Modelling deformation-induced martensite transformation in high-carbon steels

Figures & data

Table 1. Chemical compositions of the quench-and-tempered bearing steels used for model development. The asterisk (*) represents the initial carbon content before carburisation. $C_{\gamma }$ is shown beside the carbon content, and iron forms the balance of the respective compositions.

	Chemical composition / wt-%
Steel	C	Mn	Si	Cr	Ni	Mo	P	S	Cu	Al
8620 [4]	0.2* (0.987)	1.43	0.32	0.74	0.28	0.09
4320 [4]	0.2* (0.994)	0.78	0.33	0.64	1.6	0.22
3310 [4]	0.1* (0.799)	0.45	0.26	1.51	3.39	0.06
A485-M1 [5]	1.0 (0.813)	1.09	0.6	1.06	0.11		0.013	0.012
52100-QT [6]	1.005 (0.800)	0.32	0.27	1.46	0.1				0.19	0.024

Table 2. List of symbols in the present work.

$C_{\gamma }$	Carbon content in retained austenite
$a_{\gamma }$	Lattice parameter of retained austenite
$x_i$	Concentration of alloying element in wt-%
$n$	Potency of a martensitic nucleation site
${\gamma }_s$	Nucleus specific interfacial energy
$\rho$	Density of atoms in the fault plane
$\mathrm{\Delta }{G}_{Chem}$	Chemical driving force for martensitic transformation
$E_{Str}$	Elastic strain energy
$W_F$	Frictional work of interfacial motion
$\mathrm{\Delta }{G}_{Mech}$	Mechanical driving force for martensitic transformation
$\mathrm{\Delta }{G}_{Total}$	total driving force for martensitic transformation
$\frac{\mathrm{\partial }\mathrm{\Delta }G}{\mathrm{\partial }\sigma }$	Stress state of transforming martensite plate
$N_v$	Number density of nucleation sites
$N_v^0$	Total number of nucleation sites of all potencies
$\alpha$	Shape factor of potency distribution
$V_p$	Austenite particle volume
$f$	Fraction of particles to transform into martensite
$\sigma$	Applied stress
${\sigma }_C$	Critical stress for the initiation of martensite transformation
$V_{\gamma }^0$	Initial volume fraction of retained austenite before mechanical loading
$V_{\gamma }$	Volume fraction of retained austenite

Table 3. Model parameters for the implementation of Equation (7). Steel designations are included next to the values of $\mathrm{\Delta }{G}_{Chem}^{GH}$ and $W_F^{GH}$.

Parameter	Parameter values in Equation (7)
${\left(\frac{\mathrm{\partial }\mathbf{\Delta }\mathit{G}}{\mathrm{\partial }\mathit{\sigma }}\right)}^{\mathit{G}\mathit{H}}$, in J mol^−1 MPa^−1	−0.822
${\mathit{\alpha }}^{\mathit{G}\mathit{H}}$	0.866
${\mathit{\gamma }}_{\mathit{s}}$, in J m^−2	0.15
$\mathit{\rho }$, in mol m^−2	3 × 10^−5
$\mathit{f}$	0.01
$({\mathit{N}}_{\mathit{v}}^0{)}^{\mathit{G}\mathit{H}}$, in m^−3	2 × 10^17
${\mathit{V}}_{\mathit{p}}^{\mathit{G}\mathit{H}}$, in m^3	5.55 × 10^−19
${\mathit{E}}_{\mathit{S}\mathit{t}\mathit{r}}$, in J mol^−1	500
$\mathbf{\Delta }{\mathit{G}}_{\mathit{C}\mathit{h}\mathit{e}\mathit{m}}^{\mathit{G}\mathit{H}}$, in J mol^−1	−2465 (8620)
	−2444 (4320)
	−2929 (3310)
	−2905 (A485-M1)
	−2931 (52100-QT)
${\mathit{W}}_{\mathit{F}}^{\mathit{G}\mathit{H}}$, in J mol^−1	1636 (8620)
	1645 (4320)
	1429 (3310)
	1441 (A485-M1)
	1429 (52100-QT)

Table 4. Model parameters for the implementation of Equation (11).

Parameter	Parameter values in Equation (11)
${\left(\frac{\mathrm{\partial }\mathbf{\Delta }\mathit{G}}{\mathrm{\partial }\mathit{\sigma }}\right)}^{\mathit{A}\mathit{W}}$, in J mol^−1 MPa^−1	−0.86
${\mathit{\alpha }}^{\mathit{A}\mathit{W}}$	0.7899
${\mathit{\gamma }}_{\mathit{s}}$, in J m^−2	0.15
$\mathit{\rho }$, in mol m^−2	3 × 10^−5
$\mathit{f}$	0.01
${\mathit{E}}_{\mathit{S}\mathit{t}\mathit{r}}$, in J mol^−1	500
$\mathbf{\Delta }{\mathit{G}}_{\mathit{C}\mathit{h}\mathit{e}\mathit{m}}^{\mathit{A}\mathit{W}}$, in J mol^−1	−2214 (8620)
	−2150 (4320)
	−2090 (3310)
	−2623 (A485-M1)
	−2772 (52100-QT)
${\mathit{V}}_{\mathit{\gamma }}^0$	0.43 (8620)
	0.39 (4320)
	0.31 (3310)
	0.18 (A485-M1)
	0.13 (52100-QT)

Table 5. The measured and calculated ${\sigma }_C$ for the quench-and-tempered steels.

		Calculated ${\sigma }_C$/MPa
Steel	Measured ${\sigma }_C$ MPa	Equation (7), original model	Equation (11), modified model
8620	441	3987	453
4320	592	4023	592
3310	785	3170	830
A485-M1	1058	3214	715
52100-QT	1140	3168	946

Table 6. Material parameters, measured and calculated ${\sigma }_C$ for steels with alternative microstructures.

		$C_{\gamma }$	$\mathrm{\Delta }{G}_{Chem}^{AW}$	Measured ${\sigma }_C$	Calculated ${\sigma }_C$, Equation (11)
Steel	$V_{\gamma }^0$	wt-%	J mol^−1	MPa	MPa
A485-B1	0.18	0.930	−2345	722	1057
A485-B2	0.09	1.016	−2145	1436	2257
52100-B220	0.16	0.651	−3130	700	261
52100-B240	0.14	0.757	−2874	901	765
52100-B260	0.09	0.852	−2650	1070	1802
52100-QP220	0.20	0.727	−2946	731	248
52100-QP240	0.13	0.808	−2753	830	1001

Figure 1. Measured and calculated retained volume fraction ($V_{\gamma }$) of steels with quench-and-tempered microstructure.

Figure 2. Measured and calculated retained austenite volume fraction ($V_{\gamma }$) of bainitic, QP and TRIP steels. The transformation curves are shown in separate plots for clarity.

Figure 3. The change in critical stress ${\sigma }_C$ as a function of (a) solute concentration; (b) temperature; (c) $V_{\gamma }^0$.

Figure 4. (a) Required manganese and nickel concentrations for a range of critical stresses at a deformation temperature of 20°C and $V_{\gamma }^0$ of 0.43; (b) change in retained austenite volume fraction $(V_{\gamma })$ with applied stress for selected compositions.

Figure 5. (a) Required manganese and nickel concentrations for deformation temperatures between −50°C and 80°C with ${\sigma }_C$ values within a range of 400–500 MPa; (b) change in retained austenite volume fraction $(V_{\gamma })$ with applied stress for a composition of 1.4Mn-0.3Ni (wt-%) within a temperature range of −40°C to 120°C.

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