J. Mater. Sci. Technol. ›› 2021, Vol. 91: 200-214.DOI: 10.1016/j.jmst.2021.03.020
• Invited Review • Previous Articles Next Articles
Yong Lia, David San Martínb, Jinliang Wangc,a, Chenchong Wanga, Wei Xua,*(
)
Received:2020-12-17
Revised:2021-02-27
Accepted:2021-03-07
Published:2021-11-20
Online:2021-11-20
Contact:
Wei Xu
About author:*E-mail address: xuwei@ral.neu.edu.cn (W. Xu).Yong Li, David San Martín, Jinliang Wang, Chenchong Wang, Wei Xu. A review of the thermal stability of metastable austenite in steels: Martensite formation[J]. J. Mater. Sci. Technol., 2021, 91: 200-214.
Fig. 1. Temperature evolution of the amount of α'-martensite for 304 metastable austenitic stainless steel [36] and the Gibbs free energy difference between the bcc (martensite) and fcc (austenite) phases with the same composition (as calculated with Thermo-Calc) for 304 metastable austenitic stainless steel.
Fig. 2. Effect of different alloying elements on the MS temperature in alloys [27].
| Authors | MS empirical equation | Serviceable range (wt.%) |
|---|---|---|
| Relations based on linear regressions | ||
| Andrews [ | MS( °C)=539-423C-30.4Mn-12.1Cr-17.7Ni-7.5Mo | 0~0.6C; 0~4.9Mn; 0~5.0Cr; 0~5.0Ni; 0~5.4Mo |
| Eldis [ | Ms( °C)=531-391.2C-43.3Mn-21.8Ni-16.2Cr | 0.10~0.80C; 0.35~1.80Mn; 0~1.50Si; 0~0.90Mo; 0~1.50Cr; 0~4.50Ni |
| Mahieu [ | MS=539-423C-30.4Mn -7.5Si+30Al | Equation valid for TRIP steels with 0.91≤Al ≤1.73 |
| Finkler & Schirra [ | MS( °C)=635-474{C + 0.86[N-0.15(Nb+Zr)]-0.066(Ta+Hf)}-(33Mn+17Cr+17Ni+21Mo+39V+11 W) | Equation valid for high-temperature martensitic steels with 8.0~14 Cr |
| Trzaska [ | MS( °C)=541-401C-36Mn -10.5Si-14Cr -18Ni -17Mo | 0.06~0.68C; 0.13~2.04Mn; 0.12~1.75Si; 0~2.3Cr; 0~3.85Ni; 0~1.05Mo; 0~0.38 V; 0~0.38Cu |
| Lee & Park [ | MS( °C)=475.9-335.1C-34.5Mn -1.3Si-15.5Ni-13.1Cr -10.7Mo -9.6Cu +11.67ln(Dγ) | 0.1~1.0C; 0.17~1.91Mn; 0~2.28Cr; 0~2.42Ni; 0~1.96Mo; 0~0.38Si ; 0~0.2Cu; 7~225dγ(μm) |
| Li [ | Ms( °C)=540-420C-12 Cr-20Ni -35Mn -21Mo -10.5Si-10.5W+20Al+140V | 0.06~0.63C; 0~6.85Mn; 0~1.76Si; 0~1.86Cr; 0~5.0Ni; 0~0.72Mo; 0~1.2 W; 0~0.24 V; 0~0.98Al |
| Gramlich [ | MS( °C)=517-423C-30.4Mn+82Mo+37Al-700B | 0.15~0.45C; 0.68~9.94Mn; 0~0.21Mo; 0.002~0.51Al |
| Grange& Stewart [ | MS( °C)=538-350C-37.7Mn-37.7Cr-18.9Ni-27Mo | None |
| Jaffe & Hollomon [ | MS( °C)=550-350C-40Mn -35V-20 Cr -17Ni-10Cu -10Mo-8W+15Co+30Al | None |
| Kunitake [ | MS( °C)=560.5-407.3C-37.8Mn -14.8 Cr -19.5Ni-4.5Mo -20.5Cu -7.3Si | None |
| Mikula & Wojnar [ | MS( °C)=635.02-549.82C-85.441Mn-68.967Si-18.07Cr-30.965Ni-69.301Mo-6.603V+420.26Nb+553.8Ti-1746.5B | None |
| Nehrenberg [ | MS( °C)=499-292C-32.4Mn-22Cr-16.2Ni-10.8(Mo +Si) | None |
| Payson& Savage [ | MS( °C)=499-308C-32.4Mn -27Cr -16.2Ni-10.8(Si +Mo +W) | None |
| Rowland & Lyle [ | MS( °C)=499-324C-32.4Mn -27Cr -16.2Ni-10.8(Si +Mo +W) | None |
| Steven & Haynes [ | MS( °C)=561-474C-33Mn-17Cr-17Ni-21Mo | None |
| Sverdlin & Ness [ | MS( °C)=520-320C-50Mn -30Cr-20(Ni+ Mo) -5(Cu+Si) | None |
| Tamura [ | MS( °C)=550-361C-39Mn -20Cr -17V-17Ni -10Cu-5(Mo+W)+15Co+30Al | None |
| Relations based on nonlinear regressions | ||
| Wang [ | Ms( °C)=545.8e-1.362wC | Equation valid for TRIP steels with 0.2-1.6C |
| van Bohemen [ | MS( °C)=565-31Mn -13Si-10Cr -18Ni -12Mo-600[1-exp(-0.96C)] | Equation valid for plain carbon steels and 3Cr alloys with 0.15-1.8C |
| Barbier [ | MS( °C)=545-34.4Mn -13.7Si-9.2Cr -17.3Ni -15.4Mo+10.8V+4.7Co-1.4Al-16.3Cu-361Nb-2.44Ti—3448B-601.2[1-exp(-0.868C)] | 0.002~1.86C; 0~10.24Mn; 0~1.9Si; 0~17.98Cr; 0~29.55Ni; 0~5.4Mo; 0~1.19 V; 0~16.08Co; 0~3.007Al; 0~2.17Cu; 0 ~0.11Nb; 0 ~1.614Ti; 0~0.004B |
| Special equation considering the interaction among alloying elements or the morphology of martensite | ||
| Carapella [ | MS( °C)=496(1-062C)(1-0.092Mn)(1-0.033Si)(1-0.045Ni)(1-0.07Cr)(1-0.029Mo)(1-0.018 W)(1 + 0.012Co) | None |
| Liu [ | MS ( °C)=795-25000C1-45Mn-30Cr-20Ni-16Mo-5Si-8W+6Co+15Al-35V(Nb+Zr+Ti)MS ( °C)=525-350(C2-0.005)-45Mn-30Cr-20Ni-16Mo-5Si-8W+6Co+15Al-35V(Nb+Zr+Ti) | C1<0.0050.005≤C2≤0.02 |
| Andrews [ | MS( °C)=512-453C-16.9Ni-9.5Mo+217C2-71.5CMn +15Cr-67.6CCr | 0~0.6C; 0~4.9Mn; 0~5.0Cr; 0~5.0Ni; 0~5.4Mo |
| Zhao [ | Twinned martensite:MS™( °C)=420-208.33C-33.428Mn+1.296Mn2-0.02167Mn3-16.08Ni+0.7817Ni2-0.02464Ni3-2.473Cr+30Mo+12.86Co-0.2654Co2+0.001547Co3-7.18Cu-72.65N-43.36N2-16.28Ru+1.72Ru2-0.08117 Ru3Lath martensite:MSLM( °C)=540-356.25C-47.59Mn+2.25Mn2-0.0415Mn3-24.65Ni+1.36Ni2-0.0384Ni3-17.82Cr+1.42Cr2+17.5Mo+21.87Co-0.468Co2+0.00296Co3-16.52Cu-260.64N-17.66Ru | 0~1.80C; 0~26.0Mn; 0~10.0Cr; 0~34.0Ni; 0~2.0Mo; 0~59.0Co; 0~5.5Cu; 0 ~2.7 N; 0~20.1RuIf MSLM is higher than MS™, both lath martensite and twinned martensite can be present in the steel.If MSLM is lower than MS™, only twinned martensite can exist in the steel.This condition is fulfilled for some steels above a critical composition, which can be determined by settingMS™ = MS™ |
Table 1 The empirical equations of the MS temperature.
| Authors | MS empirical equation | Serviceable range (wt.%) |
|---|---|---|
| Relations based on linear regressions | ||
| Andrews [ | MS( °C)=539-423C-30.4Mn-12.1Cr-17.7Ni-7.5Mo | 0~0.6C; 0~4.9Mn; 0~5.0Cr; 0~5.0Ni; 0~5.4Mo |
| Eldis [ | Ms( °C)=531-391.2C-43.3Mn-21.8Ni-16.2Cr | 0.10~0.80C; 0.35~1.80Mn; 0~1.50Si; 0~0.90Mo; 0~1.50Cr; 0~4.50Ni |
| Mahieu [ | MS=539-423C-30.4Mn -7.5Si+30Al | Equation valid for TRIP steels with 0.91≤Al ≤1.73 |
| Finkler & Schirra [ | MS( °C)=635-474{C + 0.86[N-0.15(Nb+Zr)]-0.066(Ta+Hf)}-(33Mn+17Cr+17Ni+21Mo+39V+11 W) | Equation valid for high-temperature martensitic steels with 8.0~14 Cr |
| Trzaska [ | MS( °C)=541-401C-36Mn -10.5Si-14Cr -18Ni -17Mo | 0.06~0.68C; 0.13~2.04Mn; 0.12~1.75Si; 0~2.3Cr; 0~3.85Ni; 0~1.05Mo; 0~0.38 V; 0~0.38Cu |
| Lee & Park [ | MS( °C)=475.9-335.1C-34.5Mn -1.3Si-15.5Ni-13.1Cr -10.7Mo -9.6Cu +11.67ln(Dγ) | 0.1~1.0C; 0.17~1.91Mn; 0~2.28Cr; 0~2.42Ni; 0~1.96Mo; 0~0.38Si ; 0~0.2Cu; 7~225dγ(μm) |
| Li [ | Ms( °C)=540-420C-12 Cr-20Ni -35Mn -21Mo -10.5Si-10.5W+20Al+140V | 0.06~0.63C; 0~6.85Mn; 0~1.76Si; 0~1.86Cr; 0~5.0Ni; 0~0.72Mo; 0~1.2 W; 0~0.24 V; 0~0.98Al |
| Gramlich [ | MS( °C)=517-423C-30.4Mn+82Mo+37Al-700B | 0.15~0.45C; 0.68~9.94Mn; 0~0.21Mo; 0.002~0.51Al |
| Grange& Stewart [ | MS( °C)=538-350C-37.7Mn-37.7Cr-18.9Ni-27Mo | None |
| Jaffe & Hollomon [ | MS( °C)=550-350C-40Mn -35V-20 Cr -17Ni-10Cu -10Mo-8W+15Co+30Al | None |
| Kunitake [ | MS( °C)=560.5-407.3C-37.8Mn -14.8 Cr -19.5Ni-4.5Mo -20.5Cu -7.3Si | None |
| Mikula & Wojnar [ | MS( °C)=635.02-549.82C-85.441Mn-68.967Si-18.07Cr-30.965Ni-69.301Mo-6.603V+420.26Nb+553.8Ti-1746.5B | None |
| Nehrenberg [ | MS( °C)=499-292C-32.4Mn-22Cr-16.2Ni-10.8(Mo +Si) | None |
| Payson& Savage [ | MS( °C)=499-308C-32.4Mn -27Cr -16.2Ni-10.8(Si +Mo +W) | None |
| Rowland & Lyle [ | MS( °C)=499-324C-32.4Mn -27Cr -16.2Ni-10.8(Si +Mo +W) | None |
| Steven & Haynes [ | MS( °C)=561-474C-33Mn-17Cr-17Ni-21Mo | None |
| Sverdlin & Ness [ | MS( °C)=520-320C-50Mn -30Cr-20(Ni+ Mo) -5(Cu+Si) | None |
| Tamura [ | MS( °C)=550-361C-39Mn -20Cr -17V-17Ni -10Cu-5(Mo+W)+15Co+30Al | None |
| Relations based on nonlinear regressions | ||
| Wang [ | Ms( °C)=545.8e-1.362wC | Equation valid for TRIP steels with 0.2-1.6C |
| van Bohemen [ | MS( °C)=565-31Mn -13Si-10Cr -18Ni -12Mo-600[1-exp(-0.96C)] | Equation valid for plain carbon steels and 3Cr alloys with 0.15-1.8C |
| Barbier [ | MS( °C)=545-34.4Mn -13.7Si-9.2Cr -17.3Ni -15.4Mo+10.8V+4.7Co-1.4Al-16.3Cu-361Nb-2.44Ti—3448B-601.2[1-exp(-0.868C)] | 0.002~1.86C; 0~10.24Mn; 0~1.9Si; 0~17.98Cr; 0~29.55Ni; 0~5.4Mo; 0~1.19 V; 0~16.08Co; 0~3.007Al; 0~2.17Cu; 0 ~0.11Nb; 0 ~1.614Ti; 0~0.004B |
| Special equation considering the interaction among alloying elements or the morphology of martensite | ||
| Carapella [ | MS( °C)=496(1-062C)(1-0.092Mn)(1-0.033Si)(1-0.045Ni)(1-0.07Cr)(1-0.029Mo)(1-0.018 W)(1 + 0.012Co) | None |
| Liu [ | MS ( °C)=795-25000C1-45Mn-30Cr-20Ni-16Mo-5Si-8W+6Co+15Al-35V(Nb+Zr+Ti)MS ( °C)=525-350(C2-0.005)-45Mn-30Cr-20Ni-16Mo-5Si-8W+6Co+15Al-35V(Nb+Zr+Ti) | C1<0.0050.005≤C2≤0.02 |
| Andrews [ | MS( °C)=512-453C-16.9Ni-9.5Mo+217C2-71.5CMn +15Cr-67.6CCr | 0~0.6C; 0~4.9Mn; 0~5.0Cr; 0~5.0Ni; 0~5.4Mo |
| Zhao [ | Twinned martensite:MS™( °C)=420-208.33C-33.428Mn+1.296Mn2-0.02167Mn3-16.08Ni+0.7817Ni2-0.02464Ni3-2.473Cr+30Mo+12.86Co-0.2654Co2+0.001547Co3-7.18Cu-72.65N-43.36N2-16.28Ru+1.72Ru2-0.08117 Ru3Lath martensite:MSLM( °C)=540-356.25C-47.59Mn+2.25Mn2-0.0415Mn3-24.65Ni+1.36Ni2-0.0384Ni3-17.82Cr+1.42Cr2+17.5Mo+21.87Co-0.468Co2+0.00296Co3-16.52Cu-260.64N-17.66Ru | 0~1.80C; 0~26.0Mn; 0~10.0Cr; 0~34.0Ni; 0~2.0Mo; 0~59.0Co; 0~5.5Cu; 0 ~2.7 N; 0~20.1RuIf MSLM is higher than MS™, both lath martensite and twinned martensite can be present in the steel.If MSLM is lower than MS™, only twinned martensite can exist in the steel.This condition is fulfilled for some steels above a critical composition, which can be determined by settingMS™ = MS™ |
Fig. 3. The statistical analysis of the effects of chemical elements on the MS temperature among 20 equations, in terms of metrics including the occurrence times, the standard deviations and the coefficients of variation of the elements.
Fig. 4. Effect of austenite grain size on the volume fraction of athermally formed martensite [70].
Fig. 5. Schematic illustrations of the mechanisms governing the effect of grain size on the thermal stability of metastable austenite from the following viewpoints: (a) the stress field around the martensite [71], (b) heterogeneous nucleation [72], (c) the volume of the martensitic unit [73], (d) variations in the number of variants [76], and (e) the strength of the metastable austenite matrix [74].
Fig. 6. (a) Change in the MS temperature as a function of the loading conditions [82], (b) comparison of the experimental (blue lines) and computed (red lines) isothermal transformation curves in an Fe-Ni-Mn alloy at -196 °C under the influence of superimposed elastic stresses, σapp [88].
Fig. 7. Comparison of the effects of different influencing factors on the MS temperature.
Fig. 8. Relationship between the activation energy and embryo radius necessary to trigger martensitic transformation [91].
| Authors | Model | Hypothesis | Characterization | Direct Factors | |||
|---|---|---|---|---|---|---|---|
| CC | T | GS | SS | ||||
| KoistinenandMarburger [ | $f=1-\exp \left[\alpha\left(M_{\mathrm{S}}-T_{\mathrm{q}}\right)\right]$ | dN=φdΔGVγ→α';Vm=constant;dΔGVγ→α'/dT=constant. | (1) Expresses only the effect of temperature on the transformation process.(2) No effect of nucleation sites on the transformation process. | × | √ | × | × |
| v. Bohemen andSietsma[ | $\begin{array}{l}f=1-\exp \left[\alpha\left(T_{\mathrm{KM}}-T_{\mathrm{q}}\right)\right] \\T_{\mathrm{KM}}\left({ }^{\circ} \mathrm{C}\right)=462-273 x_{\mathrm{C}}-26 x_{\mathrm{Mn}} \\-16 x_{\mathrm{Ni}}-13 x_{\mathrm{Cr}}-30 x_{\mathrm{Mo}} \\\alpha\left(\mathrm{K}^{-1}\right)=0.0224-0.0107 x_{C} \\-0.0007 x_{M n}-0.00005 x_{\mathrm{Ni}} \\-0.00012 x_{\mathrm{Cr}}-0.0001 x_{\mathrm{M} 0}\end{array}$ | dN=φdΔGVγ→α';Vm=constant;α is linearly related to chemical composition. | (1) Expresses the effects of the temperature and chemical composition on the transformation process.(2) No effect of nucleation sites on the transformation process. | √ | √ | × | × |
| v. Bohemen[ | $\begin{array}{l}f=1-\exp \left[\alpha\left(M_{S}-T_{\mathrm{q}}\right)\right] \\\alpha\left(10^{-3} \mathrm{~K}^{-1}\right)= \\27.2-0.14 x_{\mathrm{Mn}}-0.21 x_{\mathrm{Si}}-0.11 x_{\mathrm{Cr}} \\-0.08 x_{\mathrm{Ni}}-0.05 x_{\mathrm{Mo}}- \\19.8\left[1-\exp \left(-1.56 x_{\mathrm{C}}\right)\right] \\-\frac{\ln (1-f)}{f}=1+A\left(M_{\mathrm{S}}-T_{\mathrm{q}}\right)\end{array}$ | dN=φdΔGVγ→α';Vm=constant;α is exponentially related to the carbon content and is linearly related to other elements. | (1) Emphasizes the important influence of carbon element.(2) No effect of nucleation sites on the transformation process. | √ | √ | × | × |
| Khanand Bhadeshia model[ | $\begin{array}{l}\frac{\mathrm{d} f}{\mathrm{dt}}=\mathrm{H} v \mathrm{Kmq}(1-f)^{1+\frac{1}{m}} \\H=\left(n_{\mathrm{i}}+p f-N_{\mathrm{v}}\right) \\K=\exp \left(\frac{-\Delta W_{\alpha}}{R T}\right)\end{array}$ | dN=φdΔGVγ→α';Vm=constant;dΔGVγ→α'/dT=constant;the autocatalytic factor is linearly related to f. | (1) Expresses only the effect of temperature on the transformation process.(2) Contains the effect of autocatalytic nucleation sites on the transformation process. | × | √ | × | × |
| Raghavan andEntwisle[ | $\begin{array}{l}\frac{\mathrm{d} f}{\mathrm{~d} t}=H(1-f) v K\left(\bar{V}+\frac{\mathrm{d} \bar{V}}{\operatorname{dln} N_{\mathrm{v}}}\right) \\H=\left[n_{\mathrm{i}}+f\left(p-\frac{1}{\nabla}\right)\right] \\K=\exp \left(\frac{-\Delta W_{\alpha}}{\mathrm{RT}}\right)\end{array}$ | (1) Single activation process.(2) Total nucleation sites consist of preexisting sites, autocatalytic sites and consuming sites.(3) Activation energy is constant.(4) Autocatalytic nucleation is related to f.(5) Vm satisfies Fisher's equation. | (1) Employing Fisher's equation to express the instantaneous volume of the martensite plates is impractical.(2) The effect of the grain size is reflected only in the instantaneous volume of the martensite plates and not in the nucleation rate. | × | √ | √ | × |
| PatiandCohen[ | $\begin{array}{l}\frac{\mathrm{d} f}{\mathrm{dt}}=H(1-f) v K\left(\bar{V}+\frac{\mathrm{d} \bar{V}}{\operatorname{din} N_{\mathrm{v}}}\right) \\H=\left[n_{\mathrm{i}}+f\left(p-\frac{1}{\nabla}\right)\right] \\K=\exp \left(\frac{-\Delta W_{\alpha}}{R T}\right)\end{array}$ | (1) Single activation process.(2) Total nucleation sites consist of preexisting sites, autocatalytic sites and consuming sites.(3) Activation energy is constant.(4) Autocatalytic nucleation is related to f.(5) Vm satisfies Fullman's equation. | (1) The expression of the martensite instantaneous volume is still inaccurate.(2) The effect of the grain size is reflected in only the instantaneous volume of the martensite plates and not in the nucleation rate. | × | √ | √ | × |
| Lin,Olson,andCohen[ | $\begin{array}{l}\frac{\mathrm{d} f}{\mathrm{dt}}=\int_{0}^{Q}[H(1-f) v K] \mathrm{d} Q \cdot \bar{V} \\H=\left(\frac{\mathrm{dN}_{\mathrm{i}}}{\mathrm{d} Q}+f \frac{\mathrm{d} P}{\mathrm{~d} \bar{Q}}-\frac{\mathrm{d} N_{\mathrm{v}}}{\mathrm{d} Q}\right) \\K=\exp \left(\frac{-\Delta \mathrm{Q}}{k T}\right)\end{array}$ | (1) Multiple activation process.(2) Size of preexisting nucleation sites satisfies an exponential distribution.(3) Size of autocatalytic nucleation sites satisfies a Gaussian distribution. | (1) Presents athermaland isothermal martensitic transformation simultaneously.(2) The distribution of preexisting defects and autocatalytic defects are related with grain size. | × | √ | √ | × |
Table 2 Transformation kinetics model analyses of austenite during cooling or soaking.
| Authors | Model | Hypothesis | Characterization | Direct Factors | |||
|---|---|---|---|---|---|---|---|
| CC | T | GS | SS | ||||
| KoistinenandMarburger [ | $f=1-\exp \left[\alpha\left(M_{\mathrm{S}}-T_{\mathrm{q}}\right)\right]$ | dN=φdΔGVγ→α';Vm=constant;dΔGVγ→α'/dT=constant. | (1) Expresses only the effect of temperature on the transformation process.(2) No effect of nucleation sites on the transformation process. | × | √ | × | × |
| v. Bohemen andSietsma[ | $\begin{array}{l}f=1-\exp \left[\alpha\left(T_{\mathrm{KM}}-T_{\mathrm{q}}\right)\right] \\T_{\mathrm{KM}}\left({ }^{\circ} \mathrm{C}\right)=462-273 x_{\mathrm{C}}-26 x_{\mathrm{Mn}} \\-16 x_{\mathrm{Ni}}-13 x_{\mathrm{Cr}}-30 x_{\mathrm{Mo}} \\\alpha\left(\mathrm{K}^{-1}\right)=0.0224-0.0107 x_{C} \\-0.0007 x_{M n}-0.00005 x_{\mathrm{Ni}} \\-0.00012 x_{\mathrm{Cr}}-0.0001 x_{\mathrm{M} 0}\end{array}$ | dN=φdΔGVγ→α';Vm=constant;α is linearly related to chemical composition. | (1) Expresses the effects of the temperature and chemical composition on the transformation process.(2) No effect of nucleation sites on the transformation process. | √ | √ | × | × |
| v. Bohemen[ | $\begin{array}{l}f=1-\exp \left[\alpha\left(M_{S}-T_{\mathrm{q}}\right)\right] \\\alpha\left(10^{-3} \mathrm{~K}^{-1}\right)= \\27.2-0.14 x_{\mathrm{Mn}}-0.21 x_{\mathrm{Si}}-0.11 x_{\mathrm{Cr}} \\-0.08 x_{\mathrm{Ni}}-0.05 x_{\mathrm{Mo}}- \\19.8\left[1-\exp \left(-1.56 x_{\mathrm{C}}\right)\right] \\-\frac{\ln (1-f)}{f}=1+A\left(M_{\mathrm{S}}-T_{\mathrm{q}}\right)\end{array}$ | dN=φdΔGVγ→α';Vm=constant;α is exponentially related to the carbon content and is linearly related to other elements. | (1) Emphasizes the important influence of carbon element.(2) No effect of nucleation sites on the transformation process. | √ | √ | × | × |
| Khanand Bhadeshia model[ | $\begin{array}{l}\frac{\mathrm{d} f}{\mathrm{dt}}=\mathrm{H} v \mathrm{Kmq}(1-f)^{1+\frac{1}{m}} \\H=\left(n_{\mathrm{i}}+p f-N_{\mathrm{v}}\right) \\K=\exp \left(\frac{-\Delta W_{\alpha}}{R T}\right)\end{array}$ | dN=φdΔGVγ→α';Vm=constant;dΔGVγ→α'/dT=constant;the autocatalytic factor is linearly related to f. | (1) Expresses only the effect of temperature on the transformation process.(2) Contains the effect of autocatalytic nucleation sites on the transformation process. | × | √ | × | × |
| Raghavan andEntwisle[ | $\begin{array}{l}\frac{\mathrm{d} f}{\mathrm{~d} t}=H(1-f) v K\left(\bar{V}+\frac{\mathrm{d} \bar{V}}{\operatorname{dln} N_{\mathrm{v}}}\right) \\H=\left[n_{\mathrm{i}}+f\left(p-\frac{1}{\nabla}\right)\right] \\K=\exp \left(\frac{-\Delta W_{\alpha}}{\mathrm{RT}}\right)\end{array}$ | (1) Single activation process.(2) Total nucleation sites consist of preexisting sites, autocatalytic sites and consuming sites.(3) Activation energy is constant.(4) Autocatalytic nucleation is related to f.(5) Vm satisfies Fisher's equation. | (1) Employing Fisher's equation to express the instantaneous volume of the martensite plates is impractical.(2) The effect of the grain size is reflected only in the instantaneous volume of the martensite plates and not in the nucleation rate. | × | √ | √ | × |
| PatiandCohen[ | $\begin{array}{l}\frac{\mathrm{d} f}{\mathrm{dt}}=H(1-f) v K\left(\bar{V}+\frac{\mathrm{d} \bar{V}}{\operatorname{din} N_{\mathrm{v}}}\right) \\H=\left[n_{\mathrm{i}}+f\left(p-\frac{1}{\nabla}\right)\right] \\K=\exp \left(\frac{-\Delta W_{\alpha}}{R T}\right)\end{array}$ | (1) Single activation process.(2) Total nucleation sites consist of preexisting sites, autocatalytic sites and consuming sites.(3) Activation energy is constant.(4) Autocatalytic nucleation is related to f.(5) Vm satisfies Fullman's equation. | (1) The expression of the martensite instantaneous volume is still inaccurate.(2) The effect of the grain size is reflected in only the instantaneous volume of the martensite plates and not in the nucleation rate. | × | √ | √ | × |
| Lin,Olson,andCohen[ | $\begin{array}{l}\frac{\mathrm{d} f}{\mathrm{dt}}=\int_{0}^{Q}[H(1-f) v K] \mathrm{d} Q \cdot \bar{V} \\H=\left(\frac{\mathrm{dN}_{\mathrm{i}}}{\mathrm{d} Q}+f \frac{\mathrm{d} P}{\mathrm{~d} \bar{Q}}-\frac{\mathrm{d} N_{\mathrm{v}}}{\mathrm{d} Q}\right) \\K=\exp \left(\frac{-\Delta \mathrm{Q}}{k T}\right)\end{array}$ | (1) Multiple activation process.(2) Size of preexisting nucleation sites satisfies an exponential distribution.(3) Size of autocatalytic nucleation sites satisfies a Gaussian distribution. | (1) Presents athermaland isothermal martensitic transformation simultaneously.(2) The distribution of preexisting defects and autocatalytic defects are related with grain size. | × | √ | √ | × |
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