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Journal Club Theme of June 2015: Gradient structures for optimal mechanical design

The outmost surface of engineering materials typically faces the most severe risk of damage. When such boundary conditions are given, employment of graded structures is desired to enhance the safety of the structure in an economic way [1]. Mechanically, adopted gradient structures typically involves change in Young’s modulus or strength, and are beneficial to crack shielding, reducing stress concentration, retarding shear localization, etc. In this thread of discussion, we show current progress in adopting gradient structures for achieve high strength in materials without sacrificing their ductility.

Sharp gradient by surface mechanical attrition treatment

Both strength and ductility are crucial material properties of materials used in structural applications. Like most good things, there exists a trade-off between strength-ductility in materials, which has been a long standing dilemma in materials science. The pioneer work by Lu et al [2,3] revealed that a sharp grain-size gradientby surface mechanical attrition treatment (SMAT) could dramatically increase the strength of its uniformly coarse-grained counterpart without sacrificing ductility: The usually brittle-like nanocrystalline thin layer in the surface due to SMAT (Figures 1a, 1b), combined with a transitional region with dense dislocations and the unaffected coarse-grained core, leads to a largely enhanced yielding strengthen and a failure strength close to that of the coarse-grained counter-part (Figure 1c). Motivated by the apparent grain growth after deformation, Lu et al. [2,3] proposed that mechanically driven grain boundary migration process with a substantial concomitant grain growth dominates plastic deformation of the gradient NG structure. A follow-up research by Wu et al. [4] suggested that the grain-size gradient under uniaxial tension induces a macroscopic strain gradient and converts the applied uniaxial stress to multiaxial stresses due to the evolution of incompatible deformation along the gradient depth. Thereby the accumulation and interaction of dislocations are promoted, resulting in an extra strain hardening and an obvious strain hardening rate up-turn. The SMAT technique could also be applied to metals where deformation twinning might be triggered at room temperature, so to make gradient twin structures [5,6]: Metals with a yield strength over 2 GPa while still preserving a considerable uniform elongation of 15% might be achieved.

Sharp gradient by SMAT

Figure 1: Gradient properties by Surface mechanical attrition treatment (SMAT) . (a) Illustration to show the induced structure gradient, from nanograins in the surface to coarse-grains in the core. (b) The evolution of hardness and grain size with depth. (c) The stress-strain curves of coarse-grained sample, nanocrystalline sample, and gradient sample.

Gradient nanotwin by torsion

In contrast to the surface mechanical attrition treatment, Wei et al. [7] demonstrated an effective way to realized linearly gradient materials in axial-symmetrical structures. By applying the torsion induced plastic deformation gradient along the radial direction of twinning-induced plasticity (TWIP) steel, Wei et al. [7] demonstrated an effective way around that tradeoff in the material, by introducing gradient twins. In terms of both size and density, twins increases along the radial direction of the sample (see Figures 2a to 2c). Subsequent tension shows that the yielding strength of the material can be doubled at no reduction in ductility (Figure 2d). It is shown that this evasion of strength-ductility trade-off is due to the formation of a gradient hierarchical nanotwinned structure (see Figure 2e) during pre-torsion and subsequent tensile deformation. Theoretical analysis showed that at the grain level, pre-twist introduced twins are activated in crystallographic twinning systems differ to those in subsequent tension. This switch of deformation orientations leads to the observed hierarchical nanotwinned structure. This technique could be used to pre-treat steel that requires a cylindrical shape—axles or drive shafts on cars and trains for example.

Gradient twin by pre-twisting

Figure 2: Gradient nanotwin structure along the radial direction of a pre-torsioned TWIP sample and its mechanical behavior. (a) Illustration to show gradient twin structure by pre-torsion. (b) No twins in the center (r=0) of the sample. (c) Dense twins at near the surface (r=1.0) of the sample. (d) Enhanced strength by the applied torsion of different angles. (e) Hierarchical twin structures and atomic scale details near the outermost region of the pre-torsioned sample after tensile failure. 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).

Conclusion and perspective

With the innovation of printing technology, now it is feasible to fabricate gradient structures in both constituents vary in materials and characteristic sizes [e.g., Ref. 8], we expect that the more structures with superb mechanical and other physical properties, based on the gradient design motif, could appear in the near future. Researches on quantifying correlations between gradient microstructures and properties are vital for optimizing global properties of the hierarchically structured advanced materials.


1.Suresh S (2001) Graded materials for resistance to contact deformation and damage. Science 292(5526):2447–2451.

2.Fang, T. H., Li, W. L., Tao, N. R. & Lu, K. Revealing extraordinary intrinsic tensile plasticity in gradient nano-grained copper. Science 331,1587–1590 (2011).

3.Lu, K. Making strong nanomaterials ductile with gradients. Science 345, 1455-1456(2014).

4.Wu, X. L., Jiang, P., Chen, L., Yuan, F. P.& Zhu, Y. T. Extraordinary strain hardening by gradient structure. Proc. Natl. Acad. Sci. 111, 7197-7201 (2014).

5.Wang, H. T., Tao, N. R. & Lu, K. Architectured surface layer with a gradient nanotwined structure in a Fe-Mn austenitic steel. Scripta Mater. 68, 22–27 (2013).

6.Hongning Kou, Jian Lu, Ying Li. High-Strength and High-Ductility Nanostructured and Amorphous Metallic Materials. Adv. Mater. 26, 5518–5524(2014).

7.Wei, Y. J., Li, Y. Q., Zhu, L. C., Liu, Y., Lei, X. Q., Wang, G., Wu, Y. X., Mi, Z. L., Liu, J. B., Wang, H. T. & Gao, H. J. Evading the strength-ductility trade-off dilemma in steel through gradient hierarchical nanotwins, Nature Communications 5:3580(2014).

8.L.R. Meza, S. Das, and J.R. Greer, Strong, lightweight, and recoverable three-dimensional ceramic nanolattices. Science 345, 1322-1326 (2014). 

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