**1. Introduction**

GCr15 bearing steel, with high carbon and chromium concentrations, is widely used for the rolling elements in bearing. It is routinely treated by spheroidising, quenching and tempering (QT) to obtain a microstructure comprised of spherical cementite, small amount of retained austenite and tempered martensite. Generally, bearing needs to be served under high speed and high load conditions. It has been reported [1,2] that the service temperature of ordinary bearing may reach 200 ◦C, while the aerospace bearing can be serviced up to 300 ◦C. Moreover, deterioration of bearing performance may occur during the cyclic contact loading. Microstructural development under the temperature and stress field is the crucial factor influencing the service life of the bearing steel [2,3]. Therefore, clarifying the microstructural evolution caused by the temperature and stress field to understand the mechanism of performance degradation is always an attractive topic.

Many researchers have used transmission electron microscope [4], resistivity [5], thermal analysis [6,7] and other methods to study the microstructural evolution of bearing steel during tempering or aging. There are also some studies focusing on the effect of stress on the transformation of retained austenite [8,9] and carbide precipitation [10] without an applied temperature field. Nevertheless, these studies do not consider the coupling effect of the stress field and temperature field on the microstructural transformation behaviors. Therefore, it is necessary to study the effect of stress on microstructures development during the non-isothermal process. Until now, some studies have been concentrated on the effect of stress on phase transformation behaviors, such as isothermal ferrite and pearlite transformations [11], austenite decomposition [12], martensitic phase transformations [13], bainitic phase transformation [14] and so on. However, to our best knowledge, there is still no research concerning on the microstructural transformation, and especially the cementite precipitation behaviors of GCr15 bearing steel during the non-isothermal process under applied stress.

As the non-isothermal process is close to the high-temperature tempering process for GCr15 bearing steel, the microstructure evolution during tempering should be clarified first. According to the theory of tempering, the process of tempering can be divided into several stages with the increase of temperature [15]: (1) Stage 0, 0~80 ◦C, the migration of carbon atoms to dislocation and defects [16]; (2) Stage I, 100~200 ◦C, the precipitation of ε/η transition carbides [17]; (3) Stage II, 250~350 ◦C, the decomposition of retained austenite [18]; (4) Stage III, 300~400 ◦C, the conversion of the transition carbide into cementite [19].

It is well known that the finished bearing products have gone through Stage 0 and Stage I after the traditional QT treatment, so the aim of the present work is mainly to investigate the microstructural evolution (Stage II and Stage III) during the higher tempering temperature under different tensile stresses. The kinetics parameters of microstructural development were compared and analyzed considering the effect of applied tensile stress. At the same time, the impact of applied stress on microstructural evolution during the non-isothermal process was analyzed based on microstructural analysis. In particular, the mechanism of tensile stress on cementite precipitation was discussed.

#### **2. Experimental and Theory**

The material used in the current study was GCr15 bearing steel, with the nominal composition as presented in Table 1. The experimental materials were austenitized at 860 ◦C for 15 min and followed by quenching in oil at 60 ◦C for 5 min. Then they were tempered at 160 ◦C for 2 h. After the QT heat treatment, the steel was designed to be treated under the couple action of the stress and temperature field.


**Table 1.** The chemical composition of GCr15 bearing steel (wt %).

In order to observe the microstructural evolution during the non-isothermal process under different tensile stresses, the specimens with a size of φ 10 mm × 105 mm were subjected to a continuous tensile stress (0, 20 and 40 MPa) and heated from room temperature to 300 ◦C (considering the limit service temperature of bearing and the temperature range of stage II and stage III) at the heating rate of 10 ◦C/min by means of a Gleeble 3500 thermo-mechanical simulator. The microstructure of these specimens was examined by a field-emission scanning electron microscope (FESEM, FEI Quanta 450, Hillsboro, OR, USA) and transmission electron microscopy (TEM, JEOL-2100F, Akishima, Japan). The specimens for FESEM were etched in an alcohol solution containing 4% nitric acid (volume fraction) for 10 s. The specimens for TEM were prepared by mechanically polishing and then electro-polishing in a twin-jet polisher (Struers, TenuPol-5, Ballerup, Denmark) using a solution of 10% perchloric acid and 90% acetic acid. Moreover, X-ray diffraction (XRD) data were recorded on a D/MAX-RB diffraction analyser (Rigaku, Tokyo, Japan) at 12 kW.

Activation energy, as an important kinetic parameter, can be used to evaluate the difficulty of phase transformation. The Kissinger method [20,21] and isoconversional method [22,23] are the most widely used methods to calculate activation energy, and they are usually combined with thermal analysis. In this study, for analysing the influence of tensile stress on the kinetic of microstructural evolution during the non-isothermal process, a group of specimens was heated to 500 ◦C under a 40 MPa tensile stress at different heating rate of 10, 15 and 20 ◦C/min with the aim of calculating the activation energy. It was noted that the thermal expansion curves were recorded by measuring the variation in diameter during the non-isothermal process. Considering the activation energy determined from the thermal expansion curves and heat flow curves (both as functions of the heating rate) is really close [7,24], the kinetic parameters of microstructural evolution without stress was obtained by differential scanning calorimetry (DSC) experiments using a STA449F3 thermal analyzer (Netzsch, Selb, Germany) as a comparison. The specimens for DSC were cut into φ 4 mm × 0.6 mm and then heated from ambient temperature to 500 ◦C at different heating rates of 5, 10, 15 ◦C/min, respectively. Here, pure aluminum disks were used as the reference material, and the baseline was determined by performing a rerun at the same heating rate.

The effective activation energies of different stages during the non-isothermal process were calculated by using the Kissinger equation based on the fact that the peak temperature depends on the heating rate:

$$\ln\left(T\_P^2/\mathcal{Q}\right) = Q/\mathcal{R}T\_P + \text{const} \tag{1}$$

where *TP* is the peak temperature, ∅ is the heating rate, and R is the gas constant (R = 8.314 kJ/mol). By plotting In*T*2*P*/∅ as a function of 1/*TP*, the activation energy can be obtained.

The differential isoconversional method was also employed to obtain the kinetic parameters of microstructural evolution during the non-isothermal process under different tensile stress. In this method, the reaction rate can be assumed to be a function of temperature (*k*(*T*)) and converted fraction (*f*(*α*)), which is expressed as:

$$d\mathfrak{a}/dt = k(T)f(\mathfrak{a})\tag{2}$$

where α and *T* is the converted fraction and temperature, respectively. *k*(*T*) can be obtained by the Arrhenius equation as:

$$k(T) = A \cdot \exp(-Q/\mathcal{R}T) \tag{3}$$

where *A* is the pre-exponential factor and *Q* is the activation energy. By combining Equations (2) and (3) and taking the equation to a logarithm, then the differential isoconversional method can be proposed, as follows:

$$
\ln(d\mathfrak{a}/dt) = \ln[A\cdot f(\mathfrak{a})] - \mathbb{Q}/\mathbb{RT} \tag{4}
$$

For the non-isothermal process with a constant heating rate ∅, Equation (4) can be expressed as:

$$\ln\left[\mathcal{Q}\cdot(da/dt)\right] = \ln\left[A\cdot f(\mathfrak{a})\right] - Q/\mathbb{R}T \tag{5}$$

By plotting ln[<sup>∅</sup>·(*dα*/*dt*)] as a function of 1/*T*, the slope indicates a value of *Q*/R. Then the curve of the activation energy varying with the converted fraction can be further obtained.
