Nature-Inspired Hierarchical Steels

Materials can be made strong, but as such they are often brittle and prone to fracture when under stress. Inspired by the exceptionally strong and ductile structure of byssal threads found in certain mussels, we have designed and manufactured a multi-hierarchical steel, based on an inexpensive austenitic stainless steel, which defeats this “conflict” by possessing both superior strength and ductility. These excellent mechanical properties are realized by structurally introducing sandwich structures at both the macro- and nano-scales, the latter via an isometric, alternating, dual-phase crystal phases comprising nano-band austenite and nano-lamellar martensite, without change in chemical composition. Our experiments (transmission and scanning electron microscopy, electron back-scattered diffraction, nano-indentation and tensile tests) and micromechanics simulation results reveal a synergy of mechanisms underlying such exceptional properties. This synergy is key to the development of vastly superior mechanical properties, and may provide a unique strategy for the future development of new super strong and tough (damage-tolerant), lightweight and inexpensive structural materials.


Methods
The material used in this work was an austenitic AISI 301 stainless steel with a chemical composition (in wt.%) of 16.6 Cr, 6.2 Ni, 0.4 Mo, 0.13 C, 0.45 Si, 1.7 Mn, 0.03 S, 0.03P and the balance Fe. Samples were cut into plates, 110 × 50 ×1 mm 3 in size, for heat treatment and surface nanotechnology. Samples were annealed in vacuo at 1150°C for 2 h and then quenched into water, prior to both surfaces of the specimens being treated by a Surface Mechanical Attrition Treatment (SMAT) process 31,[33][34][35] . The SMAT process is essentially a dynamic plastic deformation process. The steel plates were placed on the top side of a chamber which contains hundreds of hard balls with a diameter of 3 mm. Those balls were vibrated using high-power ultrasound so that they impacted onto the surface of the steel plates at a high speed. Essentially, the surface of the steel plates was peened with a large number of impacts over a short period of time. The plastic deformation in the surface layer coupled with the large strain and high strain rate resulted into a progressive reduction of the original micro-scale grains into nanograins. The metastable austenite of the AISI 301 was partially transformed into martensite during this dynamic plastic deformation process. A 20-kHz ultrasonic transducer was exploited as the impulse source. The chamber diameter was 70 mm and the working distance between the steel plates and the horn surface was 15 mm. Both sides of the steel plates were SMAT treated to a total time of 30 min. More details of the set-ups, procedures and mechanism of the SMAT are described elsewhere [32][33][34][35][36][37] .
For mechanical testing, treated samples were cut into dog-bone shapes with a gauge length of 30 mm and a width of 6 mm, and tested at room temperature at a strain rate of 6.7 × 10 -4 s -1 .
Seven specimens were tested to confirm repeatability. SEM and EBSD observations were performed on a JEM-6700F field-emission scanning electron microscope (SEM) equipped with an Oxford EBSD detector and HKL channel 5 software. TEM observations were carried out on a JEM-2100F transmission electron microscope with operating voltage of 200 kV. The plane-view TEM foils of the layers from certain depths were obtained by first polishing the corresponding surface layer, then mechanically polishing the sample from the untreated side until the sample reaches about the thickness of 30 µm. The treated side of the foil was protected with a resin and the foil was finally thinned down by electro-chemical polishing from the untreated side.

Theoretical Modeling
To provide fundamental basis to this experimental study, we developed a microstructurebased plasticity model to support our observations and to explain the mechanical performance of the hierarchical steel. When subjected to uniaxial tensile deformation, we can assume that the uniaxial uniform strain acts in every structural hierarchy of our steel sample. For the heterogeneous structures, the micromechanical approaches such as the self-consistent models [38][39][40] and revised mean-field methods [41][42][43] are usually applied to simulate the effective stress and strain by considering the interaction between the components. For the gradient structures, it has been proved that the rule of mixtures of Voigt model is a reasonable means to calculate the effective stress [44][45][46] . As such, the effective stress can be expressed as: where i, N, and C denote the i th layer, nanostructured region and coarse-grained region, respectively. n is the number of layers in the nanostructured region, N M is the elastic compliance tensor of dual-phased grain. The plastic strain rate is proportional to the deviatoric stress ( ) ' is the equivalent plastic strain rate which is determined by: is the equivalent strain rate and ( ) is the flow stress of the i th layer, and 0 m is the rate-sensitivity exponent. The nano-lamellae formed by the martensite are taken to be effective blocks to impede the movement of dislocations inside each grain, leading to dislocations pile-ups along the martensite/austenite interfaces.
Consequently, the dislocation pile-up zones can be created near the interfaces between the nanoband martensite and nano-lamellar austenite. Thus, the flow stress in the grains containing nanolamellae can be expressed as: , can be expressed as: where ( 0,1,2)     are the constants. a H is the thickness of austenite lamellae, and m H is the thickness of hcp ε-martensite lamellae. For the coarse grains in the core, the overall flow stress can be expressed as: where B  represents the back stress. One can find from Eqs. After carefully calibrating the model, we examined the differences of the nano-scale lamellar structure in the hierarchical steel with respect to the absence of any lamellar structure in classical gradient steels (described in the main text), as schematically illustrated in Fig. 2. Assuming that the gradient steel has a comparative microstructure with the same through-thickness grain-size variation but without nanoscale lamellae, we plot the predicted depth-dependent dislocation density in the hierarchical steel compared to that in the gradient steel in Supplementary Figure 2a.
With exactly the same grain-size gradient, the depth-dependent dislocation density for the hierarchical steel with its nano-lamellae is ~4-10 times higher than that for the comparable classical gradient steel, as seen in Supplementary Figure 2a; correspondingly, the depthdependent yield strength is up to 600 MPa higher within the layers containing nano-lamellae (down to a depth of ~300 µm below the surface) as shown in Supplementary Figure 2b.
Supplementary Figure 2c illustrates the comparison of the overall stress-strain behavior between the hierarchical steel and the comparable classical gradient steel with the same grain size gradient, and clearly shows that due to the existence of the nano-lamellae, the yield strength and flow stress are both ~400 MPa or ~50% higher than that of the classical gradient steel.
To analyze the internal stress distribution during deformation, we further depict the predicted stress-strain curves in Supplementary Figure 3a for three separated regions in hierarchical steel from surface to core through-thickness (see inset of Supplementary Figure 3a and Supplementary Figure 2). It is apparent that the yield stresses in harder outer layers (Regions I and II) are much larger than that in the softer core layer (Region III); as such, the harder outer layers enhance the overall yield strength and flow stress of the hierarchical steel. For a sample geometry with a 1 mm thickness and 100 mm width, we further plot in Supplementary Figure 3b the simulated total loading forces undertaken by each of the three regions as a function of the engineering strain. The harder outer layers (Regions I and II) can be seen to bear most of the loading forces as compared to the softer core layer (Region III). Due to the much higher average flow strength, the outermost layer (Region I) with the smallest nano-lamellae (0-100 µm depth), which occupies only ~20% of the overall volume, can sustain more than 50% of the overall load under uniaxial tension (Supplementary Figure 3a,b). Supplementary Figure 3c compares the average true stress-strain behavior of harder outer layers (Region I and II) in the hierarchical steel with that in the classical gradient steel. From this figure, it is apparent that because of the significantly higher load-bearing capacity of the outer layers (~300 μm in depth) in the hierarchical steel with its nano-scale lamellar microstructure, these outer layers can carry ~25% more of the applied load than the corresponding classical gradient microstructure at the same tensile plastic strain.
These micromechanics simulations speak to the following conclusions: 1) Assuming that the nano-scale lamellar interfaces serve as effective sources, sinks as well as strong barriers for dislocation motion during deformation, the graded nano-lamellar microstructure results in significant dislocation density increases within the hierarchical steel. More than a four-fold increase in dislocations densities within a ~300 µm depth (and about one order of magnitude increases within ~100 µm of the surface) are predicted for the hierarchical steel, as compared to that for a companion classical gradient steel without such a nano-lamellar structure. 2) Four to ten-fold higher dislocation densities and pile-ups along the nanoscale lamellar interfaces result in up to 600 MPa increase in yield strength and flow stress, and consequently a 25% increase in load-bearing capacity of the nano-lamellar structured surface layers (~300 µm in depth).
Therefore respectively, in the hierarchical steel from surface layer to core area. b. The predicted total loading forceengineering strain curves for the overall hierarchical steel as well as for each of the three separate regions within the hierarchical steel. c. The average true stress-strain behavior for Region I + Region II (~300 μm in depth) in the hierarchical steel is compared with that in the comparable classical gradient steel without nano-lamellae.

Supplementary Table 1.
Description, symbol, magnitude and equation in which the different parameters of the models appear.