6. Scheme of the nondiffusion transformation of austenite based on the constructed model.

Before discussing the equations obtained, we introduce some more useful relations characterizing the γ ! α transformation. With the γ ! α transformation, the effective atomic volume of the iron lattice changes in the sample under consideration, characterized by <sup>Δ</sup>V<sup>γ</sup> ! <sup>α</sup> and the relative volume change <sup>Δ</sup>Vγ!<sup>α</sup> <sup>V</sup><sup>γ</sup> . According to the data of [3]:

$$
\Delta V\_{\gamma \to a} = 0.268 - 1.62^\ast 10^{-4} T, \text{sm}^3/\text{mol} \tag{73}
$$

We will assume that with the formation of the α-phase, the relative change in volume is determined by the additional deformation: <sup>Δ</sup>Vγ!<sup>α</sup> <sup>V</sup><sup>γ</sup> = 3Δεα, and the compressive stress arising in the α-phase has the value.

$$
\sigma\_a = \frac{\mathbf{E}}{\mathbf{1} \cdot 2\mu} \Delta \varepsilon\_a. \tag{74}
$$

When the alloy sample is cooled by ΔT, a deformation occurs in its surface layer: εγ � αΔТ and the tensile stress σγ corresponding to this deformation:

Let σγ = 0. Let us take into account that for triaxial compression-stretching [28]:

ΔV <sup>V</sup> <sup>¼</sup> <sup>E</sup>

where E is the modulus of elasticity of steel (�2.17�10<sup>5</sup> <sup>М</sup>Pa) and <sup>μ</sup> is the Poisson

v is the propagation velocity of the microdeformation in sample (�1000 m/с) [3] and L is the characteristic distance over which the microdeformation of the shear is propagated (the size of the martensitic strips or plates). At the initial stage of the formation of the shear structure, it has a magnitude of the order of the diameter of the austenite grain (� 100 μm), and then decreases with decreasing

L22 <sup>¼</sup> v 1ð Þ ‐2<sup>μ</sup>

The cross-coefficients L12 = L21 for a nonequilibrium thermodynamic system are

Thus, we obtained simple differential equations for a nonequilibrium thermodynamic system describing the nondiffusion transformation of austenite taking into

We first transform Eq. (66) taking into account expression (62). We have:

where εα is the magnitude of deformations of the α-phase. The differential

� � ð Þ <sup>1</sup>‐2<sup>μ</sup> L22Е

This kinetic equation describes the change in the magnitude of the deformation of the <sup>α</sup>-phase in time. At <sup>t</sup> <sup>=</sup> 0, εα <sup>=</sup> 0. When the time is counted, a fast (� <sup>10</sup>�<sup>6</sup> s)

r

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dγ RT

v 1ð Þ ‐2<sup>μ</sup> LЕ

dt <sup>¼</sup> L11Δ<sup>φ</sup> <sup>þ</sup> L12σγ–L12σα: (65)

dt <sup>¼</sup> L21Δ<sup>φ</sup> <sup>þ</sup> L22σγ–L22σα: (66)

dt <sup>þ</sup> <sup>v</sup>εα=<sup>L</sup> <sup>¼</sup> L21Δ<sup>φ</sup> <sup>þ</sup> L22σγ , (67)

1 � e �v

Lt � �: (68)

E <sup>1</sup>‐2<sup>μ</sup> εα <sup>¼</sup> <sup>v</sup>

<sup>1</sup>‐2<sup>μ</sup> εα, (61)

<sup>L</sup> <sup>ε</sup>, (62)

<sup>L</sup><sup>Е</sup> : (63)

(64)

σα <sup>¼</sup> <sup>E</sup>

Then, expression (60) can be transformed as follows:

dεα

where the following values are entered:

account the influence of internal stresses.

process of transition to deformation occurs:

116

ratio (� 0.26).

Non-Equilibrium Particle Dynamics

temperature [1].

3 1ð Þ ‐2<sup>μ</sup>

dt <sup>¼</sup> L22σα <sup>¼</sup> <sup>L</sup><sup>22</sup>

From Eq. (62), we find that the coefficient L22 is equal to:

found with sufficient accuracy by the formulas proposed in [5]:

L12 <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffi L11L<sup>22</sup> <sup>p</sup> <sup>¼</sup>

Let us write the equations of motion of our system in the form:

dn<sup>α</sup>

dεα

dεα

Eq. (66) with constant coefficients (temperature) has a solution:

εα <sup>¼</sup> L21Δ<sup>φ</sup> <sup>þ</sup> <sup>L</sup>22σγ

$$
\sigma\_{\gamma} = \frac{\mathbf{E}}{\mathbf{1} \cdot 2\mu} a \Delta T. \tag{75}
$$

The existing thermal stresses in the γ phase (75) contribute to the formation of the α-phase by the shear mechanism, and the stresses arising in the α-phase compensate thermal stresses in the γ-phase. With a certain amount of α-phase, the stress equals σα = σγ arises and the further formation of the α-phase occurs according to the normal mechanism with the relaxation of the arising stresses by recrystallization. Consequently, the condition (77) corresponds to the transformation of the γ-phase by a mixed mechanism, and also to the formation of a ferrite side plates (Widmanstätten), followed by the release of the α-phase by the normal mecha-

Using the Principles of Nonequilibrium Thermodynamics for the Analysis of Phase…

DOI: http://dx.doi.org/10.5772/intechopen.83657

With a certain supercooling of ΔTi, stress compensation occurs only when the γ-phase is completely transformed into ferrite by a shearing mechanism. In this case:

L11Δφ�L12σα, σα¼σγ

with a "reticular" or acicular morphology of precipitates. Finally, for large ΔT

normal and martensitic transformations, as limiting cases.

perlite formation for high-purity eutectoid steel.

Inequality (78) determines the condition for the formation of "athermal" martensite, when the normal component does not affect the formation of the shear structure. The main effect on the rate of the γ ! α transformation, in accordance with expression (71), is due to thermal stresses in the γ phase. Thus, the constructed model of the nondiffusion austenite transformations allows us to consider the

Based on the possibility of dynamic equilibrium, expressions are found for calculating the cross-kinetic coefficients of a thermodynamic system consisting of two and three components. The values of the thermodynamic force for diffusion of carbon, kinetic coefficients and flows of a thermodynamic system describing the kinetics of carbide precipitation during the tempering of chromium steel are calculated. It has been established that the values of iron and chromium fluxes increase substantially due to the cross ratios and the significant magnitude of the thermody-

Analysis of the eutectoid transformation of austenite using the relations of nonequilibrium thermodynamics allowed us to generalize the equations of motion of the system obtained earlier by the authors of [20] and to find more accurate theoretical expressions for the perlite growth rate and its between interplate distance on the magnitude of the supercooling of steel. According to the constructed model, the perlite growth rate in the direction of the X axis has a maximum value at supercooling ΔТ = 140.0°С. The perlite growth rate calculated according to Zener's formula has a theoretical maximum value at overcooling ΔТ = 96.0°С. Consequently, the theoretical expressions (31) and (32) make it possible to describe with greater accuracy the maximum and the course of the experimental curve for the

The temperature corresponding to this supercooling is the starting point for the formation of the isothermal martensite Mni (Figure 5). Below the point Mni, the formation of the α-phase occurs by a shearing mechanism. However, the normal component of the process still has a significant value, affecting the morphology of the resulting precipitates. When supercooling a greater ΔTi, L11Δφ < L12σα, σα < σγ At temperatures below Mni, isothermal martensite or acicular ferrite is formed

L11Δφ ≪ L12σγ , (78)

nism [1].

(below Мna):

7. Conclusions

namic force (�ΔμC).

119

Comparing the values of thermodynamic forces among themselves, it is possible to classify the types of nondiffusion transformation according to the kinetic criterion. As shown in [1], p. 208, for small deviations of the system from equilibrium, the growth of crystals is more likely, controlled by self-diffusion, at large–cooperative growth. The same phase transition in a single-component system under different external conditions can take place with an independent (or slightly dependent) temperature growth rate (martensitic kinetics) and with a rate that exponentially depends on the temperature at an activation energy close to the activation energy of self-diffusion (normal kinetics). The parameter characterizing the deviation of the system from equilibrium is the supercooling of the alloy ΔT = Ac3�T, where Ac3 is the temperature of the end α ! γ of the conversion upon heating, and T is the transformation temperature. The transformation scheme for the constructed model is shown in Figure 5.

Ac1 is the temperature of the beginning of α ! γ transformation when the alloy is heated and Mni is the temperature of the onset of the formation of isothermal martensite upon supercooling of the alloy. Mn is the temperature of the onset of athermal martensite formation upon supercooling of the alloy. Mk is the temperature of the end of martensite formation upon supercooling of the alloy.

Thus, for small

$$
\Delta T: L\_{11} \Delta \rho \rhd L\_{12} \sigma\_a \rhd L\_{12} \sigma\_p,\tag{76}
$$

then the growth of α-phase crystals is determined by self-diffusion by the normal mechanism. However, as follows from Eq. (72), in this case too, the contribution of deformations (and stresses) to the conversion kinetics is very significant. In order that the condition (76) is satisfied, it is necessary that the stress level in the γand α-phases be small; for the α-phase, this is possible only in the case of relaxation of internal stresses in the alloy at high temperature by the mechanism of recrystallization.

With increasing supercooling of the alloy, the thermodynamic stimulus and the rate of normal transformation increase.

For a larger

$$
\Delta T: L\_{11} \Delta \rho \sim L\_{12} \sigma\_a > L\_{12} \sigma\_\gamma \tag{77}
$$


Figure 5.

Scheme of nondiffusion transformations from the constructed model.

Using the Principles of Nonequilibrium Thermodynamics for the Analysis of Phase… DOI: http://dx.doi.org/10.5772/intechopen.83657

The existing thermal stresses in the γ phase (75) contribute to the formation of the α-phase by the shear mechanism, and the stresses arising in the α-phase compensate thermal stresses in the γ-phase. With a certain amount of α-phase, the stress equals σα = σγ arises and the further formation of the α-phase occurs according to the normal mechanism with the relaxation of the arising stresses by recrystallization. Consequently, the condition (77) corresponds to the transformation of the γ-phase by a mixed mechanism, and also to the formation of a ferrite side plates (Widmanstätten), followed by the release of the α-phase by the normal mechanism [1].

With a certain supercooling of ΔTi, stress compensation occurs only when the γ-phase is completely transformed into ferrite by a shearing mechanism. In this case:

L11Δφ�L12σα, σα¼σγ

The temperature corresponding to this supercooling is the starting point for the formation of the isothermal martensite Mni (Figure 5). Below the point Mni, the formation of the α-phase occurs by a shearing mechanism. However, the normal component of the process still has a significant value, affecting the morphology of the resulting precipitates. When supercooling a greater ΔTi, L11Δφ < L12σα, σα < σγ

At temperatures below Mni, isothermal martensite or acicular ferrite is formed with a "reticular" or acicular morphology of precipitates. Finally, for large ΔT (below Мna):

$$L\_{11} \Delta \rho \ll L\_{12} \sigma\_{\mathcal{V}} \tag{78}$$

Inequality (78) determines the condition for the formation of "athermal" martensite, when the normal component does not affect the formation of the shear structure. The main effect on the rate of the γ ! α transformation, in accordance with expression (71), is due to thermal stresses in the γ phase. Thus, the constructed model of the nondiffusion austenite transformations allows us to consider the normal and martensitic transformations, as limiting cases.
