Strain Rate and Temperature Effects on the Strength ...

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ScienceDirect Procedia Engineering 184 (2017) 631 – 636

Advances in Material & Processing Technologies Conference

Strain Rate and Temperature Effects on the Strength and Dissipative Mechanisms in Al-Cu50Zr50 Interface Model: Molecular Dynamics Simulation Study Pradeep Gupta, Natraj Yedla Computational Materials Engineering Group, Department of Metallurgical and Materials Engineering, National Institute of Technology Rourkela-769008, India

Abstract

Molecular dynamics (MD) simulations are performed to characterize the metal (Al)-metallic glass (Cu50Zr50) interface strength and dissipative mechanisms at different strain rates and temperatures under mode-I loading. EAM (Embedded Atom Method) potential is used for modelling the interaction between Al-Cu-Zr atoms. Simulation box size of 100 Å (x) × 110 Å (y) × 50 Å (z) is used for investigation the properties of the model interface. The model is first constructed with the bottom layer Al of 50 Å and the top layer of Cu50Zr50 of 55 Å in height along y–direction. Thereafter, Cu50Zr50 metallic glass is obtained by rapid cooling at a cooling rate of 8.5 × 1011 K s-1 using NPT ensemble. The interface is deformed at strain rates of 109 s-1 and 1010 s-1 and at temperatures of 150 K and 250 K using NVT ensemble (timestep=0.002 ps). It is found that the strength of interface increases with increase of strain rate and decreases with increase in temperature. Centro symmetry parameter (CSP) is used for analysis of dissipative mechanisms operative during the deformation of the interface. It is found that the dominant deformation mechanism at the interface is by Shockley partial dislocation motion. © 2017 The Authors. Published by Elsevier Ltd. © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of the Advances in Material & Processing Technologies (http://creativecommons.org/licenses/by-nc-nd/4.0/). Conference.under responsibility of the organizing committee of the Urban Transitions Conference Peer-review Keywords: molecular dynamics; strain rate; interface; dislocations

* Corresponding author. Tel.:91-6612462569; fax: 91-6612462550.

E-mail address: [email protected]

1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the Urban Transitions Conference

doi:10.1016/j.proeng.2017.04.128

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Pradeep Gupta and Natraj Yedla / Procedia Engineering 184 (2017) 631 – 636

1. Introduction The commonly used reinforcements in Al based metal matrix composites (MMCs) are ceramic materials such as Al2O3 or SiC particles which possess an excellent combination of specific strength and stiffness at both ambient and elevated temperatures [1–4]. However, due to their low wettability, results in a porous interface, and thus deteriorates mechanical properties and increases corrosion sensitivity of the composite [5]. It is reported for the first time that by using Ni-based metallic glass (MG) in Al-alloy matrix resulted in better bonding at the interface [6]. In the recent past several types of MGs such as Fe-based, Cu-based, Zr-based and Al-based alloys mainly in the form of particles are used as reinforcements for improving the mechanical properties of Al alloys [7–10]. Thus, it can be stated that MGs have emerged as suitable substitutes for ceramic reinforcements. In the MMC, the properties of the composite can be drastically altered by nature of the interface between matrix and reinforcement, hence making it necessary to understand the characteristics of the interface [11]. For example, a hard interface decreases the toughness while that a soft interface increases the toughness [11]. In order to study the interface experimentally it is expensive and also difficult due to sensitivity to many factors such as lattice mismatch, crystal defects, the presence of impurities, thermal expansion coefficient mismatch and reactions at the interface [12,13]. Also, the mechanical properties cannot be improved unless the mechanical behavior is understood at the atomic level [12]. So, a computer simulation tool such as molecular dynamics (MD) which is conducted at the atomic level is a good alternative for studying the interface properties. Needleman [14] introduced a methodology to model the interface separation. Based on this model, the traction vector T on a crack surface in equation 1 is related to the displacement jump vector Δ across that crack surface via an interface separation potential ϕ as given below

T

wI / w' (1)

In the above methodology, large deformations and interatomic separation are based on the concept of crack tip cohesive zone [15,16] and cohesive zone models (CZM) are the popular models for modeling the interface fracture [17,18]. Using MD simulations and based on CZM, several studies have been reported on the interface characteristics of crystalline and non-crystalline materials. Spearot et al. [19] have shown that work of separation of pure bi-crystal copper grain boundary interface under mode-I is less than mode-II. Wu et al. [20] have reported that intergranular crack propagation in bi-crystal Ni is influenced by temperature, and slip bands are stronger to prevent intergranular crack growth than deformation twinning around the crack-tip. Dandekar and Shin [12] have done traction-separation studies on Al-SiC interface model in which they report that the strength of the interface decreases with increase in temperature. Further, interface studies between polyethylene and graphene suggests that separation is observed in the polymer region rather than at the interface due to strong mechanical interactions between polymer and interface [21]. In this paper, we report Al-Cu50Zr50 interface mechanical behavior under mode-I (normal to the interface) loading condition at strain rates of 109 s-1 and 1010 s-1 and at temperatures of 150 K and 250 K. All the studies are carried out using MD simulations based on CZM. We have also focussed on structural changes, dissipative mechanisms such as dislocation nucleation and their interactions during deformation. This MD simulation work is shown to provide good predictions of the interface strength and will contribute to better understanding of the deformation behavior of the interface of metal-metallic glass nano-composite.

2. Simulation procedure MD simulations in the present study are performed on LAMMPS (Large Scale Atomic/Molecular Massively Parallel Simulator) platform which is developed by Sandia Laboratory [22]. EAM potential developed by Zhou et al. [23] is used for modeling the interaction between the Al-Cu-Zr atoms. A cut-off distance of 7.1 Å is used for force calculations. The potential is valid and other details of parameters can be obtained from Ref. [23]. Moreover, the potential is used by several researchers. Phase transitions in FeCo and FeNi nanoparticles have been studied by Meng et al. [24]. Oxidation of Al layers on Ni65Co20Fe15 surface has been studied using Zhou et al. potential [23]. Furthermore, cold welding of Au and Ag nanowires [25] has been modelled using the above potential.


Fig. 1 shows the atomic position snapshot of Al (metal)-Cu50Zr50 (metallic glass) interface which is of dimension 10 nm width (x-axis) × 11 nm height (y-axis) × 5 nm thick (z-axis). Two rigid regions of dimensions 10 nm width (x-axis) × 2 nm height (y-axis) × 5 nm thick (z-axis) are created at the top and bottom of the interface model. The net force on each atom in these rigid regions is set to zero during the deformation. To obtain Al (metal)Cu50Zr50 (metallic glass) interface model we start with constructing of Al–Cu50Zr50 crystalline model. The bottom layer is filled with Al atoms (5 nm height; lattice parameter, a = 4.05 Å) and above it with Cu50Zr50 atoms which is obtained by randomly replacing 50% of Cu atoms by Zr atoms (lattice parameter of copper, a = 3.615 Å). The interface separation distance is chosen more than the equilibrium bond lengths, i.e., 3.5 Å [26]. Cu50Zr50 MG is obtained by rapid cooling from the temperature of 2300 K to 300 K at cooling rate of 8.5 × 1011 K/s (timestep = 0.002 ps) using NPT ensemble with periodic boundary conditions. The interface model is then equilibrated for 500 ps for relieving stresses generated during rapid cooling. The interface is deformed by applying uniform velocity corresponding to strain rates of 109 s-1 and 1010 s-1 to the top rigid region along [0 1 0] direction (y-axis) under nonperiodic boundary conditions. The deformation is performed using NVT ensemble and the temperature is held at 150 K and 250 K during deformation using a Nose-Hoover velocity scaling algorithm [27,28]. Strain is calculated by change in the box length along y-axis and stress is calculated using Virial stress [29]. The defects generated during deformation are visualized using centro-symmetry parameter (CSP) [30] using OVITO software [31].

Fig. 1: Atomic position snapshot of Al (metal)-Cu50Zr50 (metallic glass) interface model.

3. Results and Discussions 3.1. Effect of strain rate and temperature on the stress-strain behavior Fig. 2A shows the stress-strain plots of the interface model deformed at temperature of 150 K and strain rates of 109 s-1 (black color) and 1010 s-1. Atomic snapshots of the interface model are captured at the points on the stress-strain curve where significant changes occur. These are represented by numerical (1-5) for strain rate of 109 s-1 and numerical (1-5) enclosed in angular brackets for strain rate of 10 10 s-1. Fig. 2B shows the stress-strain plots of the interface model deformed at temperature of 250 K and at strain rates of 10 9 s-1 and 1010 s-1. In Fig. 2A, the deformation of the interface model begins with the elastic deformation up to point 2 corresponding to a strength of ~750 MPa. Straining beyond this point leads to sudden fall in the stress due to burst of dislocations. With progress of deformation the strength of the interface continuously decreases and fractures at point 5 which can be clearly seen from the atomic snapshot also. At strain rate of 10 10 s-1 the strength of the interface is much higher (~1000 MPa). The stress drops after this point and continually decreases. However, the interface does not fracture even after straining to 50 %. This could be due to amorphization of the regions close to the interface [32]. At temperature

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Fig. 2 Stress-strain curves and corresponding atomic snapshots of Al-Cu50Zr50 interface model deformed at strain rates of 109 s-1 and 1010 s-1 and at different temperatures. A: 150K, B: 150K. of 250 K and strain rate of 109 s-1 the interface yields at ~675 MPa which is lower than that at temperature of 150 K. after the yield, there is sudden drop in the stress corresponding to flow softening behavior (Fig.2B3). Upon further straining, the deformation becomes localized (Fig. 2B4) and finally thins to fracture. At strain rate of 1010 s-1, the interface yields at ~ 675 MPa and becomes pristine. Upon straining elastic deformation resumes up to a stress of ~ 950 MPa. Further straining results in sudden drop in the stress due to burst of dislocations. The interface strength decreases continuously and finally fractures at 50% strain. The corresponding atomic snapshots clearly reveal the strain localization behavior in the form of necking in the Al region (Figs. 2B4 and 2B5). 3.2 Defect analysis For visualization defects and structural changes, CSP is used and dislocation extraction algorithm (DXA) is used identify different types of dislocations (Shockley, stair rod, and perfect dislocation). Fig. 3A and Fig. 3B shows the CSP images (Fig. 3A1, Fig. 3B1) and DXA (Fig. 3A2 and Fig. 3B2) analysis of the interface model deformed at temperature of 150 K and at strain rates of 10 9 s-1 and 1010 s-1. At strain rate of 109 s-1 and strain = 0.005, it can be seen that there are no dislocations in the interface which corresponds to the elastic region of the stress-strain curve. As the stress reaches the yield stress, sudden burst of dislocations (Fig. 3A1 and Fig. 3A2) are observed in the Al region at strain of 0.02. With progress of deformation the dislocation density increases due to their interactions as observed at strain of 0.028. DXA analysis reveals the formation of partial dislocation like Shockley partial (green in color) with burger vector 1/6 and some stair rod dislocations (pink in color) with burger vector 1/6. The CSP images captured at different strains reveal parallel and V-shaped stacking faults. Despite of high stacking fault energy in Al, stacking faults are observed in the sample due to its nanoscale size [33]. At strain rate of 1010 s-1, similar features such as stacking faults are observed in the Al region of the interface. Furthermore, DXA analysis also reveals several Shockley partials and stair rod dislocations. Fig. 3C and Fig. 3D shows the CSP images (Fig. 3C1, Fig. 3D1) and DXA (Fig. 3C2 and Fig. 3D2) analysis of the interface model deformed at temperature of 250 K and at strain rates of 10 9 s-1 and 1010 s-1. With increase in temperature of deformation from 150 K to 250 K, the deformation mechanism is found to be the same as observed at 150 K temperature. However, more defects are observed as seen from the CSP images. Also, the DXA analysis reveals several Shockley partials and stair rod dislocations. The dislocation density is found to be less than that observed at 150 K temperature and is attributed to amorphization of the Al region of the interface.


Fig. 3: CSP analysis and DXA snapshots of Al-Cu50Zr50 interface model deformed at strain rates of 109 s-1 and 1010 s-1 and at different temperatures: A, B: 150 K; C, D: 250 K.

4. Conclusions Molecular dynamics simulations have been carried out to study the effect of strain rate and temperature on the AlCu50Zr50 model interface strength under mode-I loading. Based on the results, we draw the following conclusions. The interface strength decreases with increase in temperature and increases with increase in strain rate. Structural changes analyzed by CSP studies show stacking faults in the Al region of the interface despite of high stacking fault energy in Al. This is attributed to the nanoscale sample size. The dominant deformation mechanism at the interface is by nucleation of Shockley partials which interact during straining of the interface and form stair rod dislocations. The dislocation density is found to be lower at 250 K and is due to amorphization of the sample. References [1] M. Alizadeh, M.H. Paydar, Fabrication of nanostructure Al/SiC P composite by accumulative roll-bonding (ARB) process, J. Alloys Compd. 492 (2010) 231–235. [2] K. Wang, W. Li, J. Du, P. Tang, J. Chen, Preparation, thermal analysis and mechanical properties of in-situ Al 2 O 3/SiO 2 (p)/Al composites fabricated by using zircon tailing sand, Mater. Des. 99 (2016) 303–313. [3] L. Zhang, H. Xu, Z. Wang, Q. Li, J. Wu, Mechanical properties and corrosion behavior of Al/SiC composites, J. Alloys Compd. 678 (2016) 23–30. [4] M. Rahimian, N. Parvin, N. Ehsani, Investigation of particle size and amount of alumina on microstructure and mechanical properties of Al

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