For the essential role played by steels in infrastructural and overall economic development1 2, modern steelmakers are heavily involved in the development of new advanced steels, by tuning their compositions or by adopting new processing routines, to meet the increasing demands for high-performance materials2 3 4. In this field, sustained effort for innovation has led to the development of high manganese twinning-induced plasticity (TWIP) steels with exceptional combinations of formability, hardenability and ultimate strength, properties that are often attributed to the prominence of twinning-induced deformation in these materials3 4 5. First discovered in 1888 by Sir Robert Hadfield6, TWIP steels have attracted significant attention over the last decade7 due to the compelling needs of weight reduction and improved crash safety in modern vehicle components8. As shown in Supplementary Fig. 1, while the ultimate strength of TWIP steels can reach 1.4–1.6 GPa, their yielding strength is as low as ~300 MPa7. Given the general correlation between yielding strength and fatigue limit9, an important challenge is to increase the yielding strength of TWIP steels without compromising ductility. Unfortunately, traditional material processing techniques for strength enhancement, such as grain refinement10 11 12 13 or cold working, usually result in reduced ductility14. Supplementary Fig. 1 shows that strength and ductility are mutually exclusive in steels, based on data from US Steel Cooperation15, which reflects the long-standing dilemma of strength–ductility trade-off in materials science10. Significant developments have been achieved in recent years in processing metals to optimize their properties. Examples include introducing twins as second-level structures in grains16 17 18, generating relatively sharp grain size gradient19 20, or producing hierarchical structures with nanoscale grains and sub-granular solutes21, as well as gradient grains with embedded twins22 23. While these studies have substantially advanced the fundamental science of nanostructured materials24 25 26 27, it remains an open question how to scale them up to bulk engineering materials for broad industrial applications. Inspired by the ideas of introducing nanotwin structures16 17 18 and grain size gradient to enhance both ductility and strength of metals19 20, here we report a method to enhance the strength of TWIP steel by introducing a linearly graded nanotwinned structure in the material, with no trade-off in ductility and no limitations on sample dimensions. The latter will be essential in enabling practical applications of the method developed to enhance any axially symmetric structural components, including axles in machines, engines and transmission systems in mechanical, civil, aerospace, transportation, oil, automotive and energy industries. For example, with rapid population growth and the resulting demand for high-speed rail transport over much of the world in the coming century, the axles in high-speed trains pose critical safety concerns where high strength, ductility and fatigue life will be particularly desired. Results Mechanical behaviour of pre-torsioned TWIP steel The FeMnC TWIP steel is used in our study. The detailed processing in making such material is given in the Methods section. A low stacking fault energy in the range of 15–30 m Jm−2 in the austenitic structure4 is realized, which favors the formation of mechanical twins3 5 7. Such TWIP steel has a typical yielding strength of ~300 MPa but superior hardening capacity, resulting in increased uniform elongation and high ultimate strength3 5 7 8. We first apply torsion to a TWIP steel bar with dimensions shown in Supplementary Fig. 2a. The torque versus twist curve given in Fig. 1a shows not only the repeatability of experiments but also enormous hardening in the material. Typical shape of a sample with pre-torsion is given in Supplementary Fig. 2b. We first measure the variation of micro hardness of the sample along the radial direction. The hardness is clearly seen to increase along the radial direction in the sample with pre-torsion (see Fig. 1b). The stress–strain behaviours shown in Fig. 1c indicate that pre-torsion has led to substantial increases in yielding strength and also slight enhancements in ultimate strength in the tested TWIP steel samples. Supplementary Fig. 1 shows that the simultaneous attainment of both strength and ductility in FeMnC TWIP steel with pre-torsion is in striking contrast to the usual strength–ductility trade-off in steels. The hardenability, as quantified by hardening modulus, is superior for all samples subject to pre-torsion and remains at a high value till sample failure, as shown in Fig. 1d. The serrations in the stress–strain responses in TWIP steel are likely due to reorientation of some crystals during twin deformation5, which may have also resulted in the observed fluctuations in the hardening behaviour, as seen in Fig. 1d. All of our TWIP samples failed in shear mode, with and without pre-torsion, as seen in Supplementary Figs 2c and d. Microstructure evolution and deformation mechanisms To understand the mechanism of plastic deformation in TWIP samples with pre-torsion, we found it particularly insightful to examine the variations in twin density along the radial direction. Figure 2a–c presents microstructures in the sample with 180° pre-torsion at different radial positions, r/R=0, 0.5, 1, respectively. The scanning electron microscope (SEM) images reveal a gradient twin structure: the pre-torsion resulted in mechanical twins whose density increases with radial distance from the centre, with the outermost region (r/R=1) of the sample displaying the highest twin density. Figure 2d shows an electron backscatter diffraction (EBSD) image of Fig. 2c, which confirms that the band structures in Fig. 2c are indeed twin laminae. Complementary EBSD images to SEM pictures shown in Fig. 2a–c are also given in Supplementary Fig. 3. At increasing radial distance from the centre, not only the twin density increases but the twins also thicken, as seen in Fig. 2e. Figure 2f,g provides transmission electron microscope (TEM) images of twin boundaries at r/R=1.0 introduced during pre-torsion, where typical twin thickness is on the order of tens of nanometres. The twin boundaries are in general very clean, as seen in the high-resolution TEM image in Fig. 2h. Another important feature, as shown in Fig. 2a–d, is that twins in each grain are parallel and are identified as primary twins at the stage of pre-torsion. The finely spaced parallel twins can serve as barriers to inclined twinning or dislocation slip and/or source for further twinning, leading to the distinct hardening behaviours between samples with or without pre-torsion, as evidently seen in Fig. 1d. The secondary twins are very scarce right after torsion. However, upon subsequent stretching to failure under tension, the pre-torsioned samples exhibit a hierarchical nanotwinned structure with abundant secondary twins and even tertiary twins in the outermost region, as shown in Fig. 3. Figure 3a shows primary twins running from top left to bottom right (pink arrows), secondary twins in inclined orientations (blue arrows) and short tertiary twins between secondary twins parallel to the primary ones (green arrows). Secondary twins are constrained by primary twins and tertiary twins are confined between the secondary ones. Hence, the primary twins serve as effective barriers for the secondary twins, and the latter renders formation of the tertiary twins harder. Both mechanisms contribute to strain hardening during plastic deformation. Primary and secondary twins are also confirmed in the corresponding selected area electron diffraction spots with -beam incident (Supplementary Fig. 4). In addition to twin–twin interaction, activities between twin boundaries and dislocations are of particular interests for strength hardening and ductility. A dislocation approaching a twin boundary may dissociate, with one partial passing through the boundary and gliding in a conjugate slip system, and the other residing and moving along the twin boundary18 28. Combining with experimental observations, a thorough examination of possible reactions between dislocations and twin boundaries in f.c.c. metals is also available29. Figure 3b shows an HRTEM image on the formation of twin junctions when secondary twins penetrate the primary twins. Figure 3c provides an enlarged image of the yellow rectangle ‘c’ in Fig. 3b with detailed lattice arrangement of primary and secondary twins. A close view of the yellow rectangle ‘d’ in Fig. 3b, showing full and partial dislocations near the junction interface, is given in Fig. 3d. Plenty of partial dislocations are observed on the twin boundaries, as can be seen in Fig. 3e and the corresponding inverse fast Fourier transformation image (Fig. 3f). Dislocations in the yellow rectangle in Fig. 3e are identified as Shockley partials. The dissociation of such dislocations when interacting with twin boundaries avoids excessive stress concentration due to dislocation pile-up allows the material to deform and hence plays a crucial role in retaining ductility. Influence of gradient and hardening on strength and ductility The gradient twin density shown in Fig. 2 in TWIP steels with pre-torsion and the hierarchical nanotwinned structure after further tensile deformation in those twisted samples seen in Fig. 3 suggest the significance of twin gradient for retaining ductility. To explain why the combination of gradients and twin structures are so beneficial for both strength and tensile ductility, we have performed a series of finite element simulations based on isotropic plasticity (Supplementary Note 1) and crystal plasticity models that account for all the operative slip and twinning systems in TWIP steel (Supplementary Note 2). Our simulations show that the yielding strength of a gradient sample obeys the law of mixture where A denotes the area of shear plane S. This behaviour can be understood by noting that, since the sample is homogeneously deformed while yielding, any material point in the sample should be in its plastic regime. We first considered a cylindrical sample with a hard shell and soft core with distinct stress–strain behaviour (Fig. 4a). The volume fraction of the soft core is defined as f=r 2 R −2. Two volume fractions f=0.16 and f=0.64 of the soft core are considered. Using f=0.64 as an example, grains within the soft core region 0
