addition, TiN continuously precipitates from the molten SMC during the solidification process, and TiN acts as a heterogeneous nucleation site to promote the nucleation of the new phase ( figure 8(d)). The enrichment of a large amount of Ti and C in the residual molten SMC provides good conditions for the precipitation of TiC particles. Austenite and TiC undergo eutectic precipitation when the concentration of TiC in the residual molten SMC reaches its eutectic point. The amount of residual molten SMC plays an important role in the precipitation mechanisms and the morphologies of TiC particles. The precipitation of TiC particles in SMC03 follows the steps of figures 8(e)-(g). The mass fractions of Ti and C in the SMC are relatively low. When the solubility of TiC in the residual molten SMC03 reaches its eutectic point, the amount of residual molten steel is small and locate between dendrites. At this point, there is already a large amount of primary γ-phase, the eutectic γ-phase continues to grow attached to the primary γ-phase, and the eutectic TiC is left at the last solidified grain boundary or dendrite boundary; these findings are characteristic of divorced eutectic precipitation. The mass fractions of Ti and C in SMC13 are higher. The precipitation mechanism of TiC particles in SMC13 is represented by figures 8(E)-(G). When the solubility of TiC in the residual molten SMC13 reaches the eutectic point, the amount of residual molten SMC13 is still greater, and the eutectic TiC particles and the eutectic γ phase coprecipitate.

Conclusions
1. Under ideal equilibrium conditions, TiC particles have difficultly precipitating from the experimental SMCs.
However, the microsegregation phenomenon in the actual solidification process provides a good condition for the precipitation of TiC particles from residual molten SMCs.
2. The precipitation of TiC particles occurs at the end of solidification, and the SMC with high mass fractions of Ti and C precipitates TiC particles earlier. When the solidification ratio reaches 30%, 60% and 75%, SMC13, SMC06 and SMC03 start to precipitate TiC particles.
3. The eutectic particles in SMC03 and SMC06 are mainly distributed on the grain boundary, showing strip, block and irregular shapes. However, there are eutectic particles in the SMC13 grains that are flake and dendritic. There are orientation relationships between eutectic particles and matrix.
4. The mass fractions of Ti and C in SMC affect the precipitation times, particle characteristics and precipitation mechanisms of eutectic particles. TiC particles precipitate through divorced eutectic solidification when the mass fractions of Ti and C are low. When the mass fractions of Ti and C are higher, TiC particles precipitate by eutectic solidification.