1 Introduction

Over the last two decades, high-manganese twinning-induced plasticity (TWIP) steels have received considerable interest in both industries and academics [1,2,3,4,5,6], owing to the excellent combination of strength and ductility induced by the high-strain hardening capability [7] which makes them attractive for automotive applications. The excessive alloying of the Mn element serving as the austenite stabilizer ensures that TWIP steels are fully austenitic with the face-centered cubic (fcc) crystal structure at room temperature, which, however, inevitably leads to the low yield strength and prevents their use in some components demanding high deformation resistance. To overcome this limitation, a simple thermomechanical process consisting of cold rolling and a recovery heat treatment has previously been proposed and applied to the TWIP steels [8], resulting in a new type of steels with an initial microstructure containing intensive nanotwins and a high dislocation density [8]. The resultant steels are thus referred to as nanotwinned steels, showing a significantly enhanced yield strength of ~ 1400 MPa [8] compared with that of several hundreds of MPa of ordinary TWIP steels.

During the full-vehicle frontal crash, the typical strain rates encountered are in the range of 0.1–1000 s−1. The mechanical responses of metallic materials at high-strain rates tend to differ from the ones at the quasi-static loading [9,10,11]. To further judge the crashworthiness of nanotwinned steels for their potential use in automotive components, it is essential to understand their dynamic mechanical properties at various strain rates and the underlying deformation mechanisms, not limited to the quasi-static mechanical responses. However, very limited studies are available in literature [12]. In particular, the effect of strain rate on the yield strength of nanotwinned steels over a wide range of strain rates receives little attention in the literature. The objective of this work, therefore, is to uncover the strain rate sensitivity (SRS) of yield strength of a nanotwinned steel in a broad range of strain rates. A theoretical model is proposed to explain the observed transition in SRS, highlighting the important role of carbon solutes on the thermally activated dislocation activities in the nanotwinned steel, which has previously been ignored.

2 Experiments

The nanotwinned steel investigated here was produced from the original TWIP steel with the chemical composition of Fe–18Mn–0.75C–17Al–0.5Si (wt.%) and average grain size of 4.4 µm. The TWIP steel was subjected to cold rolling at room temperature with a 50% thickness reduction followed by a recovery heat treatment at 773 K for 15 min, resulting in the nanotwinned steel flat sheets with a thickness of 1.2 mm. Flat tensile specimens with the gauge dimension of 32 mm × 6 mm × 1.2 mm were cut from the plates for the room-temperature uniaxial tensile testing performed at multiple strain rates lower than 1 s−1, using the MTS 810 test system equipped with the 25-mm Epsilon extensometer. The tensile axes of these specimens are oriented along the rolling direction of the nanotwinned steel sheets. For the medium-strain rate tensile experiments (8–146 s−1), flat tensile specimens with the gauge dimension of 20 mm × 10 mm × 1.2 mm were tested by using an Instron high-strain rate machine (VHS160/100–20), and the strains were captured by the high-speed digital camera and measured using the digital image correlation (DIC) technique. High-speed tensile tests with the strain rates higher than 600 s−1 were conducted by a modified split Hopkinson bar. The tensile stresses of the high-strain rate tests were calculated from the transmitted pulse recorded by the strain gauge on the transmitted bar of the split Hopkinson bar. Strains were measured with the non-contact laser extensometer. Microstructures of the nanotwinned steel were examined using the electron channeling contrast imaging (ECCI) in a Zeiss Sigma 300 scanning electron microscope (SEM) performed at acceleration voltage of 15 kV and a working distance of 5 mm.

3 Results

Figure 1a shows the initial microstructure of the nanotwinned steel, consisting of high-density parallel bundles evenly distributed in the heavily elongated grains. These bundles are formed by the groups of nano-sized deformation twins which are introduced during the cold rolling process [8]. After cold rolling, most of the grains contain deformation twins that are active primarily in one system, consistent with the previous experimental observation [13], and some grains contain two twinning systems (Fig. 1b). A high density of dislocations can be identified in the initial microstructure, as revealed by the light contrast of dislocation patterns in Fig. 2a. The engineering stress–strain curve of the nanotwinned steel measured at 10–3 s−1 is shown in Fig. 2b, demonstrating the significantly increased yield strength σy of ~ 1400 MPa compared with that of ~ 400 MPa of the original TWIP steel. The slight strain hardening capability suggests that the dislocation density has not been saturated, possibly due to the recovery treatment process [8].

Fig. 1
figure 1

ECCI image of initial microstructure of nanotwinned steel (a) and magnified view of dashed box in a showing two twinning systems activated in a grain, with twin boundaries marked by dashed lines in different colors (b)

Full size image
Fig. 2
figure 2

ECCI image of initial microstructure showing high-density dislocations with bright contrast with inset showing magnified view of dashed box (a) and engineering stress–strain curve at 10–3 s−1 showing a yield strength of 1.4 GPa and an ultimate tensile strength of 1.55 GPa (b)

Full size image

To investigate the strain rate sensitivity of σy for the present nanotwinned steel, the engineering stress–strain curves at various strain rates near the yielding points of the nanotwinned steel are summarized in Fig. 3, from which the effect of strain rates on the yield strength can be identified. Figure 4 summarizes the variation of σy as a function of \(\mathrm{ln} \,\dot{\varepsilon }\) obtained from Fig. 3. Two SRS regimes, defined by the distinctive rate of change of σy with respect to the strain rate, are evident. At strain rates lower than ~ 1 s−1, the yield strength of the nanotwinned steel is almost insensitive to the strain rate, indicating that the strain rate sensitivity tends to be zero in this regime. In contrast, the yield strength starts to increase with increasing strain rate \(\dot{\varepsilon }\) such that the data of σy vs. \(\mathrm{ln}\,\dot{\varepsilon }\) appears to lie on a straight line.

Fig. 3
figure 3

Engineering stress–strain curves near yielding points of present nanotwinned steel, measured at a wide range of strain rates

Full size image
Fig. 4
figure 4

Variation of σy as a function of \(\ln \dot{\varepsilon }\) summarized from Fig. 3, showing two distinct strain-rate sensitivity regimes

Full size image

4 Discussion

It has been well recognized that the movement of dislocations in alloys with fcc crystal structures is affected by the strain rate [14], due to the thermally activated jumping of dislocations from local obstacles such as solute atoms and forest dislocations at finite temperatures [15, 16]. After the free gliding between neighboring obstacles, mobile dislocations are stopped in front of the local barriers for an average waiting time tw, which is strongly affected by the macroscopic strain rate of the plastically deformed specimen. This leads to the resultant rate-dependent flow stress of fcc alloys. Based on the theory of thermally activated dislocation plasticity, \(\dot{\varepsilon }\) is given by \(\dot{\varepsilon } = \dot{\varepsilon }_{0} \exp \left( {\frac{ - \Delta G}{{kT}}} \right)\), where \(\dot{\varepsilon }_{0}\) is a reference strain rate, ΔG is the Gibbs free energy for the dislocation unpinning process, k is the Boltzmann constant, and T is the temperature in Kelvin. ΔG depends on the applied stress and the specific rate-controlling mechanism as \(\Delta G = \Delta G_{0} - \tau_{{{\text{eff}}}} V\), where ΔG0 is the Helmholtz free energy, V is the activation volume which is related to the deformation mechanism, and τeff is the effective stress acting on the mobile dislocations. The resultant expression of \(\dot{\varepsilon }\) becomes [17, 18]

$$\dot{\varepsilon } = \dot{\varepsilon }_{0} \exp \left( {{ - }\frac{{\Delta G_{0} - \sigma^{{{\text{eff}}}} V/M}}{kT}} \right)$$
(1)

where \(\sigma^{{{\text{eff}}}} = M\tau_{{{\text{eff}}}}\) is the effective normal stress; and M = 3.06 is the average Taylor factor of the polycrystalline steel. Assuming that the effective stress at yielding is equal to σy, Eq. (1) can be further converted to give the expression of the strain rate-dependent yield strength as

$$\sigma_{{\text{y}}} = K\ln \dot{\varepsilon } + \sigma_{0}$$
(2)

where \(K = MkT/V\); and \(\sigma_{0} = M(\Delta G_{0} - kT\ln \dot{\varepsilon }_{0} )/V\). For a specific deformation mechanism, both K and σ0 remain constant at a fixed temperature. Therefore, it is evident that σy should be a linear function of \(\ln \dot{\varepsilon }\) for a specific deformation mechanism.

Such a linear relationship between \(\sigma_{{\text{y}}}\) and \(\ln \dot{\varepsilon }\) is evident in the rate-sensitive regime for strain rates above 1 s−1, as shown in Fig. 4. The linear fitting of the experimental data leads to K = 72 MPa, suggesting V = 10 b3 (where b = 0.254 nm) for the rate-sensitive regime. V can be seen as a signature to the deformation mechanism. The present value of 10 b3 lies in the typical range of (10–100) b3 for the nanometer-scale dislocation processes such as the cross-slip of screw dislocations [19] and dislocation emissions from interfaces in nanostructured materials [18, 20, 21]. For instance, V of nanocrystalline Ni was experimentally measured to be ~ 20 b3 [18], and a similar value of V ~ 12 b3 was reported for the nanotwinned copper [20]. The low stacking fault energy of the present nanotwinned steel promotes the planar slip of dislocation with wide stacking faults, and thus the mechanism of cross-slip may not be the controlling mechanism for the nanotwinned steel. In terms of the twin boundaries serving as the possible obstacles to dislocation motion, the mean twin spacing of the nanotwinned steel has previously been determined as ~ 30 nm [8], suggesting that the resultant V should be a few tens of b3, which is slightly larger than the experimental value. Therefore, the deformation twins, although abundant in grains, may not be the dominant obstacles controlling the thermally activated dislocation plasticity at yielding. This is consistent with the report of the nanotwinned copper [22, 23], in which a much higher density of nanotwins is achieved than those in the present material. The dislocation density ρ of the present nanotwinned steel has been estimated as 6 × 1014 m−2 [8], corresponding to the average forest dislocation spacing \(\lambda = 1/\sqrt \rho = {\text{16 nm}}\). The activation volume \(V_{{{\text{forr}}}} = \lambda b^{2}\) due to forest dislocations is thus estimated as ~ 63 b3, which is still larger than the experimental value.

After the forest dislocations and the twin boundaries have been ruled out as the dominant dislocation obstacles at yielding, it is natural to infer that the rate-controlling mechanism and the resultant small value of V are associated with the remaining obstacles undiscussed yet, i.e., carbon solutes. Experiments using atom probe tomography have directly shown the existence of the solute atmosphere surrounding dislocation cores [24] which induce short-range barriers to dislocation motion. It is thus proposed here that carbon atoms in the present nanotwinned steel may perform similarly as the Peierls barrier in the alloys with body-centered cubic (bcc) crystal structures [25], causing the local bowing out of dislocations involving the collective vibration of a few atoms to surmount the pinning of carbon atoms, similar to the kink pair mechanism in bcc alloys to surmount the Peierls barrier.

Furthermore, the relatively fast diffusion of the interstitial carbon atoms into neighboring positions suggests that such carbon-dislocation interaction mechanism with the characteristic V = 10 b3 is valid only when tw is much shorter than the average time tdiff for carbon atoms to diffuse to a position with a distance comparable to the bow-out size of the dislocation. In the proposed situation where tw > tdiff, the rate for the carbon atoms to diffuse into the core of the bowed out dislocation portion is higher than the rate for the propagation of the bow-out, leading to the constant pinning of dislocations. In other words, dislocation motion and the subsequent yielding in this case have to involve the constant carbon-dislocation interaction along the entire dislocation core, which is different from the rate-dependent bowing out process requiring only a portion of the dislocation to be thermally activated. This mechanism can also be interpreted such that a constant drag force per unit length caused by the rapid carbon diffusion has been exerted on the moving dislocations. This may explain the occurrence of the strain-rate insensitive regime in Fig. 4.

5 Conclusion

Two regimes with distinct strain rate sensitivities of yield strength are reported for the high-strength nanotwinned steel. Based on the measured activation volume which is a signature of a specific deformation process, the rate-controlling deformation mechanism of the nanotwinned steel is proposed to transfer from the constant dragging of carbon at dislocation cores to the localized dislocation bowing out process.