Dislocation array reflection enhances strain hardening of a dual-phase heterostructured high-entropy alloy

Piling-ups of geometrically necessary dislocation (GND) arrays against interfaces are known to produce hetero-deformation induced (HDI) strengthening and strain hardening to enhance the strength and ductility of heterostructured materials. Here we report an interesting dislocation mechanism that can produce strong HDI hardening: consecutive reflections of GND planar piling-up arrays near the opposite phase boundaries in a heterostructured AlCoCrFeNi2 high entropy alloy (HEA). In contrast, dislocation transmission was found at grain boundaries in the fcc phase. The discovery here provides guidance for future materials design, which may improve the combination of strength and ductility of metallic materials. GRAPHICAL ABSTRACT IMPACT STATEMENT A hitherto unknown consecutive reflection of GND arrays near phase boundaries of a heterostructured HEA is observed and proposed as a key contributor to HDI hardening.


Introduction
Since the Bronze Age, metallic materials have served mankind in nearly all aspects of life. The properties of metallic materials can be adjusted by alloying and microstructure engineering, making them one of the most widely used materials today [1]. With exacerbating global warming and the energy crisis, it has become urgent to build energy-efficient transportation vehicles, which demand strong and tough materials [2]. Consequently, new classes of metallic materials such as nanostructured materials [3][4][5][6], high entropy alloys (HEAs) interaction between the heterostructured zones produces back stress in the soft zones and forward stress in the hard zones, which collectively produce hetero-deformation induced (HDI) stress, leading to HDI strengthening and strain hardening [27,28]. Specifically, geometrically necessary dislocations (GNDs) from Frank-Read dislocation sources in the soft zone glides on a slip plane and piles up against zone boundaries. This produces back stress in the soft zones to make them appear stronger. The GND pileups also exert stress concentrations on the zone boundaries, which consequently induce forward stress in the hard zones. To produce high HDI stress, it is critical to form large numbers of GND pile-ups per unit volume. Higher back stress should lead to higher HDI stress [13].
The hypoeutectic AlCoCrFeNi 2 HEA [29] is a type of heterostructured material consisting of the fcc and bcc dual-phase structure [30]. Due to the substantial atomic size mismatch of the constituent elements, strong lattice distortion and thus high lattice friction are realized to increase the dislocation density and to slow down the dislocation speed [31], which substantially improves the chance to capture dislocation-interface interactions via in-situ TEM [32][33][34]. Here we report an interesting mechanism to produce a high density of GND pile-ups, using the dual-phase AlCoCrFeNi 2 HEA as a model material. Specifically, the phase boundaries act as barriers and reflectors to GND pile-ups so that GNDs from a single Frank-Read source can be reflected several times consecutively to produce multiple GND pile-ups, which consequently produces very high HDI strain hardening. The HEA has short range ordering, which promotes planar slip to promote the GNDs pileup against the phase boundaries during the multiple reflection of the GND arrays. A unique type of interaction between GND arrays and the zone boundaries is found. More information can be found in the Supplemental materials. Figure 1(a) shows a dual-phase heterostructure consisting of alternative face-centered cubic (fcc) and bodycentered cubic (bcc) lamellae, which was formed after annealing cold-rolled AlCoCrFeNi 2 HEA at 1200°C for 1 hour. The volume fraction of the bcc phase is ∼ 30%. The bcc zone is mainly in green color in the inverse pole figure (IPF) map (Figure 1(b1)), indicating a strong (101) texture (Supplementary Figure 2), which is consistent with Ref. [30]. The bcc lamellae are mostly single crystals, with an average length ∼ 9.1 μm and width of ∼ 2.4 μm (Figure 1(b2)). In contrast, the fcc grains are equiaxed with random orientations (Figure 1(b3)). The fcc phase has an average grain size of ∼ 6.6 μm (Figure 1(b4)).

Results and discussion
Both the grain and phase boundaries in the sample are strong barriers to dislocation slip. Figure 1(c1) shows a bright field phase boundary image. Prior to tensile straining, the phase boundary is sharp and clean, and dislocation density is low in the grain interior. Figure 1(c2) and (c3) show the selected area diffraction patterns at both sides of the phase boundary, indicating an upper fcc grain and a lower bcc grain. Figure 1 There is no specific orientational relationship between fcc and bcc phases. The phase boundary is considered an incoherent interface.
In-situ TEM can provide direct observation of dynamic interactions between GNDs and the phase boundary, as well as the evolution of the GND pile-up arrays during deformation [34][35][36][37]. Figure 2(a1) to (a3) are snapshots from Supplementary Video 1 showing dislocation slip in the interior of an fcc grain. Sluggish GND slip (Dislocations I and II, marked by the green arrows) confined in a planar array is observed. According to Refs. [38][39][40], the collective trapping effect of the 'cocktail solid solution' [41], in conjunction with the massive pile-up of dislocations, slows down the motion of GNDs. Meanwhile, the dislocation III (marked by the yellow arrow) outside of the planar array stays stationary, suggesting a confined slip in certain slip planes.
TEM observations under different two-beam conditions confirmed the Burgers vectors of the dislocations in Figure 2 as a 2 < 110 > . As shown in Figure 2(b1), three dislocations, IV, V and VI, initially glide in a planar array on a (111) plane. With increasingly applied strain, the dislocation V gradually comes to a standstill, then suddenly cross-slips onto the (111) slip plane and leaves a track which slowly fades away, while the adjacent dislocations IV and VI remain on the original slip plane (Figure 2(b2) and (b3), snapshots from Supplementary Video 2). Figure 2(c1) to (c3) are sequential snapshots showing dislocation entanglements and interactions at the intersections of planar arrays. As shown in Supplementary Video 3, planar array 3 firstly approaches and collides onto planar array 2. The array 2 is then affected by both the strain fields of arrays 1 and 3. As a result, dislocations in the array 2 tangle with incoming dislocations of the array 3 to form a dislocation network containing dislocations of different Burgers vectors. As the array 3 extends forward, additional stress is imposed by its strain field to dislocations in the array 1. There is sufficient free space on the right side of the array 1. Thus, many dislocations (marked by the red arrows) in the array 1 cross-slip onto (111) planes to the right of the figure, under the resultant stress from arrays 1 and 3. Entanglements and interactions of planar arrays are deemed to contribute to superior strain hardening [42].
Phase boundaries are major obstacles to dislocation slip in dual-phase materials, playing a dominant role in strain partitioning and HDI strengthening. Here in-situ TEM observation reveals a unique dislocation interaction with phase boundaries. Figure 3(a1) is a low magnification TEM image showing dislocation interactions with phase boundaries. The dislocation slip path exhibits a zig-zag trace in the fcc phase, as marked by the green and turquoise dash lines. As plastic deformation proceeds, GNDs pile up in an array against the phase boundary, building up a local stress concentration. Eventually, the resultant local stress drives the dislocations to cross slip to an intercepting 111 plane at the phase boundary. Consecutive cross slip of the GND arrays at the interface extends the path of dislocation slip to a new direction. Each time the dislocation path encounters the phase boundary, cross slip can occur. The process can be repeated several times to eventually form the zig-zag slip path, as shown in Figure 3(a1). It is worth noting that the phase boundary is neither totally straight nor exactly parallel to the Burgers vector of the dislocations. Thus, the incoming screw dislocation has to re-align its dislocation line near the interface prior to cross slip.
The zig-zag slip path 1 resembles in some way a reflection phenomenon. The phase boundary 'reflects' incoming dislocations like a mirror, except that the reflection paths need to be on slip planes. As shown in Figure 3(a4) to (a6), the slip path 2 develops in the same way as slip path 1. Slip paths 1 and 2 are parallel and 'reflected' at the same angle by the phase boundary, thus slip path 1 intersects with slip path 2 at the positions marked by the red dots after 'reflection' in this particular case (Figure 3(a5)). Although dislocations in paths 1 and 2 may interact at the intersection, they can eventually break away and continue to glide on their original paths. The dislocation reflection phenomenon has been captured by The fcc grains are within the size range of 2-15 μm. In this grain size range, the CRSS for dislocation slip would not change much in magnitude, despite of the varied shapes of grains. Therefore, the GND reflection mechanism can be operative in all fcc grains, if the local stress reaches a critical value (Supplementary Figure 3). However, the GND reflection mechanism is a dislocation slip based mechanism, it must be affected by the grain size effect. If the grain size is too small e.g. in the ultrafine grained regime or even smaller, the CRSS for dislocation slip will be very high [5,43], and the mean free path for dislocation slip will be too small, then the GND reflection mechanism shall theoretically cease to operate. In coarse grains with sizes of a few hundred micrometers or larger, there would be many Frank-Read sources emitting dislocations simultaneously under plastic deformation. In this case, dislocations from many different sources would interact and tangle before reaching grain boundaries, thus the chance for GND reflection would be very much limited.
GND interactions with conventional grain boundaries (GBs) are different from that with phase boundaries. Figure 3(b1) to (b3) are sequential snapshots from Supplementary Video 5. Figure 3(b1) shows three parallel GND arrays encountering a GB, building up local stress concentration. As the leading dislocation approaches the GB, contrast at the GB darkens due to stress-induced strain field (Figure 3(b2)). When the leading dislocation reaches the position approximately 100 nm to the GB, the leading dislocation is suddenly absorbed by the GB at the stress concentration site, at the same time dislocations are emitted on both sides of the GB. Although dislocation lines on the other side of the GB are not very clear due to grain misorientation, our video (Supplementary Video 5) still captured the moment when a curved dislocation segment (marked by a brown arrow) with pinned ends expanding and eventually bowing out to glide on a new slip plane (colored brown in Figure 3(b3)). The reaction between the incipient dislocation array and the GB can activate a grain boundary source to emit new dislocations on the other side of the GB [44][45][46]. Such a dislocation reaction typically leaves behind a residual dislocation at the GB. Several residual dislocations may recombine to emit a new dislocation into the original grain as indicated by the blue arrow in Figure 3(b3). Figure 4(a) shows the tensile true stress-strain curve of the annealed AlCoCrFeNi 2 HEA sample. The heterostructure contributes significantly to the observed excellent strain hardening. Strain partitioning between bcc and fcc phases promotes the HDI hardening [14] on top of the conventional forest dislocation hardening [47]. The HDI stress caused by GNDs and the effective stress caused by forest dislocation hardening can be calculated [14,27,48]: where σ HDI , σ flow , σ eff , σ u and σ r are the HDI stress, flow stress, effective stress, unloading yield stress and reloading yield stress, respectively. In practice, the HDI hardening effect is manifested by the stress-strain hysteresis loops in load-unload-reload (LUR) tensile tests [14,48]. Typical stress-strain hysteresis loops are shown in Figure 4(a) and (b). The σ r and σ u can be directly measured from the hysteresis loops. Evolutions of σ HDI , σ eff and σ HDI /σ flow with applied strain are plotted in Figure 4(c). Both the HDI and effective stresses increase with increasing strain. Note that the HDI stress increases faster than the effective stress. As a result, the ratio σ HDI /σ flow also increases with the increasing strain. Apparently, σ HDI contributes more than 50% of the flow stress at all strain levels, indicating the importance of the HDI stress in the plastic deformation. Figure 3(a) shows multiple reflections of GND pileup arrays at phase boundaries, which produces multiple GND pile-ups to effectively improve HDI strain hardening. As shown in Figure 4(c), the HDI stress continues to increase with increasing applied strain. This long-lasting HDI strain hardening is in sharp contrast with those of many other heterostructured materials [13,48] (Supplementary Figure 4 and the discussion on HDI strengthening in the Supplementary materials). The HDI stress usually quickly increases with applied strain and then approaches a saturation in heterostructured materials, because when both the soft zones and hard zones are deforming plastically, the forward stress acts to soften the hard zone, which offsets the back stress hardening in the soft zones.
The strategy of multiple reflections of GND arrays has several advantages over the GND pile-ups observed in other heterostructured materials. First, it is capable to produce multiple GND pile-ups from one Frank-Read dislocation source, which multiplies the HDI stress per unit volume. Second, this strategy also distributes the stress concentration points more uniformly to avoid breaching the zone boundary by a single pile-up of GNDs. In other words, if all GNDs in a zig-zag pileup shown in Figure 3 line up in one slip plane, the stress concentration at the pile-up head might be high enough to activate dislocations in the hard zone, or possibly initiate a crack. Third, the multiple reflections of GND arrays avoided the absorption of GNDs by the zone boundaries, as reported earlier [49]. Once GNDs are absorbed by zone boundaries, they will no longer produce back stress. The continuous GND absorption by zone boundaries is one of the reasons for the ineffective HDI strengthening observed in the brass-copper layer structure [50].
Pronounced cross slip in the grain interiors helps to release the local stress concentrations (Figure 2(c1) to (c3)), contributing to the plasticity, but to little effect of HDI hardening. GNDs pile up against conventional GBs is necessary for accommodating non-homogeneous plastic strains between grains of varied orientations [51]. Adjacent grains in the same phase have the same shear modulus, thus the GB is incapable of sustaining a toohigh stress concentration imposed by the GNDs pile-up. Instead, GNDs will be absorbed by the GB, and subsequently a GB source will be activated to emit new dislocations in the adjacent grain or back to the original grain but in another slip system, as shown in Figure 3(b1) to (b3). As a result, GNDs pile-up at GBs can induce some degree of HDI stress similar to many polycrystalline materials, but apparently the HDI stress (Bauschinger effect) is very limited [52,53]. In contrast, a zone boundary can sustain a much higher stress concentration than a conventional GB. This is because a much higher stress is needed to emit new dislocations in the adjacent zone with a higher shear modulus (Koehler effect) [54] or significantly smaller grains (Hall-Petch effect) [55]. As a result, dislocations and plastic strains are contained in the soft zones by the zone boundaries, stimulating significant HDI stresses [14].
It is of scientific importance to understand how the GND arrays cross-slip at the zone boundaries. The simplest scenario is when the zone boundary is parallel to the GND Burgers vector. Since the GNDs become pure screw dislocations when they reach the zone boundary, they can cross-slip easily without creating any residual dislocations at the zone boundary, which allows continuous cross-slip. However, this is the ideal case that can rarely occur for the reflection of GND arrays. The real situation of GND array reflections in most cases is more complex.
It can be rationalized that most GND array reflections occur at zone boundaries that are not parallel to the Burgers vector. In such a scenario, the cross-slip at the zone boundary becomes impossible because once a dislocation line lies on the zone boundary, it becomes a mixed dislocation, which cannot cross-slip. The GND can cross-slip only when its dislocation line is parallel to its Burgers vector. Based on the in-situ TEM observations, we propose a mechanism that governs dislocation cross-slip near zone boundaries. As shown in Figure 5(a1), an array of GNDs glide toward a zone boundary on an incipient slip plane, and reached the zone boundary, but cannot cross-slip because the zone boundary and the Burgers vectors have an angle of θ ( Figure 5(a2)). The following GNDs may also become mixed dislocations and stay on the incipient slip plane. These GNDs exert an expelling force to incoming GNDs. As more GNDs are pushing forward, a GND (GND IV in Figure 5(a3)) may experience enough driving force to align a segment of its dislocation line parallel to its Burgers vector and thus to enable cross-slip onto the reflection plane ( Figure 5(b1)). With continuous alignment of the dislocation line, the whole GND IV can crossslip onto the reflection plane afterward ( Figure 5(b2)). As such, the GND can cross-slip gradually from one segment first and then the whole dislocation line follows to accomplish the cross-slip [56,57]. This scenario is energetically easier and statistically more probable than aligning the whole dislocation line to transform it into a pure screw dislocation before cross-slipping. After the cross-slip of the first GND, other following GNDs cross-slip in the same way, leading to the reflection of the GND array ( Figure 5(a4)).
In the above cross-slip mechanism, the reflection of GND arrays occurs at a short distance from the zone boundary. This was indeed observed in the TEM observation. As shown in Figure 5(c), a GND segment in the left green path is straightened to align parallel with its Burgers vector prior to cross slip, as marked by the blue line, which is where incipient and reflection plane meet for the cross slip to proceed ( Figure 5(d)). Hence, the actual cross-slip location is slightly away from the zone boundary. A few dislocations are also seen between the cross-slip location and the zone boundaries. These dislocations are curved and unable to cross slip, but they provide a buffer layer that makes it possible for the following GNDs to adjust their orientation for cross-slip ( Figure 5(c)). Therefore, these GNDs between the crossslip location and the zone boundary can be considered as 'cushion' dislocations. This also increases dislocation density near the zone boundaries. Note that, there could be some geometrical issues to affect the reflection trace of planar arrays. Suppose the initial array slips in a (111) plane. If the θ is an acute or obtuse angle to the initial array, the cross slip could happen on different slip planes, such as the (111) or (111) planes. Additionally, the incident planar array may even be perpendicular to the phase boundary. In this particular case, the reflection of the dislocation array may be restrained. However, based on the EBSD result in Figure 1, it has been demonstrated that there is no specific orientation relationship between the BCC and FCC phases. Thus, such a particular case could not to be dominated in the alloy.
For an individual GND pileup, cross-slip limits the local stress concentration and number of GNDs in the pile-up. The global HDI stress measured experimentally is related to the number of GND pileups multiplied by the average number of GNDs per pileup per unit volume. In other words, the global HDI stress is related to the total number of GNDs per unit volume. The GND reflection mechanism observed here produce many GND pileups from a single Frank-Read source; A reflected GND array is actually an extension of the initial GND array emitted from a Frank-Read source. Hence a few Frank-Read sources can produce a large number of GND arrays under the GND reflection mechanism, to effectively enhance the global HDI strengthening and hardening. In addition, as mentioned above, a sufficient high driving force is needed to re-align the Burgers vectors of the dislocations for cross-slip. This driving force needs to be provided by the applied stress, which provides further hardening. In other words, there is additional hardening related to the cross-slip process.
Therefore, it is desired to design alloy compositions and heterostructures to promote this mechanism. The following factors should significantly affect the operation of the multiple reflection of GND arrays. First, planar slip is a prerequisite for this mechanism to operate. It is known that low stacking fault energy (SFE) promotes planar slip [3,4]. However, if the SFE is too low, it also promotes twinning, which could complicate or even disrupt the multiple reflection of the GND arrays. Therefore, the alloy composition should be such that it promotes the planar slip, but not twinning. In other words, the twinning fault energy should be very high in the generalized planar fault energy (GPFE) curve, which can be calculated using density-functional theory (DFT) [58,59]. In addition, high lattice frictional force also promotes planar slip [60]. The AlCoCrFeNi 2 HEA in this study meets all these compositional requirements [30,61].
The second factor is the strength difference across the zone boundary. The higher the strength difference, the harder it is for the GNDs to transmit across the zone boundary. The strengths of the zones can be affected by microstructures and textures [28]. The strength differences by differences in dislocation density, precipitation, solution hardening, grain size, etc. [43]. Texture may affect the resolved stresses on dislocation slip systems. If both soft and hard zones are textured in a way that the easy slip systems of both zones are aligned with a low misorientation angle, the chance for dislocation transmission across zone boundaries will be high [62], which lowers the probability for GND array reflection. In the current case, the hard zones are bcc phase with strong (101) texture, but the soft zones are fcc phase with randomly oriented grains. Therefore, the {110}111 slip systems of the bcc grains are in most cases oriented away from the {111}1 N 10 slip systems of the fcc grains at the zone boundaries, as shown in Figure 1(b3, d1, d2). This is one of the reasons that causes pronounced reflection of GND arrays and thus effective HDI strengthening effect.

Summary
In summary, an interesting mechanism involving multiple GND array reflection in the soft zone is found effective in producing HDI strain hardening to maintain good ductility. The GND reflection can be at the zone boundary if it is parallel to the GND Burgers vector, but otherwise it likely occurs at a distance from the zone boundary. There may be high density of cushioning dislocations between the reflection site and the zone boundary. The factors that promote multiple GND array reflection include low stacking fault energy, short-range order of solute atoms, solute atom clustering, and high strength difference across the phase boundaries. These findings provide basic guidance for designing alloys and heterostructures to employ this mechanism for superior strength and ductility.

Disclosure statement
No potential conflict of interest was reported by the author(s).