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1 Precipitation Kinetic Theory in Fe–12Ni–6Mn

This section will concentrate on the quantification or modelling of the precipitation transformation in Fe-12Ni-6Mn maraging steel. Aimed at developing cheaper alternatives than the classical 18Ni maraging steels (Table 6.2), efforts were made in Russia and Japan, studying maraging in a series of experimental Fe–Ni-Mn alloys. Research with an Fe-12Ni-6Mn alloy showed that age hardening is achieved due to precipitation of θ-NiMn in the lath martensite, the quenched structure before ageing, as observed using electron microscopy.

1.1 Theoretical Analysis of the Early Stage Ageing Process

Coherent zones, possibly with a bcc structure, form at the early stages of ageing. After these, e.g. 0.2 h at 450 °C, θ-NiMn forms well before peak hardness. Deformation occurs by dislocations cutting through these coherent zones (or precipitates). Because the increase in yield stress is proportional to the increase in hardness (ΔH) for maraging steels and applying a coherency-strengthening mechanism, one may get:

$$ {{\Updelta}}H = Ar^{1/2} f^{1/2} $$
(7.1)

where r is radius of the particle, f is volume fraction of the transformed particles and A is a coefficient relating the increase in hardness to precipitate size and fraction:

$$ A = \frac{{M_{T} }}{q}(\kappa \varepsilon )^{3/2} \mu \left( {\frac{3}{2\pi b}} \right)^{1/2} $$
(7.2)

where M T is the Taylor factor, q is a conversion constant between Vickers hardness and yield strength, κ is a numerical constant between 3 and 4, taken as 3.5, ε is a strain energy constant, μ is the shear modulus of the matrix, taken as 81 GPa and b is the dislocation Burgers vector.

Since κ, ε, μ and b are all material constants and can be obtained from the literature, the quantification of ΔH is now switched to the determination of the particle size r and precipitation fraction f.

The relationship between ageing time t and radius r of zone or precipitate (assumed spherical) is given by Zener’s parabolic relationship:

$$ r = \alpha \left( {Dt} \right)^{1/2} $$
(7.3)

where α is a constant related to the solid solubility of the precipitate and the matrix and the composition of the alloy, and D is the diffusion coefficient.

When time t is small for the early ageing stage, α can be considered as a constant and calculated following Christian’s suggestion for a spherical precipitate and small degree of supersaturation (Christian 2002):

$$ \alpha = \frac{{2^{1/2} (c_{0} - c_{\alpha } )^{1/2} }}{{(c_{\theta } - c_{0} )^{1/2} }} $$
(7.4)

where c 0 is concentration of the precipitating elements in the matrix before ageing, taken as the sum of Ni and Mn, equal to the composition of the alloy, c α is the solid solubility of the controlling elements in the parent phase and c θ is the concentration of the elements in the new phase, that is, the θ-NiMn precipitate.

The Johnson–Mehl–Avrami (JMA) equation can be used to describe the relationship between transformation fraction and time at a certain temperature:

$$ \frac{f}{{f_{\text{eq}} }} = 1 - \exp \left[ { - (kt)^{m} } \right] $$
(7.5)

where f eq is the equilibrium fraction of the precipitation (temperature dependent), k is a reaction rate constant, and m is the Avrami index.

At an early ageing stage, that is, when kt ≪ 1, the above equation reduces to the following:

$$ f = f_{\text{eq}} (kt)^{m} $$
(7.6)

Combining Eqs. (7.1), (7.3) and (7.6), one obtains:

$$ {{\Updelta}}H = A(\alpha f_{\text{eq}} )^{1/2} D^{1/4} k^{m/2} t^{(m/2 + 1/4)} = (Kt)^{n} $$
(7.7)

where n is the time exponent in the relationship between the increase in hardness and ageing time in the early stage of ageing, n = (2 m + 1)/4, and K is a temperature-dependent rate constant.

Assuming that K follows the Arrhenius type of equation:

$$ K = K_{0} \exp \left( { - \frac{Q}{RT}} \right) $$
(7.8)

where K 0 is a pre-exponential term, R is the gas constant, T is temperature (in Kelvin) and the activation energy Q for the precipitation process during ageing can be calculated. Using Eq. (7.8) to replace K in Eq. (7.7) and then taking the natural logarithms of both sides, one may get:

$$ \ln {{\Updelta}}H = n\left( {\ln K_{0} - \frac{Q}{RT} + \ln t} \right) $$
(7.9)

For a constant increase in hardness ΔH 0 at different temperatures, one will have:

$$ \ln t = \frac{Q}{RT} + \frac{{\ln {{\Updelta}}H_{0} }}{n} - \ln K_{0} $$
(7.10)

Assuming that n is constant, the activation energy Q can be obtained by plotting ln t versus 1/T, where t is the time to reach ΔH 0 at temperature T. The slope of the straight line is Q/R as can be seen from the above equation. K 0 can be obtained simultaneously from the interception of the straight line with the ln t axis. When the activation energy Q and K 0 are known, ΔH during the age hardening can be calculated using Eq. (7.7), in conjunction with Eq. (7.8).

1.2 Overall Ageing Process

There are a few assumptions in the above theory that may prohibit its application to the overall ageing process:

  1. (A1)

    coherent precipitate strengthening mechanism;

  2. (A2)

    spherical precipitate (zone or particle);

  3. (A3)

    constant activation energy;

  4. (A4)

    kt ≪ 1, which allows the simplification from Eq. (7.5) to Eq. (7.6);

  5. (A5)

    constant α for precipitate growth.

The strengthening is due to coherent precipitates before peak hardness is reached, and the particles do not change to platelets until overageing takes place. These allow assumptions A1 and A2 to be applied to describe the overall ageing period. As for the activation energy, assumption A3, this may change during the ageing process. However, when ΔH 0 takes different values, the calculations to be shown later imply that the activation energy does not vary very much. Therefore, the activation energy will be considered as a constant value in the current model.

Assumptions A4 and A5 will not be acceptable when ageing proceeds beyond the early stage. The growth constant α in Eq. (7.3) is not constant any longer when the precipitates continue to form and grow, because the composition of the matrix changes significantly when more precipitates form from the matrix. Consequently, a more accurate way to calculate r is formulated below, considering α as a function of t through the change of c 0, the composition of the matrix. Before ageing takes place, c 0 is the concentration of the precipitating elements in the alloy. Both are considered as the total amount of Ni and Mn.

From Eq. (7.3), the growth rate of particles is given by:

$$ \frac{{{\text{d}}r}}{{{\text{d}}t}} = \frac{1}{2}D^{1/2} \alpha (t)t^{ - 1/2} + D^{1/2} \frac{{{\text{d}}\alpha (t)}}{{{\text{d}}t}}t^{1/2} $$
(7.11)

so

$$ r = \int {D^{1/2} \left( {\frac{1}{2}\alpha (t)t^{ - 1/2} + \frac{{{\text{d}}\alpha (t)}}{{{\text{d}}t}}t^{1/2} } \right)} {\text{d}}t $$
(7.12)

where α can still be calculated from Eq. (7.4). However, it should be noted that the concentration in the matrix c 0, taken as the sum of Ni and Mn, changes during the ageing process simultaneously with the fraction of the precipitation f, denoted as c 0′, therefore:

$$ {{c_{0}}^\prime} = c_{0} - c_{\theta } f $$
(7.13)

Thus, for the overall ageing process, we have:

$$ {{\Updelta}}H = AD^{1/4} f_{\text{eq}}^{1/2} \left( {\int {\left( {\frac{1}{2}\alpha (t)t^{ - 1/2} + \frac{{{\text{d}}\alpha (t)}}{{{\text{d}}t}}t^{1/2} } \right)} {\text{d}}t} \right)^{1/2} \left( {1 - \exp \left( { - (kt)^{m} } \right)} \right)^{1/2} $$
(7.14)

where A is as defined in Eq. (7.2).

In Eq. (7.14), if the transformation fraction f is known (i.e., k is known), the precipitate size r can be calculated (assuming D is known), through the calculation of c 0′ and α. As a result, ΔH as a function of time and temperature can be quantitatively described.

2 Parameter Determination

2.1 Strengthening, Activation Energy and Avrami Index

In Eq. (7.14), A can be calculated when parameters M T , q, κ, ε, μ, b in Eq. (7.2) are known. The strain energy constant ε for precipitation of θ-NiMn in the α-iron matrix is:

$$ \varepsilon = \frac{{3K_{\theta } (1 + \nu_{\alpha } )\delta }}{{3K_{\theta } (1 + \nu_{\alpha } ) + 2E_{\alpha } }} $$
(7.15)

where K θ is the bulk modulus of the θ-NiMn precipitate, ν α is Poisson’s ratio of ferrite in pure iron, taken as 0.282, E α is the Young modulus of ferrite in pure iron, taken as 206 GPa (Ledbetter and Reed 1973), and δ is the linear strain accompanying precipitation from the matrix:

$$ \delta = \frac{{2(\Upomega_{\theta } - \Upomega_{\alpha } )}}{{3(\Upomega_{\theta } + \Upomega_{\alpha } )}} $$
(7.16)

where Ω α and Ω θ are the atomic volumes of the ferrite (0.01176 nm3/atom) and the θ-NiMn precipitate (0.01224 nm3/atom), respectively. Alternatively, δ can be determined from (1 + δ)3 = Ω θ α , which gives a value close to that from Eq. (7.16). The above parameters are summarised in Table 7.1. The Taylor factor M T is taken as 2.75 (Hosseini and Kazeminezhad 2009) for body-centred-cubic materials, and κ is assigned as 3.5.

Table 7.1 Values of parameters involved in the calculation of precipitation strengthening in Fe-12Ni-6Mn maraging-type alloy

The activation energy Q is calculated using Eq. (7.10), based on early ageing data. When ΔH 0 takes different values 70, 100, 150 HV, Q is determined as 141, 133 and 125 kJ mol−1, respectively. It is reasonable to treat it as a constant. In the following calculation, Q is taken as 133 kJ mol−1, the average of the above three values. Growth-related constants n and m are 0.475 and 0.45, respectively.

2.2 Reaction Rate Constant in the Johnson–Mehl–Avrami Equation

Experimental research shows that peak hardness is reached either by holding at 400 °C for 16 h, at 450 °C for 1.4 h, or at 500 °C for 0.24 h. Assuming that the precipitate fraction corresponding to peak hardness at 400 or 450 °C is known, f/f eq is known, one can obtain the value of the pre-exponential term k 0, if the reaction rate constant in the JMA equation k is assumed to follow an Arrhenius type equation with the same activation energy as K:

$$ k = k_{0} \exp \left( { - \frac{Q}{RT}} \right) $$
(7.17)

Combining Eqs. (7.17) and (7.5), one will obtain:

$$ k_{0} = \frac{{\left( { - \ln (1 - f/f_{\text{eq}} )} \right)^{1/m} }}{{t_{\text{p}} }}\exp \left( \frac{Q}{RT} \right) $$
(7.18)

where t p is the time to reach peak hardness.

The percentage of the precipitate formed at peak hardness will be determined later. As will also be shown later, the precipitation fraction corresponding to peak hardness at 400 °C is higher than that at 450 °C, which partially contributes to the stronger age hardening effect at 400 °C than at 450 °C.

2.3 Growth and Diffusion Constants

Equation (7.4) shows that α is a function of c 0, c θ and c α . In the calculations below, as discussed earlier, c 0 will be replaced by c 0′, calculated from Eq. (7.13). Both c θ and c α are to be considered as the sum of Ni and Mn in atomic fraction. Since NiMn only contains Ni and Mn, c θ always equals 1. The values of c α at different temperatures are calculated using thermodynamic software (Table 7.2, together with the equilibrium amount of NiMn precipitate). The value for c 0 is 0.1728 in atomic fraction, which is the equivalence of 0.1765 in weight fraction, that is the sum of 11.9 wt% Ni and 5.75 wt% Mn, the precise composition of the alloy studied.

Table 7.2 Data calculated with thermodynamics related to precipitation in Fe-12Ni-6Mn maraging-type alloy

At 450 °C, the average diameter of precipitates is around 3 nm after 0.2 h ageing, and 6 nm after 2 h (peak hardness). Based on these, the diffusion coefficient can be estimated. One may assume that D follows an Arrhenius-type equation with the same activation energy as K:

$$ D = D_{0} \exp \left( { - \frac{Q}{RT}} \right) $$
(7.19)

Then, the pre-exponential term D 0 can be obtained by combining Eqs. (7.19) and (7.12):

$$ D_{0} = \left( {\frac{r}{{\int {\left( {\frac{1}{2}\alpha (t)t^{ - 1/2} + \frac{{{\text{d}}\alpha (t)}}{{{\text{d}}t}}t^{1/2} } \right)} {\text{d}}t}}} \right)^{2} \exp \left( \frac{Q}{RT} \right) $$
(7.20)

2.4 Critical Nucleus Size and Precipitation Fraction at Peak Hardness

Critical nucleus size (R c) is the size of the precipitate above which the nucleus is stable and able to grow. It can be calculated as (Porter and Easterling 1981):

$$ R_{\text{c}} = \frac{{ - 2\sigma N_{\text{A}} \Upomega_{\theta } }}{{\Updelta G_{\nu } }} $$
(7.21)

where σ is the interface energy per unit area between precipitate and matrix, taken as 0.2 J m−2, N A is Avogadro’s number, and the Gibbs energy difference between the precipitate and ferrite, ΔG ν, can be calculated using thermodynamics software.

Rivera-Díaz-del-Castillo and Bhadeshia (2001) calculated the critical nucleus size taking into account the Gibbs–Thomson capillarity effect, which influences the equilibrium compositions at the particle/matrix boundary:

$$ R_{\text{c}} = \frac{{2c_{\alpha } \Upgamma }}{{c_{0} - c_{\alpha } }} $$
(7.22)

where the capillarity constant Γ is given by:

$$ \Upgamma = \frac{{\sigma N_{\text{A}} \Upomega_{\theta } }}{RT}\frac{{1 - c_{\alpha } }}{{c_{\theta } - c_{\alpha } }} $$
(7.23)

ΔG ν and R c calculated from both methods at various temperatures are listed in Table 7.3. When calculating the incubation period, the larger R c values calculated from Eq. (7.21) are used. It should be noted that even for sizes smaller than the critical radius, a parabolic growth law described by Eq. (7.3) is assumed.

Table 7.3 Driving force and the critical nucleus radius of precipitation in Fe-12Ni-6Mn maraging-type alloy

The determination of precipitation fraction f at peak hardness, f p, as a percentage of the equilibrium fraction f eq at different temperatures involves an optimisation procedure. Using the various transformation fraction values, the age hardening curves at various temperatures can be obtained. One may therefore obtain the transformation fraction value to best fit the calculated hardness curves with the experimental curves (Table 7.4). In general, peak hardness increases with decreasing temperature due to greater supersaturation giving a greater volume fraction of precipitate.

Table 7.4 Values of parameters obtained by best fitting

3 Basic Measurements

3.1 Phase Transformation Determinations

The composition of the steel used in Sects. 7.37.5 is included at the bottom of Table 6.1. The phase transformation temperatures labelled in the dilation curves are shown in Figs. 7.1, 7.2. The standard way of measuring A c3 is used by San Martín et al. (2008) and Gomez et al. (2009), where A c3 is defined as the temperature at which expansion begins again to depend linearly on temperature once the sample is fully austenitic.

Fig. 7.1
figure 1

Dilation curves of as-forged low nickel steel. a A c1A c3; b M s M f . (From Sha et al. (2011), www.maney.co.uk/journals/mst and www.ingentaconnect.com/content/maney/mst)

Fig. 7.2
figure 2

Dilation curves of as-forged steel after cooling to −196 °C. a A c1A c3; b M s M f (From Sha et al. (2011), www.maney.co.uk/journals/mst and www.ingentaconnect.com/content/maney/mst)

Koistinen and Marburger have shown for athermal martensite that the volume fraction transformed, y, at temperature T may be related to the martensite start temperature M s by an expression of the form (Chong et al. 1998):

$$ y = 1-\exp[\alpha( {M_{s}} - T )] $$
(7.24)

where α = constant, < 0, unit K−1. Rearranging and taking logarithms gives

$$ \ln ( {1-y}) = \alpha ( {M_{s} - T}) $$
(7.25)

The dilatometer curve for the as-forged steel analysed according to the Koistinen and Marburger (K–M) analysis is shown in Fig. 7.3, in the same way as shown with Fe-15 %Ni (Chong et al. 1998; Wilson and Medina 2000). The portion of the K–M curve between 378 and 340 °C probably corresponds to grain boundary massive ferrite. The remainder of the K–M curve should correspond to martensite inside the prior austenite grains. The K–M analysis can reveal different transformation processes and products, as shown by Wilson and Medina (2000), where multiple linear fitting lines were demonstrated, corresponding to different transformations in different temperature ranges during one continuous cooling experiment. That is not the case for the present maraging steel, because the vast portion of the transformation fits to one linear line.

Fig. 7.3
figure 3

K–M analysis of the dilatometer curve for the as-forged steel. (From Sha et al. (2011), www.maney.co.uk/journals/mst and www.ingentaconnect.com/content/maney/mst)

3.2 Hardness

There is a close relation between hardness and precipitation in maraging steels. The hardness, aged at 550 °C for 10 h and air cooled is 488–499 HV30. The hardness data in Fig. 7.4 show age hardening curves of the maraging steel at different ageing temperatures. When aged at the lowest temperature of 450 °C, the steel can attain the hardness of 401 HV2 after 1 h of ageing. Both 550 and 600 °C ageing temperature have led to rapid hardening responses. At 600 °C ageing temperature, the hardness reaches its peak when the ageing time is 0.25 h, with the maximum hardness of 467 HV2, followed by slow reduction to 301 HV2 after ageing for 257 h. It takes 2 h for the steel at 550 °C ageing temperature to reach the peak hardness of 496 HV2. The hardness increase rate is marginally slower than at 600 °C ageing temperature. Ageing at 450 °C gives the lowest hardness increase rate, and requires the longest time of 66 h to reach the peak hardness 500 HV2. When aged at 450 °C, the hardness keeps increasing up to and likely after the longest ageing time used at this temperature. Moreover, at the higher ageing temperature 500 °C, the maximum ageing hardness is the same as the maximum hardness at 450 °C, within error ranges. The peak hardness is 501 HV2 at 17.35 h.

Fig. 7.4
figure 4

Age hardening curves, showing the variation of hardness, with ageing time, in the maraging steel aged at 450–600 °C. (From Sha et al. (2011), www.maney.co.uk/journals/mst and www.ingentaconnect.com/content/maney/mst)

Similar peak hardness can be reached at all four ageing temperatures, but the time of reaching the peak hardness is different. This permits the presumption that similar microstructures with the peak hardness can be achieved by ageing at these four temperatures for different times. Precipitation plays a dominant role in hardness of maraging steels. Other factors are retained or reverted austenite content, and dislocation density change. In this steel, no austenite is detected by X-ray diffraction (XRD) throughout the ageing process (see Sect. 7.4.2), so this factor has no contribution. The ageing is in a temperature range of 450–600 °C. Therefore, if we assume that the dislocation density change is comparable at different temperatures when the peak hardness is reached (i.e., shorter time at higher temperatures and longer time at lower temperatures), we would lead ourselves to the belief that similar size precipitates are similarly distributed in the matrix, when the peak hardness is achieved.

It should also be noted that the hardness after ageing at 550 and 600 °C temperatures decreases not long after it reaches the peak. Moreover, the hardness keeps increasing up to and likely after the longest ageing time at 450 °C. The hardness after ageing at 500 °C temperature displays a large plateau around the peak hardness and shows almost no decrease. These interesting behaviours may be explained from two points of view. On the one hand, ageing temperatures of 450 and 500 °C are not sufficiently high for the precipitates in the steel to grow quickly, while 550 °C is high enough for them to grow to large sizes after long ageing times. Therefore, overageing happens to the steel relatively early when aged at the temperatures of 550 and 600 °C than at the temperatures of 450 and 500 °C. On the other hand, when the ageing temperature is as high as 550 °C, after a relatively long ageing time, some amount of reverted austenite may form around some nickel rich precipitates (Sha and Guo 2009). They may also be responsible for the decrease of the hardness.

The age hardening after different heat treatments, i.e. H950 (485), H950 (600), QL (485) and LQ (485) treatments, are shown in Fig. 7.5. H950 (485) treatment includes heating at 950 °C for 1 h followed by air cooling and then ageing at 485 °C. H950 (600) uses the ageing temperature of 600 °C. Q refers to half an hour at 950 °C, followed by water quenching and L refers to 2 h at 750 °C, followed by air cooling. The steel after the H950 (600) treatment reaches the peak hardness within a shortest time of about 30 min, with the lowest peak hardness value of 442 HV2, comparing with the other treatments. During H950 (600) treatment, the hardness decreases significantly after the peak hardness. H950 (600) and H950 (485) treatments only have a difference in ageing temperatures, namely ageing at 600 °C and 485 °C, respectively. When the ageing time is 64 h, H950 (485) treatment reaches its peak hardness with a value of 498 HV2. Hence, the 485 °C ageing temperature has resulted in the slower hardening response, while having a significant increase in peak hardness. QL (485) treatment takes 16 h to reach the peak hardness value of 500 HV2 and LQ (485) treatment has a similar peak hardness value of 503 HV2 when the ageing time is 8 h. Additionally, H950 (485), QL (485) and LQ (485) treatments lead to the similar increasing rate and the hardness reaches a large plateau after ageing for 8 h. At a range of 8–64 h, the hardness is close and can be considered as the same when combining standard deviation. Considering the scatter of the results, there are no differences between the hardness between 8 and 128 h.

Fig. 7.5
figure 5

Age hardening curves at two ageing temperatures (485 and 600 °C). Reprinted from Sha et al. (2012), with permission from Elsevier

Summarising the above, despite the several pre-ageing treatments, the only important variable is ageing temperature. Within experimental error all data aged at 485 °C superimpose and the steel aged at 600 °C exhibits a well-known response of reaching a peak in hardness at shorter times. There appears to be no effect of the different pre-ageing treatments.

3.2.1 Precipitation

We now continue to discuss the effect of the heat treatments on the hardness due to precipitation (this section) and overageing (Sect. 7.3.2.2). The hardness after ageing shows a pronounced increase compared to before ageing, for all treatments including the H950 treatment. Conventionally, precipitates formed during ageing should be responsible for the hardening during ageing (Askeland et al. 2010). The type of precipitates is analysed in Sect. 7.4.3.

Thermodynamic calculations indicate that Nb2C and NbC form during austenitisation (950 °C) and intercritical annealing (750 °C) (see Sect. 7.4.3). Other precipitates such as NiAl whose formation temperature is lower than 950 and 750 °C can form during subsequent cooling.

3.2.2 Overageing

The existence of austenite cannot be absolutely excluded owing to the limitation of the conventional XRD. Guo et al. (2004) stated that when the amount of austenite is lower than 2 %, conventional XRD cannot detect the austenite. Hence, even though no austenite is detected for this material, the amount of retained or reverted austenite should be considered not higher than this threshold. Additionally, for L treatment, there is no indication in XRD profile of retained austenite either. Hence, most likely, the amount of Ni element in this material is not enough to generate the reverted austenite which is formed at the expense of martensite during ageing.

The clear sign of overageing is the decrease in hardness. A possible reason of hardness decrease is precipitate coarsening (Lach et al. 2010). However, the image after H950 (600) treatment (Sect. 7.4.1) shows needle-like structures. These clear and bright microstructures are suspected to be reverted austenite which is considered to be predominately responsible for the toughness of steel (Xiang et al. 2011), but the amount of reverted austenite is too small to detect by XRD. Hence, the pronounced drop in hardness could be attributed to the reverted austenite. Accurate characterisation of the reverted austenite must be carried out to validate the hypothesis of its link with the drop of hardness.

4 Microstructure

4.1 Microscopy

The microstructure of the steel after etching (Fig. 7.6) consists of the martensite laths and the grain boundaries. After ageing for a long time at 550 or 600 °C, some dark areas are revealed, probably related to overageing products.

Fig. 7.6
figure 6

Optical micrographs before and after ageing. a As-forged; b 500 °C, 0.25 h; c 500 °C, 0.5 h; d 550 °C, 72 h. The four micrographs have a same magnification. (From Sha et al. (2011), www.maney.co.uk/journals/mst and www.ingentaconnect.com/content/maney/mst)

The martensite laths and the grain boundaries are more clearly revealed in SEM images (Fig. 7.7). Very fine precipitates are also seen, homogeneously lying on the surface. Under the TEM, the microstructure consists of martensite laths with many precipitates in the lath matrix randomly (Fig. 7.8). With increasing ageing time, small precipitates become large very slowly.

Fig. 7.7
figure 7

Scanning electron micrographs after ageing. (a) 500 °C, 32 h; (b, c) 450 °C, 66 h. (From Sha et al. (2011), www.maney.co.uk/journals/mst and www.ingentaconnect.com/content/maney/mst)

Fig. 7.8
figure 8

Transmission electron micrographs after ageing. a 500 °C, 8 h; b 550 °C, 256 h. (From Sha et al. (2011), www.maney.co.uk/journals/mst and www.ingentaconnect.com/content/maney/mst)

Table 7.5 compares the size of precipitates measured at different ageing times on SEM micrographs. The measurements on the SEM micrographs could have three sources of errors. Because some particles might have more than half of their volume embedded in the matrix and the sectioning nature of the imaging, the measured diameter might be the diameter of the exposed spherical cap instead of the diameter of the particle sphere, assuming spherical particles. This would result in underestimation of precipitate size in SEM measurements. On the other hand, the SEM might not have picked up all of the particles given the scale of the observations. This would lead to overestimation of the precipitate size due to not including the smaller particles in the counts. The two error sources would give opposite errors, and so they might cancel each other out to some extent. However, the error values shown, using standard deviations, should be mostly from the real scatter of precipitate sizes.

Table 7.5 Comparison of size of precipitates after ageing at 500 °C measured in SEM micrographs

Another source of error in SEM at such high magnifications is the local sampling. The technique cannot easily reveal any possible long-range variation of precipitate size and density, due to, for example, inhomogeneous chemical composition.

Figure 7.9 shows the microstructures after Q, H950, QL and LQ treatments prior to ageing. Many lath-like martensite packs (one example is masked in Fig. 7.9b) are clearly visible in the grain (one example is masked in Fig. 7.9e).

Fig. 7.9
figure 9

SEM images after different heating treatments without ageing. a Q; b H950; c QL; d, e, f LQ. A lath-like martensite pack is masked in b. A grain is masked in e. Reprinted from Sha et al. (2012), with permission from Elsevier

In comparison with before ageing, the microstructures after QL (Fig. 7.10b) and LQ (Fig. 7.10c) treatments comparing to that after H950 treatment (Fig. 7.10a) show that martensite matrix is more complex, in that it does not show clear, long laths, and heterogeneous.

Fig. 7.10
figure 10

SEM images after different heating treatments with ageing. a H950 (485) for 8 h; b QL (485) for 16 h; c LQ (485) for 8 h. Reprinted from Sha et al. (2012), with permission from Elsevier

The overaged microstructure after H950 (485), LQ (485) and QL (485) for 128 h, and after H950 (600) for 4 h, is given in Fig. 7.11. The matrix, martensitic structure that appears, at such high magnifications, should be treated with caution. There may be contribution from the effect of the sample preparation process, including scratch marks and etching, which is magnified with the high magnifications. Thus, not all fine features are real matrix features. Similar attention should be given for Figs. 7.9, 7.10 when magnifications at these levels are used.

Fig. 7.11
figure 11

SEM images after different heating treatments with prolonged ageing. a H950 (600) for 4 h; b H950 (485) for 128 h; c QL (485) for 128 h; d LQ (485) for 128 h. Three needle-like structures are indicated by arrows in (a), although there are more in the picture. Reprinted from Sha et al. (2012), with permission from Elsevier

4.2 X-ray Diffraction Analysis

XRD analysis is used to detect retained or reverted austenite, but no reflection peaks for fcc austenite are in the patterns after ageing at any temperature. The darkening in Fig. 7.6d does not seem to be related to austenite. Otherwise, such an austenite fraction would have been detected by XRD analysis.

Only two peaks are in the X-ray diffraction patterns, where a sharp peak occurs at 44.8° position and a small peak is at 64.9° position, in Fig. 7.12 using the example after QL treatment before and after ageing. Guo et al. (2004) quantified the precipitate fraction in maraging steel, which also gave diffraction patterns showing the existence of austenite. By comparing with Guo et al. (2004), there is no indication of peaks for retained or reverted austenite (γ) in Fig. 7.12, namely no peaks occur at 43°, 50° and 74°, the primary positions of austenite peaks.

Fig. 7.12
figure 12

XRD profiles after QL treatment without ageing and aged at 485 °C for 128 h

4.3 Thermodynamic Calculations

Thermodynamic calculations of equilibrium phases, phase fractions and their compositions in the Fe-12.94Ni-1.61Al-1.01Mo-0.23Nb-0.0046C (wt%) system are made at 450, 500, 550 and 600 °C. The phases in the calculations are liquid, fcc, bcc, hcp, diamond, graphite, σ, Laves, R, P-phase, μ, χ, MoNi α, MoNi4 β, MoNi3 γ, Al13Fe4, Al2Fe, Al5Fe2, Ti3Al, TiAl, cementite, ξ carbide, M23C6, M7C3, M6C, M3C2, V3C2, MC η, M5C2, Al3Ni, Al3Ni2, AlNi B2, AlCu θ and FeCN χ. The components in each of the equilibrium phases will be given further below when showing the calculation results.

The equilibrium phases and their mole percentages are given in Table 7.6. In this table, the fcc phase is the austenite. X-ray results show, however, that this phase does not form even after the steel is significantly overaged, for 257 h. These results, although showing the real equilibrium state, have no practical value because, in the actual ageing process of this steel at these temperatures, austenite does not form due to its slow kinetics. The reason for this is that, due to the virtually zero carbon in the bcc, the difference between austenite and bcc compositions are mainly nickel contents. Hence, the formation of austenite is controlled by the diffusion of nickel, plus the driving force for the formation of difference phases. Among the precipitation phases in Table 7.6, NiAl has a very fast kinetics (Sha and Guo 2009), as well as the carbides, because carbon has a faster diffusion rate than the substitutional elements. Because the results in Table 7.6 have no practical value, we will not continue to show and discuss the compositions of each phase in detail.

Table 7.6 Equilibrium phase mole fractions when austenite is entered in the thermodynamic calculations

The austenite phase is now excluded from the calculations, which is more relevant to the practical heat treatment of maraging steels (Table 7.7). NiAl is found to be the main precipitation phase, in agreement with an atom probe work characterising precipitates in an aluminium-containing precipitation hardening (PH) steel (Sha and Guo 2009). The calculated composition of the NiAl B2 phase is Ni53Al47. The compositions of the FeNi hcp phase and all other equilibrium phases are given in Table 7.8.

Table 7.7 Equilibrium phase mole fractions when austenite is not entered in the thermodynamic calculations
Table 7.8 Components in the calculations in each phase and their concentration ranges in atomic per cent at 450/500/550/600 °Ca

The calculated equilibrium phase mole fractions at 750 and 950 °C are given in Table 7.9. The main phase is austenite which accounts for more than 99 %, whether at 750 or 950 °C. At 950 °C, another phase is NbC accounting for 0.044 %. At 750 °C, two other phases are Nb2C and Fe2(Nb,Mo) which is a Laves phase.

Table 7.9 Equilibrium phase mole fractions in thermodynamic calculations

5 Mechanical Properties

5.1 Tensile and Impact Properties and Fractography

The tensile properties after ageing treatment at 500 °C for 2 and 6 h are similar, with tensile strength of 1594 and 1577 MPa, respectively. The reduction of area in both cases is 15 %. These testing results show that the steel has good tensile strength.

The 5 × 10 × 55 mm half-size impact energy values in as-forged condition (forged to 25.4 mm thick disc followed by air cooling), before ageing, range 21–36 J, at −196 °C to room temperature. The steel was tough in this condition because of grain refining with Nb and excess C over stoichiometry of around 160 ppm C (Wilson et al. 2008). However, the fracture toughness was low after ageing. The ductile–brittle-transition-temperature (DBTT) of the maraging steel, aged at 550 °C for 10 h, is above room temperature.

The fracture surface of the as-forged impact specimens is characterised by radial ridges (Fig. 7.13a). These shearing dimples are very big and shallow. Figures 7.13b, 7.13c show small and deep tensile dimples, with small precipitates at the bottom of many dimples, confirming that the fracture process was typically ductile. The two kinds of dimples emerging on the fracture surface on the same specimens are due to the complicated stress experienced during the impact. They also show that the steel has good toughness under the as-forged condition.

Fig. 7.13
figure 13

Fractographs of as-forged impact specimens, at increasing magnifications. a Big and shallow shearing dimples, tested at –110 °C; b small and deep tensile dimples, tested at –196 °C; c small and deep tensile dimples, tested at –110 °C. (From Sha et al. (2011), www.maney.co.uk/journals/mst and www.ingentaconnect.com/content/maney/mst)

The properties of the steel may be compared with its most equivalent but more expensive commercial counterpart, the Vascomax (2000) T-250 (Fe-18.5Ni-3Mo-1.4Ti) as follows. Following ageing treatment, T-250 has Rockwell C hardness of 49–52, equivalent to 498–544 HV10, tensile strength of 1793 MPa and reduction of area 58 %. Its room temperature full-size impact energy is 34 J. The low nickel maraging steel has matched the commercial maraging steel in its hardness and strength, but is low on ductility and toughness.

The Charpy impact energy after H950, LQ and QL treatments and then ageing at 485 °C, and after H950 treatment and then ageing at 600 °C, are shown in Table 7.10. H950 (600) treatment gives a pronounced increase in toughness of around 400 % at the expense of hardness of around 12 % comparing with H950 (485) treatment. Consistent with the hardness data in Sect. 7.3.2, all data after ageing at 485 °C are experimentally the same within experimental uncertainty.

Table 7.10 Charpy impact toughness after different heat treatments

5.2 Intercritical Annealing and the Dual-Phase Structure

In this section, we attempt to link different aspects together. The discussion with intercritical annealing and the dual-phase structure aims to explain the effect of the QL and LQ treatments on the microstructure.

For L treatment (750 °C), thermodynamically, there is no bcc phase at this temperature (see Sect. 7.4.3). It has a high possibility that the temperature/time of L treatment is not enough to transform martensite into austenite completely. Therefore, in the following cooling, even if no austenite is retained, the total amount of the fresh martensite should be less than what Q treatment would result, where Q for the austenitisation can achieve the complete transformation of martensite into austenite. QL also embodies Q treatment as the first heating step, while the further L treatment is to temper martensite which can soften martensite (Baltazar Hernandez et al. 2011). LQ treatment, where Q treatment is the second heating step comparing with QL treatment, results in more martensite to transform into austenite. Hence after subsequent quenching, more martensite is formed. There are slight differences between Q and H950, in terms of quenching media, but their hardness prior to ageing is the same, when considering standard deviation. No retained austenite has been detected after heating at around 950 °C.

Clear and long martensite laths are seen in Fig. 7.10a, but they look short and disrupted in Figs. 7.10b and 7.10c. This is probably due to the formation of the intercritical annealing product, the ‘dual-phase’ structure, which is a mixture of tempered and fresh martensite. It is noted that some precipitates form at 750 °C shown in thermodynamic calculations (see Sect. 7.4.3). Large precipitate particles may impede grain growth with ageing time more effectively than small precipitate particles. Hence, those two constituents of dual-phase have different responses to ageing. This also gives a reasonable explanation why this microstructure can only be observed after ageing. As mentioned in Sect. 7.3.1, the A c1/A c3 phase transformation temperatures are 635/871 °C. However, the A c1/A c3 phase transformation temperatures are measured during continuous heating, while the heat treating is isothermal. Thermodynamic calculations only show one phase, γ, with no bcc, at 750 °C. However, 2 h, the heating time of L treatment, may not be long enough for the transformation of martensite to austenite to complete. If so, effectively, L treatment can successfully heat the steel to an α and γ two-phase region. For two-step heating treatments, the first heating step causes the transformation of ferrite into austenite and then austenite transforms into martensite during quenching. At the second heating step, the main portion of martensite transforms into reverted austenite and the remainder of martensite is tempered and relaxed, denoted as tempered martensite. At subsequent quenching, reverted austenite transforms completely into martensite, due to no austenite detected after XRD, where the martensite is denoted as fresh martensite. Tempered martensite and fresh martensite compose a dual-phase structure, where tempered martensite is soft but lean and fresh martensite is hard but rich. The difference between QL and LQ treatments is that QL treatment sets up austenitisation as first heating step, which can transform ferrite into austenite completely. Hence, more martensite is tempered after QL treatment eventually.

This dual-phase microstructure should be responsible for the fine-grained microstructure, shown in Figs. 7.10b and 7.10c compared to Fig. 7.10a. Guo et al. (2003) gave an explanation as to why the two-step martensitic transformation of dual-phase results in the refinement of grain size. Owing to substitutional alloying elements such as Ni, Mo and Al replacing a portion of the position of iron atoms in fcc structure, there are two kinds of austenite formed, namely low-alloy and high-alloy phases, leading to two different quenching responses. The atomic concentrations in the austenite formed at high temperature (during Q treatment) and at low temperature (during L treatment) are not the same, because of the austenite composition changes as a function of temperature in the phase diagram (ASM Handbook 1992). At following quenching, the low-alloy phase transforms into martensite first. Then, the high-alloy phase starts to transform. This two-step martensitic transformation is restricted actually. The latter is constrained by surrounding martensite which is formed already. Eventually, the fine-grained microstructure is achieved. In the same paper by Guo et al. (2003), it was reported that LQ treatment nearly has no effect on grain refinement, but significant refinement can be obtained if iterating these heating procedures, namely LQLQ treatment (for QL treatment, it should be QLQL treatment).

5.3 Toughness

We now complete the discussion with the effect of the heat treatments on the toughness. The primary difference shown in the data in Table 7.10 is that the material aged at 600 °C is tougher than the material aged at 485 °C. Since the material is aged at each temperature to the peak hardness shown in Fig. 7.5, then it is obvious that the higher temperature ageing produces a material with lower hardness (e.g., 440 HV at 600 °C vs. 500 HV at 485 °C). Thus, the CVN data support the well-known observation that most materials within a given microstructural class exhibit higher toughness with a decrease in strength (Kim et al. 2008). The steel is expected to be used at around peak hardness, provided that the toughness is satisfactory.

For the steel after ageing at 550 °C for 10 h, without initial heat treatment, at room temperature, the half-size Charpy impact energy is around 4 J, and the hardness is about 455 HV2. The hardness after H950 (600) for 30 min is close, whereas the Charpy impact toughness is significantly enhanced. Therefore, low austenitisation temperature (950 °C) can achieve the significant enhancement in Charpy impact toughness compared with steel without initial heat treatment.

5.4 Summary

In summary, there is rapid age hardening across the ageing treatment temperatures of 450–600 °C. There are no significant changes of grain size and precipitates. There is no reverted austenite detected by X-ray diffraction. The steel is tough before ageing, but extremely brittle at room temperature after ageing, with high tensile strength and hardness. Thermodynamic calculations show that NiAl is the major precipitate phase at 450–600 °C.

There is different age hardening behaviour after austenitisation at 950 °C and intercritical annealing treatments of the Fe-12.94Ni-1.61Al-1.01Mo-0.23Nb (wt%) maraging steel, the steel with reduced nickel. There is no reverted austenite detected by XRD. However, some suspected reverted austenite, with a needle-like microstructure, is formed after austenitisation at 950 °C followed by ageing at 600 °C for 4 h. Laves phase, Fe2(Nb,Mo), is formed at 750 °C. The toughness after austenitisation with lower temperature is significantly increased. However, intercritical annealing treatments do not increase hardness either before or after ageing, and do not improve the toughness after ageing.