Figure 5 - uploaded by Indrasen Singh
Content may be subject to copyright.
Contour plots of normalized interaction stress corresponding to (a) NG1 and (b) NG2 with l c = 3.25 nm at E 2 = 0.03.
Source publication
Using a thermodynamically consistent non-local plasticity model, the mechanistic origin of enhancement in ductility and suppression of dominant shear banding in nanoglasses (NGs) is analysed. It is revealed that the interaction stress between flow defects plays a central role in promoting global plasticity of NGs. Specifically, we find that the int...
Citations
... In addition, the initial deformation in MG composites preferentially occurs in regions with a high free volume concentration [41]. A non-local plasticity model using finite element analysis revealed that plastic deformation in NGs can be retarded by a fine grain size [42]. These simulations emphasize that NG interfaces with excessive free volume can contribute significantly to the nucleation of shear bands. ...
... Since the softer interfaces are constrained by the harder grains, it is assumed that there are fewer transformation modes for interfaces (m = 5) than for grains (m = 40), schematically shown in Fig. 2(a). To investigate the effect of grain size on NGs, the grain sizes of the hexagonal grains [31,33,42,73,74] are assigned as 6 nm, 10 nm, 18 nm, and 38 nm, and the volume fractions of the interfaces are 43.75 %, 30.56 %, 19.00 %, and 9.75 %, respectively. A typical single grain of 6 nm composed of STZs is shown in Fig. 2(b). ...
... The indentation experiments also revealed homogeneous deformation, higher hardness, and reduced modulus in NGs than MGs [7,11,20]. An additional advantage of NGs over MGs is that their mechanical response can be tailored by tuning the grain size as reported by atomistic and finite element simulations [21][22][23][24]. Indeed, Adibi et al. [22] reported that NGs with grain size below a threshold level may exhibit a super plastic flow. ...
... The values of material parameters γ 0 , g o , c cv , ν, m and η cv are taken from the work of Anand and Su [31], and following Hirmukhe et al. [20], these are assumed to be identical for NGs and MGs. Further, the material constant b is chosen lower for NG than that for MG owing to lower steady state flow stress in the former than the latter [8,23,36]. The values of μ for NG and MG are obtained by fitting the simulated indentation load, P versus depth, h curves with the corresponding experimental data reported by Franke et al. [7]. ...
... While choosing the size of region A, it is ensured that region A is well contained within plastic zone size underneath the indenter. Further, following [21][22][23]36], the hexagonal-shaped glassy grains characterized by dimensions d 1 and d 2 along r and z directions, respectively, are considered (refer Fig. 1(c)). The values of d 1 and d 2 are taken as 9 and 11 nm, respectively, to attain an average grain size of 10 nm, as noticed in Sc-based NGs [8,38], while the width of the glassy interface is chosen as 1 nm. ...
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.
... Indeed, Wang et al. [1] reported around 17% of plastic strain in Sc-based NGs under tensile loading in contrast to catastrophic failure in MGs with identical composition. Atomistic and continuum simulations performed on NGs have shown that the strength and ductility of NGs can be tailored by tuning the grain sizes [15][16][17][18][19]. Therefore, before deploying these materials in actual applications, a proper understanding of the influence of microstructure of NGs on their mechanical behavior is essential. ...
... Like MGs, indentation response of NGs is reported to be also almost strain rate insensitive at room temperature [12], therefore, a lower value of m is considered for both the alloys. Further, Singh et al. [16] argued that the cohesion and free volume distribution should attain approximately the same saturation value at every point inside a shear band that cuts through glassy grains and glassy interfaces in NG. In addition, the free volume and cohesion distribution inside glassy grains in a NG can be assumed to be almost identical to that of MGs used to synthesize them. ...
... 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.
... 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). The biggest hurdle for NGs is that they cannot be produced with large thickness due to the limitation of the present manufacturing techniques. ...
... However, the model of Thamburaja and Ekambaram (2007) is thermodynamically consistent, derived in finite strain framework and non-local, but found to be suitable to predict the deformation behavior of MGs near and above the glass transition temperature. In order to analyse the deformation behavior of MGs at room temperature, Thamburaja (2011) modified the constitutive theory of Thamburaja and Ekambaram (2007) which has been successfully shown to capture the size dependent deformation behavior in MGs (Dutta et al., 2018;Thamburaja, 2011), MG composites (Dutta et al., 2020;Shete et al., 2017Shete et al., , 2016, NGs (Singh et al., 2014) and NG-MG nanolaminates (Hirmukhe et al., 2019). Therefore, the model of Thamburaja (2011) is employed to characterize the deformation response of MG in the present study. ...
... It must be noted from Eq. (2) that resists the enhancement in , while < 0 promotes the further evolution of . Indeed, it has been observed that spatial distribution of plays a vital role in delaying the formation of shear band and promoting homogeneous deformation in nanometre-sized notched MGs (Dutta et al., 2018;, unnotched MGs (Thamburaja, 2011), NGs (Singh et al., 2014), nanolaminates of NG-MG (Hirmukhe et al., 2019). Further, in Eq. ...
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.
... The deformation and failure mechanism of BMGs subjected to cyclically varying stresses and strains are thus a topic of scientific and technological interest. Despite this practical importance, existing experimental and simulation studies on BMGs have mainly focused on their plasticity enhancement under monotonic loading [96][97][98][99][100][101][102][103][104][105][106][107][108]. In contrast, the fatigue behaviors of both macroscopic and nanoscale MGs received much less attention and remain largely elusive [109][110][111]. ...
Metallic glasses (MGs) are often perceived as quintessential structural materials due to their superior mechanical properties such as high strength and large elastic limit. In practical applications, service conditions that introduce cyclic variations in stresses and strains are inevitably involved. The fatigue of MGs is thus a topic of research and practical interest. In this review, a brief introduction on MGs, their applications and challenges, is first provided. Next, experimental studies on fatigue behaviors of both macroscopic and nanoscale MGs are summarized. The range of topics covered include the stress-life behavior, fatigue-crack growth behavior, fatigue-fracture morphology, fatigue-failure mechanisms, as well as the effects of chemical composition, cycling frequency, loading condition, and sample size on the fatigue limits. Finally, recent progresses in simulation studies on the fatigue of MGs are discussed, with an emphasis placed on the atomic-level understanding of the fatigue mechanisms.
... Molecular dynamics (MD) simulations have revealed that NGs undergo super plastic flow for grain size below a threshold level [13]. Continuum simulations performed by Singh et al. [14] have shown that spatial distribution of stress arising due to interaction between flow defects such as shear transformation zones (STZs) plays a pivotal role in the deformation response of NGs. In addition, they found that intrinsic material length associated with this interaction stress with respect to glassy grain size governs the transition from strain localization to superplastic flow in NGs. ...
... A thermodynamically consistent, finite strain, non-local plasticity theory for MGs proposed by Thamburaja [17] is employed in this study, as it can accurately capture the size-dependent deformation behavior of NGs [14], MGs [17] and MG composites [18,19]. This model incorporates four fundamental mechanisms which governs free volume evolution in MGs. ...
... It can be seen from Eq. (2) that negative int enhances f , hence promotes further evolution of plastic strain, while 0 int > resist development of strain. Indeed, it has been demonstrated that spatial distribution of int plays a decisive role in delaying localized deformation and promoting homogeneous deformation in nano-meter sized unnotched [17] as well as notched MGs [21,22] and NGs [14]. ...
... A thermodynamically consistent, finite deformation based non-local plasticity theory for MGs proposed by Thamburaja (2011) is employed in this study. This model is chosen because it has been shown to predict accurately the size dependent deformation response in MGs Thamburaja, 2011;Thamburaja and Liu, 2014 ) and nanoglasses ( Singh et al., 2014 ). In this model, the free volume ξ is the key state variable and is a measure of defect in the material. ...
... Further, it is akin to the back stress in crystalline materials which is related to the spatial heterogeneity in the plastic shear strain field ( Bittencourt et al., 2003 ). Previous studies have shown that the spatial distribution of τ int plays a crucial role in impeding shear localization and promoting homogenous deformation in nano-size MG samples ( Thamburaja, 2011 ), nano-glass samples with reduction in nano-grain size ( Singh et al., 2014 ) and single edge notched nano-size MG specimens with sufficiently deep notches . Also, it has been shown to be the source of strain hardening in nanoscale metallic glass specimens ( Thamburaja and Liu, 2014 ) and near notch tips , which corroborate with experimental and MD simulations ( Jang and Greer, 2010;Sha et al., 2015 ). ...
... However, on comparing Fig. 19 (a)-(c), the width of the shear bands increases with l c . This is consistent with the results of Singh et al. (2014) and which showed that the shear band width in nanoglasses and single edge notched MG specimens scale with l c . Further, the effect of l c on the deformation behavior of an acute DEN specimen as seen in Fig. 19 (a)-(c) is qualitatively similar to the influence of changing the chemical composition of CuZr MG in the MD simulations ( Fig. 8 ). ...
... A thermodynamically consistent, finite deformation based non-local plasticity theory for MGs proposed by Thamburaja (2011) is employed in this study. This model is chosen because it has been shown to predict accurately the size dependent deformation response in MGs Thamburaja, 2011;Thamburaja and Liu, 2014 ) and nanoglasses ( Singh et al., 2014 ). In this model, the free volume ξ is the key state variable and is a measure of defect in the material. ...
... Further, it is akin to the back stress in crystalline materials which is related to the spatial heterogeneity in the plastic shear strain field ( Bittencourt et al., 2003 ). Previous studies have shown that the spatial distribution of τ int plays a crucial role in impeding shear localization and promoting homogenous deformation in nano-size MG samples ( Thamburaja, 2011 ), nano-glass samples with reduction in nano-grain size ( Singh et al., 2014 ) and single edge notched nano-size MG specimens with sufficiently deep notches . Also, it has been shown to be the source of strain hardening in nanoscale metallic glass specimens ( Thamburaja and Liu, 2014 ) and near notch tips , which corroborate with experimental and MD simulations ( Jang and Greer, 2010;Sha et al., 2015 ). ...
... However, on comparing Fig. 19 (a)-(c), the width of the shear bands increases with l c . This is consistent with the results of Singh et al. (2014) and which showed that the shear band width in nanoglasses and single edge notched MG specimens scale with l c . Further, the effect of l c on the deformation behavior of an acute DEN specimen as seen in Fig. 19 (a)-(c) is qualitatively similar to the influence of changing the chemical composition of CuZr MG in the MD simulations ( Fig. 8 ). ...
In this work, numerical simulations using molecular dynamics and non-local plasticity based finite element analysis are carried out on tensile loading of nano-scale double edge notched metallic glass specimens. The effect of acuteness of notches as well as the metallic glass chemical composition or internal material length scale on the plastic deformation response of the specimens are studied. Both MD and FE simulations, in spite of the fundamental differences in their nature, indicate near-identical deformation features. Results show two distinct transitions in the notch tip deformation behavior as the acuity is increased, first from single shear band dominant plastic flow localization to ligament necking, and then to double shear banding in notches that are very sharp. Specimens with moderately blunt notches and composition showing wider shear bands or higher material length scale characterizing the interaction stress associated with flow defects display profuse plastic deformation and failure by ligament necking. These results are rationalized from the role of the interaction stress and development of the notch root plastic zones.
... The constitutive behavior of BMG matrix is represented through a finite deformation non-local plasticity theory proposed by Thamburaja [25], which has been shown to capture the mechanical response of BMGs [25e28], nanoglasses [29] and BMGCs [22] well. Moreover, use of a non-local model ensures accurate representation of strain localization which is insensitive to the finite element mesh employed in the analysis [30]. ...
... Further the cohesion is assumed to decay with free volume evolution as c ¼ c o expfkðx À x T Þg where c o denotes the initial value of cohesion and k < 0 is a constant that controls free volume induced softening. It must be noted that a material length, l c is present in the model through constant s 1 in Eq. (2), which is taken as l c ¼ ffiffiffiffiffiffiffiffiffiffiffi ffi s 1 =s 2 p [22,28,29]. As in Ref. [22], dendrites are assumed to follow J 2 flow theory of plasticity with power law hardening of the following form: ...
... It must be noted that the responses of all BMGCs are nearly identical up to E 2 ~ 0.025 which suggests that the effect of AR on the mechanical response is weak in this regime. A sharp drop in stress at E 2 ~ 0.025 is observed for the monolithic BMG which implies that strain localization within a dominant SB has occurred [22,28,29]. The AR ¼ 4 case shows a similar stress drop which is comparatively less steep, smaller in magnitude and happens at a higher strain of E 2 ~ 0.03 (see Fig. 2). ...
... The quantitative understanding of the mechanism of plastic deformation of amorphous glasses arising from the local rearrangement of discrete atomic regions, at least under certain conditions, stems from the late 1970s, see [3,4]. In particular, the shear transformation zone (STZ) mechanism proposed by Argon [4] has been studied from a variety of perspectives and at a variety of scales, see, for example, [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. For a comprehensive review of recent advances in this area, see Hufnagel et al. [24]. ...
A method for solving small strain plasticity problems with plastic deformation arising from the evolution of a collection of discrete shear transformation zones (STZs) is presented. The STZs are represented as transforming Eshelby inclusions. At each instant, superposition is used to represent the solution in terms of the Eshelby inclusions, which are given analytically for an infinite elastic medium, and an image solution that enforces the prescribed boundary conditions on the finite solid of interest. The image problem corresponds to a standard linear elastic boundary value problem. Constitutive relations are specified for the kinetics of the transformation. The general three dimensional formulation is given. Solutions for compression of a plane strain block are presented that illustrate the potential of the framework.
