*Review* **Twin-Related Grain Boundary Engineering and Its Influence on Mechanical Properties of Face-Centered Cubic Metals: A Review**

**Xiaowu Li 1,2,\* , Xianjun Guan 1,3, Zipeng Jia 1,3, Peng Chen 1,3 , Chengxue Fan 1,3 and Feng Shi 1,3**


**Abstract:** On the basis of reiterating the concept of grain boundary engineering (GBE), the recent progress in the theoretical models and mechanisms of twin-related GBE optimization and its effect on the mechanical properties is systematically summarized in this review. First, several important GBE-quantifying parameters are introduced, e.g., the fraction of special grain boundaries (GBs), the distribution of triple-junctions, and the ratio of twin-related domain size to grain size. Subsequently, some theoretical models for the GBE optimization in face-centered cubic (FCC) metals are sketched, with a focus on the model of "twin cluster growth" by summarizing the in-situ and quasi-in-situ observations on the evolution of grain boundary character distribution during the thermal-mechanical process. Finally, some case studies are presented on the applications of twin-related GBE in improving the various mechanical properties of FCC metals, involving room-temperature tensile ductility, hightemperature strength-ductility match, creep resistance, and fatigue properties. It has been well recognized that the mechanical properties of FCC materials could be obviously improved by a GBE treatment, especially at high temperatures or under high cyclic loads; under these circumstances, the materials are prone to intergranular cracking. In short, GBE has tremendous potential for improving the mechanical properties of FCC metallic materials, and it is a feasible method for designing highperformance metallic materials.

**Keywords:** grain boundary engineering; mechanical property; face-centered cubic metal; special grain boundary; annealing twin

### **1. Introduction**

Early in the 1880s, Sorby first observed with an optical microscope that the microstructure of a blister steel was composed of numerous grains of various shapes and the grain boundaries (GBs) between adjoining grains. Since then, materials researchers have paid an increasing amount of attention to the GBs and interfaces (including phase boundaries) to explore a well-established method in materials design and performance improvement [1]. After the past ~140 years of study, the understanding of GBs and interfaces has significantly improved. It is now well recognized that the GB is an important component of the microstructure in polycrystalline materials and that the number, type, and distribution of GBs play critical roles in the materials' properties [2–6].

In addition, when it comes to the mechanical properties, GBs can act as the main obstacle to dislocation slip during plastic deformation, and thus become important sources of strength and work hardening of polycrystalline metallic materials [7,8]. Meanwhile, GBs may also be the preferred location for crack nucleation due to the weakened bonding strength between the atoms on both sides of the structurally disordered interface and the

**Citation:** Li, X.; Guan, X.; Jia, Z.; Chen, P.; Fan, C.; Shi, F. Twin-Related Grain Boundary Engineering and Its Influence on Mechanical Properties of Face-Centered Cubic Metals: A Review. *Metals* **2023**, *13*, 155. https:// doi.org/10.3390/met13010155

Academic Editor: Sadahiro Tsurekawa

Received: 20 December 2022 Revised: 4 January 2023 Accepted: 8 January 2023 Published: 12 January 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

higher stress concentration derived from the pile-up of dislocations [9–13]. In addition, most noteworthy, the structural order of various GBs is significantly different [14–16], so that the capacity of various GBs to resist intergranular cracks is also different [10,17–20]. Therefore, cracking is most likely to occur during plastic deformation at or along ordinary random high-angle GBs (RHAGBs) with higher structural disorder and interface energy, while special GBs with low energy (will be introduced in detail later) can generally maintain a high resistance to cracking [10,11,13,21,22].

Therefore, many researchers have made great efforts to reveal the influence of grain boundary character distribution (GBCD) optimization (also known as grain boundary engineering, or GBE) on the mechanical properties, e.g., tensile property, creep resistance, and fatigue resistance [6,12,13,23–25], and some praiseworthy research findings have been achieved in this context. While the study on the GBE approach to improving the mechanical properties of metallic materials is in progress, on the basis of further clarifying the concept of GBE, this review focuses on the latest progress in the theoretical models and mechanisms of GBE optimization and its impact on the mechanical properties. It is hoped that the summary of the recent studies of GBE may provide some valuable references for the development of advanced metallic materials that exhibit high resistances to GBE-related damage in their practical applications.

#### **2. Twin-Related GBE**

The main idea of GBE evolves from the concept of "GB design and control" proposed by Watanabe [2,3,26]. In addition, after nearly 50 years of development, GBE has emerged as a mature method that can be applied to a variety of metallic materials, such as copper alloys [6,12,27], nickel-based alloys [28–31], austenitic stainless steels [9,10,20,32,33], and lead alloys [34,35]. These materials generally have the common characteristic that their stacking fault energies are relatively low and annealing twins (ATs) are easily formed during the thermal-mechanical process (TMP); based on this, the so-called method of twin-related GBE has been well developed.

The twin-related GBE is to induce a large number of AT boundaries (or ATs), namely Σ3 GBs, in face-centered cubic (FCC) metals by the means of thermal-mechanical treatment, and other low-Σ coincidence site lattice (CSL) GBs can be further induced through the mutual interactions between two annealing twins or even between ATs and ordinary RHAGBs, thus blocking the connectivity of RHAGBs [6,36–39]. Additionally, some previous studies [10,20,40,41] have revealed that the low-ΣCSL GBs introduced by twin-related GBE exhibit a high degree of structural stability and are not prone to second-phase precipitation during medium- to high temperature annealing or welding processes. Thus, the low-ΣCSL GBs, especially in the welding heat affected zone, often exhibit a higher corrosion resistance in corrosive environments compared with ordinary RHAGBs [42]. Moreover, many investigations [9,10,17,21,43] have substantiated that twin-related GBE is an effective way to improve the intergranular corrosion resistance, intergranular stress corrosion cracking resistance, and other properties that are closely related to GBs in some FCC metals.

Consequently, the key to the realization of GBE is to induce the formation of as many annealing twins as possible during the TMP. In addition, it should be noted that only in FCC metallic materials deformed by planar-slipping of dislocations can a large number of ATs be easily induced [6]. Therefore, the twin-related GBE can only be availably applied to some FCC metallic materials with low stacking fault energy or numerous short-range order structures [6,9,41,44–46]. Many important engineering materials, such as austenitic stainless steel, nickel-based alloys, and copper alloys, are involved in this kind of material, so the twin-related GBE has received widespread attention.

#### **3. GBE-Quantifying Parameters**

As mentioned above, the main purpose of twin-related GBE is to optimize the GBCD in materials, namely, increasing the fraction of low-ΣCSL GBs and blocking the connectivity of RHAGBs. In this case, it is significantly important to know how to quantify the degree of GBCD optimization. To this end, several important GBE-quantifying parameters have been successively proposed, as summarized below.

#### *3.1. Fraction of Special GBs*

The fraction of special GBs (*f* SBs) is defined by the ratio of the length of special GBs to the total length of all GBs [20], which was most widely used in the evaluation of GBE optimization. In the statistics of *f* SBs, the CSL GBs with Σ ≤ 29 are generally regarded as the special GBs [47–49], since these types of GBs have lower energy [7,50,51], and exhibit some unique performances, e.g., lower diffusivity, lower resistivity, lower sensitivity to solute atom segregation, and higher resistance to GB sliding and crack initiation [7].

Furthermore, with the deepening of GBE studies, it has been recognized that, apart from the *f* SBs, the role of special GBs is also closely related to their location, i.e., out of or in networks of random GBs. Lehockey et al. [52] reported that the coherent Σ3 GBs were dominant in all special GBs in FCC metals with low stacking fault energy; however, most of these coherent Σ3 GBs were localized outside of RHAGB networks and cannot make any positive contributions to the tailoring of RHAGB networks. Naturally, it is difficult for these coherent Σ3 GBs to impede the intergranular stress corrosion along RHAGBs. Therefore, Lehockey et al. [52] proposed the concept of effective special GBs and suggested that only the special GBs that can block the network connectivity of the random high-angle GBs are effective in preventing the failure of materials along GBs. However, the difference in the anti-cracking properties of the same type of special GBs was even sometimes reported [20,53], so that there was as yet no unified opinion on the definition of effective special GBs. Further, it may be related to the fact that the interface index is still not considered in the current electron backscatter diffraction (EBSD) characterization. Thus, the further developments in the theory of GBs and the relevant characterization methods need to be emphasized for the better application of GBE.

#### *3.2. Distribution of Triple-Junctions*

The ultimate purpose of twin-related GBE treatment is to interrupt the network connectivity of RHAGBs and thus hinder crack propagation along RHAGBs. Therefore, how to quantify the blocking of RHAGB by the GBCD optimization is of great significance for GBE. Kumar et al. [54] proposed that the connectivity of RHAGBs can be evaluated by the statistics on the distribution of triple-junctions, which are classified as different types according to the number of special GBs they contain. For example, triple-junctions with zero, one, two, and three low-energy special CSL GBs are classified as J0, J1, J2, and J3 junctions, respectively. Among these triple-junctions, the RHAGBs are interconnected with each other at the J0 and J1 junctions, and thereby cracks can pass through the junctions without hindrance and propagate along the RHAGBs. In contrast, J3 junctions are generally too stable to meet the conditions for crack nucleation and propagation. Only at the J2 junctions can the cracks be captured by special GBs. Hence, the capture probability of cracks can be quantified by statistically calculating the distribution of *f* J2/(1 − *f* J3), where *f* J2 and *f* J3 represent the proportion of J2 and J3 junctions, respectively. Several experimental studies [6,20,55] have confirmed that there indeed exists a strongly positive correlation between the *f* J2/(1 − *f* J3) and the blocking degree of RHAGB connectivity in FCC metals.

### *3.3. Ratio of Twin Related Domain Size to Grain Size*

In the study on the mechanism of twin-related GBE, it has recently been realized that the formation of annealing twins during TMP plays an important role in increasing the *f* SBs and interrupting the network connectivity of RHAGBs, since efficiently inducing the formation of ATs can not only directly increase the fraction of special GBs but also be beneficial to decreasing the grain size. Furthermore, the quasi-in situ EBSD observation on the evolution of GBCD further indicated that the formation and growth of ATs indeed played a critical role in GBCD optimization [36]. For example, the *f* SBs in a GBE- treated material are directly related to the number of ATs in a twin-related domain (TRD), which is defined as Σ3 *n* twin cluster (namely, a large cluster of spatially adjacent twin-related grains). In light of this, Barr et al. [36] suggested that the ratio *v* of TRD size to grain size should be another important indicative indicator of GBE in polycrystalline materials. material are directly related to the number of ATs in a twin-related domain (TRD), which is defined as Σ3*n* twin cluster (namely, a large cluster of spatially adjacent twin-related grains). In light of this, Barr et al. [36] suggested that the ratio *v* of TRD size to grain size should be another important indicative indicator of GBE in polycrystalline materials.

formation of ATs can not only directly increase the fraction of special GBs but also be beneficial to decreasing the grain size. Furthermore, the quasi-in situ EBSD observation on the evolution of GBCD further indicated that the formation and growth of ATs indeed played a critical role in GBCD optimization [36]. For example, the *f*SBs in a GBE- treated

### **4. Mechanism of GBCD Optimization—"Twin Cluster Growth" Model**

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At the turn of the century, the study on the mechanism of GBCD optimization in FCC metallic materials has drawn immense attention from researchers, and several theoretical models for GBE have been proposed in succession, as shown in Figure 1. As a result, the "Σ3 GB regeneration model" [56] indicates that the coherent AT boundaries in different recrystallized grains can interact with each other to induce the formation of Σ9 GBs, and then the mobile Σ9 GBs further interact with some other Σ3 GBs, thus inducing the formation of other low-energy SBs (Figure 1a). The "high ΣCSL GB decomposition model" [57] suggests that the low-ΣCSL SBs can be derived from the decomposition of high-ΣCSL GBs (Figure 1b). According to the "special fragment model" [17], the GBCD optimization is mainly realized by the SB fragments caused by AT emitting in the RHAGB network (Figure 1c). The "incoherent Σ3 GB migration model" [58] indicates that the formation of SBs is mainly achieved by the migration of incoherent Σ3 GBs (Figure 1d). However, even though these models can explain some laws of GBCD evolution in FCC metals with low stacking fault energy to a certain extent, there still exist some obvious inadequacies due to the lack of understanding of the microstructure evolution during the TMP. On the basis of summarizing the recent in situ or quasi-in situ observations on the microstructure evolution of FCC metals, the "twin cluster growth" model is further introduced below. **4. Mechanism of GBCD Optimization—"Twin Cluster Growth" Model**  At the turn of the century, the study on the mechanism of GBCD optimization in FCC metallic materials has drawn immense attention from researchers, and several theoretical models for GBE have been proposed in succession, as shown in Figure 1. As a result, the "Σ3 GB regeneration model" [56] indicates that the coherent AT boundaries in different recrystallized grains can interact with each other to induce the formation of Σ9 GBs, and then the mobile Σ9 GBs further interact with some other Σ3 GBs, thus inducing the formation of other low-energy SBs (Figure 1a). The "high ΣCSL GB decomposition model" [57] suggests that the low-ΣCSL SBs can be derived from the decomposition of high-ΣCSL GBs (Figure 1b). According to the "special fragment model" [17], the GBCD optimization is mainly realized by the SB fragments caused by AT emitting in the RHAGB network (Figure 1c). The "incoherent Σ3 GB migration model" [58] indicates that the formation of SBs is mainly achieved by the migration of incoherent Σ3 GBs (Figure 1d). However, even though these models can explain some laws of GBCD evolution in FCC metals with low stacking fault energy to a certain extent, there still exist some obvious inadequacies due to the lack of understanding of the microstructure evolution during the TMP. On the basis of summarizing the recent in situ or quasi-in situ observations on the microstructure evolution of FCC metals, the "twin cluster growth" model is further introduced below.

**Figure 1.** Theoretical models for the GBCD optimization in FCC metals Adopted from Refs. [17,56– 58] **Figure 1.** Theoretical models for the GBCD optimization in FCC metals Adopted from Refs. [17,56–58].

Additionally, through the quasi-in situ or in situ observation of the GBCD evolution during the TMP of some FCC metals (e.g., 304, 316L austenitic stainless steels, and copper alloys) [6,36,59], it has been well recognized that the microstructural evolution during GBE treatment is mainly completed by strain-induced GB migration. For example, the Additionally, through the quasi-in situ or in situ observation of the GBCD evolution during the TMP of some FCC metals (e.g., 304, 316L austenitic stainless steels, and copper alloys) [6,36,59], it has been well recognized that the microstructural evolution during GBE treatment is mainly completed by strain-induced GB migration. For example, the ordinary RHAGBs driven by the stored strain energy migrate from the twin clusters to the deformed matrix during the annealing process of the TMP, and ATs are constantly nucleated behind the migrating GBs and grow up with the migration of GBs, as shown in Figure 2. Therefore, inducing the nucleation of as many ATs as possible is crucial to realizing the optimization

of GBCD in the process. First, the nucleation of ATs, as mentioned above, can directly increase the *f* SBs. Second, ATs with different orientations nucleated behind RHAGBs may interact with each other, thus inducing other low-energy CSL special GBs (see Figure 2b,c). Finally, the formation of ATs can induce the structural transition of migrating RHAGBs from disorder to order, which are implanted in the network of RHAGBs and thus interrupt the network connectivity. izing the optimization of GBCD in the process. First, the nucleation of ATs, as mentioned above, can directly increase the *f*SBs. Second, ATs with different orientations nucleated behind RHAGBs may interact with each other, thus inducing other low-energy CSL special GBs (see Figure 2b,c). Finally, the formation of ATs can induce the structural transition of migrating RHAGBs from disorder to order, which are implanted in the network of RHAGBs and thus interrupt the network connectivity.

ordinary RHAGBs driven by the stored strain energy migrate from the twin clusters to the deformed matrix during the annealing process of the TMP, and ATs are constantly nucleated behind the migrating GBs and grow up with the migration of GBs, as shown in Figure 2. Therefore, inducing the nucleation of as many ATs as possible is crucial to real-

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**Figure 2.** (**a**,**b**) Evolution of the twin cluster during the annealing process, where the dashed line indicates the interface between the existing twin cluster and the deformed matrix; (**c**) schematic of the formation of the AT boundary during the evolution of the twin cluster front and the formation of Σ9 GB (the inset illustrates the 111 plane trace for the growing grain (A). adopted from Ref. [36]. **Figure 2.** (**a**,**b**) Evolution of the twin cluster during the annealing process, where the dashed line indicates the interface between the existing twin cluster and the deformed matrix; (**c**) schematic of the formation of the AT boundary during the evolution of the twin cluster front and the formation of Σ9 GB (the inset illustrates the 111 plane trace for the growing grain (A). adopted from Ref. [36].

Recent studies [6,55] have shown that the deformation microstructures, including stacking faults, planar-slip dislocation structures, and deformation twins, exhibit distinctive effects on the evolution of twin clusters and thus on the GBCD optimization, as evidenced by the experimental findings of Cu-16at.% Al alloys in Figure 3. The stacking faults and planar-slip dislocation structures are fairly beneficial to the GBCD optimization, for which the formation of ATs can be induced by the ordered defects in a sequence of closely packed atomic planes at the front end of a growing twin cluster. On the contrary, deformation twins hinder the growth of twin clusters, thus impairing GBCD optimization. Therefore, the optimal prior strain for the GBCD optimization should be around the threshold strain for the appearance of deformation twins in FCC metals. Recent studies [6,55] have shown that the deformation microstructures, including stacking faults, planar-slip dislocation structures, and deformation twins, exhibit distinctive effects on the evolution of twin clusters and thus on the GBCD optimization, as evidenced by the experimental findings of Cu-16at.% Al alloys in Figure 3. The stacking faults and planar-slip dislocation structures are fairly beneficial to the GBCD optimization, for which the formation of ATs can be induced by the ordered defects in a sequence of closely packed atomic planes at the front end of a growing twin cluster. On the contrary, deformation twins hinder the growth of twin clusters, thus impairing GBCD optimization. Therefore, the optimal prior strain for the GBCD optimization should be around the threshold strain for the appearance of deformation twins in FCC metals.

In addition, some low ΣCSL GBs can also be formed when two separate twin cluster migration fronts meet together during the TMP [36,59]. These special GBs must be located in the network of random high-angle GBs, which can effectively block the connectivity of RHAGB networks.

**Figure 3.** Influence of deformation microstructures on the GBCD optimization of the Cu-16at.%Al alloy (**a**) Variation of GBE-quantifying parameters (a1: *f*SBs, a2: ratio of twin- related domain size to grain size, a3: triple-junction distribution) with the reduction ratio; (**b**) deformation microstructures at low (3%, b1), optimal (7%, b2), and high (20%, b3) reductions; (**c**) quasi-in situ EBSD observations on the evolution of microstructures during TMP treatment at an optimal stain (7% reduction, c1) and annealing at 723 K for 12 h (c2) and 36 h (c3) . adopted from Ref. [6] **Figure 3.** Influence of deformation microstructures on the GBCD optimization of the Cu-16at.%Al alloy (**a**) Variation of GBE-quantifying parameters (a<sup>1</sup> : *f* SBs, a<sup>2</sup> : ratio of twin- related domain size to grain size, a<sup>3</sup> : triple-junction distribution) with the reduction ratio; (**b**) deformation microstructures at low (3%, b<sup>1</sup> ), optimal (7%, b<sup>2</sup> ), and high (20%, b<sup>3</sup> ) reductions; (**c**) quasi-in situ EBSD observations on the evolution of microstructures during TMP treatment at an optimal stain (7% reduction, c<sup>1</sup> ) and annealing at 723 K for 12 h (c<sup>2</sup> ) and 36 h (c<sup>3</sup> ). Adopted from Ref. [6].

In addition, some low ΣCSL GBs can also be formed when two separate twin cluster migration fronts meet together during the TMP [36,59]. These special GBs must be located in the network of random high-angle GBs, which can effectively block the connectivity of RHAGB networks. Figure 4 shows the schematic diagram of the "twin cluster growth" model obtained by summing up the above research results. In the model, the ATs in twin clusters are mainly induced by the planar deformation microstructures, including stacking faults and planar dislocation structures, which are the main source of special GBs. For example, once the stacking faults in deformation microstructures encounter migrating RHAGBs, can they strongly affect a sequence of close-packed planes of recrystallizing grain and induce the transformation from a regular sequence (… ABC …) to an inverse sequence (… CBA …), as displayed in Figure 4. This is because there is a ሾ112തሿ displacement between atoms in stacking faults and in perfect crystal. The displacement can effectively reduce the necessary energy of twinning, i.e., the stacking faults can provide excessive activation energy for twinning [36,59]. Furthermore, in a twin cluster, ATs with different orientations interact with each other as they grow with the migration of RHAGBs, thus inducing some Figure 4 shows the schematic diagram of the "twin cluster growth" model obtained by summing up the above research results. In the model, the ATs in twin clusters are mainly induced by the planar deformation microstructures, including stacking faults and planar dislocation structures, which are the main source of special GBs. For example, once the stacking faults in deformation microstructures encounter migrating RHAGBs, can they strongly affect a sequence of close-packed planes of recrystallizing grain and induce the transformation from a regular sequence ( . . . ABC . . . ) to an inverse sequence ( . . . CBA . . . ), as displayed in Figure 4. This is because there is a *<sup>a</sup>* 6 - 112 displacement between atoms in stacking faults and in perfect crystal. The displacement can effectively reduce the necessary energy of twinning, i.e., the stacking faults can provide excessive activation energy for twinning [36,59]. Furthermore, in a twin cluster, ATs with different orientations interact with each other as they grow with the migration of RHAGBs, thus inducing some other special GBs. Further, at the final stage of twin cluster evolution, the intersection between separate twin clusters also induces certain special GBs. Finally, the GBCD optimization of FCC metals is fully realized by the growth of twin clusters.

other special GBs. Further, at the final stage of twin cluster evolution, the intersection between separate twin clusters also induces certain special GBs. Finally, the GBCD optimi-

zation of FCC metals is fully realized by the growth of twin clusters.

Figure 2).

**Figure 4.** Schematic diagram of the "twin cluster growth" model for the GBCD optimization in FCC metals. **Figure 4.** Schematic diagram of the "twin cluster growth" model for the GBCD optimization in FCC metals.

During the growth of twin clusters, some non-symemtric low ΣCSL GBs can also migrate in one twin cluster, such as incoherent Σ3 GBs, can reduce the interfacial energy by interacting with other special GBs in the cluster [60–62]. However, such behavior is not necessarily conducive to the increase of *f*SBs (e.g., the disappearance of the AT boundary in

**5. Influence of GBCD Optimization on Tensile Properties**  In polycrystalline metals, the fundamental parameters for evaluating the tensile properties, such as yield strength, ultimate strength, and uniform elongation, are closely related to their microstructures. For example, the well-known fine-grain strengthening (or GB strengthening) can not only effectively improve the strength but also optimize the uni-During the growth of twin clusters, some non-symemtric low ΣCSL GBs can also migrate in one twin cluster, such as incoherent Σ3 GBs, can reduce the interfacial energy by interacting with other special GBs in the cluster [60–62]. However, such behavior is not necessarily conducive to the increase of *f* SBs (e.g., the disappearance of the AT boundary in Figure 2).

#### form elongation. However, there also exists a unique effect of GBCD optimization on the tensile properties of metallic materials. Further, to eliminate the influences of precipita-**5. Influence of GBCD Optimization on Tensile Properties**

tion, phase transformation, and other special microstructures, some stable single-phase FCC metallic materials, such as austenitic stainless steel, pure copper, and copper alloys, have been selected as target materials to systematically study the influence of GBCD optimization on their tensile properties [6,12,63]. *5.1. Influence of GBCD Optimization on Room-Temperature Tensile Properties*  On the premise of a same-level grain size, the influence of GBCD optimization on the yield strength of single-phase FCC metals, such as austenitic stainless steel and copper alloys [6,63], can be negligible, while the influence on the ultimate strength is related to the role that different types of GBs play in the behavior of dislocation slipping. Moreover, In polycrystalline metals, the fundamental parameters for evaluating the tensile properties, such as yield strength, ultimate strength, and uniform elongation, are closely related to their microstructures. For example, the well-known fine-grain strengthening (or GB strengthening) can not only effectively improve the strength but also optimize the uniform elongation. However, there also exists a unique effect of GBCD optimization on the tensile properties of metallic materials. Further, to eliminate the influences of precipitation, phase transformation, and other special microstructures, some stable single-phase FCC metallic materials, such as austenitic stainless steel, pure copper, and copper alloys, have been selected as target materials to systematically study the influence of GBCD optimization on their tensile properties [6,12,63].

#### the mode of dislocation slipping is also different in various materials due to differences in *5.1. Influence of GBCD Optimization on Room-Temperature Tensile Properties*

stacking fault energy, short-range order, and friction stress [44,64]. Additionally, for the FCC materials with an extremely low stacking fault energy, a perfect dislocation is very likely to dissociate into two partial dislocations (extended dislocations) that are separated by the stacking fault, and the two partial dislocations are On the premise of a same-level grain size, the influence of GBCD optimization on the yield strength of single-phase FCC metals, such as austenitic stainless steel and copper alloys [6,63], can be negligible, while the influence on the ultimate strength is related to the role that different types of GBs play in the behavior of dislocation slipping. Moreover, the mode of dislocation slipping is also different in various materials due to differences in stacking fault energy, short-range order, and friction stress [44,64].

Additionally, for the FCC materials with an extremely low stacking fault energy, a perfect dislocation is very likely to dissociate into two partial dislocations (extended dislocations) that are separated by the stacking fault, and the two partial dislocations are constrained to move in a slip plane and cannot cross slip, so that their deformation behavior

is generally dominated by the planar slip of dislocations and deformation twinning [65,66]. It is well known that the special GBs are high-angle GBs with low Miller indices, a small disorder degree, and low interfacial energy [51,67]. The slip planes on both sides of the interface are often continuous but with a certain turning angle, which allows some dislocations to slip across the interface. However, it must be noted that dislocations in FCC metals can slip only after the partial dislocations recombine into a perfect dislocation. According to the inverse relationship between the equilibrium width of an extended dislocation and the stacking fault energy [7], dislocations in FCC metals with an extremely low stacking fault energy are not so easy to slip across the special GBs. In this case, the functions (in terms of mechanical behavior) of special GBs are similar to those of ordinary RHAGBs. Figure 5 shows a case study regarding the influence of GBE on the roomtemperature mechanical properties of Cu-16at.% Al alloy with an extremely low stacking fault energy (6 mJ/m<sup>2</sup> ). As a result, the GBE treatment has little effect on the tensile strength of the Cu-16at.% Al alloy at room temperature (Figure 5a), but it improves the ductility to a certain extent due to the fact that special GB can improve the deformation uniformity, the capacity of maintainable work hardening, and the resistance to intergranular cracking (Figure 5b) [6]. ior is generally dominated by the planar slip of dislocations and deformation twinning [65,66]. It is well known that the special GBs are high-angle GBs with low Miller indices, a small disorder degree, and low interfacial energy [51,67]. The slip planes on both sides of the interface are often continuous but with a certain turning angle, which allows some dislocations to slip across the interface. However, it must be noted that dislocations in FCC metals can slip only after the partial dislocations recombine into a perfect dislocation. According to the inverse relationship between the equilibrium width of an extended dislocation and the stacking fault energy [7], dislocations in FCC metals with an extremely low stacking fault energy are not so easy to slip across the special GBs. In this case, the functions (in terms of mechanical behavior) of special GBs are similar to those of ordinary RHAGBs. Figure 5 shows a case study regarding the influence of GBE on the room-temperature mechanical properties of Cu-16at.% Al alloy with an extremely low stacking fault energy (6 mJ/m2). As a result, the GBE treatment has little effect on the tensile strength of the Cu-16at.% Al alloy at room temperature (Figure 5a), but it improves the ductility to a certain extent due to the fact that special GB can improve the deformation uniformity, the capacity of maintainable work hardening, and the resistance to intergranular cracking (Figure 5b) [6].

constrained to move in a slip plane and cannot cross slip, so that their deformation behav-

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**Figure 5.** Effect of GBCD optimization on the room-temperature tensile properties of the Cu-16at.% Al alloy (**a**) Comparisons of the tensile properties of non-GBE and GBE samples (**b**) Influences of GBE on the deformation (b3, b4) and cracking (b1, b2) behaviors adopted from Ref. [6] **Figure 5.** Effect of GBCD optimization on the room-temperature tensile properties of the Cu-16at.% Al alloy (**a**) Comparisons of the tensile properties of non-GBE and GBE samples (**b**) Influences of GBE on the deformation (b<sup>3</sup> , b<sup>4</sup> ) and cracking (b<sup>1</sup> , b<sup>2</sup> ) behaviors adopted from Ref. [6].

In materials with a high stacking fault energy and numerous short-range order structures, their deformation mode is still dominated by planar slip of dislocations because of the "glide plane softening" effect [68]. However, the dislocations in such materials are generally perfect dislocations or extended dislocations with a low width. As mentioned above, it is much easier for such dislocations to propagate across special GBs, which is equivalent to an increase in the average free path of dislocations [68]. According to the Kocks-Mecking model [69], the increment rate of dislocations reduces with the increase of the dislocation free path, and thereby, the work hardening behavior of these materials should be lowered by the GBCD optimization. Therefore, the ultimate tensile strength of such materials may be reduced to a certain extent after GBE treatment despite an improvement in ductility, which still needs to be further confirmed experimentally.

It is worth noting that, regardless of any materials, the destruction of the RHAGB network by special GBs should be beneficial to inhibit crack propagation, which is conducive to the improvement of ductility.

#### *5.2. Influence of GBCD Optimization on High-Temperature Tensile Properties*

Due to the continuous progress of socioeconomics, more attention has been paid to the performance of materials in some harsh environments. For instance, the mechanical performance of metallic materials at high temperatures has been particularly emphasized because it involves several important livelihood and national defense industries, such as nuclear power, aviation, and aerospace.

Previous studies [70,71] indicated that the stacking fault energy of metallic materials increased as the environmental temperature elevated, which induced the dislocation slipping mode to change from planar slip to wavy slip. Accordingly, the probability of dislocation recovery would be significantly increased, thus weakening the work-hardening capacity of materials. In addition, as the temperature reaches a high level, the dynamic recrystallization would also happen in metallic materials. Consequently, the appearance of dynamic recrystallization further increases the consumption of dislocations. Further, dislocation recovery and dynamic recrystallization are important factors causing hightemperature softening. In fact, these two unfavorable factors are closely related to the GBCD in materials. For example, due to the lower ability of RHAGBs to channel dislocation slip, the strain or stress concentration tends to happen near the ordinary RHAGBs during plastic deformation, which results in a rapid increase in the strain energy. On the one hand, the high density of dislocations gathered near RHAGBs, especially under the influence of high temperature, would cause a stronger dynamic recovery behavior, thus inducing a higher softening behavior. On the other hand, the high strain energy provides an extra driving force for the dynamic recrystallization occurring at GBs, which further aggravates the softening phenomenon. As a result, the high *f* SBs introduced by GBE treatment can effectively weaken these two adverse effects occurring at GBs.

The reason that GBE-induced special GBs are capable of weakening the recovery of dislocations is due to the fact that the lower interfacial energy, coupled with the lower lattice distortion, will induce more moving dislocations to slip across special GBs [12], thereby reducing the local density of dislocations near the GBs. Meanwhile, GBE can reduce the Gibbs free energy of materials and thus inhibit the nucleation and growth of recrystallized grains at random high-angle GBs under high-temperature deformation, which is the major reason why GBE can weaken the dynamic recrystallization. Figure 6 shows our recent work about the influence of GBE on the mechanical properties of a Cu-16at.% Al alloy at a high temperature of 723 K and different strain rates [12]. As a result, due to the reasons above mentioned, the high-temperature strength and ductility of FCC metals (e.g., Cu-16at.%Al alloy) can be synchronously improved by a GBE treatment (Figure 6a) under the premise that dynamic recovery and recrystallization occurs more easily at a lower strain rate of 10−<sup>4</sup> s −1 (Figure 6(b2)), and the corresponding evidences for the suppressive effects of GBE on the GB cracking and dynamic recrystallization at a lower strain rate of 10−<sup>4</sup> s −1

are given, respectively, in Figure 6(c1,c2) (inverse pole figure maps) and Figure 6(c3,c4) (TEM images). strain rate of 10−4 s−1 are given, respectively, in Figure 6(c1,c2) (inverse pole figure maps) and Figure 6(c3,c4) (TEM images).

**Figure 6.** Influence of GBE on the tensile properties and deformation behavior of Cu-16at.% Al alloy at 723 K and at different strain rates. Comparisons of GBCD (**a**) and tensile property (**b**) between GBE and non-GBE samples, and the experimental evidence for the suppressive effects of GBE on the GB cracking (inverse pole figure maps c1,c2) and dynamic recrystallization (TEM images c3, c4). adopted from Ref. [12] **Figure 6.** Influence of GBE on the tensile properties and deformation behavior of Cu-16at.% Al alloy at 723 K and at different strain rates. Comparisons of GBCD (**a**) and tensile property (**b**) between GBE and non-GBE samples, and the experimental evidence for the suppressive effects of GBE on the GB cracking (inverse pole figure maps c<sup>1</sup> ,c2 ) and dynamic recrystallization (TEM images c<sup>3</sup> , c<sup>4</sup> ). adopted from Ref. [12].

#### **6. Influence of GBCD Optimization on Creep Properties**

As the service temperature exceeds half of the melting point, the creep will generally become a crucial threat to the service safety of polycrystalline metallic materials. It is well known that the creep of metallic materials mainly originates from dislocation-climbing and GB-slipping [8]. Apparently, there is a great difference in the structural stability of various types of GBs under high-temperature deformation. In this case, the resistance of various GBs to dislocation slip should be different. Therefore, the GBE treatment is bound to have a certain impact on the creep resistance of polycrystalline metallic materials. various GBs to dislocation slip should be different. Therefore, the GBE treatment is bound to have a certain impact on the creep resistance of polycrystalline metallic materials. Firstly, the lowered Gibbs free energy in GBE samples signifies that a relatively

As the service temperature exceeds half of the melting point, the creep will generally become a crucial threat to the service safety of polycrystalline metallic materials. It is well known that the creep of metallic materials mainly originates from dislocation-climbing and GB-slipping [8]. Apparently, there is a great difference in the structural stability of various types of GBs under high-temperature deformation. In this case, the resistance of

*Metals* **2023**, *13*, x FOR PEER REVIEW 11 of 19

**6. Influence of GBCD Optimization on Creep Properties** 

Firstly, the lowered Gibbs free energy in GBE samples signifies that a relatively higher activation energy for creep is needed under a high-temperature constant load. Secondly, the higher lattice order of the special GBs suppresses the dislocation decomposition at the GBs and thus significantly inhibits the GB slipping [72]. Finally, it is difficult to form cavities on the interface of special GBs by the decomposition of dislocations at high temperature, which greatly improves the resistance to creep failure in GBEed materials [72–75]. For instance, Lehockey and Palumbo [72] reported that the significant reductions in bulk primary creep strain and steady-state creep rate can be realized and the cavitation damage at GBs can be greatly suppressed in nickel by increasing the fraction of special GBs, as shown in Figure 7. In another case study, Was et al. [75] observed that the creep resistance of Ni-16Cr-9Fe alloys can also be effectively improved by the GBE treatment. In short, the GBE treatment is indeed a well-established method to improve the creep resistance of metallic materials. higher activation energy for creep is needed under a high-temperature constant load. Secondly, the higher lattice order of the special GBs suppresses the dislocation decomposition at the GBs and thus significantly inhibits the GB slipping [72]. Finally, it is difficult to form cavities on the interface of special GBs by the decomposition of dislocations at high temperature, which greatly improves the resistance to creep failure in GBEed materials [72- 75]. For instance, Lehockey and Palumbo [72] reported that the significant reductions in bulk primary creep strain and steady-state creep rate can be realized and the cavitation damage at GBs can be greatly suppressed in nickel by increasing the fraction of special GBs, as shown in Figure 7. In another case study, Was et al. [75] observed that the creep resistance of Ni-16Cr-9Fe alloys can also be effectively improved by the GBE treatment. In short, the GBE treatment is indeed a well-established method to improve the creep resistance of metallic materials.

**Figure 7.** Influence of GBE on the creep properties of nickel. (**a**) Comparisons of creep curves for nickel samples with various fractions of special GBs (Sf); (**b**) Effect of the fraction of special GBs on the steady-state creep rate and total primary creep strain; (**c**) Relative proportion of RHAGBs (Σ > 29) and special GBs (Σ1–Σ29) showing cavitation in the sample with the Sf = 45. adopted from Ref. [72] **Figure 7.** Influence of GBE on the creep properties of nickel. (**a**) Comparisons of creep curves for nickel samples with various fractions of special GBs (Sf); (**b**) Effect of the fraction of special GBs on the steady-state creep rate and total primary creep strain; (**c**) Relative proportion of RHAGBs (Σ > 29) and special GBs (Σ1–Σ29) showing cavitation in the sample with the Sf = 45. adopted from Ref. [72].

#### **7. Influence of GBCD Optimization on Fatigue Performance**

**7. Influence of GBCD Optimization on Fatigue Performance**  It is a known fact that at least half of the mechanical fracture in metal components is caused by the fatigue failure of materials [76]. In order to improve the fatigue resistance of materials, numerous studies have been carried out on the understanding of fatigue deformation behavior and fatigue cracking mode. It has been understood that the fatigue cracking of materials mainly arises from the strain localization under cyclic loading [77, It is a known fact that at least half of the mechanical fracture in metal components is caused by the fatigue failure of materials [76]. In order to improve the fatigue resistance of materials, numerous studies have been carried out on the understanding of fatigue deformation behavior and fatigue cracking mode. It has been understood that the fatigue cracking of materials mainly arises from the strain localization under cyclic loading [77,78]. Moreover, the fatigue cracking mode was found to be closely dependent upon the service environment, the type of fatigue load, etc. [44,79,80]. In addition, under a low cyclic load or a relatively low temperature, fatigue cracks tend to initiate along slip bands in FCC materials; however, as the load or temperature increases, they will be more likely to form at GBs [79,81]. Furthermore, it was easier for the fatigue cracks of polycrystalline FCC materials to nucleate along slip bands under a tension-compression cyclic load than at GBs under a tensile-tension fatigue load [82]. It should be noted that, in polycrystalline

metallic materials, the capacity of different types of GBs to resist fatigue cracking is also significantly different. For example, in the study of the fatigue damage behavior of copper bicrystals, Li et al. [83] indicated that, compared with ordinary RHAGBs, coherent twin boundaries have a higher resistance to fatigue cracking. Pan et al. [84] demonstrated that the cyclic stress response is independent of the loading history in nano-twin strengthened polycrystalline copper, which is beyond all doubt beneficial for the fatigue performance. Therefore, the twin-related GBE is regarded as a feasible method to improve the fatigue properties of metallic materials.

Lehockey et al. [85] explored the effect of GBE treatment on the fatigue properties of alloy 738 and alloy V-57 through tensile-tensile fatigue tests at room temperature. The high *f* SBs introduced by GBE treatment in alloys 738 and V-57 effectively improved the fatigue lives of these two alloys. They suggested that the main reason for the GBE-induced improvement in fatigue properties should be attributed to the influences of GBE on the precipitation behavior in these two alloys [85].

In order to probe a pathway to improve the low-cycle fatigue life of FCC metals via GBE, our recent work [13] examined the tension-tension fatigue behavior of the non-GBE and GBE Cu-16at.% Al alloys at relatively high stress amplitudes, and it was found that an appropriate GBE treatment (i.e., cold rolled with 7% reduction and annealed at 723 K for 72 h) can effectively improve the stress-controlled tension-tension low-cycle fatigue life of Cu-16at.%Al alloys (Figure 8a). The GBE treatment can lead to a greater capability of compatible deformation (Figure 8b) and a higher resistance to GB cracking (Figure 8c), and thus effectively hinder the cyclic strain localization and cracking at GBs, especially at increased stress amplitudes, so that the sensitivity of fatigue life to stress amplitude can be weakened by GBE in Cu-16at.% Al alloys. This research strongly demonstrated that the GBE method can be regarded as an efficient pathway to improve low-cycle fatigue resistance of FCC metals.

In addition, through an in situ observation on the fatigue crack growth in SUS304 austenitic stainless steel, Kobayashi et al. [86,87] confirmed that the fatigue cracking resistance of special GBs is significantly better than that of RHAGBs, as shown in Figure 9. In this work, the polycrystalline specimen (Type A) with a higher fraction of low-ΣCSL boundaries shows a lower crack propagation rate compared with the specimen (Type B) with a lower fraction of low-ΣCSL boundaries (Figure 9a), since the higher fraction of low-ΣCSL boundaries significantly improves the resistance to intergranular cracking (Figure 9b).

Furthermore, the room-temperature fatigue resistance of metallic materials can be improved by a GBE treatment, which can optimize the deformation uniformity and the resistance to intergranular cracking. As mentioned above, the intergranular cracking tendency of polycrystalline metallic materials becomes more obvious at high temperatures; in this case, it will naturally raise the question of whether the effect of GBE on fatigue performance will become more significant or not. For this reason, Gao et al. [81] investigated the fatigue cracking behavior of nickel-based superalloy ME3 at high temperatures of 973 K and 1073 K, and they found that the intergranular fatigue cracking behavior in the target material indeed became significant with increasing temperature; however, it can be effectively suppressed by a GBE treatment, especially at the higher temperature of 1073 K rather than the lower temperature of 973 K. Therefore, GBE is more efficacious and helpful for improving the high-temperature fatigue resistance of metallic materials.

**Figure 8.** Effect of GBE on the Fatigue Performance of Cu-16at.% Al Alloy. (**a**) Comparison of the fatigue lives of non-GBE and GBE samples at different stress amplitudes; and comparisons of the deformation uniformity (**b**) and cracking behavior (**c**) of non-GBE and GBE samples fatigued at a stress amplitude of 175 MPa. adopted from Ref. [13] **Figure 8.** Effect of GBE on the Fatigue Performance of Cu-16at.% Al Alloy. (**a**) Comparison of the fatigue lives of non-GBE and GBE samples at different stress amplitudes; and comparisons of the deformation uniformity (**b**) and cracking behavior (**c**) of non-GBE and GBE samples fatigued at a stress amplitude of 175 MPa. adopted from Ref. [13].

In addition, through an in situ observation on the fatigue crack growth in SUS304

austenitic stainless steel, Kobayashi et al. [86,87] confirmed that the fatigue cracking resistance of special GBs is significantly better than that of RHAGBs, as shown in Figure 9. In this work, the polycrystalline specimen (Type A) with a higher fraction of low-ΣCSL boundaries shows a lower crack propagation rate compared with the specimen (Type B) with a lower fraction of low-ΣCSL boundaries (Figure 9a), since the higher fraction of low-ΣCSL boundaries significantly improves the resistance to intergranular cracking (Figure

9b).

**Figure 9.** shows that GBE improves the fatigue propagation resistance in SUS304 austenitic stainless steel. (**a**) Comparisons of GBCD and crack propagation rates of Type A and Type B samples (**b**) Influence of GBCD on the local propagation rate of fatigue cracks Adopted from Ref. [86] **Figure 9.** Shows that GBE improves the fatigue propagation resistance in SUS304 austenitic stainless steel. (**a**) Comparisons of GBCD and crack propagation rates of Type A and Type B samples (**b**) Influence of GBCD on the local propagation rate of fatigue cracks Adopted from Ref. [86].

Furthermore, the room-temperature fatigue resistance of metallic materials can be improved by a GBE treatment, which can optimize the deformation uniformity and the resistance to intergranular cracking. As mentioned above, the intergranular cracking tendency of polycrystalline metallic materials becomes more obvious at high temperatures; in this case, it will naturally raise the question of whether the effect of GBE on fatigue performance will become more significant or not. For this reason, Gao et al. [81] investigated the fatigue cracking behavior of nickel-based superalloy ME3 at high temperatures of 973 K and 1073 K, and they found that the intergranular fatigue cracking behavior in Gao et al. [32] recently found that the GBE has little visible effect on the tensioncompression fatigue property of 316LN austenitic stainless steel under a high temperature (573 K) salt solution, as shown in Figure 10a. In this work, the fatigue cracks of 316LN austenitic stainless steel mainly nucleated and propagated along slip bands (Figure 10b) due to the influence of hydrogen embrittlement, which was hardly restricted by special GBs. Accordingly, the GBE treatment may effectively improve the fatigue properties of metallic materials, for which intergranular cracking is the dominant cause of fatigue damage, but it has little effect on the fatigue damage along slip bands. Additional, in-depth work still needs to be done to elucidate the definite effect of GBE on the fatigue properties of various metallic materials.

the target material indeed became significant with increasing temperature; however, it can be effectively suppressed by a GBE treatment, especially at the higher temperature of 1073 K rather than the lower temperature of 973 K. Therefore, GBE is more efficacious and

Gao et al. [32] recently found that the GBE has little visible effect on the tension-compression fatigue property of 316LN austenitic stainless steel under a high temperature (573 K) salt solution, as shown in Figure 10a. In this work, the fatigue cracks of 316LN

helpful for improving the high-temperature fatigue resistance of metallic materials.

austenitic stainless steel mainly nucleated and propagated along slip bands (Figure 10b) due to the influence of hydrogen embrittlement, which was hardly restricted by special GBs. Accordingly, the GBE treatment may effectively improve the fatigue properties of metallic materials, for which intergranular cracking is the dominant cause of fatigue damage, but it has little effect on the fatigue damage along slip bands. Additional, in-depth work still needs to be done to elucidate the definite effect of GBE on the fatigue properties

of various metallic materials.

**Figure 10.** Effect of GBE on the fatigue performance of 316LN austenitic stainless steels in hightemperature salt solutions. (**a**) Relationship between strain amplitude and fatigue life for GBE and non-GBE samples; (**b**) Crack propagation in GBE and non-GBE samples. Adopted from Ref. [32] **Figure 10.** Effect of GBE on the fatigue performance of 316LN austenitic stainless steels in hightemperature salt solutions. (**a**) Relationship between strain amplitude and fatigue life for GBE and non-GBE samples; (**b**) Crack propagation in GBE and non-GBE samples. Adopted from Ref. [32].

#### **8. Summary 8. Summary**

On the basis of reaffirming the concept of GBE, this review summarizes the recent development of twin-related GBE, including the theoretical models and mechanisms of GBE optimization, and emphatically concentrates on the applications of GBE to improve the mechanical properties of polycrystalline metallic materials. The theoretical models of twin-related GBE have been relatively well developed, except for some technical problems (e.g., the determination of effective special GBE). This review has strongly demonstrated the powerful and fruitful applications of twin-related GBE in improving the various mechanical properties of polycrystalline metallic materials, e.g., tensile ductility at room temperature, strength-ductility match at high temperature, creep resistance, fatigue life, etc. On the basis of reaffirming the concept of GBE, this review summarizes the recent development of twin-related GBE, including the theoretical models and mechanisms of GBE optimization, and emphatically concentrates on the applications of GBE to improve the mechanical properties of polycrystalline metallic materials. The theoretical models of twin-related GBE have been relatively well developed, except for some technical problems (e.g., the determination of effective special GBE). This review has strongly demonstrated the powerful and fruitful applications of twin-related GBE in improving the various mechanical properties of polycrystalline metallic materials, e.g., tensile ductility at room temperature, strength-ductility match at high temperature, creep resistance, fatigue life, etc. Therefore, the twin-related GBE should be a feasible solution to the design of high-performance materials in the future. However, most of the existing research was just conducted on a laboratory scale, and it is still lacking in the application of practical engineering. Therefore, exploring low-cost and reliable methods to realize GBE is still a major challenge to its application. In addition, the application of GBE to optimizing the fatigue properties of FCC materials has an excellent prospect for being developed into a novel pathway, which is worthy of being further investigated.

**Author Contributions:** Conceptualization, X.L.; writing—review and editing, X.L., X.G.; consulting literature, Z.J., P.C., C.F., F.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was financially supported by the National Natural Science Foundation of China (NSFC) under Grant nos. 51871048 and 52171108 and the Fundamental Research Funds for the Central Universities under Grant no. N2202007.

**Acknowledgments:** Special thanks to the Analytical and Testing Center, Northeastern University, China.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The abbreviations and their original meanings appear in this review.


#### **References**


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