Strain-induced solid-state coating of TWIP steel sheets with zinc

The hot-rolled 2-mm-thick sheets of high-manganese austenitic TWIP steel X40MnCrAl and 0.5-mm-thick pure Zn sheets, cut in 30-mm-wide and 150-mm-long plates, were utilised in this study. The TWIP steel has a chemical composition (in wt%): 18.9–Mn, 1.7–Cr, 1.2–Al, 0.4–C, 0.3–Si, and balance of Fe.

To maintain controlled temperatures within the interface zone and prevent uncontrolled temperature drops resulting from contact with the cold rolls, the Zn plate was positioned as an internal layer between two TWIP steel plates, forming a material ‘sandwich’. The stack of plates was secured at one end using a wire passed through all the plates of the ‘sandwich’ to prevent shifting and separation during rolling. The initial plate stack, as shown in Fig. 1, was rolled with thickness reductions of 50% and 70% at temperatures of 100, 200, 300, and 380 °C. This rolling process was carried out using a ‘Dinkel’ rolling mill with a 200-ton capacity, rolls with a diameter of 350 mm, and an angular velocity of 1.26 s⁻¹.

The average strain rate, \(\dot{\varepsilon }\), was calculated using the following expression, [9]:where \({V}_{r}=220\) mm/s is the linear velocity at the roll surface; \({L}_{d}\) is the length of deformation zone along axis of symmetry; \({t}_{0}\) and \({t}_{f}\) are the initial and final thickness of the stack, respectively.

The average strain rate calculated using Eq. (1) was 7.4 and 9.4 s⁻¹ for stacks rolled to 50 and 70% thickness reduction, respectively. Furthermore, it should be noted that distribution of strain is not uniform along cross section of the stack, with less strain induced in the steel layers and very large strain in the Zn layer, as illustrated schematically in Fig. 1. The strain, calculated from actual layers thickness after rolling, was one order of magnitude higher in Zn layer compared to TWIP sheets. These values for all rolling trials are presented in Table 1. Therefore, the strain rates in layers of steel and Zn differ by one order of magnitude and are temperature and strain dependent. Effective strain in TWIP steel layers is shown graphically as function of temperature for rolling at 50 and 70% thickness reduction in Fig. 2. It can be seen that the strain introduced in steel layers increases with temperature and reaches maximum at 300 °C, but then drops sharply when the temperature reaches 380 °C. That can be explained by momentous rise of temperature above Zn melting temperature due to high strain deformation, discussed in the next paragraph.

High strain rate rolling obviously resulted in temperature rise, especially in the middle of samples, which can be estimated using the following expression, [9]

where \({\sigma }_{e}\) is equivalent stress (1300–1050 MPa for TWIP steel and 40–3 MPa for Zn, in the temperature range 100–400 °C); \({\varepsilon }_{e}\) is equivalent strain (Table 1); c is the specific heat (527–622 J kg⁻¹ K⁻¹) for TWIP steel and 398–508 J kg⁻¹ K⁻¹ for Zn, in the temperature range 100–400 °C, [10]); ρ is the density of the material (7850 and 7134 kg/m³ for steel and zinc, respectively); and J is the mechanical equivalent of the heat (1.064–1.19 for steel and 1.111–1.333 for nonferrous metals).

Taking the average value of effective strain (\({\varepsilon }_{e}^{{\text{TWIP}}}=0.365; {\varepsilon }_{e}^{{\text{Zn}}}=1.12\) for 50% thickness reduction) and (\({\varepsilon }_{e}^{{\text{TWIP}}}=0.505; {\varepsilon }_{e}^{{\text{Zn}}}=1.55\) for 70% thickness reduction) across the range of deformation temperatures, and using expression (2) the temperature rise due to rolling was calculated (Table 3) (Sect. "Analytical evaluation of bonding mechanisms during rolling"). The temperature rise in the TWIP layers ranges from 65 to 96 °C for 50% reduction and 90–133 °C and 70% reduction, respectively, and it is ten times larger than temperature rise in a zinc layer. However, it should be noted that the surface of Zn plate rolled at temperature 380 °C to 70% reduction was in the close contact with steel plates heated to the temperatures 513 °C, which is significantly higher than Zn melting point and resulted in the incipient melting at the contact surface.

Eight samples in total were processed and analysed. The initial microstructure of both constituent materials before rolling can be also seen in Fig. 1. The average grain size of TWIP steel plate before rolling was about 11 µm, and initial average grain size of Zn plate was about 180 µm.

A relative intensity, K, of the characteristic X-ray radiation of Zn as a function of the energy of primary electrons, E, can be presented aswhere \(I\left(E\right)\) and \({I}_{{\text{std}}}\left(E\right)\) are intensities of the characteristic Zn X-ray radiation emitted from a specimen and from a uniform standard (ZnTe), respectively. In the framework of the technique employed in the present study, \(I\left(E\right)\) and \({I}_{{\text{std}}}\left(E\right)\) were calculated as follows

Here, \(C\left(\rho x\right)\) is the concentration profile of Zn (weight fraction) along the depth \(x\) in the studied specimen; \({C}_{{\text{std}}}\) is the Zn content in the standard; \(\Phi \left(\rho x, E\right)\) and \({\Phi }_{{\text{std}}}\left({\rho }_{{\text{std}}}x, E\right)\) are depth distributions of Zn atoms ionisations in the studied specimen and in the standard, respectively; \(f\left(\rho x\right)\) and \({f}_{{\text{std}}}\left({\rho }_{{\text{std}}}x\right)\) are functions taking into account absorption of characteristic Zn radiation; \(\rho\) and \({\rho }_{{\text{std}}}\) are densities of the studied specimen and the standard, respectively.

The Const appearing in Eqs. (4) and (5) depends on several instrument parameters, such as the electron probe current, a collection angle of X-ray detector, the detector efficiency, etc. Since measurements of intensities of the characteristic X-ray radiation from the sample and from the standard at each energy were done at the same analytical conditions, the Const in Eqs. (4) and (5) is cancelled.

Generally, functions \(\Phi\) and f also depend on the sample chemical composition for nonuniform samples. However, as the solubility of Zn in Fe and Mn in the studied temperature range is only a few weight percent, the assumption was made that \(\Phi \left(\rho x, E\right)\) and \(f\left(\rho x\right)\) are independent on Zn distribution \(C\left(\rho x\right)\). Depth distributions functions for steel and Zn were taken in the form suggested in [13]. For \(f\left(\rho x\right)\) a conventional equation [14] was used:where \(\mu\) is the mass absorption coefficient of Zn characteristic radiation by a considered matrix (the studied steel and ZnTe, respectively) and \(\theta\) is the take off angle of X-ray radiation (30° in the present case).

The concentration profile of Zn in steel, under the assumption of diffusion-controlled penetration, is taken as follows:where C₀ is the concentration at the surface, parameter \(\alpha =\frac{1}{2\rho \sqrt{{D}^{*}t}};\) \(\rho\) is steel density; t-estimated time of ‘apparent diffusion’; and \({D}^{*}\) is an ‘apparent diffusion coefficient’ of Zn in TWIP steel. This new term, ‘apparent diffusion coefficient’, is introduced in the present work and discussed in Sect. "Analytical evaluation of bonding mechanisms during rolling"

Finally, from the Eq. (3), \(k\left(E\right)\) is expressed as:

Unknown parameters \({C}_{0}\) and α in Eq. (8) were found by fitting the measured experimental data \(k\left(E\right)\) to function (8) using the least square method. The minimisation criterion for fitting is described by a ‘fit index’:where \(k\left({E}_{i}\right)\) was calculated using Eq. (8) for each level of energy \({E}_{i}\). The \({k}_{i}\) is the measured value of relative intensity for this energy \({E}_{i}\); \(\sigma \left({k}_{i}\right)\) is the standard deviation of \({k}_{i}\); and n is the number of energies used.

As shown by SEM images, samples after rolling exhibited a well-formed bonding between steel and Zn layers at all temperatures and strains. Typically, the physical mechanisms aiding the interface formation under plastic co-deformation of two metals with imposed hydrostatic pressure involve: (i) deformation-induced atom intermixing; (ii) accelerated atomic diffusion; and, possibly, (iii) formation of intermetallic phases.

The Fe–Zn equilibrium phase diagram shows the possibility of Г, Г₁, ς, δ_k, δ_p—high temperature Fe–Zn intermetallic phases formation [15]. As shown in ref. [16], long annealing at 400 °C results in formation of all these phases. Considering that the temperature range during co-rolling was below 400 °C, and the short time of the rolling (below 1 s), the intermetallic phases were not expected to form, which was confirmed by SEM and TEM observations. Therefore, apparent bonding during co-rolling of TWIP and Zn sheets could form only by mechanisms (i) and/or (ii). The classical diffusion equation with concentration-independent diffusion coefficient.

should be complemented by a drift term when the diffusion occurs simultaneously with plastic deformation [17]where D and D’ are the intrinsic and dynamic diffusion coefficients in the static material and in the material undergoing plastic deformation, respectively, and v is the drift velocity defined as \(v=\dot{\varepsilon x}\), (12.9 and 15.3 mm/s at the surface of the stack rolled to 50 and 70%, respectively). Our estimates show that the drift correction to the static penetration depth is below 5 nm and, therefore, the drift term in Eq. (11) can be neglected. Therefore, a classical Erf-function solution (7) of the diffusion equation, as discussed in Sect. "Analytical model for analysis of EPMA results", is considered adequate.

It should be noted that most of the diffusion studies in the Fe–Zn system have been performed on diffusion of Zn in α-Fe, while the data on Zn diffusion in γ-Fe are scarce. The accumulated literature data on lattice (L) and grain boundary (GB) diffusion of Zn in α-Fe [18‐24] covers the temperature range 400–900 ºC and shows that GB diffusion is much faster than lattice diffusion. Both coefficients \({D}^{L}\) and \({D}^{{\text{GB}}}\) diminish with temperature decrease within this interval, but the bulk diffusion coefficient drops by eleven orders of magnitude, while the GB diffusivity only drops by six orders of magnitude. The ratio of the GB and lattice diffusion coefficients increases with decreasing temperature and reaches eight orders of magnitude at 400 °C, Table 2.

As will be described in the Sect. "Microstructure characterisation after rolling", the microstructure after rolling-induced severe plastic deformation is highly defective, with multiple randomly-oriented fast diffusion paths which are in non-equilibrium state. Such nanostructures contribute to enhancement of diffusivity far beyond what would be expected from the greater contribution of GB diffusion due to increased volume fraction of GBs [25].

Based on the correlations proposed by Gust et al. [21], Kang et al. [19] have claimed that, despite the bulk diffusivity of Zn in α-Fe being higher than that of Zn in austenite, the GB diffusion of Zn in γ-Fe is faster than in α-Fe. This may be related to the differences in atomic structure of the GBs in bcc and fcc Fe. However, the diffusion coefficients in Table 2 do not support this statement, as these values were calculated in assumption that activation energy of the GB diffusion is about 0.6 of activation energy of bulk diffusion. Unfortunately, no experimental values on bulk and GB diffusion in the low temperature range employed in this study are available in the literature and, therefore, the relevant diffusion coefficients were estimated by Arrhenius extrapolation of the high-temperature data from the literature [18‐24]. These extrapolated values served as a reference for comparison with ‘apparent diffusion coefficients’ presented in Sect. "Calculations of apparent diffusion coefficient".

It is shown in ref. [23] that considerably higher than predicted (see Table 2 and Fig. 3) depth of Zn penetration along austenite GBs was observed in TWIP steel, where high-angle grain- and twin boundaries were contributing to Zn penetrations. This may be associated with stress-assisted GB diffusion [26], or fast penetration of Zn along pre-melted Zn-rich GBs [27]. Such layers of disordered quasi-liquid Zn-rich phase have a thickness of a few interatomic distances and may occur at the GBs below the melting point of pure Zn [27].

It is also important to note that deformation-induced crystal defects and internal stresses introduced during rolling could trigger the intensified stress-induced diffusion during post-rolling cooling in air. To estimate the contribution of post-rolling diffusion to intermixing, the time of cooling (from the maximum temperature T’ to the temperature T, in °C, close but higher than the room temperature of 20 °C), Δt, should be estimated. To this end, we employed the following relationship [28]where V is the volume of the stack, A is the outer surface area of the stack after rolling, and \(\overline{h }\) is the convective heat transfer coefficient at the surface (25.2–26.9 W m⁻² K⁻¹). The results of calculations of temperature rise due to rolling (see Eq. (2)) and time of cooling to the room temperature (Eq. (12)) are presented in Table 3 for all samples. Cooling of the stack to the temperature of T = 25 °C takes between 12 and 17 min.

These data (Table 3) further are used to fit the model (3, 4, 5, 6, 7, 8, and 9) to experimentally measured intensities obtained by ‘primary electrons energy variation’ method and calculate the ‘apparent diffusion coefficient’ of Zn in TWIP steel. Though, naturally, the most intensive diffusion occurs during initial stages of cooling when the stack is still hot, we will use the estimate based on Eq. (12) as a higher bound of the actual diffusion time. This means that the effective diffusion coefficient obtained in the framework of our model with the time taken from Table 3 only represents the lower bound estimate of the true diffusion coefficient. Moreover, though the actual deformation time during rolling (about 1 s) is much shorter than cooling time, the defects introduced by rolling move during the deformation. This movement introduces additional, ballistic intermixing that cannot be described in terms of classical diffusion Eq. (10) at the actual deformation temperature [29]. We will also use the actual rolling time in the framework of our model to estimate the upper bound of apparent diffusion coefficient. In this respect, it should be noted that several studies demonstrated that the rate of mass transfer during severe plastic deformation is many orders of magnitude higher than that for conventional bulk or GB diffusion [30, 31].

The initial microstructure of the TWIP sheets after hot rolling, shown in the insert of Fig. 1, consisted of equiaxed grains with a mean grain size (determined by the intercept length method) of \(11\pm 8\) µm, and with visible presence of annealing twins. The EBSD map of initial microstructure is presented in Fig. 4.

The SEM observations of the samples after rolling at different temperatures showed the formation of highly defected structure, with dislocation cells, severe twinning and microbands. The representative microstructural features are shown in Figs. 5, 6, 7, 8, and 9. As can be seen from Table 1 the lowest strain in the TWIP steel layers is achieved after rolling with 50% thickness reduction, at temperature 100 °C. At this level of strain, increase in dislocation density appears as dislocation walls and self-organising cells. Very few deformation twins were visible in favourably oriented grains (Fig. 5), while grains seem not elongated in the rolling direction. This observation is consistent with results presented in [32] that at small strain the microstructure mainly consists of dislocation substructures with less than 20% of all grains containing primary deformation twins.

With temperature increase to 200 °C the strain in TWIP steel layer also increased above 0.3, and the system of double shear microbands about 400 nm apart at 45° to the rolling direction appears. Rolling direction (RD) is indicated in Fig. 6 by a black vertical arrow. It can be noted that grains have elongated parallel to the rolling direction with twinning significantly intensified. The appearance of shear band is expected in fcc metals with high stacking fault energy when the strain hardening rate remains almost constant (stage III according to classification in ref. [32]) within strain level 0.3–0.4 and their directions coincide with maximum shear stress planes in rolling.

The maximum strain in TWIP steel layer after both 50 and 70% thickness reduction was obtained when rolling was performed at 300 °C (Figs. 7 and 8). It is noticeable that the twinning activity increased significantly and most of the grains contain deformation twins, including primary and secondary twin systems (see insert in Fig. 7). Similarly, the deformation twinning was observed in the samples rolled at 300 °C with 70% thickness reduction. More elongated grains in the rolling direction can be seen in Fig. 8.

The high density of defects in the sample rolled at 300 °C increases the probability that some of them were absorbed by the high-angle GBs and transformed them into highly non-equilibrium state [30]. The diffusivity of such non-equilibrium GBs is by several orders of magnitude higher than that of the GBs in well-annealed coarse grain polycrystals.

At the rolling temperature of 380 °C, the heat generated by plastic deformation led to momentary temperature rise exceeding Zn melting point, and therefore, the strain introduced into TWIP steel plates surrounding Zn becomes smaller. Moreover, as the temperature in TWIP steel layer exceeds 400 °C the twinning propensity decreases, similarly to observations made in ref. [33], which leads to twinning suppression and favours dislocation glide and formation of microbands (Fig. 9). The small number of twins were observed in SEM micrograph of Fig. 9b, but well-developed dislocation cells could be seen within most of the grains (Fig. 9c). This was confirmed also by TEM imaging (Fig. 10a). Furthermore, the TEM images revealed the presence of nano-twins adjacent to interface, where the grain refinement is intensified, similarly to trend observed in ref. [34].

The EDS/TEM elemental maps of the interface zone with its characteristic intermixing and diffusion regions have been acquired for all samples. The concentration line scan profiles in samples rolled at 100 °C exhibit random concentration fluctuations in a wide range of 0.25–1 µm, which means that mechanical intermixing mechanism is responsible for formation of interface layer at this temperature. Similar results were obtained for 50 and 70% thickness reduction (Fig. 11.

The width of intermixing zone is consistent with the results of AFM analysis of TWIP steel sheet surface topography, which yielded the average deviation from a mean height of R_a = 0.47 µm. The asperities of the initial rough surface of TWIP steel sheets penetrate softer Zn sheet and cause a turbulent flow of Zn and steel along the interface due to severe shear strain, similar to the interface morphologies observed during severe plastic deformation of stacks of dissimilar materials [35, 36].

When rolling is performed at 200 °C the concentration line profiles acquired at the contact between steel asperities and zinc suggest that, in addition to intermixing, the interdiffusion within 90–150-nm-wide zone has occurred (Fig. 12). The width of this zone is well above the spatial resolution limit of the EDS analysis.

It should be noted that the contributions of both mechanical intermixing and interdiffusion to the interface morphology and composition are visible within approximately 1-µm-wide zone in the samples rolled at 300 and 380 °C (Figs. 13 and 14). However, due to complicated boundary shape, the separation of these two contributions is not possible. Moreover, the interfaces in the EDS/TEM elemental maps are, generally, not in the edge-on position, which means an additional, geometry-related broadening of the interface interdiffusion zone. Nevertheless, based on statistical analysis of several concentration line profiles for each studied sample we proposed the range of Zn penetrations depth related to Zn diffusion into TWIP steel, see Fig. 15.

To define the ‘apparent diffusion coefficient’ of Zn in Fe, \({D}^{*}\), from the experimentally measured penetration depth, x, presented in Fig. 15 and time, t, given in Table 3, we used Einstein–Smoluchowski equation:

The results of this estimation obtained from STEM-EDS data and use of Eq. (13) (presented in Fig. 17 by black squares), obviously are less precise than data obtained by direct measurements. Therefore, to estimate the Zn penetration profile with higher precision and better statistics, the EDS-PEEV method was employed.

The detailed description of \({D}^{*}\) calculations based on the PEEV method and analytical model (3, 4, 5, 6, 7, 8, and 9) is given in Sect. "Characterisation techniques". The fitting of the experimentally measured dependencies of the intensity of the characteristic Zn X-ray radiation on the energy of primary electron beam with the analytic model summarised in Eqs. (3, 4, 5, 6, 7, 8, and 9) is illustrated in Fig. 16, and the resulting ‘apparent diffusion coefficients’ of Zn are listed in Table 4. In Table 4, \({D}_{l}^{*}\) represent lower bound of this coefficient accounting for time of cooling to the room temperature, while the values \({D}_{u}^{*}\) represent the upper bound of this coefficient relevant to the rolling time only. Obviously ‘apparent diffusion coefficient’ during rolling, \({D}_{u}^{*}\), is heavily affected by ballistic intermixing and is two orders of magnitude higher than \({D}_{l}^{*}\).

The ‘apparent diffusion coefficients’ of Zn in TWIP steel (\({D}^{*}\)) obtained by two methods are shown in Fig. 17 by black squares (from STEM-EDS data) and by blue and yellow circles (by the PEEV method). The extrapolated literature data for diffusion coefficient for Zn along grain boundaries in austenitic Fe is shown in Fig. 17 for comparison (red line).

Obviously, that ‘apparent diffusion coefficient’ of Zn in TWIP steel is several orders of magnitude higher than \({D}^{{\text{GB}}}\), but its temperature dependence is rather weak. The corresponding activation energy formally determined from the Arrhenius plot for the strain of 50%, 23 ± 12 kJ/mol, is much lower than the activation energy of Zn diffusion along the GBs both in γ-Fe (170 kJ/mol) and α-Fe (162 kJ/mol).

Let us first consider whether the high apparent diffusivity of Zn in TWIP steel uncovered in the present work can be attributed to the non-equilibrium state of GBs, as has been observed in several studies of ultrafine grain materials produced by severe plastic deformation [25, 30, 37]. However, our microstructure observations of the as-rolled TWIP steel samples did not reveal the formation of new high-angle GBs. With the original grain size of 11 µm, the contribution of the GB diffusion to the interface intermixing would be highly localised, which was not confirmed by our EDS/STEM elemental maps (see Figs. 11, 12, 13, and 14). Therefore, we attribute the accelerated interface intermixing to the dislocations which are moving during rolling-induced plastic deformation. Such moving dislocations may drag along the solute (Zn) atoms strongly interacting with the dislocation elastic field. Moreover, the elastic strain field of the curved dislocation accelerates the dislocation pipe diffusion [38, 39]. It should be noted that high dislocation densities were observed in the TWIP steels deformed in the temperature range from room temperature to 200 °C, [40]. Finally, the atomistic core structure of the moving dislocations and grain boundaries is different from that of their static counterparts and may be a factor responsible for accelerated diffusion [41]. It is interesting that the obtained low value of the activation energy for ‘apparent diffusion coefficient’ of Zn in TWIP steel is very close to the activation energy for self-diffusion in liquid Zn, 21 kJ/mol [42]. Though it may be a random coincidence, this may indicate that the Zn-rich dislocation cores responsible for ballistic intermixing exhibit a quasi-liquid (pre-melted) atomic structure and correspondingly low activation energy for diffusion. The existence of such pre-melted or solute-enriched dislocation cores has been discussed in several studies [43‐45].

In general, the data presented in Fig. 17 prove that there are two contributions into ‘apparent coefficient of diffusion’, namely, diffusion itself and deformation-induced mass transfer, which is not sensitive to the temperature, but sensitive to imposed strain. The convergence of ‘apparent diffusion coefficient’ and of GB diffusion coefficient of Zn in γ-Fe at the highest studied temperature of 380 °C (the GB diffusion can be considered as a benchmark of the fastest diffusion process in the TWIP steel) indicates that contribution of ballistic intermixing is higher at lower temperatures, but at higher temperatures the contribution of diffusion dominates.