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(a) 2D Axisymmetric FE model of cylindrical specimen along with 'Berkovich equivalent' conical rigid indenter with half cone angle of 70.3 0 employed in indentation simulations. (b) FE model of cylindrical sample considering microstructure of NG in a region A, while homogenized NG in region B. (c) Enlarged view of region A and a grain whose size is characterized by length d 1 and d 2 .
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Finite element simulations of indentation on Sc75Fe25 nanoglasses (NGs) and metallic glass (MG) ribbons are performed by employing extended Drucker Prager (EDP) and Von-Mises plasticity model, and pressure sensitive index, α is determined by fitting recent experimental data. It is found that yield behavior of NG is better characterised by pressure...
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... are performed using the pressure insensitive (Von-Mises) and pressure sensitive (extended Drucker Prager (EDP)) plasticity The axisymmetric FE simulations of Berkovich indentation on cylindrical specimens are performed using 'Berkovich equivalent' conical rigid indenter with spherical tip ( R = 200 nm) and semiapex angle of 70.3 ° [32] . Fig. 1 (a) displays FE discretization of sample using four-node quadrilateral axis symmetric elements in r − z plane along with the indenter geometry. The size of the specimen is chosen as 40 ( L s / R ) × 30 ( H s / R ) to ensure that plastic zone is well contained below indenter so that boundary effects on indentation response could be ...
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... size of the specimen is chosen as 40 ( L s / R ) × 30 ( H s / R ) to ensure that plastic zone is well contained below indenter so that boundary effects on indentation response could be minimized [16] . Further, all nodes on the bottom and left side edges are constrained to move in z and r direction, respectively, while a constant displacement rate is applied to the rigid indenter through a reference point RP attached to it ( Fig. 1 (a)). ...
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... and larger r p in NGs are due to their high α, which might be because of presence of free volume rich interfaces. Therefore, a fundamental question "what is value of α for interfaces in NGs?" arises. To address this, FE simulations of indentation on NG1 are repeated by modeling the microstructure of NG (i.e. GGs and GIs), as displayed FE model in Fig. 1 (b). Since α is expected to influence deformation only after commencement of plastic yielding, microstructure is modeled only in the region (region 'A' in Fig. 1 (b)) just underneath indenter, while a homogenized NG is considered outside this region i.e., region 'B' ( Fig. 1 (b)). Note that region A is significantly larger than r NG 1 p ...
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... of α for interfaces in NGs?" arises. To address this, FE simulations of indentation on NG1 are repeated by modeling the microstructure of NG (i.e. GGs and GIs), as displayed FE model in Fig. 1 (b). Since α is expected to influence deformation only after commencement of plastic yielding, microstructure is modeled only in the region (region 'A' in Fig. 1 (b)) just underneath indenter, while a homogenized NG is considered outside this region i.e., region 'B' ( Fig. 1 (b)). Note that region A is significantly larger than r NG 1 p noted in Fig. 3 (c). Following [1-8 , 14 , 40] , shape of the GGs is assumed to be hexagonal, and their size is characterized by dimensions d 1 and d 2 along r and ...
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... and GIs), as displayed FE model in Fig. 1 (b). Since α is expected to influence deformation only after commencement of plastic yielding, microstructure is modeled only in the region (region 'A' in Fig. 1 (b)) just underneath indenter, while a homogenized NG is considered outside this region i.e., region 'B' ( Fig. 1 (b)). Note that region A is significantly larger than r NG 1 p noted in Fig. 3 (c). ...
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... that region A is significantly larger than r NG 1 p noted in Fig. 3 (c). Following [1-8 , 14 , 40] , shape of the GGs is assumed to be hexagonal, and their size is characterized by dimensions d 1 and d 2 along r and z directions, respectively ( Fig. 1 (c)). Here, d 1 and d 2 are chosen as 9 and 11 nm, respectively, to achieve average grain size of 10 nm , as observed in experiments [6] , while interface width is taken as 1 nm [6] which results in a volume fraction of GGs, V g f = 0.73. ...
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Despite its significance in fundamentally understanding mechanical behaviors of metallic glasses, the effect of elastic heterogeneity on plastic deformation and thereby nanotribological behavior of metallic glass thin films (MGTFs) remains an open question. By a combination of nano-scratch, nano-DMA and nanoindentation tests, we have investigated i...
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... Unlike crystalline metals and alloys in which plastic deformation is almost exclusively a function of the deviatoric part of the stress tensor, plasticity in amorphous materials such as BMGs and glassy polymers is pressure sensitive, i.e., the hydrostatic stress also plays a role in the flow behaviours [33][34][35][36][37]. Typically, pressure sensitivity results in an elevation in the flow stress of the material when hydrostatic compression is superposed on the shear stresses. ...
... Based on the modified expanding cavity model developed by Narasimhan [38], Patnaik et al. [39] concluded that the pressure-sensitive plastic flow in BMGs leads to significantly higher constraint factors than that in crystalline metals during indentation. This is attributed to the fact that the material underneath the indenter yields under the influence of the hydrostatic stresses that are exerted by the surrounding elastic cavity [33][34][35][36][37]. While C is sensitive to the geometry of the indenter, it is generally in the range of 3-4.5 for amorphous alloys [33][34][35][36][37] and between 1 and 3 for crystalline alloys [40,41]. ...
... This is attributed to the fact that the material underneath the indenter yields under the influence of the hydrostatic stresses that are exerted by the surrounding elastic cavity [33][34][35][36][37]. While C is sensitive to the geometry of the indenter, it is generally in the range of 3-4.5 for amorphous alloys [33][34][35][36][37] and between 1 and 3 for crystalline alloys [40,41]. ...
... Nanoglasses comprising glassy grains (GIs) separated by glass interfaces (GIs) appears to provide extensive tensile elongations [10]. The limited experimental results show that profuse secondary shear bands (SSBs) in NGs compared to the MGs of identical compositions, and the molecular dynamic (MD) simulations show that the presence of GIs will enable increased nucleation sites for shear bands [11][12][13][14][15][16][17][18][19][20]. A detailed experimental investigation of the effect of temperature, stress state, and strain rate on the mechanical behavior of NGs under various external conditions will provide further insights into understanding the differences in deformation mechanisms in NG and MGs. ...
Nanoindentation experiments are performed on a binary Pd-Si metallic glass (MG) and nanoglass (NG) using Berkovich and cube-corner indenters to investigate the effect of indenter geometry on the deformation behaviour. A large number of pop-ins in the load vs. displacement curves and a higher pile-up of material around the indenter are observed for sharper cube-corner indenter compared to the Berkovich indenter. In case of both the indenters, NG displays lower hardness than the MG due to the presence of higher free volume and lack of any clusters in the glassy grains or interfaces. Further, the hardness is observed to decrease with indentation load signifying the indentation size effect (ISE) in hardness. The discrete plasticity ratio, Ψ defined as the ratio of pop-in displacement, ∆hdis to the total displacement, htot is used to estimate the influence of serrations on total plastic deformation and characterize the nature of the plastic flow. The Ψ indicates that the deformation mode is independent of indenter geometry for both the glasses.
... The variation of H with the loading rate for both NG and MG obtained at P max of 4 mN is plotted in Fig. 5a. It can be noticed from the figure that, at all the loading rates, NG exhibits a higher H than the MG, consistent with the previous experimental and simulation studies [15][16][17][48][49][50][51]. Besides this, the H decreases with an increased loading rate for both the NG and MG samples. ...
... Following this, it is expected that Cu-Zr NGs should exhibit a lower H as compared to MGs, contrary to the current experimental results (Table 3) Recently, it has been observed that the number of clusters and their size can be varied by thermal annealing, which influences the β relaxation kinetics and mechanical properties [16,[59][60]. Further, the high free volume present in the GIs also causes an increase in pressure sensitivity index during the plastic deformation, thereby leading to an increase in the hardness of NGs [48]. With the help of a modified expanding cavity model applicable, Narasimhan J o u r n a l P r e -p r o o f [61] has observed higher H in materials having higher pressure sensitivity index due to the large elasticity continuum surrounding the indentation zone. ...
The strain rate sensitivity, m, of a binary Cu60Zr40nanoglass (NG) and metallic glass (MG) are investigated using nanoindentation. Indentations were performed at different loading rates in the range of 0.26 to 8 mN/s, which gives equivalent indentation strain rates over three decades. The load vs. displacement curves of MG exhibited noticeable displacement bursts at low loading rates, which gradually decreased with increasing loading rate suggesting a transition from more to less severe heterogeneous plastic flow. While in the case of NG, no noticeable displacement bursts are present at any of the loading rates suggesting a near homogeneous plastic flow. In both NG and MG, the hardness decreases with increasing loading rate, resulting in negative strain rate sensitivity, m. The m for NG is higher than the MG, indicating a more homogeneous flow underneath the indentation. Interface indentation experiments and subsequent analysis of the deformation zone showed a larger number of fine secondary shear bands (SSBs) in NG as compared to the primary shear bands (PSBs), while the plastic flow in MG is accommodated mostly by the PSBs. The findings of the current study will help improve the understanding of the plastic deformation behavior of NGs and provide insights for designing the novel microstructural architecture of amorphous alloys with improved ductility.
... In this section, the effect of parameters D and V on the variation of hardness along the SMATed layer is investigated by performing 2D axisymmetric finite element simulations of Berkovich indentation using a "Berkovich equivalent" conical-spherical rigid indenter (refer to Fig. 14b) [47,48]. Figure 14a shows finite element discretization of SMATed target ( 6000(L) × 6000 nm(H) ) using the four-noded axisymmetric element with reduced integration (CAX4R) along with rigid spherical indenter in the r − z plane. ...
In surface mechanical attrition treatment (SMAT), the processing parameters like the diameter of hardened steel balls/shots (D) and their impact velocity (V) are crucial in affecting the mechanical properties of the materials. This study is focused on understanding the effect of D and V on microstructural and hardness variation during the SMAT process. The SMAT has been performed on AISI 304L steel using 3-mm and 8-mm diameter balls with a combination of 1 m/s and 10 m/s impact velocity. Microstructure of the SMATed material shows twin distribution near the top surface changeover from coarser to finer when V increases from a low to significantly high value, whereas it changes marginally with an increase in D. Nanoindentation experiments performed along the depth of SMATed material reveal that the near-surface hardness is mainly governed by V and weakly influenced by D. However, the hardened layer thickness is enhanced by increasing either of these parameters. The complementary finite element (FE) simulations of the single impact SMAT process are performed using the rate-dependent Johnson–Cook plasticity model to provide the mechanistic reasons for the behavior observed from the experiments. A strategy to determine the hardness-depth profile of SMATed steel through FE simulations is developed. The hardness behavior of the SMATed steel is linked to the effects of D and V on the residual equivalent stress and equivalent plastic strain at the surface. The hardness away from the surface is influenced by the shot size and shot velocity. The empirical relations that show the dependence of hardness on the SMAT parameters are determined.
... NGs have exhibited excellent mechanical properties in comparison to MGs of identical composition, owing to their unique microstructure consisting of glassy grains separated by glassy interfaces [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. These interfaces are characterized by low density [5], excess free volume [18], and higher sensitivity to hydrostatic/normal stress [19,20]. Consequently, these interfaces facilitate nucleation of multiple shear bands which are uniformly distributed throughout the volume of the material leading to prolonged homogeneous deformation in NGs. ...
... Fig. 1(a) shows the geometry of rigid indenter and FE discretization of the specimen using four-noded axisymmetric elements in r − z plane. The size of specimen (40(L s /R) ×30(H s /R)) is chosen to be sufficiently large to avoid interaction of plastic boundaries with free surfaces of the specimen to ensure boundary effects on indentation response to remain minimal [19,20,37]. A constant displacement rate in z direction is imposed on the indenter through a reference point RP (refer Fig. 1(a)). ...
Nanoglasses (NGs) have shown large tensile ductility and hardness than metallic glasses (MGs) used to synthesized them. The mixed mode (I and II) fracture experiments and complementary finite element (FE) simulations reported significant influence of applied mode mixity on the crack tip plasticity and fracture toughness of MGs. However, no such study has been under taken for NGs which are synthesized from MGs only. Therefore, two-dimensional, plane strain, FE analysis on the stationary crack in nanoglass (NG) and metallic glass (MG) subjected to mixed mode (I and II) loading conditions are performed under small scale yielding (SSY) conditions by employing the constitutive model for MGs. It is found that the crack tip plasticity is markedly affected by mode mixity in both NGs and MGs, and the shear bands ahead of crack tip appears to be more diffused in the former than the latter. Further, the plastic zone size ahead of the crack tip in NG is larger than that for MG for identical loading conditions. Also, FE simulations predict enhancement in fracture toughness of both the alloys with increase in the mode I contribution. In addition, the results suggest that the NGs may not exhibit larger fracture toughness than MGs with identical composition, although they exhibit larger tensile ductility.
... Given the completely different microstructures of NGs and MGs, the ISE in the former is expected to be significantly different from the latter with identical composition, though it has not been investigated until now. Further, Hirmukhe et al. [38] have shown that the plastic deformation in NGs is more pressure sensitive than MGs due to high pressure sensitivity of interfaces in the former. However, the effect of pressure sensitivity on the ISE in glasses is not investigated and thus, the mechanism governing ISE in NGs and MGs is not well understood. ...
... A highly refined mesh is employed below the indenter to capture the distribution of SBs better, while relatively coarser mesh is used in the region away from the indenter. The size of the specimen is chosen as 25R(L s ) × 20R(H s ) to ensure that the plastic zone is well contained beneath the indenter and the boundary effects on indentation response are minimized [38,45]. Further, all the nodes on the left side and bottom edges are restrained from moving along r and z directions, respectively, while a constant displacement rate is applied to the rigid indenter through a reference point RP attached to it ( Fig. 1(a)). ...
... The size of 'Region A' is ensured to be sufficiently larger than the plastic zone size below the indenter. Following MD [15,17] and FE simulations on NGs and NG-MG composites [16,38,49], the shape of grains is assumed to be hexagonal whose size is characterized by dimensions d 1 and d 2 along r and z directions, respectively (refer Fig. 1(c)). These values are taken to be 4 and 10 nm, respectively, to achieve an average grain size of 7 nm, which is similar to the size observed in the experiments by Nandam et al. [12], while interface width is taken as1 nm. ...
In this work, binary Cu60Zr40 nanoglasses (NGs) and melt spun ribbons (MGs) are synthesized by using magnetron sputtering in an inert gas condensation (IGC) system and standard melt-spinning, respectively. The bonded interface experiments through micro-indentation, and nanoindentation experiments at different peak loads are conducted on both glasses. In addition, complementary finite element (FE) simulations are performed using finite strain viscoplastic constitutive theory for amorphous metals. The bonded interface experiments reveal smooth and almost semi-circular shaped shear bands in MG, while the formation of wavy shear bands is observed in NG. Further, the primary shear band densities in the MG is higher than that in NG, while the plastic zone size below the indenter is larger in the latter than the former. Furthermore, nanoindentation experiments show that the hardness in NGs as well as MGs decreases with increase in indentation depth signifying both alloys exhibiting the indentation size effect (ISE). However, the ISE is found to be more pronounced in MGs than NGs. The FE simulations show that the less pronounced ISE in NGs is due to the slower softening primarily because of higher friction coefficient, μ in them.
... However, one should look at the above analysis with a degree of caution as we have neglected the effect of free volume and the variation of the local atomic structure in the interfacial or core regions. In fact, Hirmukhe et al. [32] have recently used finite element simulations to study the effect of free volume in the interfacial regions to understand the higher strength in Sc 75 Fe 25 nanoglasses compared to metallic glasses. They have found that the pressure sensitivity of the glass-glass interfacial regions creates an additional hardening www.mrs.org/jmr ...
Strain localization during plastic deformation drastically reduces the shear band stability in metallic glasses, ultimately leading to catastrophic failure. Therefore, improving the plasticity of metallic glasses has been a long-standing goal for several decades. In this regard, nanoglass, a novel type of metallic glass, has been proposed to exhibit differences in short and medium range order at the interfacial regions, which could promote the formation of shear transformation zones. In the present work, by introducing heterogeneities at the nanoscale, both crystalline and amorphous, significant improvements in plasticity are realized in micro-compression tests. Both amorphous and crystalline dispersions resulted in smaller strain bursts during plastic deformation. The yield strength is found to increase significantly in Cu–Zr nanoglasses compared to the corresponding conventional metallic glasses. The reasons for the mechanical behavior and the importance of nanoscale dispersions to tailor the properties is discussed in detail.
Graphic Abstract
... With this motivation, Gleiter and coworkers (Jing et al., 1989;Gleiter, 2008;Gleiter, 2009;Gleiter, 2013;Gleiter, 2016) proposed the concept of nanoglasses (NGs) consisting of glassy grains (GGs) separated by glassy interfaces (GIs) of higher free volume, and later, several researchers have successfully fabricated NGs using different manufacturing routes (Gleiter et al., 2014;Nandam et al., 2017;Ivanisenko et al., 2018;Nandam et al., 2020). Extensive studies have been conducted on NGs to investigate their mechanical and functional properties using both experiments and simulations (Chen et al., 2011;Ritter et al., 2011;Sopu et al., 2011;Wang et al., 2011;Ritter and Albe, 2012;Adibi et al., 2013;Albe et al., 2013;Witte et al., 2013;Wang et al., 2014;Adjoud and Albe, 2016;Sniadecki et al., 2016;Nandam et al., 2017;Hirmukhe et al., 2019;Arnold et al., 2020;Singh et al., 2020a;Singh et al., 2020b;Hirmukhe et al., 2020;Katnagallu et al., 2020;Nandam et al., 2020). A series of MD simulation studies have been performed on NGs with different GG sizes and observed that the plasticity increases with the decreasing size of the GGs. ...
In this work, the deformation behavior of as-prepared (AP) and structurally relaxed (SR) Cu–Zr–based nanoglasses (NGs) are investigated using nano- and micro-indentation. The NGs are subjected to structural relaxation by annealing them close to the glass transition temperature without altering their amorphous nature. The indentation load, p , vs. displacement, h , curves of SR samples are characterized by discrete displacement bursts, while the AP samples do not show any of them, suggesting that annealing has caused a local change in the amorphous structure. In both the samples, hardness (at nano- and micro-indentation) decreases with increasing p , demonstrating the indentation size effect. The micro-indentation imprints of SR NGs show evidence of shear bands at the periphery, indicating a heterogeneous plastic flow, while AP NG does not display any shear bands. Interestingly, the shear band density decreases with p , highlighting the fact that plastic strain is accommodated entirely by the shear bands in the subsurface deformation zone. The results are explained by the differences in the amorphous structure of the two NGs.
... However, the strength of such composites is compromised considerably due to lower yield strength of the soft phases. NGs are comprised of dense amorphous regions separated by fine glassy interfaces (Jing et al., 1989) which exhibit excess free volume (Ritter et al., 2011;Şopu et al., 2009), lower density (Fang et al., 2012) and higher sensitivity to the hydrostatic stress (Hirmukhe et al., 2020). These interfaces facilitate the nucleations of multiple shear bands leading to more homogeneous distribution of plastic strain and enhanced ductility in NGs (Adibi et al., 2013;Singh et al., 2014). ...
Cellular metallic glasses (MGs) have been found to be a potential candidate for structural and functional applications due to their attractive properties such as high strength to weight ratio, excellent energy absorption and enhanced plastic deformation. The experiments have shown transition in deformation mode from global failure caused by localization in a shear band to the local failure by damage confined to few cells with reduction in relative density of specimen from a large to moderate value. The mode of deformation again changes over to the collective buckling of ligaments through row by row collapse when the relative density is decreased to a sufficiently lower level. The atomistic simulations on nanoscale cellular MGs have also reported transition from localized but confined to few cells to almost homogeneous deformation with increasing cell size. They have also shown strain localization in a dominant shear band for cell spacing along diagonal direction above a threshold value which was correlated to shear band width in monolithic MG. However, it is not clear as to why and how the shear band thickness in monolithic MG controls the threshold cell-spacing. Therefore, 2D plane strain finite element (FE) simulations of compressive loading are performed on nanoscale cellular MGs using thermodynamically consistent finite strain non-local plasticity model. The present FE simulations successfully predict the two transitions in deformation mode as observed in MD simulations and experiments. It is found that the interaction stress associated with the flow defects such as shear transformation zones (STZs) plays an important role in the deformation response of cellular MGs. Results show that the transition in deformation behavior is governed by the ratio of cell-wall thickness to the intrinsic material length associated with interaction stress. Also, the moderate change in sample size has marginal effect on the deformation response of MG cellular structure. The present work may provide guidelines for designing cellular MG structures capable of showing enhanced plastic deformation for practical engineering applications.
Numerical analysis using explicit code LS-DYNA has been carried out to study the penetration characteristics of a spherical fragment of Ø6mm diameter and conical fragments with apex angles 40°, 60°, 80° and 100° of identical mass made of Stainless Steel (SS 304). The spherical and conical fragments impact on Steel 1006 target plates of 6, 3 and 1 mm thickness at 500 to 2000 m/s impact velocity range in the simulation models. The simulation model employed for the spherical fragment of Ø6 mm diameter in the present study has been validated with experimental data available in the literature. The validated simulation model has been extended to analyse the penetration characteristics of conical fragments with apex angles 40° to 100°. Johnson–Cook (J-C) model, a strain rate-dependent plasticity model supplemented with the Gruneisen equation of state (EoS) and an erosion contact algorithm, have been used in the simulation models to capture the penetration characteristics of the spherical and conical fragments at high velocities. The penetration characteristics have been determined from simulation models in terms of residual velocity and residual kinetic energy of the fragment. The conical fragment with 40o apex angle indicated better penetration characteristics than other fragment shapes considered in the current study.
