**3. Correlation of structure and mechanical properties**

a radius in between of Zr and Cu atoms, the three atomic sizes can adjust the coordination polyhedron around the Cu atom, and increases the possibility of comfortable arrangements to reach FI. Furthermore, the negative mixing heat of Al with Zr and Cu drives Al to scatter in the Cu-Zr matrix. A more ideal ratio of 0.905 of Zr-Al atoms make Al surrounded by Zr become the topologically optimal way for FI packing. Similar with the binary Cu-Zr MG mentioned above, the FIs in this ternary MG overlapped and connected with the bonding forms of tetrahedral sharing (TS, same as IS), FS, ES, and VS, and then interconnected with each other resulting in the formation of networks (shown in **Figure 4**). The degree of connectivity of FI might serve as the backbone of the MG structures, and induced the more stable structure and improvement of mechanical properties in ternary glass compared with the binary glass. A further study taken by Tang suggested that those SRO clusters with low degree five-fold symmetry structure could also tend to form interconnected networks [17]. But different with the solid-like networks formed by FI clusters, the low five-fold symmetry clusters built up liquid-like networks. Compared with the solid-like networks, the liquid-like ones were less

**Figure 4.** (a) A supercluster consisting four types of connections VS, ES, FS and TS; (b) a large supercluster consisting of over 700 atoms; (c) higher degree of connectivity of FI shown in Cu-Zr-Al MG compared with (d) Cu-Zr MG [13].

resistant to shear events and usually fertile sites for plastic deformation.

34 Metallic Glasses - Properties and Processing

The correlation of structure and mechanical properties is a central theme of materials research, no matter crystalline materials or amorphous ones. The properties of MGs change pronouncedly with the internal structures change. Several works have been done for the influence of changes in composition proportions and variation in the processing conditions for MGs of a fixed composition, but what really governs the properties of MG from the sight of atomic-level structures has to be concerned for its quantitative and predictive theory establishment. The icosahedral cluster structures usually have a more dense packing efficiency, and the distributions are not even in space with connection of icosahedral existing. Thus, the MG structure has intrinsic fluctuations, and the local atomic-level area has heterogeneity in structure and dynamics, and the nanoscale mechanical heterogeneity had been proved with the using of dynamics force microscopy [18]. The mechanical response of MG sample can be significantly influenced by various local structure motifs, relative fractions, and their distributions in space. In other words, the structural heterogeneity necessarily leads to mechanical heterogeneity and decide the mechanical behavior of the MG [10, 19].

According to Wakeda's investigations on the shear deformation of Cu*<sup>x</sup>* Zr1*-x* (*x =* 0.30–0.85) MGs, the local geometrical structures had large variation with the change of proportions, and affected the yield and fracture behavior of the MGs [20]. With application of Voronoi polyhedral analysis method, the local structures were characterized by pentagons and free volume, and these two factors were found related to each other. The pentagonal regions corresponded to the densely packed structure and nonpentagonal regions corresponded to the free volume structure. With shear simulation taken on the various MGs, it was found the pentagon-rich region tends to undergo elastic deformation, while the pentagon-poor was easily deformed plastically. Pentagon-rich local area had more formation of fivefold symmetry structure, and more relevant to the FI cluster, thus the aggregation of pentagons could be regard as formation of SRO. The results indicated the pentagonal SRO contributed the structural stability as well as elastic strength, while the opposite ones closely related to yield and fracture behavior in MGs.

The preparation processing of MG also has a significant influence on the formation of SRO cluster types and contents, and induces local SRO structure heterogeneity in MG. Cheng found that the mechanical behavior and dynamics responses varied with different cooling rates of MG [11]. When applied the same tensile loading procedure to the MG samples prepared under different cooling rates, the sample with lower cooling rate showed a strong tendency to form a single and highly localized SB, while the one with higher cooling rate had a more homogeneous deformation. To obtain a quantitative evaluation of strain localization, the degree of strain localization parameter was defined as:

 $\mu$ 

the degree of strain localization parameter was defined as:

$$\psi = \sqrt{\frac{1}{N} \sum\_{l=1}^{N} \left( \eta\_l^{\text{Miss}} - \eta\_{\text{nse}}^{\text{Miss}} \right)^2} \tag{2}$$

where, a larger *ψ* means larger fluctuations in the atomic strain and a more localized deformation mode. The strain localization degree *ψ* was found negatively correlated with cooling rates and positively correlated with the fraction of Cu-centered FI clusters. A shear deformation simulation also showed the MG with lower cooling rate had higher shear stress compared with higher cooling rates. And the analysis on shear modulus showed a consistent tendency with strain localization phenomenon. These results showed the dynamics heterogeneity have a significant dependence on cooling rate, and revealed that the MG structure and mechanical behavior can be regulated by controlling the quenching process and cooling rates.

Since SBs formation is a significant signal for catastrophic failure of MG, the structure evolution analysis of SBs is necessary for the dynamics investigation during a deformation. Cao et al. studied the correlation of cluster evolution with the shear localization initiation in a Cu-Zr MG in the SB regime [21]. Fractions of several dominant cluster types in the SB forming region were analyzed during deformation, as shown in **Figure 5**. The breakdown of FI clusters was identified as a structural signature of the initiation of shear localization. With distorting of the FI backbone into less-shear-resistant, uncomfortable clusters, the shear localization propagating to a major SB with a velocity close to speed of voice. Feng et al. took quantitative treatment on the atomic structure of SBs in Cu-Zr MG and found the "liquid-like" features of SB [22]. With the method of H-A analysis, bonded pair types and distributions in SB are more similar to supercooled liquid compared with the MG matrix (shown in **Figure 6**). The SRO analysis results showed heterogeneous structure distribution in clusters. Zr-centered <0,2,8,5 > clusters exhibited strong spatial correlations and tendency to connect with each other in the SB, and formed interpenetrating solid-like backbone in SB (shown in **Figure 7**). Ju et al. took another view on the correlation of the mechanical properties and the local structural rearrangement of Mg-Zn-Ca MG by using H-A analysis method [23]. From the H-A index analysis on the system, the numbers of 1551 and 1431 local structures decreased with the increasing strain until 0.05, and the H-A indices of different types remained almost constant when the strain became larger than 0.05. The distributions of atomic local shear strain during the tension process showed the stages of the initialization of STZs, the extension of STZs, and the formation of shear bands along a direction 45° from the tensile direction.

The researching work about MG structure revealed the interconnection of icosahedra clusters was the intrinsic nature of MGs. The networks forming by neighboring icosahedra to medium range is negligible for the correlation of structure and mechanical properties in MGs. Lee et al. extended the structural hierarchy to a longer range by connecting MRO structures to large networks [24]. As we mentioned above, the MRO structures are constructed by connecting the neighboring SROs with each other. In Lee's works, interpenetrating connection of icosahedra (ICOI) structure was constructed by icosahedra, and it was illustrated as a typical MRO structure to explore correlation of structure and mechanical properties. To find out which pattern motif mostly contributed to structure stability, the potential energy of the center atom of the individual

**Figure 7.** Connectivity of the network formed by the central atoms of the <0,2,8,5 > clusters [22].

**Figure 6.** Comparison of several bonded pair types in the matrix, the SB, and supercooled liquid [22].

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**Figure 5.** Variations of five dominant SRO clusters with the sample strain increasing in the SB region [21].

Mechanical Properties and Deformation Behaviors of Metallic Glasses Investigated… http://dx.doi.org/10.5772/intechopen.76830 37

**Figure 6.** Comparison of several bonded pair types in the matrix, the SB, and supercooled liquid [22].

simulation also showed the MG with lower cooling rate had higher shear stress compared with higher cooling rates. And the analysis on shear modulus showed a consistent tendency with strain localization phenomenon. These results showed the dynamics heterogeneity have a significant dependence on cooling rate, and revealed that the MG structure and mechanical

Since SBs formation is a significant signal for catastrophic failure of MG, the structure evolution analysis of SBs is necessary for the dynamics investigation during a deformation. Cao et al. studied the correlation of cluster evolution with the shear localization initiation in a Cu-Zr MG in the SB regime [21]. Fractions of several dominant cluster types in the SB forming region were analyzed during deformation, as shown in **Figure 5**. The breakdown of FI clusters was identified as a structural signature of the initiation of shear localization. With distorting of the FI backbone into less-shear-resistant, uncomfortable clusters, the shear localization propagating to a major SB with a velocity close to speed of voice. Feng et al. took quantitative treatment on the atomic structure of SBs in Cu-Zr MG and found the "liquid-like" features of SB [22]. With the method of H-A analysis, bonded pair types and distributions in SB are more similar to supercooled liquid compared with the MG matrix (shown in **Figure 6**). The SRO analysis results showed heterogeneous structure distribution in clusters. Zr-centered <0,2,8,5 > clusters exhibited strong spatial correlations and tendency to connect with each other in the SB, and formed interpenetrating solid-like backbone in SB (shown in **Figure 7**). Ju et al. took another view on the correlation of the mechanical properties and the local structural rearrangement of Mg-Zn-Ca MG by using H-A analysis method [23]. From the H-A index analysis on the system, the numbers of 1551 and 1431 local structures decreased with the increasing strain until 0.05, and the H-A indices of different types remained almost constant when the strain became larger than 0.05. The distributions of atomic local shear strain during the tension process showed the stages of the initialization of STZs, the extension of STZs, and

behavior can be regulated by controlling the quenching process and cooling rates.

36 Metallic Glasses - Properties and Processing

the formation of shear bands along a direction 45° from the tensile direction.

**Figure 5.** Variations of five dominant SRO clusters with the sample strain increasing in the SB region [21].

**Figure 7.** Connectivity of the network formed by the central atoms of the <0,2,8,5 > clusters [22].

The researching work about MG structure revealed the interconnection of icosahedra clusters was the intrinsic nature of MGs. The networks forming by neighboring icosahedra to medium range is negligible for the correlation of structure and mechanical properties in MGs. Lee et al. extended the structural hierarchy to a longer range by connecting MRO structures to large networks [24]. As we mentioned above, the MRO structures are constructed by connecting the neighboring SROs with each other. In Lee's works, interpenetrating connection of icosahedra (ICOI) structure was constructed by icosahedra, and it was illustrated as a typical MRO structure to explore correlation of structure and mechanical properties. To find out which pattern motif mostly contributed to structure stability, the potential energy of the center atom of the individual

localization of SBs under the same mechanical loading. To describe the plastic flow and reveal the deformation transition mechanism, the initiation of SBs from a shear transformation is a fundamental problem for the starting. One of the most popular explanations is STZ theory raised by Argon [27]. According to the theory, STZs are the clusters composed of tens to hundreds of atoms, and the basic elements undergoing the plastic flow in MG. When a shear stress is applied on the MG, the atoms in the cluster have relative movements, and deformation takes place inside the cluster. The distortion of STZ is an activation process, and needs a certain activation energy and volume, to transfer a STZ from a high energy state to a lower one.

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The propagation of a SB from a collection of STZs is next problem to be concerned. Ogata et al. performed shear deformation on Cu-Zr bulk MG with MD simulations [28], and observed the nucleation and localization of SBs during shear deformation. The nucleation of SB was taken place from a local atomic rearrangement like STZ, and this local deformation induced releasing of elastic strain energy in the shear plane, and activated the generation of more STZs. Then, the STZs interacted with each other and formed a SB in the shear direction. Furthermore, the generation of SB enhanced the elastic strain energy of the surrounding materials in the in-

Shimizu et al. described the propagating and developing of SB as a growth process of embryonic shear band (ESB) [29, 30]. An ESB appeared at the concentrator of a group of activated STZs. When the far-field shear stress exceeds the glue traction with temperature rising induced by frictional heating, and the length of the ESB increased to a critical length over 100 nm, the ESB would become maturing to a localized SB. An aged-rejuvenation-glue-liquid (ARGL) SB model was used for the description of the shear front, and four zones were defined as aged glass, rejuvenated glass, glue, and liquid (illustrated in **Figure 9**). The temperature distributes from room temperature at aged glass end to over the glass transition temperature at the liquid end. Their model was supported by the temperature rising phenomenon, which can reach a maximum over 1000 K, can also be verified from the research work by Lewandowski et al. [31]. They planted a fusible tin coating to observe the temperature rise during bend-test on MG, and observed melting in the SBs formation area, thus deduced that local temperature rise

For a further understanding on SBs, the mechanical properties of SBs were investigated by Zhou et al. by testing samples with pre-existing SBs with tensile MD simulations [32]. It was demonstrated that pre-deformation lowered material strength and triggered enhanced strain fluctuation before sample yielding, leading to highly dispersed plastic shearing in the entire

plane directions, made the spreading of SB more localized.

in the bands can reach a few thousand kelvin.

**Figure 9.** The aged-rejuvenation-glue-liquid (ARGL) shear band model [29].

**Figure 8.** The breaking of ICOI networks in the during shear deformation [24].

icosahedra participating in the connection scheme of each patterns were calculated. It was found the icosahedra with volume shared type had a lower potential energy and stable structure, Cu65Zr35 had larger fractions of ICOIs with close connection of ICOIs compared to Cu50Zr50, and together with more dense atomic packing. With addition of shear simulations, Cu65Zr35 was found more resistant to applied load and showed higher elastic modulus and yield stress. The highly connected MROs constituted a compact icosahedral network over an extended range, which was resistant to stress-induced shear transformations under applied load. The breaking of ICOI networks during shear deformation are shown in **Figure 8**. This work presented the connectivity of MROs and showed its significant influence on the mechanical properties of MG.
