Effect of Rare Earth Elements on Microstructure and Hot Workability of AISI T15 High Speed Steel

Abstract

To investigate the effect of rare earth elements (REEs) on hot workability and the microstructure evolution of AISI T15 high-speed steel (HSS), hot compression tests were conducted using a Gleeble-1500D thermal simulation machine at the temperature of 1000–1150°C and the strain rate of 0.01–10 s⁻¹. The experimental results show that the flow stress of the modified samples by REEs is lower than that of REEs-free samples under the same conditions, indicating that REEs cause a reduction in deformation resistance (stress level) and improve the deformability of the as-cast high alloy steels at elevated temperatures. A hyperbolic-sine function was adopted to characterize the flow stress as a function of deformation temperature and strain rate and the apparent activation energy of T15 HSS before and after adding REEs were determined to be approximately 557.3 kJ/mol and 513.97 kJ/mol, respectively. Therefore, it is inferred that REEs are beneficial to the occurrence of dynamic recrystallization (DRX), which has also been demonstrated through the determination of characteristic points on the stress-strain curves and the evolution of microstructure. The metallographic analysis also indicates that REEs refine the recrystallized grains and eutectic carbide network and make the deformed microstructure more uniform. Additionally, the maps of power dissipation and instability based on the Dynamic Materials Modeling approach (DMM) were established to evaluate the effect of REEs on hot workability.

1. Introduction

High-speed steel (HSS) is widely used to fabricate cutting tools and wear-resistant components because of its great microstructure stability, prominent mechanical properties and excellent toughness at elevated temperatures.^1,2,3) For this type of steel, there contains numerous alloying elements, mainly W, Mo, Cr, V, Co, etc.^4,5,6,7) Such excellent performance of high-speed steel is largely attributed to the dissolution of alloying elements and the precipitation of carbides. Especially, the sizes, distribution, morphology and content of carbides in the matrix have a critical impact on the comprehensive properties of materials.^8,9) Whereas the higher alloy content facilitates the formation of carbides segregation in the solidification structure and causes the non-uniformity of the microstructure. The composition modification, forging or rolling process and heat treatment are commonly used means to improve the structural homogeneity of high-speed steel. Rare earth elements (hereinafter referred to as REEs) are known to be effective modifiers used to optimize the microstructure and refine the grain. Studies^10,11) show that the total content of eutectic carbides is decreased and distributed into a discontinuous network, and the as-cast structure is refined after adding REEs. To our knowledge, the optimization of the microstructure is usually beneficial to the plastic deformation of the material. The uniformity of the structure and the reduction of eutectic carbides can effectively avoid stress concentration and promote the migration of the slip surface. As an important working technique, hot plastic deformation is broadly applied in industrial fields to improve the performance of the material. However, the deformation of materials is an extremely complicated process, especially for materials with poor plasticity. Unreasonable thermal deformation parameters will cause structural distortion and energy segregation, leading to the initiation of crack sources, even cracking and destruction of the material; Consequently, research on the hot deformation behavior of metal materials at elevated temperatures is of great significance to the formulation of hot working process parameters and the analysis of plastic deformation mechanisms. Thermal compression testing is a proven and effective method to simulate the thermal deformation process of materials.

At present, some research on thermal deformation behavior is carried out on alloy steel, such as pipeline steel,¹²⁾ high strength steel,¹³⁾ plasticity steel,¹⁴⁾ and PM tool steel.¹⁵⁾ Unfortunately, up to now, there is relatively little literature about the influence of REEs on hot deformation behavior of as-cast steel with high content in carbon and alloy. So the purpose of this study is to concentrate on the effect of REEs addition on the hot deformation behaviors of as-cast T15 HSS using the isothermal compression tests conducted at different deformation temperatures and strain rates. The difference among the stress-strain curves, the hot deformation activation energy and constitutive model, DRX behavior and microstructure evolution during hot plastic deformation are analyzed to understand deformation mechanisms and the effect of the modifier. Additionally, processing maps of the experimental steels are established to evaluate the effect of REEs on workability. The findings of this study can be served as a reference for further research.

2. Materials and Methods

The experimental materials used in the present investigation were fabricated via vacuum induction melting (VIM). The basic chemical composition (wt.%) of the ingot detected by direct reading spectroscopy is C, 1.59; W, 12.4; Mo, 0.5; Cr, 4.2; V, 5.1; Co, 5.2; Fe to balance. Here, one was called as T15, the other modified by 0.1% REEs was marked as T15RE. The cylindrical compression samples of 15 mm in length and 8 mm in diameter were machined from the ingot, and all the samples were ground to reduce the surface roughness before the experiment.

Isothermal compression tests were conducted on a Gleeble-1500D thermal simulation machine. The samples were first heated to 1180°C at a rate of 10°C/s and soaked for 5 min for austenitizing to obtain a uniform distribution of the alloying elements before testing. Subsequently, it was cooled down to different deformation temperatures (1000°C, 1050°C, 1100°C and 1150°C) at a speed of 3°C/s, and isothermally maintained for 1 min to homogenize. The samples were then compressed to the extent of 60% deformation by single-pass isothermal compression at various strain rates of 0.01 s⁻¹, 0.1 s⁻¹, 1.0 s⁻¹ and 10 s⁻¹. Finally, water quenched was adopted to retain the high-temperature deformation morphology of the samples. The detailed experimental process is shown in Fig. 1. After the experiment, the deformed samples were cut along the compression axis for the observation of microstructure. The grain structures of the deformed samples were observed and analyzed by using an Olympus PM3 optical microscope (OM). Figure 2 shows the phase equilibrium diagram of T15 HSS calculated by the thermodynamic software JMatPro. From the phase diagram, it can be markedly seen that only austenite phase, MC-type and M₆C-type carbides retain within the temperatures range of 1000–1150°C, and no other phase is generated, namely holding the same microstructure for all samples before deformation. The content of the austenite phase increases with increasing the deformation temperature, while that of both carbides decreases slightly. Due to the lack of corresponding REEs modules, the effect of REEs on the equilibrium phase diagram of T15 HSS cannot be predicted by software. The equilibrium phase diagram drawn in this study is mainly intended to understand the approximate microstructure composition of the steel before deformation, which has little effect on the final experimental results.

Fig. 1.

The schematic diagram of thermal simulation test. (Online version in color.)

Fig. 2.

The phase equilibrium diagram at 950–1210°C for AISI T15 high-speed steel. (Online version in color.)

3. Results and Discussion

3.1. Microstructure of the As-cast High-speed Steel

Figure 3 shows the typical microstructure of as-cast high-speed steel (samples T15 and T15RE) with an average grain size of approximately 20–40 μm, which is mainly composed of black iron matrix and white networks of eutectic carbide. And a large amount of small-sized carbide is also precipitated in the grains. Compared with the network structure in Fig. 3(a), that of T15RE is broken to some extent by adding REEs, and more matrix structure is linked together (see Fig. 3(b)), thus improving the comprehensive performance of the material. The fishbone M₆C-type carbide is formed owing to containing a large sum of elements W and C, as revealed in Fig. 3(c). At higher magnification (Fig. 3(d)), It is seen obviously that the network structure of eutectic carbides is more dispersed and refined. The fish-bone carbide in the ledeburite structure is refined, which becomes shorter, thinner, and tends to be isolated or distributed more homogeneously in a discontinuous network. In addition, the total amount of carbides is reduced. The volume fraction of the carbides of T15RE is estimated to be about 28.05% by Image J software, which is smaller than that of T15 (about 39.51%).

Fig. 3.

The as-cast microstructure of both T15 and T15RE steels: (a) low magnification, T15; (b) low magnification, T15RE; (c) high magnification, T15; (d) high magnification, T15RE.

3.2. Effects of REEs on Hot Deformation Behavior

3.2.1. True Stress-strain Curves

In the process of thermal compression deformation experiment, a series of the true stress-strain curves of experimental steel are obtained by data recording and post-processing, which are frequently used to reveal the variation of flow stress as deformation temperature and strain rate change, as shown in Fig. 4. All true stress-strain curves in the figures exhibit a similar shape characterized as a single peak behavior under different deformation conditions, which is a representative manifestation of the occurrence of DRX behavior.

Fig. 4.

True stress-strain curves of the as-cast high-speed steel under different deformation conditions: (a) $\dot{\epsilon }$=10 s⁻¹; (b) $\dot{\epsilon }$=1.0 s⁻¹; (c) $\dot{\epsilon }$=0.1 s⁻¹; (d) $\dot{\epsilon }$=0.01 s⁻¹. (Online version in color.)

Also apparently, it is seen that the flow stress curves are sensitive to the changes in deformation temperature and strain rate. At the initial stage of deformation, the flow stress climbs rapidly as the strain increases until reaching the maximum value called the peak stress. Afterward, the flow stress gradually decreases and approximatively approaches a stable state little by little. Actually, in the whole course of compression deformation at elevated temperatures, the thermoplastic evolution mechanism of metallic materials is an endlessly competitive process of work hardening and dynamic softening. Before reaching the peak stress, work hardening plays a dominant role due to the increase of dislocation density. As the strain increases, dynamic softening including dynamic recovery (DRV) and DRX dominates, which can counteract or partially counteract the influence of work hardening, leading to a decline of the flow stress. When softening and work hardening reach a dynamic equilibrium, the flow stress will attain a stable state, viz., keeping stress unchanged with the strains rising. Moreover, the peak stress and the steady-state stress increase with the decrease of deformation temperature or the increase of strain rate. When seen as a whole, the flow stress has a distinct change whether the strain rate or the deformation temperature is varied, which means that the deformation temperature and strain rate have a non-negligible effect on the flow stress.

Additionally, the flow stress of the REEs-treated steel (T15RE) is lower than that of REEs-free steel (T15) under the same conditions, except for a few data points caused by artificial errors, differences between samples or other factors. The phenomenon demonstrates that REEs cause a reduction in deformation resistance (stress level) and improve the deformability of the as-cast high-alloying steel, which is attributed to a more uniform microstructure, the refining of eutectic carbide network and lesser segregation of elements, etc.^16,17) It should be noted here that the action mechanism of REEs on T15 HSS in this study is different from that in low-alloy steel or other metal materials. In previous reports, some segregated REEs atoms at the grain boundaries can inhibit the movement of dislocations, thereby increasing the strength of the material.^18,19) In this study, however, REEs greatly optimize the morphology and content of the network structure of eutectic carbide with higher hardness, resulting in a reduction in deformation resistance (flow stress), which is beneficial to the hot plastic working of materials.

3.2.2. The Constitutive Equations and Deformation Activation Energy

As stated above, thermoplastic deformation of the materials is considered to be a dynamic evolution process of energy and microstructure. In the process, the modified Arrhenius equation proposed and verified by Sellars and Tegart,²⁰⁾ which is a hyperbolic-sine mathematics model comprising the thermal deformation activation energy and deformation temperature, is frequently adopted to describe the relationship among the flow stress (σ), strain rate ($\dot{\epsilon }$) and temperature (T) during hot compression deformation of materials, given by:²¹⁾   

$$\dot{\epsilon }=\text{A}{\left[\text{sinh}\left(\alpha \sigma \right)\right]}^{\text{n}}\text{exp}\left(-\text{Q}/\text{RT}\right)$$(1)

Furthermore, at low stress (ασ<0.8) and high stress (ασ<1.2), the relationship between flow stress and strain rate can also be expressed by a power function and an exponential function respectively, as shown in Eqs. (2) and (3):   

$$\dot{\epsilon }={\text{A}}_{\text{1}}{\sigma }^{{\text{n}}_{\text{1}}}$$(2)

  

$$\dot{\epsilon }={\text{A}}_{\text{2}}\text{exp}\left(\beta \sigma \right)$$(3)

Where A₁, A₂, A, n₁, n, α, β are constants independent of experimental conditions, here α=β/n₁; A is a structural factor; n is the stress exponent, Q is the thermal deformation activation energy (kJ/(mol·K)); R is the gas constant (8.314 J/(mol·K)) and T is the absolute deformation temperature (K).

Similar to high-temperature creep, the plastic deformation of metallic materials in elevated temperatures also has a thermally activated process. As a vitally important indicator for reflecting the difficult degree of material deformation, the deformation activation energy may be derived as follows:   

$$\text{Q}=\text{R}{\left[\frac{\partial \text{ln}\dot{\epsilon }}{\partial \text{ln}\left[\text{sinh}\left(\alpha \sigma \right)\right]}\right]}_{\text{T}}{\left[\frac{\partial \text{ln}\left[\text{sinh}\left(\alpha \sigma \right)\right]}{\partial \left(\text{1}/\text{T}\right)}\right]}_{\dot{\epsilon }}=\text{Rn}K$$(4)

Notably, when the parameters are known, the thermal deformation activation energy and constitutive equations can be obtained to describe the rheological properties of materials at elevated temperatures. To take T15RE as an example, the process of determining the material constants is briefly described, and the peak stress σ_p here is selected to solve the parameters in the constitutive equations.

Based on the stress-strain curves of T15RE and combined with the above equations, the plot of $\text{ln}\dot{\epsilon }$ vs. lnσ_p and the plot of $\text{ln}\dot{\epsilon }$ vs. σ_p are shown in Figs. 5(a), 5(b), respectively. By utilizing the linear regression method, the average values of the slopes in both figures representing n₁ and β separately are calculated as n₁=8.03, β=0.04, so α=β/n₁=0.0055. Analogously, the relationship curves of $\text{ln}\dot{\epsilon }$ vs. ln[sinh(ασ_p)] and ln[sinh(ασ_p)] vs. 1000/T are plotted in Figs. 5(c), 5(d), and the average values of the slopes are determined as n=5.95 and K=10.39, respectively. Consequently, the apparent activation energy of T15RE is obtained, viz., Q_T15RE=513.97 kJ/(mol·K). The data points basically have a good linear relationship with the regression line in the figures, indicating that calculated parameters have good accuracy.

Fig. 5.

The relation curves for obtaining parameters of the constitutive equation: (a) lnσ_p vs. $\dot{\epsilon }$; (b) σ_p vs. $\dot{\epsilon }$; (c) ln[sinh(ασ_p)] vs. ln$\dot{\epsilon }$; (d) ln[sinh(ασ_p)] vs. (1000/T). (Online version in color.)

Furthermore, the relationship between the strain rate and the deformation temperature can also be represented by the Zener-Hollomon parameter (Z parameter) in an exponential function,^22,23) as follow:   

$$\text{Z}=\dot{\epsilon }\text{exp}\left(\text{Q}/\text{RT}\right)=\text{A}{\left[\text{sinh}\left(\alpha \sigma \right)\right]}^{\text{n}}$$(5)

The relationship curve between lnZ and ln[sinh(ασ_p)] is plotted, as presented in Fig. 6, which is adopted to solve the constant lnA by seeking the intercept of the regression curve. Ultimately, the value of the parameters A is determined to be 8.18×10¹⁸.

Fig. 6.

The relationship curve of lnZ and ln[sinh(ασ_p)]. (Online version in color.)

By repeating steps as described above, all the unknown relevant parameters in the constitutive equation of T15 steel are determined, i.e., ${\text{n}}_{\text{1}}^{*}$=8.54, β^*=0.044, α^*=0.0052, n^*=6.33, A^*=4.37×10²⁰, respectively, and then Q_T15=557.33 kJ/mol. What is certainly clear is that the thermal deformation activation energy of T15RE is lower than that of T15. Put another way, the addition of REEs causes the decrease of the activation energy, implying that the occurrence of DRX behavior is more easily achieved.²⁴⁾

Moreover, according to the definition of the hyperbolic sine function and the inverse function, the flow stress in Eq. (5) can be expressed as follows:²⁵⁾   

$$\sigma =\left(\text{1}/\alpha \right)\text{ln}\left\{{\left(\text{Z}/\text{A}\right)}^{\text{1}/\text{n}}\text{+}{\left[{\left(\text{Z}/\text{A}\right)}^{\text{2}/\text{n}}+\text{1}\right]}^{\text{1}/\text{2}}\right\}$$(6)

And thus, substituting the determined parameter values into the Eqs. (5) and (6), the constitutive equations for T15 and T15RE described by the Z parameter during hot deformation are determined respectively, as shown below:   

$$\begin{array}{l}{\sigma }_{\text{T15RE}}=\\ \text{1}/\text{0}\text{.0055ln}\left\{{\left(\text{Z}/\left(\text{8}\text{.18}\times {\text{10}}^{\text{18}}\right)\right)}^{\text{1}/\text{5}\text{.95}}\text{+}{\left[{\left(\text{Z}/\left(\text{8}\text{.18}\times {\text{10}}^{\text{18}}\right)\right)}^{\text{2}/\text{5}\text{.95}}+\text{1}\right]}^{\text{1}/\text{2}}\right\}\end{array}$$(7)

  

$${\text{Z}}_{\text{T15RE}}=\dot{\epsilon }\text{exp}\left(\text{513}\mathrm{\hspace{0.17em} }\text{970}/\text{8}\text{.233T}\right)$$(8)

  

$$\begin{array}{l}{\sigma }_{\text{T15}}=\\ \text{1}/\text{0}\text{.0052ln}\left\{{\left(\text{Z}/\text{(4}\text{.37}\times {\text{10}}^{\text{20}}\right)}^{\text{1}/\text{6}\text{.33}}+{\left[{\left(\text{Z}/\text{(4}\text{.37}\times {\text{10}}^{\text{20}}\right)}^{\text{2}/\text{6}\text{.33}}+\text{1}\right]}^{\text{1}/\text{2}}\right\}\end{array}$$(9)

  

$${\text{Z}}_{\text{T15}}=\dot{\epsilon }\text{exp}\left(\text{557}\mathrm{\hspace{0.17em} }\text{330}/\text{8}\text{.233T}\right)$$(10)

3.3. Eigenvalues on True Stress-strain Curves

As is well-known, the stress-strain curves derived from thermal compression experiments are closely related to the microstructure evolution of the materials during hot deformation, and the former is the external embodiment, while the latter is the internal essence. And it is not difficult to discover the variation trend of curves at different deformation temperatures and strain rates from the true stress-strain curves, whereas it can be quite arduous to locate eigenvalues directly on the curves, especially critical strain and corresponding critical stress. Scholars at home and abroad have done numerous studies on the method of extracting the eigenvalues from the stress-strain curves, among which the second-order derivative method described by Poliak and Jonas^26,27,28) is widely adopted to determine the eigenvalues. In this method, the work hardening rate (θ=dσ/dε), frequently used to research DRX behavior, is treated as a function of flow stress. The critical stresses for the occurrence of DRX are obtained from the inflection points on the θ vs. σ curves under different deformation conditions. Based on the basic knowledge of partial differentiation, it can be known that the relationship equation can be derived as follows: −∂(lnθ)/∂ε=−∂θ/∂σ. So the critical stresses are alternatively available by solving the inflection points on the lnθ vs. ε curves or the minimums points (−∂²(lnθ)/∂ε²=0) on the −∂(lnθ)/∂ε vs. ε curves, analogously corresponding to the inflection points on the θ vs. σ curves or the minimums points (−∂²θ/∂σ²=0) on the −∂θ/∂σ vs. σ curves, respectively.

In this section, the relationship curves of work-hardening rate versus true strain at a strain rate of 1.0 s⁻¹, 10 s⁻¹ for deformed samples are plotted, as shown in Fig. 7, where the solid lines with various colors represent T15, while the dashed lines belong to T15RE. In the case of Fig. 7(a), the logarithm of work hardening exhibits a downward trend as strain increases. More specifically, the natural logarithm of the work hardening rate expresses an initial decrease, followed by passing a gentle slope stage, and finally continues to decrease with increasing strain. The characteristic behavior is more pronounced at a higher temperature. The first inflection points on the lnθ vs. ε curves mean the beginning of DRX, and besides, it is also found that the inflection point in the figure moves to the left as the temperature rises. The gentle slope stage is the hardening stage, and the length of the gentle slope stage at higher temperature is shorter than that at low temperature, viz., the shorter of hardening stage, which indirectly illustrate that the higher the deformation temperature, the more conducive to the initiation of the DRX behavior, and the more intense. Compared to Fig. 7(a), the shape of more curves shown in Fig. 7(b) shows similarity to some degree, demonstrating that the influence of temperature on the work hardening rate is relatively weakened at a higher strain rate.

Fig. 7.

The relationship curves of work-hardening rate versus true strain at different deformation conditions: (a) The lnθ vs. ε curves at 1.0 s⁻¹; (b) The lnθ vs. ε curves at 10 s⁻¹; (c) The −∂(lnθ)/∂ε vs. ε ln curves at 1.0 s⁻¹; (d) The −∂(lnθ)/∂ε vs. ε curves at 10 s⁻¹. (Online version in color.)

In addition, a more discovery, the inflection points on the lnθ vs. ε curves for T15RE appear earlier than that for T15 in general, as illustrated in Figs. 7(a), 7(b), that is, the DRX behavior is more likely to occur in the thermal deformation process due to REEs effect, and the phenomenon is more significant and easier to identify in Figs. 7(c), 7(d), which is consistent with the calculation results above of the thermal deformation activation energy.

According to the curves in Fig. 7, the characteristic values on true stress-strain curves for T15 and T15RE at a strain rate of 10 s⁻¹, 1.0 s⁻¹ with various deformation temperatures, including the peak stress and the critical stress, as well as corresponding to the peak strain and the critical strain, are determined, and plotted as a function of the deformation temperatures, as shown in Fig. 8.

Fig. 8.

The relationship curves between characteristic values and deformation temperatures. (a) ε_p vs. T; (b) ε_c vs. T; (c) σ_p vs. T; (d) σ_c vs. T. (Online version in color.)

As far as the eigenvalues in the present studied material are concerned, more clear differences and information among them can be discovered in Fig. 8 instead of the curves in Fig. 7. In plain sight, the higher the deformation temperature, the smaller the eigenvalues on the strain-stress curves, and the smaller the strain rate, the smaller the eigenvalues. As a case of the peak stress, the values of peak stress for T15 at the strain rate of 1.0 s⁻¹, 10 s⁻¹ and at 1000°C are 303.5 MPa and 357 MPa respectively, while corresponding that for T15RE are 284.9 MPa and 334 MPa, which are relatively smaller. As regards the critical stress, it is the same as the peak stress case. For example, the value of critical stress for T15 steel at 1000°C with the strain rate of 1.0 s⁻¹and 10 s⁻¹ are 301.1 MPa and 353.7 MPa respectively, larger than that of T15RE determined as 281.6 MPa and 332 MPa at the same conditions. And although the gap between the corresponding values gradually decreases with the increase of temperature, the characteristic always exists, irrespective of deformation temperatures and strain rates. The phenomenon further indicates that the plastic deformation capacity of T15 steel has been significantly improved during hot compression due to the REEs effect. In terms of strain, adding REEs likewise plays a positive and promotional role in reducing the corresponding strain values. No matter is peak strain, critical strain, always appears ahead of time, except for a few individual points, as shown in Figs. 8(c)–8(d). A series of modifications, such as controlling grain boundary segregation, reducing apparent activation energy and the number of grain boundaries, can lower the “threshold” of certain reactions in the deformation process, making it more likely to occur.

It should be emphasized that some errors may be generated because of involving the polynomial fitting and the derivation of the curves in the process of seeking the eigenvalues, which further affect the accuracy of the results, and yet the solution method is still of great reference value for studying the effect of REEs on the DRX behavior of T15 HSS.

3.4. Microstructure Evolution after Thermal Deformation

A series of the deformed microstructure images of the experimental steels are shown in Figs. 9 and 10, which are used to study the microstructure evolution with different deformation conditions, as well as the effect of REEs on which. After hot compression, the deformed grains have been basically equiaxed, and the eutectic carbides are generally distributed in a network along the grain boundary.

Fig. 9.

Typical microstructures of the samples deformed at a strain rate of 1.0 s⁻¹and different temperatures of (a) 1050°C/T15; (b) 1100°C/T15; (c) 1150°C/T15; (d) 1050°C/T15RE; (e) 1100°C/T15RE; (f) 1150°C/T15RE. (Online version in color.)

Fig. 10.

Typical microstructures of the samples deformed at a temperature of 1000°C and various strain rates of (a) 10 s⁻¹/T15; (b) 0.1 s⁻¹/T15; (c) 0.01 s⁻¹/T15; (d) 10 s⁻¹/T15RE; (e) 0.1 s⁻¹/T15RE; (f) 0.01 s⁻¹/T15RE.

Figure 9 shows the microstructure of samples deformed at a strain rate of 1.0 s⁻¹ and different deformation temperatures of 1050°C, 1100°C and 1150°C, respectively. When the deformation condition is 1.0 s⁻¹ and 1050°C, the original microscopic morphology is significantly improved due to the DRX effect, compared with the as-cast microstructure. The network structure of eutectic carbides is also crushed, and part of the carbides along the grain boundaries are decomposed during austenitizing and dissolved in the matrix, which leads to the reduction of eutectic carbides between grains. Yet there are still many large-sized carbides that fail to decompose at this temperature and show an uneven distribution after deformation as exhibited in Fig. 9(a). As the deformation temperature increases, the migration rate of grain boundaries increases, making the grains gradually grow. Even some eutectic structures also begin to aggregate to form a banded structure, as shown in the red dashed area (see Fig. 9(c)). These characteristic structures with hard and brittle properties are prone to stress concentration during high-temperature plastic deformation. Particles or interfaces that easily cause crack initiation may be formed, leading to rheological instability of the material, which is also consistent with the law of instability zone in the processing map. Furthermore, the differences in grain size and carbides distribution between T15 and T15RE are glaringly obvious with different strain rates and deformation temperatures. Under the same deformation conditions, the modified sample has a more uniform microstructure distribution, smaller grains, and less carbide. Figure 10 represents the deformed microstructure of the samples compressed at the deformation temperature of 1000°C and the strain rates of 1.0 s⁻¹, 0.1 s⁻¹, 0.01 s⁻¹. When the strain rate range is 0.1–1.0 s⁻¹, a good microstructure can be obtained, with fine grains, uniform carbide distribution and no coarse network structure. However, as the strain rate decreases, the deformed microstructure of the samples gradually presents a trend of grains growth and carbides network coarsening. This is because the reduction in strain rate can provide more sufficient time for atomic diffusion and grain boundary migration, which will promote the growth of recrystallized grains. Similarly, adding REEs is favorable to optimizing microstructure at a deformation temperature of 1000°C regardless of the strain rate. No coarse banded structure is observed in T15RE samples, but more small-sized carbides with a polygonal or nearly spherical shape, just as illustrated in Figs. 10(d)–10(f). As well known, due to the larger atomic radius than iron atoms, the doped REEs atoms tend to occupy defects in the microstructure to reduce the free energy of the system, such as vacancies, dislocations, grain boundaries, phase interfaces, instead of forming a solid solution. It is pointed out in the literature that REEs can improve the equilibrium solid solubility product of carbide-forming elements in the austenite zone, reduce the solution temperature of carbides, and then promote the dissolution of more alloying elements into the matrix during austenitizing.^29,30) Previous relevant studies have also shown that the interaction coefficient of REEs with carbide forming elements are all negative in metal materials, namely decreasing the activity of these elements,^31,32) which means that the segregated REEs can effectively retard the diffusion of solute atoms, thereby inhibiting the precipitation of carbides from the matrix during solidification. Therefore, the degree of segregation of alloying elements and the size and content of eutectic carbides network, whether in the original as-cast microstructure or the deformed microstructure, have been improved after adding REEs. Meanwhile, the segregated REEs at the grain boundary can reduce the interface energy and slow down the migration of grain boundaries to inhibit the growth of grains at elevated temperatures. Besides, REEs can reduce the anisotropy of the interface energy of the carbide particles, making the velocity vectors of interface migration in each direction approximate, and so the more carbides tend to be polygonal or nearly spherical instead of lamellar after deformation. Compared with the REEs-free samples, a series of optimizations and adjustments brought by REEs finally made the microstructure more uniform and improved the overall performance of the material.

3.5. Hot Workability of Steel

To further comprehend the effect of REEs on the hot workability and the regularity of experimental materials during thermoplastic deformation, it is necessary to study the processing map proposed by Prasad and Gegel.^33,34) To date, the processing map based on the dynamic material model (DMM) has been widely adopted to optimize hot working processes of metallic materials, such as superalloy,³⁵⁾ Titanium alloys,³⁶⁾ Aluminum alloys,³⁷⁾ and Magnesium alloys.³⁸⁾ In the DMM model, the total power P consists of two complementary parts, which can be defined as follows:   

$$\text{P}=\sigma \dot{\epsilon }={\int }_{\text{0}}^{\dot{\epsilon }}\sigma \mathrm{d}\dot{\epsilon }+{\int }_0^{\sigma }\dot{\epsilon }\mathrm{d}\sigma =\text{G}+\text{J}$$(11)

Where G is the energy dissipation of the material during plastic deformation, the majority of which is converted to heat; J is the energy dissipation in the process of microstructure evolution, including dynamic recovery, recrystallization, etc.

The efficiency of power dissipation may be represented by the symbol η, which is used to indicate the workability of the materials at a variety of temperatures and strain rates and determined by the ratio of a non-linear power dissipation occurring instantaneously within the material to an ideal linear power dissipation,²³⁾ given by:   

$$\eta =\text{J}/{\text{J}}_{\text{max}}=\text{2m}/\left(\text{m}+\text{1}\right)$$(12)

Where m is the strain rate sensitivity exponent and ultimately determined at a given strain and deformation temperature, which is described as:³⁹⁾   

$$\text{m}=\frac{\text{dJ}}{\text{dG}}{|}_{\epsilon \text{,T}}=\frac{\text{dln}\sigma }{\text{dln}\dot{\epsilon }}{|}_{\epsilon \text{,T}}$$(13)

The variation of the efficiency of power dissipation η with temperature and strain rate in the three-dimensional space is always plotted as a contour map in a two-dimensional plane with temperature and strain rate as axes, expressing iso-efficiency contours.⁴⁰⁾ Figure 9 shows the comparisons of the efficiency of the power dissipation η for both T15 and T15RE steels at strains of 0.45, 0.65 and 0.85 respectively via a series of contour color fill maps. Wherein the efficiency values in the red domain are larger than 0.3 (η ≥ 30%), which is mainly located at a lower strain rate, and the efficiency value increases with the decrease of strain rate. There are two small red domains at strains of 0.45, 0.65 and 0.85 for T15 in Figs. 9(a)–9(c), while there exists one large red domain for T15RE, as shown in Figs. 9(d)–9(f). Besides, the area of the red domain increases as true strain increases. The efficiency value of dissipation power related to DRX is generally considered to be 30–50%.^40,41,42) REEs increases the range of power dissipation coefficient of the steel, making it more prone to the DRX process during thermal deformation, which can homogenize microstructure and refine the precipitated phase, thereby improving the material performance.

The parameter $\xi (\dot{\epsilon })$ is proposed based on the extremum principle of irreversible thermodynamic, served as an instability criterion for determining whether rheological instability occurred, and can be written as:⁴³⁾   

$$\xi \left(\dot{\epsilon }\right)=\mathrm{\partial }\text{ln}\left[\text{m}/\text{(1}+\text{m)}\right])/\mathrm{\partial }\text{ln}\dot{\epsilon }+\text{m}<\text{0}$$(14)

In terms of Eq. (14), it may be inferred that the flow instability region will be generated when $\xi (\dot{\epsilon })$ becomes negative, which is frequently represented by the shaded area in processing maps.

Processing maps of the specimens deformed at a strain of 0.85 are generated by contouring the efficiency of power dissipation η and the instability parameter $\xi (\dot{\epsilon })$ within the temperature range from 1000°C to 1150°C and the strain rate range from 0.01 s⁻¹ to 10 s⁻¹, as shown in Fig. 10. The various numbers on the contour lines represent the different efficiency of power dissipation η. Generally, the stability domains are mainly located somewhere with higher η, indicating that more heat energy is dissipated by the evolution of microstructure (mainly DRX). Meanwhile, the instability regions are more inclined to occur at the deformation conditions of higher strain rates and lower deformation temperature (the larger LT cyan shaded area at low temperatures). And by contrast, the instability mechanism is more sensitive to high strain rate than deformation temperature. For T15 HSS, a larger instability region is generated at a strain rate of 1.0–10 s⁻¹ and overlays the entire tested deformation temperature range. While there exist three small instability domains for T15RE as follows: one occurs at the temperature of 1000°C to 1035°C and the strain rate of 0.4 s⁻¹ to 1.5 s⁻¹, and another occurs at the temperature of 1030°C to 1055°C and the strain rate of 4.47 s⁻¹ to 10 s⁻¹. At a higher strain rate, the dislocation generated in the deformation process cannot be timely transferred due to insufficient deformation time and accumulated at grain boundaries, causing stress concentration. And while at a lower temperature, the small driving force of atoms causes rheological instability easily as well. And the third region lies in the temperature from 1065°C to 1150°C and the strain rate from 0.17 s⁻¹ to 1.78 s⁻¹, despite having a maximum efficiency of the power dissipation of over 36%. This phenomenon demonstrates that flow instability can still occur in some areas with a higher efficiency, which is attributed to the mismatch between heat accumulation and consumption.⁴⁴⁾ The thermal energy produced by deformation fails to be diffused rapidly owing to the poor thermal conductivity of the material and local energy segregation is generated. Besides, the LT cyan shadow area in Fig. 10(b) is visibly reduced. To wit, the addition of REEs expands the hot working window of high-speed steel, consequently optimizing its hot workability.

In this study, the optimum processing condition for T15 steel is in the deformation temperature range from 1000°C to 1030°C and strain rate range from 0.01 s⁻¹ to 0.03 s⁻¹, while that of T15RE is at the temperature of 1000–1130°C with a strain rate of 0.01–0.06 s⁻¹.

Fig. 11.

Power dissipation maps at the strain of (a) 0.45/T15; (b) 0.65/T15; (c) 0.85/T15; (d) 0.45/T15RE; (e) 0.65/T15RE; and (f) 0.85/T15TR. (Online version in color.)

Fig. 12.

The processing maps of both T15 and T15RE steels with a strain of 0.85. The LT cyan regime corresponds to the flow instability region ($\xi (\dot{\epsilon })$ < 0): (a) T15; (b) T15RE. (Online version in color.)

4. Conclusion

(1) All true stress-strain curves show a single peak characteristic associated with DRX behavior, and the flow stress curves are sensitive to the changes in deformation temperature and strain rate. During deformation, REEs addition causes a reduction in deformation resistance (flow stress level) under the same conditions and improves the deformability of the as-cast T15 steel.

(2) The constitutive equations that describe the flow stress as a function of strain rate and deformation temperature are developed for both T15 and T15RE steels, and the hot deformation activation energy of about 513.97 kJ/mol for T15RE steel is lower than that of T15 steel (557.3 kJ/mol), indicating the DRX behavior occurs more easily.

(3) Eigenvalues on true stress-strain curves via the evolution of the Poliak and Jonas method are determined. The peak stress and critical stress, as well as the corresponding peak strain and the critical strain, will all decrease with the increase of deformation temperature and decrease of strain rate, and adding REEs can reduce the numerical value of the corresponding eigenvalues of AISI T15 steel.

(4) The deformed grains have been basically equiaxed and the eutectic carbides are mainly distributed in a network along the grain boundary. A higher temperature or lower strain rate will promote the growth of recrystallized grains. The network structure of eutectic carbides at the grain boundary after adding REEs is significantly refined, and the grains are more uniform.

(5) Processing maps based on the dynamic material model (DMM) at the strain rate of 0.01–10 s⁻¹ and deformation temperature of 1000–1150°C with a strain of 0.85 are established. The efficiency of power dissipation η after adding REEs increases with the increase of true strain, and the instability region associated with cracks is more prone to occur at a higher strain rate and a lower temperature. The optimum heat processing window is identified to be 1000–1030°C and 0.01–0.03 s⁻¹ for T15, while 1000–1130°C and 0.01–0.06 s⁻¹ for T15RE.

Acknowledgment

This work was supported by Fundamental Research Funds for the Central Universities (FRF-TT-20-04 and FRF-GF-19-005B). The authors also would like to thank the support from Ms. Yan Zhang, during the hot compression tests performed at the Gleeble thermal simulator.

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