Molecular dynamics simulation of tensile behavior of ... - Springer Link

Journal of Mechanical Science and Technology 27 (1) (2013) 43~46 www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-012-1231-8

Molecular dynamics simulation of tensile behavior of diffusion bonded Ni/Al nanowires† Zhenjiang Hu1,2, Junjie Zhang2,*, Yongda Yan1,2, Jiuchun Yan2 and Tao Sun2 1

Key Laboratory of Micro-systems and Micro-structures Manufacturing of Ministry of Education, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China 2 Center for Precision Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China (Manuscript Received November 25, 2011; Revised July 10, 2012; Accepted August 29, 2012) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract Interfaces play key roles in determining mechanical properties of materials. In current work we perform molecular dynamics simulations of diffusion bonding to evaluate the effect of temperature on the morphology of the Ni/Al interface and the strength of the diffusion bonded Ni/Al nanowires. The centro-symmetry parameter is adopted to identify defect atoms generated. Simulation results show that the thickness of the Ni/Al interface has strong dependence on the temperature of diffusion bonding. Following uniaxial tension tests indicate that the yield strength of Ni/Al nanowires is smaller than both the single crystalline Ni and Al nanowires, because of the Ni/Al interface acting as dislocation source and the mobilization of pre-existing dislocations at high temperature. It is shown that the mechanical properties of diffusion bonded Ni/Al nanowires strongly depend on the temperature. Keywords: Diffusion bonding; Nanowire; Tension; Molecular dynamics; Mechanical property ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction Diffusion bonding, as one of the typical solid-state welding processes, is widely used in fields of aerospace, biotechnology, mechanical engineering, and medicine, etc. [1-4]. During diffusion bonding, metallic atoms diffuse into adjacent material to form atomic bonds on the interface with the aid of high pressure and/or temperature, and consequently functional components of small and large dimensions can be obtained. Recently, diffusion bonding has been proposed to fabricate large-scale electrically interconnected metallic nanowire networks [5, 6]. With the increasing miniaturization in asfabricated components, a fundamental understanding of the atomistic mechanisms of diffusion bonding and the subsequent mechanical properties of diffusion bonded components is essentially required to obtain nanocomponents of high quality. While experimental investigation of diffusion bonding is suffering from the resolution limitation of measuring apparatus, theoretical approach such as molecular dynamics (MD) simulation has been widely used to obtain atomic insights into diffusion bonding. To develop the optimal parameters that yield superior mechanical properties of the diffusion bonded components, it is *

Corresponding author. Tel.: +86 451 86412934 Fax.: +86 451 86415244 E-mail address: [email protected] Recommended by Editor Maenghyo Cho © KSME & Springer 2013 †

crucial to understand the formation mechanisms of the interface formed during diffusion bonding and its subsequent deformation behavior under external loads. The morphology and properties of formed interface have strong dependence on a number of process parameters, such as temperature, pressure, time, and surface quality, etc. Chen et al. performed MD simulation of diffusion bonding Cu-Ag, and reported that the thickness of interfacial region is strongly dependent on the stress state [7]. They further evaluated the effects of temperature and surface roughness on the diffusion bonded Cu/Al interface using MD simulation. They found that a higher temperature yields larger thickness of the interface [8]. Despite valuable insights into the diffusion bonding of bulk materials obtained by previous studies, less information is known about the atomistic mechanisms of diffusion bonding of nanowires and their mechanical properties. Therefore, in this work we perform MD simulations of diffusion bonding and subsequent uniaxial tension tests to evaluate the effect of temperature on the morphology and mechanical property of diffusion bonded Ni/Al nanowire, which has promising multifunctional applications ranging from magnetic sensors to memory alloys [9, 10].

2. Simulation method As depicted in Fig. 1(a), the MD model of the diffusion bonding of Ni/Al nanowires consists of a single crystalline Ni nanowire contacting with a single crystalline Al nanowire,

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Z. Hu et al. / Journal of Mechanical Science and Technology 27 (1) (2013) 43~46

strain rates of all the uniaxial tensions are the same as 2.64e9/s. The CSP is utilized to identify the defect structures generated during diffusion bonding and following uniaxial tension processes. All the MD simulations are performed by using LAMMPS code with numerical integration step of 1 fs [13]. The VMD and Atomeye are adopted together to visualize MD data and generate MD snapshots [14, 15].

3. Results and discussion Fig. 1. MD model of diffusion bonding of Ni/Al nanowires: (a) Planar view of Ni/Al nanowires; (b) the Ni/Al interface.

Fig. 2. Planar views of diffusion bonded Ni/Al nanowires (top row) and Ni/Al interfaces (bottom row).

both of which are of face centered cubic (FCC) lattice structure. An embedded atom method (EAM) potential developed for Ni-Al system is utilized to describe the atomic interactions in the Ni/Al nanowires [11]. Both of the Ni and Al nanowires have a square shape with the same transverse dimensions of 4.05 nm and 4.05 nm in X [100] and Z [001] directions. The lengths in Y [010] direction for Ni nanowire and Al nanowire are 3.52 nm and 4.05 nm, respectively. Non-periodic boundary condition (PBC) is applied in three directions, and the bottom layer of the Al nanowire and the upper layer of the Ni nanowire are fixed. It should be noted that in order to amplify the effect of Ni/Al interface on the mechanical properties of diffusion bonded Ni/Al nanowires, the size of transverse direction is comparable with the length size to obtain large volume fraction of the Ni/Al interface. Fig. 1(b) shows the crystalline Ni/Al interface formed due to the lattice mismatch between dissimilar Ni and Al lattices. Atoms are colored according to the calculated values of centro-symmetry parameter (CSP) [12]. The as-created Ni/Al nanowires are first relaxed under 0 bar at 1 K for 50 ps, and then subjected to diffusion bonding at different temperatures for 50 ps, both are in the isothermal-isobaric NPT ensemble. In order to investigate the effect of temperature on the diffusion bonding of Ni/Al nanowires, four temperatures, as 1 K, 300 K, 500 K, and 700 K, are considered. After the completion of diffusion bonding processes, uniaxial tension tests of the diffusion bonded Ni/Al nanowires are then performed by applying opposite constant velocities to the fixed bottom Al and upper Ni layers in the microcanonical NVE ensemble. The temperature of uniaxial tension is consistent with the diffusion bonding process. The

3.1 Effect of temperature on Ni/Al interface The top row in Fig. 2 shows the planar views of the diffusion bonded Ni/Al nanowires at different temperatures. There is Ni/Al interface formed between the Al nanowire and the Ni nanowire after diffusion bonding at each temperature. However, the thickness of the Ni/Al interface strongly depends on the diffusion bonding temperature: the higher the temperature, the thicker the interface. At low temperature the Ni/Al interface mainly originates from the lattice mismatch between dissimilar Ni and Al lattices. Therefore, the thickness of the Ni/Al interface at the temperature of 1 K is on the same order of magnitude with the FCC unit cell. At high temperature, however, the pronounced thermal effect facilitates the break of metallic bonds and subsequent diffusion of atoms, which consequently leads to larger thickness of the Ni/Al interface. We also note, two-way diffusion between Ni and Al atoms is observed in current work, which is distinctly different from the one-way diffusion of from the Cu side into the Al side reported in the Ref. [8]. This can be attributed to the discrepancy in the size of transverse directions. Instead of the infinite large Ni/Al interface caused by applying PBC in transverse directions in the Ref. [8], in current work the Ni-Al system possesses finite sizes in three dimensions, which strongly refrains the one-way diffusion due to the presence of large volume fraction of free surface. In addition, the top row in Fig. 2 shows that the size of the diffusion bonded Ni/Al nanowires expands significantly after diffusion bonding at higher temperatures of 500 K and 700 K. The bottom row in Fig. 2 shows that there are dislocations emitting from the Ni/Al interface formed at higher temperature, as highlighted by the black circles in Fig. 2(c) and (d). While the formed interface is crystalline at low temperature, it is mainly amorphous at high temperature in addition to the presence of dislocations. 3.2 Effect of temperature on tensile behavior of diffusion bonded Ni/Al nanowires Above analysis indicates that the Ni/Al interface of diffusion bonded Ni/Al nanowires is strongly depended on the diffusion bonding temperature. We subsequently evaluate the effect of temperature on the mechanical property of the diffusion bonded Ni/Al nanowires by performing uniaxial tension test. For comparison purpose, unixial tension tests of the single crystalline Ni and Al nanowires at 1 K are also performed. Fig. 3 plots the stress-strain curves obtained during the tension

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Table 1. Mechanical properties of diffusion bonded Ni/Al nanowires at different temperatures.

Young’s modulus (GPa)

1K

300K

500K

700K

127.94

84.30

61.86

57.23

Yielding stress (GPa)

4.76

4.12

3.27

1.99

Flow stress (GPa)

1.70

2.30

2.35

1.50

Fig. 3. Stress-strain curves during uniaxial tensile of three nanowires at 1 K.

Fig. 5. Stress-strain curves during unixial tensile of diffusion bonded Ni/Al nanowires at different temperatures. Fig. 4. Instantaneous defect structure in nanowires at yielding point: (a) Ni; (b) Al; (c) Ni/Al.

processes of the single crystalline Ni nanowire, the single crystalline Al nanowire, and the diffusion bonded Ni/Al nanowires at 1 K. For the single crystalline Ni nanowire, the stress first increases rapidly during elastic deformation. Young’s modulus E, defined as the ratio of stress to strain, can be calculated from this linear curve. The calculated values of Young’s modulus for the single crystalline Ni, the single crystalline Al, and the diffusion bonded Ni/Al nanowires are 155.65 GPa, 90.91 GPa, and 127.94 GPa, respectively. It indicates that the diffusion bonded Ni/Al nanowires has higher stiffness than the single crystalline Al nanowire. After reaching a critical strain of 8.5% at which the stress reaches the maximum value, i.e. tensile yielding stress, the stress for the single crystalline Ni nanowire drops dramatically caused by initiation of plasticity. The tensile yielding stress for the single crystalline Ni nanowire, the single crystalline Al nanowire, and the diffusion-bonded Ni/Al nanowires is 13.23 GPa, 7.73 GPa, and 4.76 GPa, respectively. Fig. 4 presents instantaneous defect structures of the single crystalline Ni nanowire, the single crystalline Al nanowire, and the diffusion bonded Ni/Al nanowires at the onset of plasticity. Atoms are colored according to calculated CSP values, and perfect FCC atoms are eliminated to show defect structures clearly. It can be seen that for the single crystalline Ni and single crystalline Al nanowires, initial dislocations nucleate homogeneously from four edges of free surface. In addition, the defect structures present perfect symmetry at low temperature of 1 K. In contrast, initial dislocation nucleates

Fig. 6. Planar view of diffusion bonded Ni/Al nanowires after tension: (a) 1 K; (b) 300 K; (c) 500 K; (d) 700 K.

heterogeneously from the Ni/Al interface of the diffusion bonded Ni/Al nanowires at the yielding point, and only one {111} slip plane is activated first. Therefore, the tensile yield stress is smaller for the diffusion bonded Ni/Al nanowires than either the single crystalline Ni or the single crystalline Al nanowires. It indicates that the Ni/Al interface acts dislocation source to emit initial dislocation, which lowers the strength of the diffusion bonded Ni/Al nanowires in comparison with both the single crystalline Ni and single crystalline Al nanowires at the same temperature. Fig. 5 plots the stress-strain curves obtained during tensile processes of the diffusion bonded Al/Ni nanowires at different temperatures. The calculated Young’s modulus, tensile yield stress, and plastic flow stress are listed in Table 1. It indicates that both the Young’s modulus and tensile yield stress decrease with increasing temperature. This phenomena can be interpreted by larger amplitude of atoms fluctuating around its balance position at higher temperature, which leads to that atomic bond is easier to be broken under applied load than lower temperature. In addition, the mobilization of preexisting dislocation generated in diffusion bonding at high

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temperature also contributes to the lower yielding stress. Fig. 6 presents planar views of diffusion bonded Ni/Al nanowires after the completion of tension processes. It is interesting to observe that plastic deformation only occurs in the Al nanowire part for all the four diffusion bonded Ni/Al nanowires. It is seen from Fig. 6 that dislocation density first increases with increasing temperature when temperature is low. Furthermore, work hardening is more serious in the diffusion bonded Al nanowire at 300 K due to strong dislocation reaction and cross slip. Upon further increase of temperature, however, dislocation density decreases and creep plays more pronounced role in the plastic deformation of nanowires at high temperature of 700 K. Fig. 6 also demonstrates that the cross section size of the neck formed during tension process first increases with increasing temperature, but then decreases at 700 K.

4. Conclusions In summary, we perform MD simulations of diffusion bonding and following uniaxial tension to investigate the effect of temperature on the morphology of the Ni/Al interface and the mechanical property of the diffusion bonded Ni/Al nanowires. Simulation results demonstrate that the diffusion bonded Ni/Al nanowires possess larger stiffness than the single crystalline Al nanowire. The Ni/Al interface acts as dislocation source to emit initial dislocation, which leads to lower tensile yielding stress in comparison with the single crystalline Ni or Al nanowires at the same temperature. It is found that the thickness of the Ni/Al interface increases with increasing temperature. The Young’s modulus and tensile yield stress of the diffusion bonded Ni/Al nanowires are both lower at higher temperature. The plastic deformation of the diffusion bonded Ni/Al nanowires during tension process is dominated by dislocation activity at low temperature and creep at high temperature, which leads to different dependence of flow stress on the temperature.

Acknowledgment The authors gratefully acknowledge financial support of the Natural Science Foundation of Heilongjiang Province of China (E200833), China Postdoctoral Science Foundation (2012M511463), and the Heilongjiang Province Postdoctoral Science Foundation (LBH-Z11143), Open Foundation of State Key Laboratory of Physical Chemistry of Solid Surface, Xiamen University (201112).

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Zhenjiang Hu is currently an associate professor at Center for Precision Engineering, Harbin Institute of Technology. His research interests are micro/nanoFabrication, diffusion bonding welding, development of AFM-based nanoscratching apparatus.

Junjie Zhang is currently a research faculty at Center for Precision Engineering, Harbin Institute of Technology. His research interests are nanoscale friction and wear of nanomaterials, computational nanomechanics.