3.2 A kinetics model of martensite transformation under cyclic loading
By combining the TI model [20] with the Smaga model [22], a kinetics model which can describe the transformation law of retained austenite under the cyclic loading is obtained, as shown in Eq. (1). According to the volume fraction of martensite measured in the experimental steel, and based on the kinetics model of martensite transformation under the cyclic loading with TI model and Smaga model, the kinetics model of martensite transformation under cyclic loading of the experiment steel is established.
$${f}_{M}=k{\epsilon }_{a}{[1\text{exp}\left(\varPhi {S}_{p}\right)]}^{m}$$
1
Where k, Φ, m are material parameters, εa is the strain amplitude, Sp is the true cumulative plastic strain, and fM is the volume fraction of martensite.
$${ S}_{p}=4N{\epsilon }_{a}^{p}$$
2
Where \({\epsilon }_{a}^{p}\) is the true plastic strain amplitude at half of the fatigue life (0.5 Nf) and N is the cycle number (C).
$${\epsilon }_{a}^{p}={\epsilon }_{a}\frac{{\sigma }_{a}}{E}$$
3
Where \({\sigma }_{a}\) is the stress amplitude (MPa) at half the fatigue life (0.5 Nf), and E is the elastic modulus (MPa).
By introducing Eq. (2) and Eq. (3) into Eq. (1), it can be concluded that:
$${f}_{M}=k{\epsilon }_{a}{\left\{1exp\left[4\varPhi N\left({\epsilon }_{a}\frac{{\sigma }_{a}}{E}\right)\right]\right\}}^{m}$$
4
According to Eq. (4), the kinetics model parameters are determined by fitting the measured data of α´ martensite transformation of the experimental steel under the strain amplitude of 1.1%, as shown in Table 2.
Table 2 Fitting values of material constants
Material constants

k

Φ

m

Fitting value

4

0.502

1.2

The values of material constant in Table 2 are brought into Eq. (4), and the kinetics model of martensite transformation under the cyclic loading is obtained as follows:
$${f}_{M}=4{\epsilon }_{a}{\left[1{exp}\left(2.008N{\epsilon }_{a}^{p}\right)\right]}^{1.2}$$
5
The curves of the above kinetics model under different strain amplitudes are shown in Fig. 7. The correlation between the values of the cyclic loading test and the kinetics model is more than 90%. It can be seen that the model can accurately describe the volume fraction of martensite transformation under the cyclic loading.
By deriving the kinetics curve of martensite transformation under the cyclic loading, the curve of martensite transformation rate with cycles is obtained, as shown in Fig. 8. It can be seen from the figure that the martensite transformation rate of the experimental steel is not constant under the cyclic loading. The transformation rate gradually increases at the initial stage of cyclic deformation. And after reaching the peak, it gradually decreases to zero. Moreover, at the initial stage of cyclic deformation, the larger the strain amplitude is, the larger the martensite transformation rate is, and the earlier it reaches the peak. From the law of strain amplitude of 0.5%, 0.7%, and 0.9% in Fig. 8, it can be seen that the larger the strain amplitude is, the faster the martensite transformation reaches saturation, that is, the larger the strain amplitude is, the faster the martensite transformation rate drops to zero.
3.3 The microscopic mechanism of martensite transformation under cyclic loading
In this study, quasi insitu cyclic test with a strain amplitude of 1.1% was carried out to study the microscopic mechanism of martensite transformation under the cyclic loading. The five cycles selected were 0, 5, 15, 50 and 150 (fatigue), respectively. The specimens for microscopic observation were cut from the center position of the gauge section.
3.3.1 EBSD analysis
Figure 9 is the EBSD analysis diagram of the experimental steel at the initial state and different cycle numbers. Due to the large scanning step set in the test, it belongs to the micron level, while ε martensite belongs to the nanometer level, and ε martensite can not be identified. The observation of ε martensite is analyzed by TEM in the following. Figure 9(a) shows the microstructure at the initial state after solution treatment at 1050 ℃, with bodycentered cubic(BCC) structure in red and facecentered cubic(FCC) structure in green. It can be seen from the EBSD images that the overall morphology and orientation of the two phases are not obvious, and the austenite with FCC structure is distributed in the ferrite matrix with BCC structure as an island. There are also a few red areas in austenite, which can be divided into two types. The first type is distributed at the intersection of austenite grain boundaries with a strip shape; The second one is distributed in the austenite grain, which is wedgeshaped. These red areas may be α´ martensite with the BCC structure produced during the solution treatment.
In Fig. 9, the ferrite and the α´ martensite are both BCC, so both of them are marked in red. The α´ martensite is produced by austenite, which is located in the austenite. It can be seen from the figure that the straininduced α´ martensite is in the shape of a sieve, as shown in the yellow dotted line in Fig. 9.
It can be seen from Fig. 9(b) that only a small portion of austenite grains can produce martensite at the 15th cycle, which indicates that the austenite has poor stability and it is easy to transform into martensite, but it has a low volume fraction. According to Fig. 8, the volume fraction and the rate of martensite transformation change with cycles, it can be seen that the volume fraction of martensite transformation is less in the range of 0 to 15 cycles (0C < N ≤ 15C). But the transformation rate increases rapidly, and it reaches the peak at the 15th cycle; α´ martensite still increases with the increase of cycles (N > 15C). Compared with the EBSD diagram at the 15th cycle, the EBSD diagram at the 50th cycle shows that the amount of martensite increased. The martensite is flaky, and the austenite tends to be sievelike. This phenomenon is more obvious in the fatigued specimen. According to Fig. 8, the rate of martensite transformation gradually decreases after 15 cycles, but the volume fraction of martensite still increases gradually and reaches the maximum at fatigue. The transformation rate drops to zero at the same time.
Martensite transformation is affected not only by the stability of austenite, but also by the strain of the parent phase. It can be seen from Fig. 9 that the transformation of austenite does not occur uniformly under the cyclic loading. Martensite transformation occurs only in a portion of austenite at the initial cyclic stage. With the increase of austenite strain, martensite transformation occurs in a larger portion of austenite at the later stage of cyclic loading. It can be seen from the figure that in addition to a small portion of martensite in austenite grains, martensite is also produced at austenite grain boundaries at the initial cyclic stage. This is because there are stress concentrations at grain boundaries, where much more strain is obtained preferentially, thus reaching the starting point of martensite transformation preferentially, and then martensite transformation occurs.
Previous studies have shown that the transformation of austenite is related to the orientation of austenite grains, which is relative to strain direction under uniaxial tensile. As shown in Fig. 10 combined with Fig. 9, for the austenite grain orientation in the experimental steel under the cyclic loading with a strain amplitude of 1.1%, the martensite transformation mainly occurs in the austenite with grain orientation < 101 > after 15 cycles; The austenite with grain orientations < 001 > and < 101 > produce martensite transformation after 50 cycles, and the austenite with grain orientations < 001>, < 101 > and < 111 > both produce martensite transformation at fatigue. Therefore, with the increase of cumulative plastic strain under the cyclic loading, the austenite grain orientations corresponding to the degree of difficulty for martensite transformation are < 101>, < 001>, < 111 > from easy to difficult.
It is found that the austenite with grain orientation < 101 > is much more at the original state by analyzing the grain orientation diagram. Thus more austenite grains are prone to transform into martensite, and the martensite transformation rate is larger at the initial cyclic stage; The more stable retained austenite with grain orientations < 101 > and < 111 > are not easy to transform into martensite. Thus the martensite transformation rate begins to decrease, as shown in Fig. 10, with a strain amplitude of 1.1%.
3.3.2 TEM analysis
In order to further explore the nucleation of martensite transformation in experimental steel under the cyclic loading, TEM analysis was carried out on the experimental steel with different cycles with a strain amplitude of 1.1%. For the nucleation of martensite transformation, previous studies have shown that the nucleation position of martensite transformation may include the intersection of shear bands, the intersection of shear bands and grain boundaries, the intersection of grain boundaries, and the position of the shear band, etc [28]. Figure 11 shows the microstructure of the austenite in the original state. It can be seen that there are a large number of stacking faults and a small number of dislocation lines. It can be inferred that these stacking faults provide nucleation positions for the subsequent formation of ε martensite and α´ martensite.
Fig. 12 shows the microstructure of the experimental steel at the 5th cycle. The deformed band structure running through the whole austenite grain is parallel distributed in the austenite, which is white in the dark field diagram, indicating that these structures are different from the structure of the matrix and they are the newly formed phase. According to the relevant literature, ε martensite is a thin strip, so it can be inferred that the fine strip structure is ε martensite. Compared with the original state, austenite grains produce phase transformation and ε martensite. In addition, compared with the TEM diagram of the original state in Fig. 11, the stacking fault density is also significantly reduced. This is because the winding and superposition of the stacking fault is the intermediate step of transformation from austenite to ε martensite, and the density of the stacking fault decreases due to the formation of ε martensite [29].
Figure 13 shows the bright and dark field diagrams of the microstructure of austenite at fatigue. It can be seen from Fig. 13a and b that in addition to the strip structures (ε martensite), there are also block structures in austenite. The comparison between the bright and dark field diagrams shows that the strip structures are different from the block structures. As a consequence, it can be inferred that the block structures are α´ martensite. In addition, it can be seen from the figure that a portion of α´ martensite is produced at the intersection of ε martensite and the other portion produced on ε martensite. Figure 13c and d are the bright and dark field diagrams of austenite at another location. The lamellar structure in austenite grain can be identified as α´ martensite by diffraction pattern, which means the α´ martensite is the martensite transformation that is produced in austenite grain.
In conclusion, there are three microscopic mechanisms of α´ martensite transformation under cyclic loading. In the first case, austenite first transforms into ε martensite, then from ε martensite to α´ martensite, and α´ martensite nucleates at the intersection of ε martensite; In the second case, austenite first transforms into ε martensite, then from ε martensite to α´ martensite, and α´ martensite nucleates on ε martensite; The third is that austenite transforms directly into α´ martensite.