High Temperature Mechanical Behavior of Aluminum- Cu50Zr50Metallic Glass Interface

Molecular dynamics (MD) simulations are carried out to determine interface strength between aluminum (metal) and Cu50Zr50 (metallic glass) at temperature of 500 K and at strain rate of 108 s-1. Simulation box of size 100 Å (x) × 110 Å (y) × 50 Å (z) is used for the above studies. At first Al-Cu50Zr50 crystalline interface model is built with the base layer-Al of 50 A and the top layer-Cu50Zr50 of 55 Å along y-direction. Later Cu50Zr50 metallic glass is obtained by quenching at a cooling rate of 4 x 1012 Ks-1. NPT ensemble is used in metallic glass preparation simulation. The interface model is then equilibrated at 300 K for 500 ps to relieve the internal stresses. EAM (Embedded Atom Method) potential is used for modelling the interaction between Al-Cu-Zr atoms. The interface strength of Al-Cu50Zr50 model interface is determined by applying load in the directions normal (mode-I) and parallel (mode-II) to the interface. NVT ensemble is used for the deformation studies. In mode-I for perfect and cracked interface, the interface fractures in the Al-region via necking. Sticking of the Al-atoms to the metallic glass is observed in both the loading conditions. Also, multiple voids are nucleated at the interface.


Introduction
Among the advanced materials for aviation, defense and automobile applications, Al-based metal Matrix composites (MMC) are of extraordinary mechanical properties, including low density, high elastic modulus, strength, good fatigue and good wear resistance [1][2][3]. The main drive behind the advancement of MMC is the likelihood to tailor their properties to meet particular requirements, which renders this sort of material remarkable in correlation with general engineering materials [4]. In common MMCs, the most broadly utilized reinforcement are ceramic, for example, Al2O3 or SiC, as fibers, flakes or particulates [5]. In any case, the interfaces between the reinforcement and the metal matrix are generally not good, which brings about very permeable (porous) materials and poor wettability which reduces the mechanical properties and also reduces prolonged consumption life of the MMCs. To take care of this issue, metallic glasses have been proposed as a novel reinforcement in MMCs [6][7][8][9], considering the metastable/amorphous nature of the metallic glass materials. The metallic glass reinforcement, containing practically metallic components, are accepted to be better with the metal matrix and to bring about better interface [10][11][12][13]. They are viewed as reasonable for use as reinforcement in light metal with moderately low melting temperature, for example, Al and Mg metals matrix. Mechanical properties of the composite are influence by the interface between reinforcement and the matrix. Moreover when the size of the reinforcement is reduced to the nano level, remarkable improvement in the mechanical properties like high elastic strain and large yield stress are observed [12] due to high interface strength. Deformation mechanisms such as Dislocation glide, twinning are impossible or too expensive to experimentally observe because experimental equipment are very sensitive to factors like crystal defects, impurities, lattice mismatch etc. [14]. To study the interface properties at nano scale, computer simulation like molecular dynamics (MD) offers a good alternative. In present study, we aim at investigating the deformation behavior of the interface between the aluminum and Cu50Zr50 metallic glass subjected to mode-I and mode-II loading at temperature of 500 K and strain rate of 10 8 s -1 .

Simulation method and model
We performed MD simulation on LAMMPS (Large Scale Atomic/Molecular Massively Parallel Simulator) [15] platform. The interaction between the Al-Cu-Zr atoms during mode-I and mode-II deformation is used by EAM potential developed by Zhou et al. [16]. As per the EAM, the total energy E of the crystal is expressed as below ,, where, the pair energy represented by ( ij  ) between the atoms i and j separated by a ( ij r ) distance, and the embedding energy ( i F ) associated with embedding an atom i into a local site with an electron density ( i  ).The following equation calculate the electron density where, e f represents the scaling constant and for pure metals its value is 1, e r represents the equilibrium nearest neighbour distance and  is additional parameter for the cutoff. The generalized elemental pair potential equation is given by [16] 20 20 Where, A , B ,  ,  and re are represented as fitted parameters, and k and  are two additional parameter for cutoff. The pair potential for a and b species are given below: The potential stated above is found to well fit to fundamental material properties, for example, lattice constants, elastic constants, bulk modulus, vacancy development energies and it predicts accurately the heat of solution of alloy. For instance, Meng et al. [17] effectively utilized Zhou potential parameters to study phase transitions in FeCo and FeNi nanoparticles. The EAM potential parameters utilized for Al, Cu and Zr are shown in Table 1.

Simulation of interface
Simulation box represented in Fig. 1 with dimension 100 Å (x) × 110 Å (y) × 50 Å (z) is used for the prediction of interface strength of Al (metal)-Cu50Zr50-(metallic glass). At first Al-Cu50Zr50 crystalline model is constructed with the bottom layer (Al) of 50 Å (Al-atoms represented as red colour) and the top layer of 60 Å (Cu50Zr50) in height along y-direction (Cu-atoms and Zr-atoms are represented as blue and yellow in colour respectively). NPT ensemble is used in metallic glass preparation simulation. Isothermal-isobaric (npt) ensembles which updates the position and velocity for atoms in the group each timestep. Thereafter, a cooling rate of 4 × 10 12 K/s is used to obtain Cu50Zr50 metallic glass by rapid cooling. To relieve the stresses interface model is equilibrated at 500 K for 500 ps. A defect (void) interface model is obtained by deleting atoms in the interface region of 20Å diameter. Mode-I and mode-II loading is used to determine the fracture strength of Al-Cu50Zr50 (perfect and defect) model interface. For mode-I, loading direction is y-axis [0 1 0] while for mod-II it is z-axis [0 0 1]. Periodic boundary condition is used along z-direction for mode-II loading while non-periodic boundary condition in all the directions for mode-I. All the simulations are carried out at timestep of 0.002 ps, strain rate of 10 8 s -1 and temperature of 500 K. The perfect and defect interface model is allowed for full separation under tensile load.

Results and discussion
The simulation results of the perfect interface and cracked interface simulated at temperature of 500 K and deformed at strain rate of 10 8 s -1 for mode-I and mode-II will be presented here. The engineering strain is calculated by comparing the boundary distance from the reference configuration of the undeformed structure in both the x and y -directions. Similar methodology was also used in the studies of Dandekar and Shin [18], and Zhou et al [19] Figs. 2(a) and 2(b) shows the stress-strain relation of the interface simulated at 500 K for strain rate of 10 8 s -1 under mode-I and Figs. 2(c) and 2(d) for mode-II conditions for perfect and cracked sample respectively. The regions on the stress-strain curve where changes occur in the interface have been numbered (1-4). The corresponding atomic position snap shot are shown in Figs. 3(a-d). The centro-symmetry parameter [20] is used to observe plastic deformation mechanism features and are shown in the Figs. 4(a-d). Simulated stress-strain features of the interface at temperature of 500 K and strain rate of 10 8 s -1 from its beginning stage to final stage of fracture are shown in Fig. 2(a-d). The disfigurement of the interface (glass and crystalline locale) starts with versatile distortion from its beginning state to the first yield state (Fig. 2a) ~121.9 MPa relates to strain of 0.019 in mode-I deformation and reaches to maximum stress of 181.94 MPa. When crack is introduced in the interface (Fig. 2(b)), yield strength and the maximum strength decreases. The stress-strain features are more serrated due to vibration of atoms about the mean positions at such high temperatures [21]. Fig. 3a and Fig. 3b shows the atomic position snapshots of the interface without and with void at the centre of the crystalline (aluminum) and metallic glass (Cu50Zr50) interface simulated at temperature of 500 K and deformed strain rate of 10 8 s -1 under mode-I condition. It can be seen that with progress of deformation amorphization of the crystalline region of the interface occurs along with nucleation of voids. In the interface with crack, its closure occurs as strain increases. The load bearing capacity decreased in the presence of void. Figs. 4a-d show centro-symmetry parameter of the perfect and defect interface under mode-I and mide-II loading conditions. It can be clearly seen that defects are nucleated in the crystalline region of the interface. Corresponding to mode-I of Fig. 2 (a) at point 1, two Shockley partials (Fig. 5) with burgers vector 1/6<112> are observed. At higher strains dislocations are not observed due to amorphization of the crystalline region at high temperature, as the atoms randomized for amorphization and dislocation dissolves [24].

Conclusions
 The stress-strain curve is more serrated due to deformation carried out at high temperature.  Yield strength and maximum strength is high for perfect interface.  During mode-I loading, the fracture occurs by necking in the aluminium region of the interface.  Void closure occurs during progress of deformation in the cracked interface.  Adhesion of the Al atoms at the interface has been observed for mode-I and mode-II loading.  Centro-symmetry parameter (CSP) revel amorphization of the interface in the early stages of the deformation due to high temperature.  Vacancies are observed in the crystalline region of the interface.  Formation of dislocations at high temperature is very low due to amorphization.