SCIENCE CHINA Physics, Mechanics & Astronomy • Research Paper •
September 2010 Vol.53 No.9: 1716–1719 doi: 10.1007/s11433-010-4094-y
Atomistic simulations of the effect of a void on nanoindentation response of nickel ZHU PengZhe*, HU YuanZhong & WANG Hui State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China Received March 11, 2010; accepted July 13, 2010
Three-dimensional molecular dynamics simulations have been performed to investigate the effect of a void on the nanoindentation of nickel thin film. The radius and depth of the void are varied to explore how they influence the nanoindentation. The simulation results reveal that the presence of a void softens the material and allows for a larger indentation depth at a given load compared to the no void case. The radius and depth of the void have a major effect on the indentation behaviors of the thin film. It is also observed that the void will collapse during the nanoindentation of crystal with void. And when the indentation depth is sufficiently large, the void will disappear. It is found that the indentation depth needed to make the void disappear depends on the void size and location. nanoindentation, molecular dynamics simulations, void PACS: 46.55.+d, 46.50.+a, 02.70.-c, 31.15.-p
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Introduction
Atomistic simulations have been used widely in the past to study the nanoindentation and have provided valuable insights into the mechanisms underlying materials response [1–6]. Pioneering work of atomistic simulations of nanoindentation was conducted by Landman et al. in 1990 [1]. Since then a large number of atomistic simulations have been performed to explore the behaviors of nanoindentation. For example, Kelchner et al. [2] used atomistic simulations to study the dislocation nucleation during the indentation on Au(111) substrate and Li et al. [5] studied nucleation and propagation of dislocations in indented solid Al by means of molecular dynamics simulations. Most of the previous simulations focused on materials without defects, but the materials in the engineering always have various defects such as grain boundary, surface steps and voids. Thus, atomistic simulations have been performed
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to investigate the effect of defects on nanoindentation. Zimmerman et al. [7] studied surface step effect upon nanoindentation of Au(111) crystal. Lilleodden et al. [8], Feichtinger et al. [9], and Ma et al. [10] explored the grain boundary effects and Tan et al. [11] employed the static atomistic simulations to investigate the effect of a void on the nanoindentation of copper(111). In addition to atomistic simulations, Yu et al. [12] used the quasicontinuum method that combines the finite element method and molecular dynamics simulations to study the effects of a nanocavity on the nanoindentation of copper film with a hard frictionless indenter. Thin films of Ni and Ni alloy have been widely used in micro-electro-mechanical systems (MEMS) [13,14] and magnetic storage systems [15,16]. Moreover, defects such as voids significantly affect the performance of materials [11]. Therefore, in this work we employ classical molecular dynamics simulations to investigate the effect of a single void on the nanoindentation of Ni(001). The goal of the investigation is to elucidate the effects of a single void on the material deformation behavior. phys.scichina.com
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ZHU PengZhe, et al.
Sci China Phys Mech Astron
2 Simulation methodology In this work, the nanoindentation is carried out on a single crystal nickel thin film with FCC structure. The schematic representation of the simulation model is shown in Figure 1. The x, z and out-of-plane y direction coincide with the [100], [001] and [010] crystallographic direction, respectively. The size of the Ni thin film is 50a0×50a0×20a0, where a0 is the lattice constant of Ni (a0=0.352 nm). A spherical void with a certain radius r is embedded under the surface of the Ni film directly beneath the indenter by removing some atoms. The distance between the center of the void and the top surface is h=r+d, where d is the distance between the inner upmost point of the void and the top surface of the thin film. The atoms are cataloged into three groups: rigid, thermostat and Newtonian atoms. Three layers of atoms at the bottom of the thin film are kept fixed serving as rigid atoms [1]. The four layers of atoms adjacent to the rigid atoms at the bottom of the film are thermostat atoms, in which the temperature is maintained by Langevin thermostat [17]. All the other atoms are Newtonian atoms which are unconstrained. Periodic boundary conditions are imposed in the x and y directions, which represent the infinite boundary of the thin film. The rigid atoms form a fixed boundary condition for the bottom of the film. The top surface of the film is free. In order to avoid the effect of thermal vibration on simulation results, we focus on a low temperature of T=1 K. The Newton’s equations of motion are integrated with a velocity-Verlet algorithm with a time step of 1 fs. The embedded atom method (EAM) potential is used to describe the interaction between the nickel atoms in the film. The EAM potential has been widely used in molecular dynamics simulations of metallic systems [18,19]. It was successfully used in our previous study [20]. In particular, the EAM potential for Ni developed by Mishin et al. [21] is adopted. A repulsive potential [2] is used to represent the spherical indenter. The repulsive potential is described by equation:
Figure 1 Schematic representation of the model.
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V (r ) = Aθ ( R − r )( R − r )3 ,
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(1)
where A is a force constant, θ ( R − r ) is the standard step function, R is the indenter radius, and r is the distance from each Ni atom to the center of the indenter. The force constant is usually on the order of several eV/Å3 [2,8]. In this work we choose A=3.3 eV/Å3 [2]. The indenter has a radius of R=4.5 nm. We have checked that the conclusions obtained from our simulations are not affected by the indenter radius in the range of R=3–5 nm. The simulation of nanoindentation process consists of an equilibrium stage and an indentation stage. In the equilibrium stage, the system is relaxed to its equilibrium configuration. In the second stage, indentation is modeled by lowering the indenter at a constant velocity of 10 m/s. Although the indentation speed in our simulations is several orders higher than that of nanoindentation experiments (10−6–10−9 m/s), it is slow enough to allow equilibrium of the system. And the indentation speed of 10 m/s was chosen in the nanoindentation of Ni thin film by Nair et al. [22]. To view the evolution of defects during nanoindentaion, we use the centrosymmetry parameter defined by Kelchner et al. [2], which has been proven to be effective for FCC crystals. The centrosymmetry parameter is zero for an atom in a perfect FCC material under any homogeneous elastic deformation and positive values for an atom near a defect such as a cavity, a dislocation or a free surface.
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Results and discussion
Figure 2(a) shows the load-depth curves for nanoindentation performed without a void and with a void located at various depths d with a fixed radius. Meanwhile, Figure 2(b) shows the load-depth curves for nanoindentation performed without a void and with a void with various radii at a fixed depth d. According to Figure 2, compared to the no void case the presence of a void softens the material and allows for a larger indentation depth at a given load. Also in Figure 2(a) as the depth of the void increases, the slope of the load-depth curves in the elastic stage increases as expected, while for the fixed depth d the slope of the load-depth curves in the elastic stage decreases with the increase of the void radius, as can be seen from Figure 2(b). A unique phenomenon in the indentation of crystal with void is the collapse of the void, which softens the material. The typical evolution of the void collapse during nanoindentation is shown in Figure 3. The void parameters are r=1.5 nm and d=0.6 nm.The deformation pattern is depicted with the centrosymmetry parameter (CSP). The atoms with CSP values above 0.5 correspond to defective atoms [23]. The atoms with CSP below 0.5 are assumed to be in the perfect FCC configuration and are removed in Figure 3(a)– (d). Figures 3(a) and 3(e) show the atomistic configuration after relaxation. Figure 3(b) presents the snapshot at the
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ZHU PengZhe, et al.
Sci China Phys Mech Astron
September (2010) Vol. 53 No. 9
Figure 2 Load-depth curves for two void parameters: (a) at various depths with the fixed radius r=1.5 nm and (b) with various radii at the fixed depth d=0.6 nm.
indentation depth of 0.25 nm. As can be seen, in the elastic deformation stage the top surface of the void is compressed. It can also be seen that the atoms with CSP larger than 0.5 are only those near the void surface and substrate surface, indicating that most of the atoms retain the near-perfect lattice structure during the elastic deformation. Then the dislocations nucleate as shown in Figure 3(c). Obvious collapse of the void can also be observed [24]. The nucleation and movement of dislocations and the collapse of void continue until the maximum indentation depth (see Figures 3(d) and 3(f)).
Figure 3 Snapshots of the evolution of the void collapse during the nanoindentation. The void parameters are r=1.5 nm, d=0.6 nm. Figures 3(a)–(d) are the snapshots of the indentation process for the indentation depths of 0, 0.25, 0.55 and 0.95 nm. Figures 3(e) and 3(f) are the x-z plane cross- section snapshots of the indentation process for the indentation depths of 0 and 0.95 nm. The atoms are colored according to their centrosymmetry parameters.
When the indentation continues and the indentation depth is sufficiently large, the void will disappear as expected since many atoms near the indenter are pushed into the void vacancy [11]. Figure 4 shows the x-z plane cross-section snapshots of indentation process for different voids at indentation depths when the voids disappear. The indentation depth is 1.35 nm when the void disappears for the void with r=1.5 nm and d=0.6 nm (Figure 4(a)). The indentation depths are 1.5 nm for the void with r=1.5 nm and d=0.9 nm (Figure 4(b)) and 1.85 nm for the void with r=2 nm and d=0.6 nm(Figure 4(c)). The results clearly show that the indentation depth needed to make the void disappear is related to the void size and location. For voids with the same size(r), as the depth of void (d) increases, the indentation depth required to make the void disappear also increases. For voids with the same depth (d), as the size of the void(r) increases, the indentation depth needed to make the void disappear increases as well. In our simulations no crack is observed during the indentation process. Besides, stress may concentrate at the internal surface of the void and the stress concentration will prompt the void to collapse during indentation [11].
4
Conclusions
In this paper, the effect of a void on the nanoindentation of nickel thin film is explored using molecular dynamics simulations. It is found that the material softens and a larger depth is needed at a given load due to the presence of a void.
Figure 4 x-z plane cross-section snapshots of the indentation process for different voids at indentation depths when the voids disappear. The atoms are colored according to their centrosymmetry parameters.
ZHU PengZhe, et al.
Sci China Phys Mech Astron
The simulation results also reveal that both the radius and depth of a void significantly influence the nanoindentation response of thin film. As the depth of the void increases, the slope of the load-depth curves in the elastic stage increases. For the fixed depth the slope of the load-depth curves in the elastic stage decreases with the increase of the void radius. It is observed that the void will collapse during the nanoindentation of crystal with void. And when the indentation depth is sufficiently large, the void will disappear. It is found that the indentation depth needed to make the void disappear is related to the void size and location. For voids with the same size, as the depth of void increases, the indentation depth required to make the void disappear also increases. For voids with the same depth, as the size of the void increases, the indentation depth needed to make the void disappear increases as well. This work was supported by the National Natural Science Foundation of China (Grant Nos. 50730007 and 50721004) and the State Key Development Program for Basic Research of China (Grant No. 2009CB724200).
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