Effects of forging temperature and velocity on nano-forming process
using molecular dynamics simulation
Shiang-Jiun Lin
a, Cheng-Da Wu
b, Te-Hua Fang
b,⇑, Li-Min Kuo
a aDepartment of Mold and Die Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan
b
Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan
a r t i c l e
i n f o
Article history:
Received 25 February 2011
Received in revised form 28 April 2011 Accepted 3 May 2011
Available online 31 May 2011 Keywords: Nanoforging Temperature Elastic recovery Molecular dynamics Velocity
a b s t r a c t
The nanoforging process of a pure copper nanorod (workpiece) is studied using molecular dynamics (MD) simulations based on embedded atom method (EAM) potential. The effects of the forging temperature and the forging velocity are evaluated in terms of molecular trajectories, pressure, internal energy, and a radial distribution function. The simulation results clearly show that the internal energy of the work-piece and the pressure exerted on it during the forging process decrease 50% and 7% with increasing forg-ing temperature from 300 to 620 K; however, the internal energy and pressure increase 207% and 20% with increasing forging velocity from 50 to 90 m/s, respectively. During the forging process, a special atomic structure in (1 0 1) and ð1 0 1Þ slip planes was observed, and that represents the site of generation of dislocation and growth nucleation. When severe plastic deformation occurs, the high-energy atoms in the workpiece are significantly distributed along the direction of the slip plane due to the packing of defect structures. When the forging velocity increases, the density of the workpiece becomes more non-uniform. The forged workpiece has similar distributions of atomic density after the elastic recovery for various forging temperatures and forging velocities.
Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction
With increasing demand for micro/nanopatterns, the develop-ment of nanofabrication technology has become a priority. Two main top-down approaches, photolithography [1] and maskless lithography [2–4], are widely used for fabricating miniaturized electronic, mechanical, optical, and microfluidic devices on large-area substrates. Photolithography is a process that uses light to transfer a geometric pattern from a photo mask to a light-sensitive chemical, called a photoresist or simply resist, onto the substrate. Problems encountered in conventional photolithography include the light diffraction limit, scattering, and the chemical property of the photoresist material. Maskless lithography is widely used for precise nanofabrication, with laser light, electrons, ions, or physical pressing being used to produce various nanostructures on a substrate. The most popular technique is like nanoimprint lithography (NIL), which offers a sub-10-nm feature size and high throughput at low cost[5–7].
Nanoforging might be a feasible top-down approach for fabri-cating or modifying a workpiece into the desired shape. Molecular dynamics (MD) simulation is an effective tool for studying material behavior and system design at the nanometer scale, and it provides
detailed deformation information at the atomic level. Atomic sim-ulation avoids experimental noise and turbulence problems and can be used to analyze molecular trajectories and thermodynamic properties. Many nano-systems have been analyzed using MD, such as surface friction[8,9], nanoscratch [10], lubrication [11], nanoimprint[12,13], contact[14], and nanoindentation behavior
[15,16].
Forging is a manufacturing process that shapes a material using localized compressive forces. This work investigates the effect of forging temperature and velocity on the nanoforming process using MD simulation. The results are discussed in terms of molec-ular trajectories, pressure, internal energy, and a radial distribution function.
2. Methodology
A schematic MD model of the nanoforging process is illustrated
inFig. 1. The model consists of a punch (active mold), a fixed mold
(passive mold), and a nanorod workpiece. The molds and the work-piece is made of nickel (Ni) and copper (Cu) with perfect face-centered cubic (FCC) metal atoms, respectively. To focus on the behavior of the workpiece formation, the two molds (marked pur-ple) are set to be rigid atoms, whereas the Cu atoms of the work-piece (marked orange) are set to be Newtonian atoms. The initial nanoforging system is controlled to be at a temperature of 300 K.
0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.commatsci.2011.05.008
⇑Corresponding author. Tel.: +886 7 3814526 5336. E-mail address:[email protected](T.-H. Fang).
Computational Materials Science 50 (2011) 2918–2924
Contents lists available atScienceDirect
Computational Materials Science
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m m a t s c iA periodic boundary condition (PBC) is imposed on surface plane Y (which is in contact with the punch). In mathematical models and computer simulations, a PBC[17]is often used to simulate a large system by modeling a small part that is far from its edge. The dimensions of the Ni punch are 1.0 (length) 1.9 (width) 12.0 (height) nm, those of the Cu workpiece are 8.5 (length) 1.9 (width) 2.7 (height) nm, and those of the cavity of the passive mold are 1.2 (length) 1.9 (width) 8.5 (height) nm. To
investi-gate the influences of the forging temperature and velocity on the nanoforming process, the temperature and velocity vary in the ranges of 300–620 K and 30–100 m/s, respectively.
The embedded atom method (EAM) potential model is adopted for simulating the interactive behavior between workpiece-work-piece (Cu–Cu) and workworkpiece-work-piece-mold (Cu–Ni) atoms. The EAM po-tential, initially developed by Daw and Baskes [18], has been proven to be a good potential format for metal atoms. The potential assumes that the crystal energy is the sum of a pairwise potential and an energy required to embed an atom into a local medium with a given electron density. In EAM potential, the total energy of E can be expressed as:
E ¼1 2 X i;j;i–j /ijðrijÞ þ X i Fið
q
iÞ ð1Þwhere
u
ijis the pair energy between atoms i and j separated by rij, and Fiis the energy required to embed atom i into a local site with electron densityq
ijq
ijcan be calculated using:q
i¼X
j;j–i
fjðrijÞ ð2Þ
where fj(rij) is the electron density at the site of atom i arising from atom j at a distance rijaway. The generalized pair potentials were chosen to have the form:
Fig. 1. Schematic MD model of nanoforging process.
Table 1
EAM potential parameters for Cu[20].
re fe qe a b A B j k
2.556162 1.554485 22.150141 7.669911 4.090619 0.327584 0.468735 0.434307 0.86214
Fig. 2. Snapshots of nanoforging process at a temperature of 300 K at time steps of (a) 30, (b) 60, (c) 90, (d) 109 (cavity completely filled), (e) 109.3 (unloading), and (f) 112 ps (completely unloaded). The atoms are colored according to their magnitude of internal energy (J).
ergy of the workpiece and the pressure exerted on it increase with increasing forging velocity. This is due to the atoms being greatly deformed by the punch, and the dislocations and stack faults in the workpiece not having sufficient time to recover or adjust. More force is thus required for further plastic deformation. The effect of work hardening is also large for high-velocity forging. To clearly understand the effect of forging velocity on the pressure experi-enced by the workpiece at different forging stages,Fig. 8shows the variation of the slope of pressure versus forging velocity for each forging stage. The physical meaning of the slope of the pres-sure is the required prespres-sure per unit of strain. InFig. 8, the slope of the pressure slightly increases with forging velocity at stages 1 and 2, and then greatly increases with increasing forging velocity at stage 3. At stage 3, the required compressive loading is very large, and the force directly increases with the forging velocity. The slopes at stages 2 and 3 are 3.8–7.2-fold and 17.0–24.0-fold larger than that at stage 1, respectively.
3.4. Effect of forging temperature and velocity on radial distribution function
A radial distribution function (RDF) (or pair correlation func-tion), g(r), describes how the atomic density varies as a function of the distance from one particular atom.Fig. 9shows g(r) at a tem-perature of 300 K and a forging velocity of 30 m/s for different forg-ing stages. InFig. 9, the g(r) for a perfect FCC structure represents the distribution of atomic density of the Cu workpiece after the thermal equilibrium process. The position of the high narrow peaks in order is 0.255, 2.80, and 0.360 nm, which correspond to the min-imum energy separation for Cu, respectively. At stage 1, the num-ber of peaks decreases, and the height of the main peak (0.255 nm) significantly increases due to the small deformation of the work-piece. With further loading, the height of the peak slowly de-creases, and its width becomes wider. The position of the main peak shifts to the left side (the distance between atoms decreases) at stage 2. When the cavity is about to be filled, the main peak exhibits a larger shift due to greatly higher compressive loading, less free space, and denser atomic packing. At stage 3, the structure exhibits a short-range order, and the position of the main peak de-creases to about 0.22 nm.
Fig. 10shows the relationship between g(r), forging
tempera-ture, and forging velocity for the workpiece in the filled cavity and the forged workpiece. In general, the distance between atoms increases with increasing temperature due to an increase in kinetic energy. However, the simulation results show that the effect of temperature on g(r) is not obvious for both the filled cavity (a) and the forged workpiece (c). This is due to all atoms being largely constrained in the small cavity; they have little free movement when the cavity has been completely filled. In addition, the effect of adhesion can be neglected due to the high-velocity unloading. ComparingFig. 10a and c, the workpiece has similar distributions of atomic density after the elastic recovery process for various forg-ing temperatures. Observforg-ing the effect of forgforg-ing velocity shown in
Fig. 10b, the behavior of g(r) at the completely filled stage is a little
different from that for the effect of temperature (Fig. 10a). When the forging velocity increases, the main peaks become higher and narrower, and additional small peaks appear in the g(r) curve due to the nonuniform atomic distribution for high-velocity forg-ing, as shown in the snapshots in Fig. 4. After elastic recovery
(unloading), the position and height of main peaks in the g(r) curve become similar for various forging velocities. This indicates that lots of disordered structures and defects under high-velocity forg-ing have been readjusted and rearranged.
4. Conclusion
This study conducted an MD simulation to investigate the ef-fects of forging temperature and velocity on the nanoforming pro-cess. The following conclusions were obtained:
(1) During the forging process, a special atomic structure in (1 0 1) and ð1 0 1Þ slip planes can be observed, and the high-energy atoms in the workpiece are significantly distrib-uted along the direction of the slip plane due to the packing of defect structures.
(2) The internal energy of the workpiece and the pressure exerted on it during the forging process decrease with increasing forging temperature.
(3) The internal energy of the workpiece and the pressure exerted on it during the forging process increase with increasing forging velocity.
(4) The workpiece has similar distributions of atomic density after the elastic recovery process for various forging temper-atures and velocities.
Acknowledgment
This work was supported by the National Science Council of Tai-wan under Grants NSC 97-2221-E-151-059-MY3 and NSC 099-2811-E-151-002.
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