Molecular dynamics based modelling of the dislocation motion in bulk nanostructuring of a FCC material

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1 Molecular dynamics based modelling of the dislocation motion in bulk nanostructuring of a FCC material ALICE BURUIANA, MIHAELA BANU, ALEXANDRU EPUREANU, FELICIA STAN Manufacturing Science and Engineering Department Dunarea de Jos University of Galati, Faculty of Mechanical Engineering Domneasca Street 111, , Galati ROMANIA Mihaela.Banu@ugal.ro Abstract: Materials nanostructuring by severe plastic deformation (SPD) have attracted much interest in the last decade due to their physical and chemical properties. During severe plastic deformation of metals, at the nanostructuring level of nm grain size, dislocations arrange in ordered patterns and the plastic behavior is mainly controlled by the motion of crystal lattice. In order to model the motion of the deformation mechanisms, the present paper proposes the molecular dynamics method applied to copper severe plastic deformation in order to investigate the pattern of the elastic fields generated by the dislocations within the deformation. Key-Words: Nanostructuring materials, Dislocation mechanisms, Molecular dynamics, FCC materials, Modelling 1 Introduction In the last decade, nanocystalline and ultra-fine grain (UFG) materials processed by severe plastic deformation methods (SPD) have been the subject of intense study for a lot of researchers. Due to the fact that at 50 nm the classic deformation mechanisms are not available any more, researchers as [15,16,17,18,19] and others have done TEM and HRTEM investigations in order to observe the physical phenomena that determine the plastic deformation. In case of ductile copper, it has been observed the twining mechanism. Deformation twinning the mechanism that accommodates plastic deformation in copper, is thought to be directly related to the particular nanostructures, which has not been observed in their coarse-grained counterparts. Yielding of the materials occurs immediately after an elastic springback state which is governed by the appearance of defects in the crystal lattice. The most existing results concerning deformation mechanisms in the nanostructured materials with grain size lower then 200 nm are based on indirect techniques to investigate the appearance and interactions of these defects. In order to understand these key features of plastic deformation from atomic point of view, molecular dynamic technique is used (MD). Molecular dynamics is using real physical and chemical models that become very important in determining the properties of materials. Most MD techniques consider a small number of dislocations and refer to specific dislocation mechanisms, such as cross slip, dislocation cutting process or dislocation nucleation from cracks. This paper presents the modeling of a dislocation by MD technique in bulk nanostructured copper obtained by equal channel angular process (ECAP). 2 Experimental conditions for generating the model Nanocrystalline and ultra-fine grain materials processed by severe plastic deformation (SPD) methods has been the subject of intense study in the last years. Among all the well known SPD methods, some of the most important are the equal channel angular pressing in 2D (2D-ECAP) and 3D (3D- ECAP) because they have the advantage to produce large samples. The 2D-ECAP process was first invented by Segal in 1977 in Russia in order to achieve large strains and later other researchers extended this method in order to produce UFG materials with superior mechanical properties [12,13]. In the 2D-ECAP process a square or cylindrical bar is compressed from one section of continuous profile channel to another section. The second section of the profile is oriented to the first one to an angle, called channel angle, Φ=2φ and an outer arc of curvature, ψ. ISSN: ISBN:

2 In the 2D-ECAP method, the plastic deformation of the material is caused by simple shear in a thin layer at the crossing plane of the channel sections. Despite non-uniform strain distributions, the amount of equivalent plastic strain generated can be estimated as [Rosochowski et al., 2004]: 2/ 3 cos, (1) where is the amount of strain and φ is the die channel. For the case when 2φ=90º, the plastic strain is always ε=1.15. Extrapolation of strength from a strain rate of 10 4 s 1 to the one greater than 10 6 s 1 becomes problematic, because strain rate cannot be increased by orders of magnitude without increasing the pressure. For an ECAP process done for 0-8 passes, the yield stress varies from 148 to 200 MPa and the dislocation density (x10 14 m -2 ) is between 1.64 and By ECAP process we can say that a high value of yield stress is obtained, the yield stress is a function of ECAP pass numbers and the rate strain hardening of ECAP is very low compared to the unprocessed material. The channel angle Φ is the most important experimental factor that influences the ECAP process because it dictates the total strain imposed in each pass and it has a direct influence on the nature of the material microstructure. Most experiments report that the channel angle is between 90º and 120º. Once the channel angle is increased the microstructure of the processed material becomes less regular and there are higher fractions of grain boundaries having low angles of disorientation. Some experiments revealed the fact that using a die having the channel angle Φ=60º it is possible to produce excellent microstructures, with the average grain size smaller than the die having Φ=90º, so the grain size for pure Al were ~1.1μm for Φ=60º and ~1.2 μm for Φ=90º [Furuno et al., 2004]. The major disadvantage of the die with Φ=60º is that requires a high pressure during the process. The ECAP process is usually done using highcapacity hydraulic presses, with the pressing speed between 1-20 mm s -1. This pressing speed has no influence on the size of the ultrafine grains because slower speeds produce equilibrate microstructures. During the process, when the pressing speed is increased the yield stress has constant values. Another important factor in the ECAP process is the pressing temperature, because it can be easily controlled. For pure Al, when increasing the temperature during the process there is an increase of the equilibrium grain size, with the temperature between 0-700º K and the grain size between μm and also an increasing annihilation of dislocations within the grains. An important role in the ECAP process is played by the back-pressure because it helps improving the workability of the samples. Without back-pressure it is found that cracks usually appear after passes, but with a back-pressure of 300 MPa, the samples have no cracks for more than 16 passes. Another important advantage of the back-pressure is that during the process, it helps the material to become more uniform. The deformation mechanism of the nanostructured materials is not completely known. Researchers reported that twinning and grain boundary sliding are the main mechanisms that lead to the deformation. The present paper proposes one new step in understanding how FCC (face-centered cubic) deforms under ECAP conditions by means of the molecular dynamic simulation, particularly for copper. 3 Creating the molecular dynamic model Molecular dynamic (MD) simulations have been used to study the atomic-scale processes that occur during plastic deformation of polycrystalline aggregates of nanocrystalline grains because at this scale no experimental model is able to catch the real deformation mechanism. The simulations suggest that nanocrystalline metals accommodate externally applied loading, by means of grain boundary sliding and the emission of partial dislocations that run across the grains [1,8]. The MD simulations also suggest that grain boundary sliding and the partial dislocation emission are triggered by atomic shuffling and free volume migration in the grain boundaries. For creating our molecular dynamic model we have used the trail representation set up by [2,3,4,5,6,7]. 3.1 Creating the geometry Recent TEM investigations have showed that ductile copper consists of irregular-shaped grains with random orientations. Grain sizes are between 100nm and 1μm, and each grain contains a high density of growth twins of the 111/[112] type. Starting from the ISSN: ISBN:

3 trail representation build up by [6,10,20,21,] we have created our own molecular models, as shown in figure 1 (a, b, c, d). d) e) f) Fig. 1 Schematic model of two dislocation process: a) trail of partial point defects, d) vacancy tube [Buehler et al., 2005], b) trail of partial point defects, e) vacancy tube, our generated models, c) and f) 2D section through the dimensional elastic field for both cases. For creating the molecular model we use the lattice orientation of the ductile copper, which is a facecentered-cubic (FCC) material. The FCC materials have larger interstitial spaces, being capable of retaining other atoms with atomic radius r=0,146a, where a is the lattice constant. For ductile copper a=3.61aº, the minimal distance between two atoms is Aº and the atomic radius is r=1.278aº. 3.2 Determining the atomic ID In the dislocation mechanisms presented above, the atoms around the dislocation, in both cases, have different potential energies due to the fact that the dislocation produces an elastic field that makes these atoms different than the neighbor atoms. For Cu-Cu atomic interactions between workpiece atoms, the well established embedded atom (EAM) method potential can give realistic description of the material. According to EAM, the total atomic potential energy is expressed as: 1 Etot ij ( rij ) F( i ) i (2), 2 ij 1 where Φ ij is the interaction energy between two atoms i and j, F i is the embedded energy of the atom I, ρ i is the density of atom I, induced by all the other atoms. 3.3 Simulation conditions The model simulations used for investigating the molecular dynamics simulations were carried out in copper (μ = 42 GPa, Poisson's ratio ν = 0.347, b = nm, indenter radius r i =50nm, elastic module E=123GPa and an estimated shear strength of the crystal G/2π=7.6GPa). The simulation uses a number of 149 atoms in a cell size of 6.9x6.9 μm with a time step of ns with a shear stress τ max =10.7GPa, in the conditions of a diffusion process. Diffusion is a mechanism that creates thermal activated salts for the atoms. In order to achieve these salts the temperature has to vary at least with a few degrees and eventually ISSN: ISBN:

4 these slats describe the trajectories of each atom. Our MD simulations used periodic boundary conditions with reflecting walls with the temperature between º K and the internal pressure between 0.5 and 2 MPa. 4 Results and interpretations During the simulations, once we increase the temperature and the internal pressure is constant, the kinetic energy also increases. When we decrease the pressure and the temperature is constant, the kinetic energy decreases, bellow the average value. For the second type of dislocation, when we decrease the pressure and the temperature is constant, the kinetic energy does not decrease so much, is still above the average value. The total energy depends both on the temperature and the pressure. When both parameters increase, the total energy also increases. In both cases, when the temperature was constant and we increased the external pressure, the pressure inside the simulation cell increased significantly. The velocity distribution increased once with the temperature, it lost part of its intensity. d) e) f) Fig. 2 Graphs of kinetic energy: a), b), c) for the trail of partial point defects; d), e) and f) for the vacancy tube Fig. 3 Variation of total energy as a function depending on time ISSN: ISBN:

5 Fig. 4 Pressure as a function depending on time, for different values for the temperature and external pressure a) b) Fig. 5 Trajectories for a) trail of partial point defects and b) for vacancy tube, in the final stage of simulation The snapshots of the atoms movement under the conditions similar to the ECAP process show the that the atoms from the elastic field around the dislocation spread in many directions similar to a diffussion process. The amount of kinetic energy for trails of partial point defects is less then the kinetic energy of the vacance tube. The next step in the investigation will concentrate on the shape of the trajectory in order to have the possibility to predict the pattern of the deformation. This will facilitate the control of the manufacturing process by ECAP in order to design the material with desired mechanical properties. 5 Conclusions The more and more developed applications of the materials with high level of mechanical properties such superplasticity and stiffness lead to connect the manufacturing processes with the physical ISSN: ISBN:

6 investigation of the phenomena that occur inside the materials. In the present paper, molecular dynamic simulation was used to model the movement of the atoms placed around the two kind of dislocations for ductile copper during its nanostructuring by ECAP severe plastic deformation process. The results underline the importance of considering the shape of the trajectories of these atoms during the process with the goal of predicting the geometrical loci. If the loci could be known, the macroscale simulation of the ECAP process can be improved by considering within the constitutive model of an internal variable tat describe such nanoscale phenomenon. The results obtained are the first approach for the multi-scale analysis of the ECAP process by finite element modelling. Acknowledgements The present researches are developed with the financial support of the Romanian Research Program PN II, specific program IDEAS 1758/2008, financed by the Romanian Ministry of Education and Research. Special thanks to the Center for Polymer Studies, Boston University, USA for allowing us to use molecular dynamics software VMDLv References: [1] Allen M. P., Introduction to Molecular Dynamic Simulation, Computational Soft Matter, NIC Series, Vol. 23, ISBN , 2004, pp [2]Bringa E.et al., Ultrahigh Strength in Nanocrystalline Materials, Science 309, 1838 (2005) [3] Budrovic Z., Footprints of deformation mechanisms during in-situ X-ray diffraction: nanocrystalline and ultrafine grainded materials, 3463, 2006.Dir.:HelenaVan Swygenhoven [4] Budrovic Z. et al., Plastic Deformation with Reversible Peak Broadening in Nanocrystalline Nickel, Science304, 273 (2004) [5] Buehler M., Large-scale hierarchical molecular modeling of nanostructured biological materials, J. of Comp. and Th. Nanoscience, 3(5), (2006); [6] Buehler M.,et. al., The dynamical complexity of work-hardening: a large-scale molecular dynamics simulation, Acta Mech Sinica, 21, (2005) [7] Chen Zheng and Yong-Wei Zhang, A Molecular Dynamics Study of the Effect of Voids on the Deformation Behavior of Nanocrystalline Copper, Journal of Nanomaterials, Volume 2007 (2007) [8] Drexler K. E.,Toward Integrated Nanosystems: fundamental Issues in Design and Modeling, Journal of Computational and Theoretical Nanoscience,3,1-10 (2006) [9] Hemker K., Understanding How Nanocrystalline Metals Deform, Science304, 221 (2004) [10] H.Haddadi, S. Bouvier, M. Banu, C. Maier and C. Teodosiu, Towards an accuarate description of the anisotropic behaviour of sheet metals under large plastic deformations Modelling, numerical analysis and identification, International Journal of Plasticity, 22, 12, Pages , (2006) [11] Li L., Wei W., Lin Y., Lijia C. and Zheng L., Grain boundary sliding and accommodation mechanisms during superplastic deformation of ZK40 alloy processed by ECAP, J.of Mat.Sci., 41(2), (2006) [12] Olejnik L., Rosochowski A., Methods of fabricating metals for nano-technology, B. Polish Academy of Sciences, 53, 4, (2005) [13] Rosochowski A. et al., Metal Forming technology for producing bulk nanostructured metals, Steel grips 2 suppl. Metal Forming (2004), pp [14] S. Pendurti and S. Jun, In-Ho Lee, Cooperative atomic motions and core rearrangement in dislocation cross slip, Appl. Phys. Lett. 88, (2006) [15] Simokawa T. et al., Grain size dependence of the relationship between inter- and intragranular deformation of nanocrystalline Al by molecular dynamic simulation, Phy. Rev. B71, (2005) [16] H. Van Swygenhoven, Dislocation propagation versus dislocation nucleation, Nat Mater Nov ; 5 (11): (2006) [17] Uchic M. et al., Sample Dim. Influence Strength and Crystal Plasticity, Science 305,986 (2004) [18] V. Yamakov, D. Wolf, S. R. Phillpot, A. K. Mukherjee and H. Gleiter, Deformation-mechanism map for nanocrystalline metals by moleculardynamics simulation, Nat. Mat. 3, (2003) [19] D. H. Warner, W. A. Curtin& S. Qu, Rate dependence of crack-tip processes predicts twinning trends in f.c.c. metals, Nat. Mat. 6, (2007) [20] Teodosiu C., Large Plastic Deformation Of Crystalline Aggregates, Springer-Verlag Vienna ISBN / EAN: , (1997) [21] Y. Wang, J. Li, A. V. Hamza, and T. W. Barbee, Jr., Ductile crystalline amorphous nanolaminates, Applied Physical Science, July 3, 2007 _ vol. 104 _ no. 27 _ (2007). ISSN: ISBN: