A Review on Heterogeneous Nanostructures: A Strategy for Superior Mechanical Properties in Metals

Abstract

Generally, strength and ductility are mutually exclusive in homogeneous metals. Nanostructured metals can have much higher strength when compared to their coarse-grained counterparts, while simple microstructure refinement to nanoscale generally results in poor strain hardening and limited ductility. In recent years, heterogeneous nanostructures in metals have been proven to be a new strategy to achieve unprecedented mechanical properties that are not accessible to their homogeneous counterparts. Here, we review recent advances in overcoming this strength–ductility trade-off by the designs of several heterogeneous nanostructures in metals: heterogeneous grain/lamellar/phase structures, gradient structure, nanotwinned structure and structure with nanoprecipitates. These structural heterogeneities can induce stress/strain partitioning between domains with dramatically different strengths, strain gradients and geometrically necessary dislocations near domain interfaces, and back-stress strengthening/hardening for high strength and large ductility. This review also provides the guideline for optimizing the mechanical properties in heterogeneous nanostructures by highlighting future challenges and opportunities.

1. Introduction

High strength in metals is always favorable in industry, while the elevation in strength is usually accompanied with the drastic loss in ductility [1,2,3,4,5,6]. High strength in metals can be achieved by grain refinement or cold working [1,7,8,9,10]. For the last several decades, severe plastic deformation has been extensively utilized to produce nanocrystalline (NC) or ultrafine-grained (UFG) metals with ultra-high strength [1,7,8,9], while the low strain hardening and the resultant limited ductility restrict their practical applications [2,3,4,5]. Thus, the main challenge is to design novel microstructures to restore an acceptable ductility in the high-strength metals and evade the strength–ductility trade-off.

Metals with both high strength and large ductility are always desired for the structural applications, and such demands have been realized in the last decade by the novel strategy: tailoring the microstructures at nanoscale, i.e., the design of heterogeneous nanostructures [2,3]. These heterogeneous nanostructures include heterogeneous grain/lamellar/phase structures [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33], gradient structure [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65], nanotwins [66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115], and nanoprecipitates [116,117,118,119,120]. One common feature in these heterogeneous nanostructures is that there always exist various domains with dramatically different strengths, although the geometrical patterns and the structural sizes of the domains might vary widely [3,14,15,16,17]. The inhomogeneous plastic deformation in different domains would cause stress/strain partitioning and strain gradients at the domain interfaces [3,14,15,16,17]. And the strain gradients should produce geometrically necessary dislocations (GNDs) and extra-hardening for better performance in mechanical properties [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30].

In this regard, we will present a review in recent advances for heterogeneous nanostructures, and the addressed points are focusing on mechanical properties, microstructure characterization, and deformation physics. In this review, experimental work, numerical simulations and theoretical analysis are all discussed.

2. Heterogeneous Grain/Lamella/Phase Structures

Heterogeneous grain/lamella/phase structures, either with or without dual/multiple constituent phases [17,18,19,20,21,22] and precipitates [23,24] have been regarded as a new class of ideal candidates for structural applications due to their high strength and excellent ductility [2,3]. In this type of materials, the interplays between different adjoining microdomains with different grain sizes, phase constitutes, and/or dislocation substructures are crucial to understand the mechanical behaviors and guide the designing of ultra-strong materials with good tensile ductility [2,3,11,12,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29].

2.1. Hetero-Interfaces and Deformation Mechanisms

Hetero-interfaces in heterogeneous grain/lamella/phase structures are the domain boundaries created during fabrication and developed with the applied straining, and such interfaces bear striking similarities to the conventional grain boundaries (GBs), albeit obvious differences also exist between them [14,18]. In homogeneous materials, the flow stresses exerted on moveable dislocations due to the presence of GBs generally are short-ranged, whereas in heterogeneous grain/lamella/phase structures the extra flow stresses, exerted on the hetero-interfaces due to the directional pile-ups of GNDs, usually are long-ranged [3,13,121]. As a result, the GND pile-ups nucleated by inhomogeneous plastic flow also give rise to an additional inhomogeneous stress locally at the hetero-interfaces because the creation of the GND pile-ups against the hetero-interfaces hinders the successive sliding of mobile dislocations [3,14]. More importantly, the hetero-interfaces are mechanical incompatibility interfaces, which can accommodate inhomogeneous plastic deformation and release the stress concentration [28,122,123]. The hetero-interface is a kind of strain constraint interface that displays a dynamic existence between various adjacent hard/soft microdomains during loading [14]. The main functions of the hetero-interface include: i) accommodating local plastic strains; ii) providing extra strain hardening and additional strengthening effects [13,15,16]. It is well-known that the hetero-interface is the main factor governing the strengthening and strain-hardening behaviors of heterogeneous grain/lamella/phase structures. On one hand, the hard microdomains do not need to bear large plastic strain during deformation, while provide ultra-high strength to the whole sample due to the dynamically strain partitioning and the load transferring mechanisms [122,123,124,125,126,127]. On the other hand, the plastic straining of the soft microdomains occurs under the multiaxial stress constraints of the surrounding hard microdomains, thus their own strain hardening and strengthening can be greatly enhanced [16,18,53], resulting in better strength and ductility for the whole sample [13,16,17,18,19].

In fact, the superior mechanical properties of heterogeneous grain/lamella/phase structures can be attributed to the synergistic strengthening and strain hardening due to the mechanical incompatibility at the hetero-interfaces between adjacent soft/hard domains during plastic deformation [16,25]. Upon tensile loading, both the soft and hard domains are elastically deformed firstly, and after that, the soft domains yield first with increasing applied strain while the hard domains still deform elastically, which can create a strain gradient accommodated by GND pile-up at the hetero-interfaces [121,128]. The pile-up of GNDs in turn produces long-range back-stress strengthening to enhance global yield stress [13,16,121]. Since the back stress at the hetero-interface is high and is subsequently relieved to a certain extent due to the plastic deformation of a portion of hard domains, a macroscopic flow-stress dip or a transient hardening phenomenon may occur in the macroscopic stress–strain curves soon after an overall yielding, which depends on the competition between the stress relaxation of hard domains and the hardening of soft domains [28,123,129,130,131].

2.2. Heterogeneous Grain Structures

As one of the most important microstructural parameters, the grain size plays a crucial role in controlling the yield strengths and strain-hardening behaviors in various metallic materials [1,4,5,6,7,8,9,10]. The domains in heterogeneous grain structure (HGS), containing grains with different sizes varying from nanometers to micrometers [14,17,18], and hence display dramatic strength difference from one domain to another according to the well-known Hall–Petch relationship.

According to the Considère criterion, tensile uniform elongation of high-strength metals can be effectively improved if plastic strain instability is suppressed [132]. One of the most effective methods for delocalizing plastic instability and enhancing strain-hardening rate is to fabricate HGS, which are composed of both nanograins (NGs) and coarse grains (CGs) [17]. Such materials with HGS have two and even more peaks in their grain size distributions which span widely through several orders of magnitude in general [17,18,133,134,135]. Accordingly, excellent synergy of high strength and good ductility has been observed in the resultant materials with HGS, due to their extraordinary strain-hardening capacities [14,17,18]. For example, the bi- and multi-modal microstructures were reported to have both high tensile yield strength and large uniform elongation in copper by simultaneously improving the dislocation accumulation capability and brittle-crack initiation resistance [18,133,134]. Although the deformation mechanisms of these approaches are still not fully understood, it can be generally inferred that the existence of the constrained soft CGs suppresses strain localization and enables extra strain-hardening, prolonging uniform elongation at high flow stresses, while the NGs bear load transfer and provide high strength [16,17,124,126]. The key factor in materials with HGS is that the plastic deformation is non-homogenous and the local deformation incompatibility can promote the macroscopic plastic strain in a more effective manner.

Since back stress hardening plays an important role during the plastic deformation of materials with HGS, the origin and the definition of back stress should be discussed first. The term “back stress” was first used in Fisher’s research on the strengthening behaviors in a precipitation hardening alloy [136]. The back stress was referred as a reverse average stress of the Orowan dislocation loops around the precipitated particles against the successive emitted dislocations from Frank–Read (F–R) sources, i.e., the critical effective stress impeding F–R dislocations. In Fisher’s investigation [136], the residual dislocation shear-loops around the particles were equivalently treated as the transformed strain prescribed in a classical Eshelby’s inclusion problem [137] to deal with this stress state, which generates the average internal stress in the matrix to hinder the subsequent forward deformation. Brown et al. [138,139] proposed that the residual shear dislocation loops around the hard precipitates can impede the subsequent dislocation sliding in the matrix, resulting in formation of the source-shortening stress. The concept of the original Fisher’s back-stress is referred by the so-called Orowan stress after the addition of inhomogeneous internal stress [139]. The concept of back stress was further extended by Brown and Stobbs [138], and Asaro [140] in the hardening model of dual-phase materials. They proposed that the incompatibility strains between the hard phase and the soft matrix can induce a long-range internal stress, which makes the dual-phase structure susceptible to reverse deformation. Later on, the concept was further extended to the long-range (internal) back stress between the soft and hard microdomains due to the micro-inhomogeneous strain during plastic deformation, which is the concept of back stress currently used [141,142]. In the earlier quantitative analysis of back stress by Cottrell [143], Orowan [144,145] and Embury [146], half of the difference between the forward and reverse flow stresses in Bauschinger testing was consistently used to characterize the magnitude of back stress, and hence the back stress was often called the Bauschinger stress. Wilson et al. [147] conducted an X-ray diffraction study on the non-relaxed lattice strains during deformation of a two-phase microstructure, and further demonstrated that permanent softening is ~1.9 times of the back stress when reverse loading reduces internal stress to zero. This experimental result was consistent with the prediction of the aforementioned Orowan’s model [144]. Furthermore, a large number of experimental results have shown that back stress plays a crucial role in the strain hardening, strengthening and mechanical properties of materials with non-homogeneous microstructures [121]. According to the Orowan’s model [144], the macroscopic flow stress of materials with heterogeneous structure can be denoted as following:

σ_flow = σ₀ + σ_forest + σ_back,

(1)

where σ₀ is the initial resistance against occurrence of dislocation sliding, σ_forest is the dislocation resistance derived from the interactions between movable dislocations and forest dislocations, and σ_back is the long-range back stress due to the extra GND-induced hardening.

According to the definition of strain-hardening rate Θ = ∂σ/∂ε, when the changes in testing temperature and strain rate can often be ignored during the quasi-static tensile deformation [132], the Equation (1) can be rewritten as:

Θ_flow = Θ_forest + Θ_back,

(2)

where Θ denotes the macroscopic strain-hardening rate, and Θ_forest and Θ_back are forest hardening rate and back-stress hardening rate, respectively. It can be seen that the back-stress hardening rate is essential for the enhancement of the overall strain-hardening rate of materials with HGS, and thus a scientific basis for exploiting and providing the potential hardening mechanism associated with monotonic plastic deformation has been proposed by Wu et al. [3].

We presented an analytical model to calculate the back stress based on the hysteresis loops observed in tensile loading-unloading-reloading test [53]. Upon tensile loading, yielding starts in larger grains, while small ones still remain elastic. The applied load will be transferred from large grains to small ones [148]. Upon unloading, the macroscopic stress decreases and the large grains are subjected to a compression stress when the small grains reach the completely unloaded state [122]. Upon subsequent compressive loading, the whole sample initially behaves elastically until the large grains enter in the plastic regime first in compression, a situation that will take place at a much lower absolute value compared to the initial tensile flow stress because of the pre-compression of large grains [53]. As a consequence, an asymmetry in the macroscopic forward (tensile) and reverse (compressive) yield stresses will occur (so-called Bauschinger effect [53,122]), and this effect characterizes the development of back stress [16,53]. Therefore, back stresses develop in terms of the load transferring from large grains to small ones, whereas the strain partitioning from small grains to large ones [148]. This is evidenced by the large width of hysteresis loops and high hardening rate due to back stress. Both the dynamic load transferring and strain partitioning along with the tensile straining lead to the increasing back stress [16,17,53].

Experimental studies have been conducted on the mechanical properties and deformation mechanisms of HGS in single-phase metals [16,18], dual-/multiple-phase alloys [20,21], and transformation-induced plasticity (TRIP)/twinning-induced plasticity (TWIP) steels [22,23], emphasizing on the back-stress-induced strengthening/hardening effects. Early research on metals with HGS started with synthesizing their microstructures [149,150]. Recently, great efforts and growing scientific interests have been focused on tailoring multi-scale hierarchical microstructures in a nanostructured matrix and achieving a synergistic strengthening/hardening from the combined effects of both grain refinement and extra hardening [14,16,123]. More recently, we [17] reported a simultaneous improvement of both strength and ductility in a single-phase fcc medium-entropy alloy (MEA) with dynamically-refined HGS. The MEA with HGS can be produced by a conventional heat-treatment of partial recrystallization annealing, which is currently a well-developed processing route at a low cost.

The grains can be efficiently refined for the MEA in situ during tensile deformation due to its low stacking fault energy (SFE) [151,152], thus reinforcing the HGS and increasing the back stress to promote strain hardening and hence uniform elongation. Compared with the MEA with homogeneous UFG structure [86], the MEA with HGS has a significant higher uniform elongation and a similar flow stress. The dynamic grain refinement in HGS accommodates plastic deformation by facilitating the successive emission of SFs in new orientations (Figure 1a). This dynamic grain refinement induced plasticity (GRIP) effect by architecting HGS is therefore much like TRIP and TWIP in facilitating strain hardening and plastic flow [153,154]. In addition, the small grains are generated mainly at GBs and triple junctions of larger grains, where damage is more susceptible to initiate [1,17]. Thus, GRIP effect has beneficial influences on increasing fracture toughness, in addition to delaying plastic instability such as premature necking in tensile deformation. The dynamic grain refinement can also further reinforce the heterogeneity in HGS, and thereby increase the back-stress-induced strain hardening, suppressing the strain localization and prolonging the tensile uniform elongation. In consequence, the tensile uniform elongation of the MEA with HGS was enhanced up to 20% even when the yield strength was improved to above 1 GPa (Figure 1b) [17].

Similar to the above processing approach, Slone et al. [87] produced another type of HGS with partially recrystallized microstructure in a similar MEA. Striking hysteresis loops are also observed not only in the sample with HGS at the early stage of plastic deformation, but also in the partially recrystallized sample with relatively homogeneous grain structure at end stage of uniform deformation. This result just further confirms that back-stress hardening plays a key role at a high stress level. It is well known that the dynamic generation of twin bundles during deformation and the consequent hardening can build a superior back-stress effect in TWIP steels with the conventional equilibrium CG structure [154]. Similarly, the role of architecting HGS for enhancing strain-hardening capacity in metals was well discussed in this paper. However, there are some obvious discrepancies between these two studies [17,154], though both the small NGs and the twin bundles are associated with the partial dislocations emitted from GBs and triple junctions. In Slone’s case [87], a back stress can indeed be developed into a large magnitude due to the formation of the large amount of twin bundles during tensile testing in conventional CG microstructures. For our HGS, it should be noted that there are definitely deformation twins formed inside grains during tensile deformation, while these twins are the corner twins and these twins subsequently evolve into newly-formed NGs during further deformation [17]. In other words, twinning-induced back stress in our HGS should have played a smaller role in the strengthening and strain hardening during the tensile deformation.

It has attracted great interests for optimizing the strength–ductility synergy by tailoring the HGS. More and more experimental results have shown that the effect of back stress in providing extra strengthening and strain-hardening capacity for the materials with HGS. Although these studies have been conducted on the various HGSs with different morphologic and crystallographic features, these microstructures do share one common characteristics: there is a dramatic difference in flow stress between different microdomains. This large difference in flow stress is often caused by huge heterogeneities in microstructure, crystal structure or composition in these domains. The domain sizes could be in the range of micrometers to millimeters, and the domain geometries can vary dramatically. It is indicated that heterogeneous microstructures can achieve a large accumulation of GNDs especially at the hetero-interfaces during inhomogeneous deformation, which in turn causes significant back stress, resulting in enhanced overall strain-hardening capacity. Therefore, how should the hetero-interfaces be designed? The hetero-interfaces should be designed to improve the constraints on soft domains exerted by the surrounding hard domains during plastic deformation, which is important for accommodating GNDs, bearing strain gradient, and inducing back stress [16,121]. The spatial distribution and morphology of hetero-interfaces, including geometric and microstructural characteristics, should have great influences on the mechanical behaviors of HGS. Thus, domain size, domain distribution, domain morphology, soft/hard domain volume fraction, and local discrepancies in yield strength and strain-hardening behavior between any two adjacent domains should be properly designed to optimize the mechanical properties of HGS [2,3].

2.3. Heterogeneous Lamella Structures

According to the above-mentioned strategies for inducing high back-stress, the heterogeneous lamella structure (HLS) presents a near-ideal heterogeneous structure due to both the high density of domain interfaces and the adjustable volume fractions for soft/hard domains in such microstructure [16,23]. Our recent results have shown that a commercially-pure Ti with HLS, which possesses the spatial distribution of the alternating hard and soft lamellae with their both widths ranging from a few to a dozen micrometers, presents enhanced tensile strength–ductility synergy (Figure 2a) [16]. Such Ti with HLS unprecedentedly surpasses its CG counterpart in strain hardening and consequently produces both larger ductility and higher strength (Figure 2b–d). The Ti with HLS was fabricated by asymmetric rolling followed by partial recrystallization annealing, which produced a strong local micro-hardness variation between the alternating hard and soft lamellae, as well as a slight macroscopic structural gradient with recrystallized grains of a few micrometers near the surface and recovered ultrafine-grains in the central region. In addition, the soft CG lamellae consisting of recrystallized grains are intermixed with the relatively harder UFG lamellae at microscopic scale. The HLS produces a strong internal mechanical incompatibility and long-range back stress at macroscopic scale from the surface to the center as well as at microscopic scale between adjacent lamellae (Figure 2e). During the deformation of HLS, the GNDs are gradually generated and blocked by hetero-interfaces to induce back stress (Figure 2f). This extra strain hardening induces even higher overall strain hardening in Ti with HLS than that in CG Ti, which is usually believed to be impossible [16].

This enhanced tensile properties for HLS as compared to these for uniform structure can also be attributed to the local variations in the hardness between alternating recovery and recrystallized lamellar domains [16,53]. This hardness difference needs to be large enough to generate local incompatibility of plastic deformation and local extra hardening for improvement in global hardening. In a summary, larger local gradients and higher local GNDs render the better mechanical performances, such as yield strength, strain-hardening rate, and uniform elongation [16,26,53]. The local variation in hardness in the deformed state is small, but it is enhanced after recovery and partial recrystallization annealing. This has been verified by micro-hardness testing on recovered and recrystallized lamellae [16]. The best combination of strength, strain-hardening rate and uniform elongation should be associated with the optimized difference in hardness between soft and hard lamellae. Moreover, the spatial distribution of the alternating hard and soft lamellae, rather than a random distribution of irregular grains and soft/hard domains, should have better performance on mechanical properties [3,16].

Recent studies on copper/bronze laminates by Huang et al. have revealed possible existence of an optimum layer thickness for the best mechanical properties [25,155]. In-situ microstructural examinations during tensile deformation revealed pile up of high-density GNDs at the hetero-interfaces. This result suggests that interface-affected zone likely exists and has a width of a few microns, which is the key factor to maximize the back-stress hardening. When the spacing between the hetero-interfaces is large, the density of GNDs should be low. While too small spacing would cause the overlapping of the distributions of GNDs for neighboring interfaces, resulting in decreasing strain hardening and tensile ductility. Thus, a proper spacing between the hetero-interfaces has been identified to be about 15 µm for generating the best tensile properties for the copper/bronze laminates [25].

2.4. Heterogeneous Phase Structures

The transient strain-hardening phenomenon has been experimentally observed in the various metals and alloys with either a simple homogeneous grain microstructure or a complex multi-scale hierarchical grain/phase microstructure [14,16,17,28]. In simple metals, this phenomenon is generally attributed to the heterogeneous distributions of GBs and dislocation substructures, such as dislocation cells and dislocation walls [156,157]. However, the transient phenomenon has not yet been completely understood in heterogeneous structure [14,16,17], which is much more complex than that of homogeneous materials because of discrepancy in deformation behaviors between neighboring microdomains/phases. To better understand this issue, we conducted a synchrotron-based in-situ tensile testing on a Fe-16Mn-10Al-0.86C-5Ni high specific strength steel (HSSS) with heterogeneous microstructure, in order to clarify the possible micro-mechanisms underlying the elasto-plastic deformation and back-stress hardening of this heterogeneous phase structure (HPS). This investigation would also help for understanding of the transient strain-hardening phenomena in materials with heterogeneous microstructure [28].

The HSSS with heterogeneous microstructure shows a remarkable feature of the elasto-plastic deformation behavior, resulting in a pronounced hardening transition on the stress–strain curves during an early stage of deformation (Figure 3a) [28]. This phenomenon can be attributed to inhomogeneous deformation occurring in this dual-phase steel because of the microstructural heterogeneities and long-range back stresses arising from plastic incompatibilities between alternating-distributed phases with different responses of mechanical properties. In fact, a composite-type elasto-plastic deformation prevails in most high strength steels [14,16,17,28,53]. This is due to the plastic deformation heterogeneity between the constituents, phases and grains with different mechanical responses and even orientations relative to an externally applied stress. This will lead to the presence of long-range internal stress, i.e., back stress, which evolves with applied strain because of intra- and inter-granular variations of plastic strains, and the evolved back stress has a strong impact on the strain-hardening behaviors and macroscopic mechanical properties [29,158,159]. It is a great challenge to investigate the strain hardening behaviors associated with the back stress in the HPS since it is a complex interplay between individual phases due to the presence of hetero-phase interfaces [28]. More importantly, both the load redistribution and strain partitioning will take place in HPS during plastic deformation [28]. These effects enable not only high capacity of strain hardening but also a large uniform elongation in a composite-type microstructure [28,122].

Upon the applied tensile strain, the axial lattice strains in both soft austenitic matrix and hard B2 phase can roughly be divided into a three-stage evolution, i.e., elastic deformation, elasto-plastic transition, and plastic co-deformation up to overall necking (Figure 3b) [28]. In the stage of elastic deformation, both the axial lattice strains of austenitic matrix and B2 phase coincide well and increase linearly. During the elasto-plastic transition stage, the lattice strain of austenite firstly deviates from linearity, while the lattice strain of B2 phase still increases linearly. With the further tensile strain, a rapid drop in lattice strains of both austenite and B2 phases is observed clearly. In the stage of plastic co-deformation, the axial lattice strains of both austenitic matrix and B2 phase begin to rise nonlinearly, but with different slopes. Moreover, the transition process can be subdivided into two sub-stages according to the plastic yielding first in austenite and soon afterwards in B2 phase. In the first sub-stage (II₁), a grain-to-grain yielding takes place first in soft austenitic matrix due to varying Schmid factors and strain-hardening behaviors of individual austenite grains. During the second sub-stage (II₂), a rapid drop of lattice strain in B2 phase appears, indicating that B2 phases start to yield for accompanying the decline in load shedding from softer austenite to harder B2 phase through hetero-phase interfaces.

The unique up-turn hardening in the stress–strain curves observed in HPS can therefore be attributed to the nature of elasto-plastic transition [28,122]. Under tensile loading, soft phase will deform plastically first. However, they are constrained by still elastic-deformed hard phase such that dislocations in soft one are piled up and blocked at hetero-phase interfaces. GNDs will also be generated at hetero-phase interfaces due to the plastic strain incompatibility [28,121]. This produces the back stresses to make it difficult for dislocations to slip in soft phase until the surrounding hard phase starts to yield at larger applied strain. As a consequence, both inter-phase back stresses and intra-phase back stresses occur, which are attributed to the progressive yielding of grains and phases [28,129]. This is the reason why a much high back-stress hardening is visible exactly at the transient stage (elasto-plastic deformation stage). The high strain hardening is therefore originated from both back-stress hardening and forest dislocation hardening in both phases. Moreover, once the B2 phase yields, rapid relaxation of elastic stresses and strains on the hetero-phase interfaces causes a rapid stress-drop [28,129]. Afterwards, the macroscopic strain-hardening rate resumes to rise up gradually as a consequence of the back stresses resulting from the strain incompatibility together with rapid dislocation multiplication in both phases [28]. The development of the back stress during plastic deformation of two-phase microstructure due to dynamic strain partitioning and yield stress mismatch was also described in other research [123,124,129,154].

In fact, back stress strengthening/hardening has also been reported in nanocomposites [122], dual-phase alloys [28] and TRIP/TWIP steels [160]. He et al. [23] have developed another similar HPS coupled with V-containing nanoprecipitates in medium-Mn steel, i.e., the so-called deformed and partitioned (D&P) steel [23]. Based on the experimental observations and theoretical analysis, they have proposed that the high dislocation density in the D&P steel not only increases the yield strength, but also enables a large ductility by the glide of existing mobile dislocations and by the controlled release of TRIP effect, resulting in an ultrahigh yield strength reached to above ~2 GPa, 50% higher than that of the conventional high-strength steels, together with a comparable uniform elongation. Besides, a Lüders-like nonuniform deformation behavior is exhibited in such D&P steel during tensile deformation, and the more in-depth mechanisms have not yet been revealed.

3. Gradient Structure

Materials from nature and biological systems, such as bamboos, teeth and seashells, have been found to have gradient structure from the surface to the interior and exhibit exceptional mechanical properties [30]. Learning from nature, mankind has designed gradient structure in engineering materials to achieve novel and superior physical and mechanical properties [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65]. These mechanical properties include uniaxial tensile properties, dynamic properties and fatigue properties. For gradient structured metals with exceptional mechanical properties, the strength/hardness generally shows a gradient along the depth. As a result, the microstructures (grain size, phase fraction, twin volume fraction/twin thickness, and texture/orientation) display an apparent gradient along the depth.

3.1. Fabrication Methods

In 1999, a concept of surface nanocrystallization on metals and alloys was introduced for the first time [35], a gradient structure was produced by surface mechanical attrition treatment (SMAT) and nanostructured (NS) grains were formed at the surface layer by repetitive severe plastic deformation (Figure 4a). In 2003, the SMAT technique was utilized to enhance the efficiency of nitriding process [38]. The grain size was refined and a fraction of GBs was increased in the surface layer during SMAT. Thus, the nitriding kinetics of the surface treated iron were significantly improved since GBs can be considered as well-known high ways for diffusion processes [38]. Later on, another surface nanocrystallization technique, surface mechanical grinding treatment (SMGT) at cryogenic temperature Figure 4b, has been used to fabricate a gradient nano-microstructured surface layer on copper and the grain size at the topmost surface was as small as 22 nm [41].

3.2. Tensile Behaviors of Gradient Grained Structures

The tensile properties of gradient structured metals were started to be investigated since 2008. A new microstructure, multiple layered structure with gradient grain size in each layer, has been obtained by SMAT technique and subsequent warm co-rolling technology, and excellent tensile properties have been revealed in this new microstructure [40]. The compression residual stress and deflection of cracks by the interface between the nanostructured layers have been found to play important roles for achieving high ductility in this periodically layered gradient structure [40]. As we know, NC metals can have much higher strength when compared to their CG counterpart, while NC metals are believed to be intrinsically brittle under uniaxial tensile loading. When the NC copper film is confined by a CG layer in the gradient structure, strain localization can be suppressed and large uniform tensile ductility can be achieved [42]. The intrinsic deformation mechanisms for large tensile plasticity of NC copper surface layer in gradient structure have been revealed by Fang et al. [42] for the first time, and the substantial grain growth by mechanically-driven GB migration process has been proposed to be the dominant plastic deformation mechanism of this gradient NS layer (Figure 5). These “in-situ” coarsened grains help to regain strain hardening and dislocation plasticity in the surface layer. More recently, a critical grain size of 165 nm was identified in the gradient structured copper during uniaxial tension, tension-induced softening was observed for grains smaller than this critical grain size while tension-induced hardening was found for grains larger than this critical grain size [46]. The observed softening was attributed to the grain growth in the small grains while the strain-induced hardening in the large grains was due to dislocation multiplication and formation of dislocation walls/cells.

Using the same SMAT technique, we have produced a gradient structure in an IF steel and large tensile ductility was achieved in the NS surface layer of IF steel without apparent grain growth when confined by the CG substrate [14]. These observations suggested that the varying propensities for flow instability between different layers in the gradient structure can induce stress-state change to suppress the strain localization in the NS surface layer [14]. Extra synergic strengthening and extra hardening were also induced by strain gradient to help tensile ductility, and the strain gradient was due to the mechanical incompatibility between different layers during the elasto-plastic stage and the co-deformation stage in the gradient structure [14,15]. An obvious up-turn for strain hardening rate was also observed due to the stress-state change and the strain gradients (Figure 6). As we know, the strain gradients are generally accommodated by the pileup of GNDs at the interfaces, which in turn generates long-range back stress between the hard NS surface layer and the soft CG core. We proposed a simple equation to calculate back stress from the tensile unloading-reloading hysteresis loop based on its deformation physics, and also reported strong back stress strengthening/hardening in the gradient structured IF steel [14]. Using the tensile load-unload-reverse compressive load testing, we also reported extraordinarily larger Bauschinger effect in the gradient structure compared to the CG counterpart and proposed to use the reverse yield softening as a quantitative parameter to represent the Bauschinger effect [53]. This parameter can be utilized to evaluate the magnitude of back stress hardening for exceptional tensile properties in heterogeneous materials.

Moreover, we reported an “in-situ” evolution of the induced strain gradients in a gradient-structured metals during uniaxial tension [57]. We found that the lateral strain gradients increase with increasing applied tensile strain, and the strain gradients increase faster and the back-stress hardening plays more important role at the elasto-plastic transition stage. It is well known that NS metals typically fail soon after yielding under uniaxial tensile loading, starting with strain localization. Thus, low tensile ductility in NS metals is ascribed to strain localization, so one always tries to avoid localization, but never think about how to utilize it. We illustrated for the first time how to adopt the good point of localization, i.e. collecting vast strains for ductility, and to avoid its shortcoming, i.e. fast instability, by stabilizing localized shear band in the gradient structure [63]. This novel strategy overturned our traditional understanding for strain localization. We exhibited for the first time that localization may induce ductility, instead of catastrophic failure. This enhanced ductility in the gradient structure was fulfilled by the shear band delocalization: shear bands were initiated soon after yielding in the NS surface layer, while were delocalized by propagating along the gage length during the tensile loading, and synergistic work hardening was induced by back stress hardening from the strain gradients in both the axial and depth directions [63].

3.3. Tensile Behaviors for Other Types of Gradient Structures

Besides the gradient structure with grain size gradient, other types of gradient structures (i.e., gradients for phase fraction, twin volume fraction/twin thickness, and texture/orientation) also showed great potential for achieving superior tensile properties [27,47,51,56,59]. Wei et al. [47,51,56] applied pre-torsion deformation to a cylindrical twinning-induced plasticity steel sample to generate gradient of twin volume fraction along the radial direction (Figure 7). They found that the yield strength of the gradient twinned structure can be doubled without sacrifice of tensile uniform elongation compared to the untreated CG sample, evading the strength–ductility trade-off dilemma. The enhanced tensile properties in the gradient twinned structure have been attributed to two points: (i) the formation of a gradient hierarchical nanotwinned structure during the pre-torsion deformation and the subsequent tensile loading; (ii) this hierarchical nanotwinned structure is generated in the sequential torsion and tension deformation by activating different twinning systems. Cheng et al. [13] fabricated a dual gradient structure of grain size and twin thickness by direct-current electrodeposition method. This dual structural gradient was found to show superior work hardening and strength that can exceed those of the components of the gradient structure. The enhanced tensile properties have been attributed to a unique patterning of ultrahigh densities of dislocations in the grain interiors: bundles of concentrated dislocations, a special type of GNDs (Figure 8). These bundles of concentrated dislocations were induced due to the nature of gradient, were not available in the homogeneous samples [64].

We generated dual gradients with respect to grain size and martensite phase fraction in a TRIP steel by SMAT technique [27]. A design strategy was reported to combine the both benefits from gradient structure and TRIP effect, and the reported TRIP-gradient steel was found to take advantage of both mechanisms, prolonging the TRIP effect to large strains [27]. Significant heterogeneity for strength exists not only macroscopically between the hard surface layer and the soft center layer, but also microscopically between the soft austenite domains and the hard martensite walls. Thus, the martensitic transformation was found to be triggered successively along the depth with tensile loading due to the strain partitioning between soft and hard areas, enabling the martensitic transformation to last to a larger tensile strain. As a result, the reported TRIP-gradient steel displayed an excellent combination of high strength and ductility due to both the dynamic strain partitioning and the TRIP effect. The SMAT technique was also utilized to fabricate the dual gradient structure of grain size and orientation in a Mg alloy [59]. The stronger strain hardening and higher tensile ductility were attributed to the pyramidal dislocations activated in the whole sample and higher dislocation density induced by grain-size gradient in the dual gradient structure.

3.4. Dynamic Behaviors of Gradient Structures

It is well known that the plastic flow behaviors and the observed flow stresses in metals and alloys highly depend on the loading rate. The materials display dramatically different mechanical behaviors at high strain rates due to the substantial adiabatic temperature rise, thermal softening, inertial and strain rate effects, and the formation of adiabatic shear band (ASB) compared to those at quasi-static strain rates [52,58,65]. A few studies have been conducted to focus on the dynamic behaviors of gradient structures [43,52,58]. Jérusalem et al. [43] have conducted a series of ballistic tests on the gradient structures to build two length scales as optimization parameters for ballistic performance: one is the intrinsic length scale (the finest grain size and the grain size gradient), and the other one is the extrinsic length scale (the thickness of the samples). Proper choice of these two length scales can lead to the best ballistic properties. Strain hardening behaviors and strain rate sensitivity (SRS) of gradient grained iron under compressive loading over a wide range of strain rates (5 × 10⁻⁴–10⁴ s⁻¹) have been investigated in our recent work [52]. The gradient grained iron was found to show apparent strain hardening behaviors at all investigated strain rates, and the extra hardening at all strain rates were believed to be due to the back stress hardening induced by the plastic deformation incompatibility between different layers in the gradient structures. The dynamic SRS of the gradient grained iron was found to be slightly higher than that of the CG counterpart, which is controversial to the general observation that SRS should decrease with decreasing grain size for BCC metals [161]. This enhanced SRS in the gradient structure was attributed to the additional increase in dislocation density by the GNDs associated with the strain gradients and the back stress hardening. The dynamic shear behaviors of a gradient structured TWIP steel have been investigated in our recent paper [58]. The gradient structured TWIP steel was observed to have better dynamic shear properties over the homogeneous counterparts, which can be attributed to the suppression of ASB nucleation and propagation in the gradient structure (Figure 9). The propagation velocity of ASB in the gradient structures was found to be one order of magnitude lower than that in the homogeneous counterparts. Moreover, the well-known maximum stress criterion on ASB nucleation for homogeneous materials was found to be no longer valid for the gradient structures.

3.5. Fatigue Behaviors of Gradient Structures

In structural applications, most materials and components fail under cyclic loading, thus the fatigue behaviors of metals and alloys have attracted extensive interests, in which a few papers have focused on the fatigue mechanisms of the gradient structures [39,45,49,61]. Roland et al. [39] have investigated the fatigue behaviors of a gradient-structured 316L stainless steel, and significant improvement of the fatigue limit has been achieved in the gradient structure. The fatigue properties can be further improved by a short post-annealing treatment, which can be attributed to a recovery at the GBs leading to a reduction of the internal stress (Figure 10). The similar fatigue behaviors have also been observed in a gradient structured martensitic stainless steel [45], the torsion fatigue strength of the gradient structure is 38% higher than that of the original material and an additional 8% increment in fatigue strength was achieved after a post-annealing treatment. The enhanced fatigue properties can be attributed to the formation of the gradient structure with a hard surface layer with a high structural homogeneity. Huang et al. [49] have investigated the fatigue behaviors of an AISI 316L stainless steel with gradient structures and found that the fatigue strength of the gradient structure is significantly improved in both the low- and high-cyclic fatigue regimes compared to that of the original material. Moreover, the fatigue ratio (the fatigue limit divided by the ultimate tensile strength) was also apparently elevated in the gradient structure. Due to the hard surface layer, these enhanced fatigue properties can be attributed to the suppression of the initiation of cracks and accommodation of a remarkable cyclic plastic strain amplitude. Mechanically driven abnormal grain growth has been observed in a gradient grained copper under strain-controlled cyclic loading [61]. This abnormal grain growth was observed to start from the ultrafine grained subsurface layer and eventually move to the NS top surface layer with increasing cycles. They have attributed the enhanced fatigue properties of the gradient structured copper to the abnormal grain coarsening and the formation of dislocation patterns, which in turn accommodate the cyclic plastic strain and postpone the formation of extrusions/intrusions at the surface for improving the cyclic properties.

3.6. Theoretical and Numerical Work for Gradient Structures

The above-mentioned experimental evidences have shown that the enhanced mechanical properties (uniaxial tensile, dynamic and fatigue) can be achieved by the gradient structure, while the detailed mechanisms underlying the observed mechanical behaviors still need further investigations and how the mechanical properties can be optimized in the gradient structure need be clarified by theoretical and numerical modeling. In the past decade, several approaches (i.e., dislocation density-based continuum plasticity modeling [48,54,55], dislocation mechanism-based size-dependent crystal plasticity modeling [64], Crystal plasticity finite element modeling [65] and molecular dynamics (MD) simulation [60]) have been utilized to understand the strengthening and strain hardening behaviors. Li et al. [48,54] have developed a dislocation density-based continuum plasticity model to reveal the extra strain hardening behaviors in the gradient structure of IF steel, in which the nonuniform deformation of the lateral surface, the interaction of different layers along the depth, GNDs and back stress were considered (Figure 11). A simple physical law with two dimensionless parameters has been established to build the correlation between the strong extra strain hardening and the nonuniform deformation of the lateral surface, and these two parameters can be determined by experimental data. Based on the dislocation density-based continuum plasticity model, the strain hardening rate up-turn as observed in experiments was well reproduced and a strength–ductility map was plotted, in which the gradient structure clearly shows much more superior mechanical properties to their homogeneous counterparts. They have attributed the high strain hardening rate of the gradient structure to the generation of abundant GNDs in the NS surface layers through analyzing the evolutions of GNDs density distribution and back stress. Zeng et al. [65] have investigated the mechanical behaviors of the gradient grained copper using crystal plasticity finite simulations. They revealed both gradients of stress and plastic strain in the cross-section of the gradient grained copper under uniaxial tensile loading, these spatial gradients were found to be due to the progressive yielding of each layer along the depth during the tensile deformation. GNDs can be generated by these plastic strain gradients, which is contrast to the widely studied strain gradient plasticity induced by nonuniform deformation (i.e., torsion, bending and indentation at small scales).

Lu et al. [64] have incorporated multiple dislocation evolution, damage evolution, and mechanically-driven grain growth into a dislocation mechanism-based size-dependent crystal plasticity model to predict the tensile behaviors of the gradient grained copper. The simulated results have revealed the strengthening and the strain hardening mechanisms based on the spatial distribution and the evolution of microstructure and damage and have demonstrated the ability to optimize the strength and the ductility of the gradient grained copper. Zhu et al. [55] have developed a mechanism-based dynamic plastic model to describe the strain-rate dependent flow behaviors in gradient nanotwinned austenite stainless steels. These theoretical simulation results have indicated that the dynamic properties of the gradient nanotwinned austenite stainless steels are highly sensitive to the twin spacing and the twin volume fraction, and this mechanism-based dynamic plastic model can be used to well predict the plastic response of the gradient nanotwinned metals under a wide range of strain rates. Lin et al. [60] have combined experimental observations and molecular dynamic simulations to reveal the optimal grain size distribution profile of the gradient structure. The results have indicated that the surface roughening of CGs and strain localization of NS grains can be effectively suppressed by the interaction between CG grains and NS grains, resulting in the observed strong strain hardening and the superior uniform elongation. The aforementioned theoretical and numerical simulations have provided not only promising methodologies of producing gradient structure with optimizing mechanical properties, but also models for understanding the deformation mechanisms in the gradient structures.

4. Nanotwinned Structure

Nanotwinned (NT) structure has been proven to be a useful strategy for achieving ultra-high strength with acceptable ductility in face-centered cubic (FCC) metals, especially in FCC metal and alloys with low SFE. Twin boundaries (TBs) in crystalline materials are efficient and easy-controlled interfaces that can interact with dislocations, similar to GBs [12]. TBs can be introduced into grains during deposition processing (so-called growth twins), plastic deformation (so-called deformation twins) or annealing of deformed structures (so-called annealing twins). Due to the lower energy, TBs usually exhibit much higher thermal and mechanical stabilities compared with high-angle GBs [66]. It was shown that introduction of twins for designing material structures offers substantial strengthening while preserving acceptable ductility, especially when the density of twins is high and the size of twins is at the nanoscale. On one hand, TBs can block dislocation sliding and dislocations can be piled-up at TBs for improving strength in materials. Upon further plastic deformation, twins may be transformed into NGs via shear banding or high-angle GBs by dislocations accumulation [66]. On the other hand, TB could nucleate and emit dislocations during plastic deformation when the stress concentration at TBs is high enough. Atomistic and MD simulations have also shown that TBs can assist dislocation generation [67]. The main factors affecting the strengthening of TBs are the spacing of TBs and the volume fraction of twins. In recent years, numerical research indicated that when the spacing of TBs decreases to nanoscale, the strengthening effect is particularly remarkable, and the other mechanical properties in metals, such as ductility, strain rate sensitivity, wear resistance, fatigue performance, fracture toughness, can also be significantly improved [68,69,70,71,72,73].

4.1. Strength and Ductility

Strength and ductility are the important mechanical properties of metals and alloys, but there exists a trade-off dilemma between them, limiting the potential use of many structural metals and alloys. Numerical research have proven that the strength can be effectively elevated in metals and alloys without much sacrifice of ductility [74,75,76]. Especially in copper, the strength of NT Cu can reach impressive gigapascal scale, over more than fifteen times of its CG counterpart [75]. The electro-deposited Cu sample with high density of nanoscale growth twins showed that the strength and ductility can increase simultaneously with decreasing TB spacing when the mean grain size keeps constant [74,75,76,77] (Figure 12a and Figure 13). The strengthening effect of TBs is analogous to that of conventional GBs. The in-situ transmission electron microscope (TEM) and other postmortem TEM investigations showed that TBs are strong barriers to dislocations, and glissile partial dislocations can be generated at TBs for accommodating plastic deformation, which releases the local stress concentration and promotes further plastic deformation [66,78,79,80]. Another approach to introduce nanotwins in metals and alloys was severe plastic deformation (SPD) technique, which can generate grain refinement and deformation twinning. For materials with low SFE, such as Cu-Zn [80,81], Cu-Al [82,83], FeCoCrNiMn [84,85], CoCrNi [17,86,87], and other high/medium entropy alloys (H/MEAs), twinning is easier to occur than slipping, especially at the low temperature [88] and high strain rate [89]. Nanostructured Cu sample by means of dynamic plastic deformation (DPD) at liquid nitrogen temperature and subsequent short-time annealing showed surprisingly good strength–ductility combination [90]. The annealed structure as a typical heterogeneous structure, containing nano-grains with nanotwins and static recrystallized grains, showed excellent performance in work hardening ability. The similar heterogeneous structures also work effectively in Cu-Zn and Cu-Al alloys, as shown in Figure 12c,d [80,91]. High manganese TWIP steels are perfect candidates in crash safety of automobile due to their excellent work hardening capability, but the TWIP steels with CG structure usually have low yielding strength [92]. A gradient NT structure [47] was generated by applying torsion to double the yielding strength without reduction of ductility in a TWIP steel. In addition, multiple twins can promote plastic deformation in metals and alloys, while higher order twins are difficult to form in the metals and alloys with high SFE [94,95]. Five-order twins were fabricated in pure silver (Ag) with extremely low SFE by SMAT and uniaxial pre-loading [96]. The Ag with multiple twins can improve its strength by over three times without sacrificing ductility when compared to the CG counterpart. The hierarchical NT structures in FCC metals have been proposed to be a novel structure to bring out higher strength/ductility than NT counterparts due to their unique deformation phenomena [97].

4.2. Strain Rate Effect and Activation Volume

Mechanical performance of metals and alloys is always sensitive to strain rates, especially for NC metals [98,99,100,101,102,103]. The SRS can be defined as: $m=\partial ln\sigma /\partial ln\dot{\epsilon }$, where $\sigma$ is the flow stress and $\dot{\epsilon }$ is the strain rate. SRS generally reflects the ability of materials to resist localized deformation when deformation is unstable at higher strain rate [71,98,99,100,101,102,103]. In general, the high SRS means higher elevation in flow stress with increasing strain rate. Enhancing SRS could prevent early onset of necking and nonuniform plastic deformation at a higher strain rate. TBs, which serve as a special kind of boundaries with low energy, can obstruct dislocation motion for providing higher strength and larger SRS. Activation volume of plastic deformation reflects the mechanism of rate-controlling deformation. The activation volume of NT-Cu was measured to be about dozens of b³ (here, b is the Burgers vector of Cu, b = 0.265 nm), much lower than that for UFG-Cu without twins (several hundred of b³), in which the main rate-controlling deformation mechanism might be forest dislocation interaction. Tensile strain rate jump tests [99] and different strain rate tensile tests [71] have revealed that NT-Cu with higher density of nanotwins can have a higher elevation of flow stress with increasing strain rate. The flow stress for the samples of NT-Cu with a mean TB spacing of 15 nm (referred to NT-Cu-fine) can be elevated more than 150 MPa when the strain rate increases from 10⁻⁵ to 10⁻² s⁻¹. However, the corresponding elevation value for the samples of NT-Cu with a mean TB spacing of 100 nm (referred to NT-Cu-coarse) is only about 50 MPa. In addition, the average grain size for both NT-Cu-Fine and NT-Cu-Coarse samples is similar (about 400–500 nm), excluding the grain size effect. The TEM observations of NT-Cu-fine samples after deformation showed that TBs are curved comparing to the straight TBs before test and high-density dislocations are observed to pile up along TBs. Stress-relaxation tests are standard methods to measure strain hardening rate, SRS, activation volume and mobile dislocation density. The TB spacing always has significant influences on the NT Cu’s mechanical performance [104]. The NT-Cu with high density of twins show a much lower exhaustion rate of mobile dislocations as the applied stress increases, when compared to NC Cu without twins [105]. These results suggest that TBs can preserve mobile dislocations more effectively. MD simulations have indicated that dislocations may propagate into the adjacent part of twins by cutting through TBs when dislocations interact with Σ3 coherent TBs in NT-Cu [99], which would contribute to sufficient strain hardening by the mobile dislocations at the coherent TBs.

4.3. Fatigue and Damage Tolerance

Fatigue behaviors of materials refer to the mechanical properties subjected to cyclic loading [70]. In applications, more than ninety percent of the metal components or structures fail due to fatigue loading, which is normally tension-tension or tension-compression cyclic loading. The corresponding theories and experiments have been proposed and studied for homogeneous materials, such as the Griffith fracture theory, the J-integral and the Paris’s low. However, the fatigue and fracture deformation mechanisms of the materials with heterogeneous structures are still far from well understood [106,107,108,109,110]. Pan et al. reported a history-independent and stable cyclic response in highly-oriented NT-Cu samples [70]. They defined the so-called “necklace” dislocations, which carry plastic deformation strongly correlating across multiple TBs. The corresponding simulations indicated that the “necklace” dislocations move collectively back and forth along the TBs under cycle loading, so there was no damage accumulation by the cyclic stresses in the samples. The coherent TBs usually are generated in materials as an ideal toughening “phase” to prevent stress concentration and improve fracture resistance. The in situ TEM observations [106] and MD simulations [107,108,109,110] revealed that a zigzag crack path was remained in the thin foil of NT Cu during fracture process due to the dislocation pile up against TBs and across TBs, as shown in Figure 14. The detailed analysis of MD results revealed that the mechanism of fracture involves the dislocation-mediated local thinning ahead of the crack tip instead of cleavage fracture. On one hand, the zigzag mode of crack path would cause more energy dissipation compared to a straight crack path. On the other hand, there was also small section of crack along coherent TBs which have higher fracture resistances than incoherent GBs. Therefore, TBs could increase the fracture resistances effectively [111,112,113,114,115,116,117,118,119,120,121,122]. Xiong et al. have indicated that 316L stainless steels with bundles of nanoscale deformation twins have beneficial to enhance the fracture resistance [113,114]. The results showed that the twinning bundles constrict void initiation in nano-grain matrix, coincidently resist crack propagation by acting as crack bridging ligaments.

The desirable mechanical properties, such as high strength, high ductility, high SRS, high damage tolerance, can be obtained in materials with nanotwins [66,115]. The enormous chanllenges fall in the processing of higher density of nanotwins, especially for materials with high SFE. This deserves futher deep investigations in the future.

5. Nanoprecipitate

Precipitation strengthening is a common approach to enhance the strength of materials. However, the particles in large size usually cause stress concentration due to deformation incompatibility, leading to microvoids, microcracks and even earlier fractures. Nanoprecipitate can solve this dilemma and obtain both high strength and large ductility in metals and alloys.

Liu et al. fabricated the La₂O₃ nanoparticles in the nanostructured molybdenum (Mo) alloys, which exhibit an unprecedented combination of strength and ductility [116]. The intragranular La₂O₃ nanoparticles could generate and store dislocations, prolonging ductility with high strength in nanostructured Mo alloys. The particles also play an efficient role as barriers to dislocation slipping. The TEM images showed that the dislocations are pinned by nanoparticles and generated around the nanoparticles. The spatial distribution and density of the nanoprecipitates also influence work-hardening ability. By aging treatment, nanoprecipitates with rich content of Ni, Ti and Al were dispersed in medium-Mn alloys [117]. The strength and the uniform elongation were both elevated effectively due to the nanoprecipitates [117]. The intragranular precipitates promote ductility in martensite by accumulating dislocations. Precipitation strengthening is also considered to be an effective strengthening mechanism in HEAs. Fu et al. designed and fabricated an Fe₂₅Co₂₅Ni₂₅Al₁₀Ti₁₅ dual-phase HEA that contains an FCC matrix (γ) with a small volume fraction of body-centered cubic (BCC) phase [118]. There are some primary nanoprecipitates γ′ and secondary nanoprecipitates γ* in FCC matrix. Based on the observation of in situ compression tests in the TEM, dislocation slipping was observed to be impeded by shearing both the primary precipitates γ′ and the secondary precipitates γ*. Thus, the HEA with high density of hierarchical intragranular nanoprecipitates shows an unprecedented tensile yield strength, which is ~1860 MPa.

We [119] developed an electroplating protocol in pure Ni to deploy NGs inside large grains: so-called nanodomained Ni (Figure 15c). These nanodomains can block dislocations and leave ample room for dislocation to entangle and store in the large grains, resulting in simultaneous high strength and large ductility and evading the strength–ductility trade-off. The conventional nanostructured Ni has a higher strength, but the uniform elongation decreases drastically with decreasing grain size, as shown in the curves of A, B and C in Figure 15a. Figure 15b summarizes the typical “banana curve” (trade-off) for the Ni and Cu with homogeneous structure (the blue region) by normalized yield strength and normalized uniform tensile elongation (ductility). Outside of the blue region, the green dashed line shows the data with an outstanding combination of strength and ductility for Cu and other steels with heterogeneous structures. The nanodomained Ni stands out as an exception with its NG-level strength and CG-like ductility. And the tensile stress–strain curve of the nanodomained Ni (Figure 15a, curve F) shows the higher work hardening rate than that of the Ni with other structures, which is the reason for such a large uniform elongation. High resolution post-mortem TEM observations of indicate much higher dislocation density near the boundaries of the domains (Figure 15d). The MD simulations have also confirmed this phenomenon [120].

As shown in Figure 16, moving dislocations are observed to be blocked and pinned by the domain boundaries. Although the average domain diameter is as small as about 7 nm and the volume fraction is around 2.4%, these domains appear to be stable upon tensile deformation. Such heterogeneously architected nanostructure has been proven to be a valuable strategy to evade the strength–ductility trade-off in pure metals [117,118,119,120].

6. Conclusions, Future Perspective and Challenges

In this paper, the plastic behaviors and the corresponding deformation physics for heterogeneous grain/lamellar/phase structures, gradient structure, NT structure and structure with nanoprecipitates have been reviewed. The design concept for these heterogeneous structures is to delocalize strain concentration for improving ductility through extra hardening effects. These heterogeneous structures have can increase opportunities for dislocation storage by GNDs over the homogeneous counterparts. These GNDs are generated by the strain gradients and the plastic deformation incompatibility between different domains with dramatically varying mechanical properties. Thus, unexpected high uniform elongation can be achieved for high strength metals and alloys, evading the strength–ductility trade off. These deformation mechanisms and deformation physics are applicable not only to the uniaxial loading condition but also to the dynamic and fatigue conditions.

In one hand, one may think to raise the microstructure inhomogeneity to achieve stronger strain gradients and better extra strain hardening, on the other hand the interfaces with too large microstructure inhomogeneity might not be strong enough to accommodate the high strain gradients and the high density of GNDs, resulting in a quick failure at the interfaces and a lower ductility. The size and spacing of the domains are also critical for optimizing the mechanical properties of heterogeneous structures. Smaller domains can generate more interfaces, resulting in more spaces for a higher density of GNDs and better ductility. However, too-small domains may cause the overlapping of GNDs distributions between neighboring domains, resulting in decreasing ductility. Thus, how to control the microstructure heterogeneity to obtain optimizing mechanical properties remains an unresolved issue and needs extensive experimental and theoretical efforts in the future. Moreover, manufacturing the desired microstructure with predesigned heterogeneity is a great challenge. Previous studies on the dynamic behaviors of heterogeneous structures were conducted in an “in-situ” manner; however, "in-situ" dynamic experiments with accurate measurements of temperature rise history and strain field history must be developed to better understand these dynamic processes. Experimental evidence for the fatigue behaviors of heterogeneous structures are also limited, and more research should be conducted to obtain a comprehensive understanding on fatigue mechanisms (including fatigue crack growth behaviors, cyclic softening/strengthening behaviors) in the future. Moreover, additional efforts should focus on the fracture toughness, impact toughness, superplastic behaviors and thermal stability of the heterogeneous structures.