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Molecular dynamics simulation of mechanical characteristics of CuZr bulk metallic glasses

using uni-axial tensile loading technique

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2014 Phys. Scr. 89 115701

(http://iopscience.iop.org/1402-4896/89/11/115701)

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Molecular dynamics simulation ofmechanical characteristics of CuZr bulkmetallic glasses using uni-axial tensileloading technique

Fayyaz Hussain1, Muhammad Imran1, Muhammad Rashid3, Hafeez Ullah2,Abdul Shakoor1, Ejaz Ahmad1 and S A Ahmad4

1Materials Simulation Research Laboratory (MSRL), Department of Physics, Bahauddin ZakariyaUniversity, University Campus, Bosan Road, 60800, Multan, Pakistan2 Laser and Optronics Laboratory, Department of Physics, Bahauddin Zakariya University, UniversityCampus, Bosan Road, 60800, Multan, Pakistan3Department of Physics, COMSATS Institute of Information Technology, 44000 Islamabad, Pakistan4Department of Physics Simulation Laboratory, The Islamia University of Bahawalpur, Pakistan 63100

E-mail: fayyazhussain248@yahoo.com and anam_iub@yahoo.com

Received 13 February 2014, revised 26 June 2014Accepted for publication 2 September 2014Published 23 October 2014

AbstractIn the present study, a three-dimensional molecular dynamics simulation is performed to elaboratethe mechanical strength of bulk metallic glasses (BMGs). The radial distribution function (RDF) isused to predict the structural disorder that appeared during the quenching provided for BMGsprocessing. The mechanical behavior is investigated using uniaxial tensile loading through stress–strain curves. It is observed that during tensile loading, the yield strength of Cu50Zr50 increaseswith the increase in the strain rate, and it quickly attains the maximum value. Soon after the samplefractures without entering into the plastic region. To elucidate the effects of componentconcentration, we design BMGs with the following three configurations: Cu25Zr75, Cu50Zr50 andCu75Zr25. It is revealed from the results that samples with a lower Cu concentration have a higherdegree of short-range ordering and lower yield strength, and vice versa. To analyze thesignificance of crystalline–amorphous interfaces, we designed four cylindrical core–shellnanorods with Cu cores and BMGs shells. It is observed that the mechanical strength of the core–shell nanorod is significantly higher compared to the pure BMGs nanorod.

Keywords: BMGs, uniaxial, core-shell, mechanical strength

(Some figures may appear in colour only in the online journal)

1. Introduction

Recent developments in science and technology have enabledscientists to discover a new class of materials for high-techapplications while offering better performance [1]. Industrialapplications require materials that exhibit maximum efficiencyunder optimum conditions. Researchers have introduced manynew materials with novel characteristics, such as carbon nano-tubes, graphene and so on. Among these materials, metallicglasses are of great interest because of their unique mechanical

characteristics. Metallic glasses have attracted considerableattention from material scientists and thus they have emerged asa prospective field of research in recent years [2]. The recentdiscovery of new glass-forming compositions has made it mucheasier and more promising to design bulk metallic glasses.

Bulk metallic glasses (BMGs) exhibit excellentmechanical properties, such as high corrosion resistance, highstrength and excellent forming and shaping ability [3]. Someof their excellent properties compared to those of crystallinematerials made them strong candidates for engineering and

| Royal Swedish Academy of Sciences Physica Scripta

Phys. Scr. 89 (2014) 115701 (6pp) doi:10.1088/0031-8949/89/11/115701

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commercial applications [4]. BMGs can be processed in awide range of different component concentrations, includingthose based on Fe, Al, Ag and Mg. [5]. Among these cate-gories of BMGs, the Zr-based BMGs have excellentmechanical properties [6]. Previous studies have shown thatCu- and Zr-based BMGs have relatively better glass-formingability (GFA) compared to other BMGs [7]. However, brit-tleness at room temperature is one of its curial drawbacks [8];therefore, it is necessary to prepare Cu- and Zr-based BMGswith less brittleness and relatively higher hardness. For thispurpose, thin-film metallic glasses (TFMGs) have recentlybeen prepared experimentally by using sputtering techniques.Research has shown that binary Cu- and Zr-based TFMGsexhibit wider temperature and compositional range. TheCu/Zr–Cu crystalline/amorphous system has been describedwith different thicknesses and has proved that high strengthand large tensile elongation occur before fracture [9].

Recently, various computational techniques have beenwidely used to characterize the BMGs in two- and three-dimensional phases [9] in a more vigorous way (atomicscale), which is sometimes impossible with an experimentalset up. The mechanical properties of Cu46Zr54 BMGs havebeen investigated with the help of nano-indentation and uni-axial compression tests through MD simulation [9]. The MDstudies have shown the stability of Cu50Zr50 icosahedralclusters that were softly landed on the surface of Cu50Zr50BMGs [9]. The plastic deformability of high-density fluc-tuated states due to different thermal quenching processes ofthe binary Cu67Zr33 BMGs have been explored using MDsimulation [10]. MD simulations employing the Finnis andSinclair potential have reported the presence of short-rangeatomic ordering in Cu60Zr40 BMGs [16]. The atomic order inCu–Zr BMGs has been characterized by using an x-rayabsorption fine-structure method, as well as through MDsimulation. The atomic description of glass formation andstructural analysis of the Cu46Zr54 BMGs has been exploredusing the MD studied [11]. The actual problem during thefabrication of BMGs is to provide the high cooling ratenecessary to achieve better GFA; however, this is much moredifficult to achieve under laboratory conditions [12].

In the current study, the main aim is to characterize thestructural and mechanical behavior of Cu–Zr BMGs undervarious conditions. The structural disorder of BMGs isexplored using the radial distribution function (RDF), andmechanical behavior is elaborated using uni-axial tensile tests(employing the stress–strain data recorded during the uniaxialloading process). To analyze the significance of crystallineamorphous interfaces, we have designed a cylindrical core–shell nanorod with a crystalline Cu core and a BMGs shell.

2. Details of simulation process and interatomicpotential

The typical configuration of BMGs simulation cells is shownin figure 1. The nanorods have dimensions of60 Å× 30 Å× 30 Å along, [1 0 0] [0 1 0] and [0 0 1] direc-tions, respectively, and contain 4779 atoms. The initial

nanorod sample has B2 structure with randomly mixed Cuand Zr atoms. A large-scale Atomic/Molecular MassivelyParallel Simulator (LAMMPS) [13] is used to perform thesimulation throughout this work. Periodic boundary condi-tions are employed in all three dimensions. The sample is firstheated above the melting temperature (up to 2000 K). Sec-ondly, we equilibrated it at that temperature for 500 ps and,finally, cooled it by quenching at a cooling rate of 2 K ps−1

down to 300 K with a temperature step of 200 K. After eachtemperature step, the sample is allowed to equilibrate for200 ps. Finally, the sample is equilibrated at 300 K for a totaltime of 1000 ps. The time step for the entire simulation pro-cess is 1 fs.

Furthermore, we modeled a core–shell nanorod with a Cucore and BMG shell to achieve better mechanical properties,as shown in figure 8. For this purpose, we designed fournanorod samples (Cu50Zr50, Cu/Cu25Zr75, Cu/Cu50Zr50 andCu/Cu75Zr25). All the samples were processed using thetechnique of heating above the melting temperature and thencooling down (rapidly quenching) to room temperature. Thelength and radius of all the samples are 100 and 40 Å,respectively, whereas the core–shell nanorods have a Cu coreof radius 25 Å. The samples consist of a total of 41608 atoms,enough to achieve the stable core–shell BMG nanorodsshown in figure 8.

There are three types of interactions possibly occurringbetween Cu and Zr atoms in the simulation box, i.e. Cu–Cu,Zr–Zr and Cu–Zr. These interactions can be created using awell known generalized EAM potentials developed by M IMendelev et al [14]. The total energy Ei of an atom i is

⎛⎝⎜⎜

⎞⎠⎟⎟∑ ∑ραβ Φ= +α α β

≠ ≠

E F r r( )1

2( )i

j i

ij

j i

ij

Where F is the embedding energy that is a function of theatomic electron density ρ Φ is a pair-potential interaction andα and β are the element types of atoms i and j.

3. Results and discussion

3.1. Mechanical behavior of Cu50Zr50 BMGs

To conduct the structural analysis, we calculated the RDFduring the cooling process and plotted it against the intera-tomic distance. This gave valuable information about thestructural disorder of the sample. The RDF values calculatedduring the cooling process at various temperatures are shownin figure 2. In this graph, each individual RDF curve shows acomplete loss of structural order of the sample when it iscooled down to 300 K. The peak height decreased with thetemperature, which is evidence that the structural stability ofthe sample increases with the relative decrease in the tem-perature. It can also be observed from figure 3 that the sam-ples at lower temperatures are relatively more stable becauseof the limited motions of the atoms.

The basic simulation process involves the deformation ofa BMG nanorod by stretching it from both ends with constant

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Phys. Scr. 89 (2014) 115701 F Hussain et al

velocity to ensure uni-axial tensile loading and constant strainrate (109 s−1), as presented figure 4. This can be seen in thestress-versus-strain graph in figure 7. The engineering stressinitially increases with the increase in the value of strain (inthe elastic region) and then suddenly fracture occurs withoutentering into the plastic region. It is observed that the value ofstress suddenly decreases to a significantly low value, whichindicates that the Cu50–Zr50 BMGs is brittle in nature.

3.2. Effect of strain rate on the mechanical behavior of Cu50–Zr50 BMGs

In order to investigate the effects of strain rate on themechanical response of the nanorod, we subjected it todeformation with three velocities (0.01, 0.1 and 1 Å ps−1)related to three constant strain rates of the order 108, 109 and1010 s−1, respectively. The resulting stress-versus-straincurves are compared as shown in figure 5. It can be observedfrom the figure that there is a significant change in themechanical response of BMGs for different strain rates. Theblue line shows the curve of highest strain rate (1010 s−1), thered curve represents (109 s−1), and the black curve representsthe lowest strain rate (108 s−1). It is revealed that the yield

Figure 1. (a), (b) and (c) showing final amorphous structures for Cu25Zr75, Cu50Zr50 and Cu75Zr25; yellow and blue colors represent Zr andCu atoms, respectively.

Figure 2. Radial distribution functions of Cu50Zr50 at differenttemperatures.

Figure 3. Total energy of Cu50Zr50 at different temperatures.

Figure 4. To deform the sample, constraints are applied on both endsof the sample along the x-axis to ensure uniaxial tensile loading withconstant strain rate (109 s−1), Cu50Zr50. It is observed thatdeformation of BMGs rods occur randomly without specificdirection, which confirms the glassy behavior of the rods.

Figure 5. Uniaxial tensile loading stress VS strain for Cu50Zr50 atdifferent strain rates.

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Phys. Scr. 89 (2014) 115701 F Hussain et al

strength of the nanorod increases with the increase in thestrain rate, i.e. it is higher for highest value of the strain rate,and vice versa. Whereas the fracture occurs relatively soonerat the highest strain rate compared to the lower strain rate, itindicates that the nanorod appears relatively more brittle tothe higher strain rates, and vice versa.

3.3. Effect of component concentrations in CuxZr100− x BMGs

To investigate the effect of component concentrations on themechanical behavior of binary BMGs, we designed threeBMGs samples with different Cu and Zr concentrations, i.e.Cu25Zr75, Cu50Zr50 and Cu75Zr25, as shown in figure 1. Firstof all, the BMGs samples with different concentrations wereprocessed using the method of heating above the meltingtemperature and then rapidly cooling them down to roomtemperature (300 K) with a very high quenching rate on theorder of 2 K ps−1. The RDF curves can provide valuableinformation to ensure the effect of component concentrationson the final structure and stability of the BMGs in this regard.The resulting RDF curves for all three samples were com-pared at room temperature, as shown in figure 6. The RDFcurves for Cu25Zr75, Cu50Zr50 and Cu75Zr25 are representedby black, red and blue colors, respectively. Glass formationcan be analyzed from the peaks of RDF curves of samples.The first peak of the RDF curve is at maximum for theCu25Zr75 configuration and at minimum for the Cu75Zr25configuration, whereas Cu50Zr50 has an intermediate value.This is evidence that final structures will be significantlydifferent for the three configurations.

To investigate the effect of component concentrations onmechanical behavior, the three samples were subjected to uni-axial tensile loading at a constant strain rate on the order of109 s−1. The resulting stress–versus-strain graphs are plottedin figure 7 for comparison. The curves for three samples,Cu25Zr75, Cu50Zr50, and Cu75Zr25, are represented by thecolors of blue, red, and black, respectively. It is clear from thefigure that the yield strength of the sample increases as the Cuconcentration in the sample increases, whereas the brittleness

was also found to increase with the increase of Cu con-centration, and vice versa. The mechanical behavior of thethree nanorod samples can be summarized by combining theobservations from figures 6 and 7. It is observed that forCu25Zr75, the RDF peak has highest value, whereas the yieldstrength is lowest; however, Cu75Zr25 exhibits highest yieldstrength and lowest value of RDF peaks. These observationsindicate that the sample with highest Cu concentrationappears to be relatively harder and more brittle, while pos-sessing better glassy structure compared to the lower Cuconcentrations. The Cu50Zr50 lies in between both samples inall of its mechanical responses. The results are in completeagreement with previously reported work [15–18].

3.4. Effect of Cu core on mechanical behavior of CuZr BMGs

To observe the effect of core–shell structure on the mechan-ical properties of the nanorod, four BMGs samples (Cu50Zr50,Cu/Cu25Zr75, Cu/Cu50Zr50 and Cu/Cu75Zr25) were subjectedto deform using the uni-axial tensile loading process. For thispurpose, both ends of the nanorod were constrained to movein opposite directions with a constant strain rate on the orderof 109 s−1, as shown in figure 9. The resulting stress-versus-strain curves for all the samples are plotted in figure 10 forcomparison. It can be elaborated from figure 10 that the yieldstrength of core–shell nanorods (for all core–shell config-urations) is significantly higher compared to a simple BMGsnanorod. This increase in the yield strength is due to theinterface present between the crystalline Cu core and amor-phous shell nanorod; such interface is called ‘crystallineamorphous interfaces’ (CAI). The presence of CAI sig-nificantly enhances the yield strength of the core–shellnanorod. The fracture in core–shell nanorods takes placerelatively sooner compared to a pure Cu50Zr50 nanorod,which is evidence that presence of CAI significantly enhancesthe brittleness of the nanorod. These results are in agreementwith previously reported work [19–20].

Figure 6. RDF for Cu25Zr75, Cu50Zr50 and Cu75Zr25.Figure 7. Uniaxial tensile loading stress VS strain for Cu25Zr75,Cu50Zr50 and Cu75Zr25 at constant strain rate.

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4. Conclusions

It is concluded from the results of the uni-axial tensiledeformation of the Cu50Zr50 BMGs nanorod that the fracturetakes place without considerable plastic deformation, con-firming that Cu50Zr50 BMGs are brittle. The results also showthat the yield strength for a Cu50–Zr50 nanorod increases withan increase in the strain rate, while fracture occurs earlier incase of higher strain rate, and vice versa. Thus, at a higherstrain rate, the nanorod appears to be more brittle; however, itappears stronger compared to those with a lower strain rate.We designed CuZr BMGs with three different component

concentrations to achieve BMGs with better mechanicalproperties. Results show that the nanorod with a lower Cuconcentration has a lower yield strength and higher prob-ability of the existence of short-range ordering, whereasBMGs with higher Cu concentrations appear to be stronger,more brittle, and possessing better GFA. The current resultsare well consistent with previously reported experimental andtheoretical results with the same component configurations ofthe Cu50Zr50 sample. [21–22]. It is also concluded from theobservations that the presence of CAI significantly enhancesthe mechanical strength and brittleness of core–shell nanorodscompared to those of its pure BMGs counterpart of the samedimensions.

Acknowledgements

This work is carried out in the Department of PhysicsSimulation Lab, The Islamia University of Bahawalpur,Bahauddin Zakariya University Multan Pakistan and is par-tially supported by Higher Education Commission (HEC) ofPakistan.

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Figure 8. Initial configuration of simulation cell having length and radius 100 Å and 40 Å, respectively; (a) Cu50Zr50 (b) Cu core Cu50Zr50shell (core with radius of 25 Å).

Figure 9. Deformation behavior of Cu core BMGs shell sampleunder uni-axial tensile loading with constant strain rate 109 s−1.

Figure 10. Uniaxial tensile loading stress VS strain for various core–shell configuration.

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