The EBSD and TEM analysis results show that the sizes of martensite structure are affected by cooling rate. The block size of the water-quenched sample is the smallest. According to solid phase transformation theory, martensite transformation is a typical representative of non-thermal activated solid phase transformation, which belongs to the first level phase transformation whose mode is nucleation and growth. The characteristic of martensite phase transformation is non-diffusion and shear transformation whose speed is very fast and controlled by nucleation. There is still dispute about martensite nucleation theory. The generally accepted view is that most of the martensite transformation is nonhomogeneous nucleation and the homogeneous nucleation only happens under special conditions [9]. According to classical nucleation theory, the nucleation ratio is illustrated as follows [9].

$I={N}_{0}\omega exp(\frac{-Q}{kT})exp(\frac{-\mathrm{\Delta}{G}^{\ast}}{kT})$(5)where *I* is nucleation ratio; *N*_{0} is the assumed number of potential nucleus; *ω* is oscillation frequency of atoms which is related with surface area of nucleus; *Q* is the activation energy for each atom movement; *△G** is the activation energy for nucleation; *k* is Boltzmann constant; *T* is temperature. Although formula eq. (5) is derived from homogeneous nucleation, the form is same as nonhomogeneous nucleation. The difference is that *N*_{0} is the assumed number of potential nucleus for non-uniform nucleation and the *△G** is the activation energy for nonhomogeneous nucleation.

During martensitic transformation, *ω* and *Q* are considered as constant. ${N}_{0}\omega exp(-Q/kT)$ is a parameter which decreases with increasing undercooling. The activation energy for nucleation, *△G**, reduces exponentially with decreasing temperature. Therefore, $exp(-\mathrm{\Delta}{G}^{\ast}/kT)$ increases with decreasing temperature. The collective effect of two parameters, ${N}_{0}\omega exp(-Q/kT)$ and$exp(-\mathrm{\Delta}{G}^{\ast}/kT)$, results in increasing of the nucleation ratio of martensite firstly and then decreaseing with increasing undercooling. The schematic diagram is shown in Figure 19. There is a largest nucleation ratio with a suitable undercooling and the nucleation ratio is reduced with too small or too large undercooling. Undercooling has effect on nucleation ratio and finally influences martensitic effective grain size for nucleation controlled martensite transformation. There is a relationship between cooling rate and undercooling. The undercooling increases with increasing cooling rate due to the decreased phase transformation temperature. Therefore, the nucleation ratio was reduced by too slow and too fast cooling rate. From the experimental results, it is speculated that the undercooling with 10% NaCl-water quenching be over the tip of the nose in Figure 19, while with oil or water quenching below the tip of the nose.

Figure 19: The schematic diagram of relationship between undercooling and nucleation ratio.

There is an obvious coarsening of carbides in tempered samples with increasing cooling rate. Dislocations affect precipitation behavior of carbides on tempering. The alloying atoms segregate on boundaries and dislocations firstly and promote nonhomogeneous nucleation of carbides. When the cooling rate is slow, the dislocation density in the sample is relatively less. There are more lattice distortion and residual stresses in the sample with fast cooling rate. Therefore, the dislocation density is higher with fast cooling rate.

Low dislocation density reduces the amount of carbides precipitation on dislocations and promotes more carbides precipitation in matrix. However, when the cooling rate is too fast, the dislocation density in the sample increases obviously which increases the amount of carbides precipitation on dislocations. The dislocations accelerate diffusion of carbon and alloying atoms and results in coarsening of carbides. Meanwhile, the amount of small size carbides precipitation in matrix reduces.

When cooling rate is slow, the dislocations are less and the amount of large size carbides precipitated on dislocations is also less. At the same time, small carbides are homogeneously nucleated in matrix and the precipitation strengthening effect is obvious. With increasing cooling rate, the dislocation density increases, which is beneficial for improving strength, but the amount of large carbides precipitating on dislocations also increases with result of reduction of the amount of small size carbides precipitating in matrix. Therefore, the precipitation strengthening effect is reduced. In addition, the martensite structure is coarse with too fast cooling rate, which is detrimental for strength, which is the reason that the strength increment is not obvious with 10% NaCl-water quenching. The strength of water quenched and tempered sample is almost 20 MPa higher than that of oil-quench and tempered sample, because of the refined blocks and laths. The strength of 10% NaCl-water quenched and tempered sample is a little higher than that of water quenched and tempered sample, maybe because of the refined martensitic laths. The block boundary is the most effective grain boundary for strength of lath martensite, since the block boundary significantly restricts the movement of dislocations [20, 21, 22, 23]. The martensitic lath width is also refined with increasing cooling rate. The lath boundaries can also act as barriers to dislocation movement and have a strengthening effect [23, 24].

When cooling rate is appropriate (the undercooling is near the tip of nose in Figure 19), the martensite nucleation ratio increases and get refined martensite effective grain size. The amount of high angle grain boundaries increases with martensite structure refinement which is beneficial for improving toughness. When cooling rate is too slow or too fast, the nucleation ratio is reduced which results in coarsening of effective grain size and reducing the high angle grain boundaries and deteriorates toughness.

Besides martensite structure, carbides precipitation on tempering also has effect on toughness. The carbides are coarse with fast cooling rate due to high dislocation density. During plastic deformation, there is stress concentration on large carbides which accelerates the cracks initiation. Besides, the martensite structure and the carbides are coarse with fast cooling rate. The large size carbides promote cracks initiation and coarse structure accelerates cracks propagation. Therefore, too fast quenching cooling rate reduces impact toughness significantly.

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