Handbook of Materials Modeling pp 773-792 | Cite as

# Atomistic Calculation of Mechanical Behavior

## Abstract

Mechanical behavior is stress-related behavior. This can mean the material response is driven by externally applied stress (or partially), or the underlying processes are mediated by an internal stress field; very often both are true. Due to defects and their collective behavior [1], the spatiotemporal spectrum of stress field in a real material tends to have very large spectral width, with non-trivial coupling between different scales, which is another way of saying that the mechanical behavior of real materials tends to be multiscale. The concept of stress field is usually valid when coarse-grained above a few nm; in favorable circumstances like when crystalline order is preserved locally, it may be applicable down to sub-nm lengthscale [2]. But overall, the atomic scale is where the stress concept breaks down, and atomistic simulations [3, 4, 5] provide very important termination or matching condition for stress-based theories. Large-scale atomistic simulations (chap 2.27) are approaching μm lengthscale and are starting to reveal the collective behavior of defects [6]. But studying defect unit processes is still a main task of atomistic simulation.

### Keywords

Migration Anisotropy Argon Brittle Tungsten## Preview

Unable to display preview. Download preview PDF.

### References

- [1]R. Phillips,
*Crystals, Defects and Microstructures: Modeling Across Scales*, Cambridge University Press, Cambridge, 2001.CrossRefGoogle Scholar - [2]T. Zhu, J. Li, K.J. VanVliet, S. Ogata, S. Yip, and S. Suresh, “Predictive modeling of nanoindentation-induced homogeneous dislocation nucleation in copper,”
*J. Mech. Phys. Solids*, 52, 691–724, 2004.MATHCrossRefADSGoogle Scholar - [3]M. Allen and D. Tildesley,
*Computer Simulation of Liquids*, Clarendon Press, New York, 1987.MATHGoogle Scholar - [4]D. Frenkel and B. Smit,
*Understanding Molecular Simulation: From Algorithms to Applications*, 2nd edn., Academic, San Diego, 2002.Google Scholar - [5]J. Li, A.H.W. Ngan, and P. Gumbsch, “Atomistic modeling of mechanical behavior,”
*Acta Mater.*, 51, 5711–5742, 2003.CrossRefGoogle Scholar - [6]F.F. Abraham, R. Walkup, H.J. Gao, M. Duchaineau, T.D. De laRubia, and M. Seager, “Simulating materials failure by using up to one billion atoms and the world’s fastest computer: work-hardening,”
*Proc. NatlAcad. Sci. USA.*, 99, 5783–5787, 2002.CrossRefADSGoogle Scholar - [7]J. Schiotz, F.D. Di Tolla, and K.W. Jacobsen, “Softening of nanocrystalline metals at very small grain sizes,”
*Nature*, 391, 561–563, 1998.CrossRefADSGoogle Scholar - [8]V. Yamakov, D. Wolf, S.R. Phillpot, and H. Gleiter, “Dislocation-dislocation and dislocation-twin reactions in nanocrystalline Al by molecular dynamics simulation,”
*Acta Mater.*, 51, 4135–4147, 2003.CrossRefGoogle Scholar - [9]J. Schiotz and K.W. Jacobsen, “A maximum in the strength of nanocrystalline copper,”
*Science*, 301, 1357–1359, 2003.CrossRefADSGoogle Scholar - [10]V. Yamakov, D. Wolf, S.R. Phillpot, A.K. Mukherjee, and H. Gleiter, “Deformationmechanism map for nanocrystalline metals by molecular-dynamics simulation,”
*Nat. Mater.*, 3, 43–47, 2004.CrossRefADSGoogle Scholar - [11]H. VanSwygenhoven, P.M. Derlet, and A.G. Froseth, “Stacking fault energies and slip in nanocrystalline metals,”
*Nat. Mater.*, 3, 399–403, 2004.CrossRefADSGoogle Scholar - [12]A.J. Haslam, V. Yamakov, D. Moldovan, D. Wolf, S.R. Phillpot, and H. Gleiter, “Effects of grain growth on grain-boundary diffusion creep by molecular-dynamics simulation,”
*Acta Mater.*, 52, 1971–1987, 2004.CrossRefGoogle Scholar - [13]A. Hasnaoui, H. VanSwygenhoven, and P.M. Derlet, “Dimples on nanocrystalline fracture surfaces as evidence for shear plane formation,”
*Science*, 300, 1550–1552, 2003.CrossRefADSGoogle Scholar - [14]A. Latapie and D. Farkas, “Molecular dynamics investigation of the fracture behavior of nanocrystalline alpha-Fe,”
*Phys. Rev. B*, 69, art. no.-134110, 2004.Google Scholar - [15]M.H. Muser, “Towards an atomistic understanding of solid friction by computer simulations,”
*Comput. Phys. Commun.*, 146, 54–62, 2002.CrossRefADSGoogle Scholar - [16]M. Urbakh, J. Klafter, D. Gourdon, and J. Israelachvili, “The nonlinear nature of friction,”
*Nature*, 430, 525–528, 2004.CrossRefADSGoogle Scholar - [17]C.L. Kelchner, S.J. Plimpton, and J.C. Hamilton, “Dislocation nucleation and defect structure during surface indentation,”
*Phys. Rev. B*, 58, 11085–11088, 1998.CrossRefADSGoogle Scholar - [18]J.A. Zimmerman, C.L. Kelchner, P.A. Klein, J.C. Hamilton, and S.M. Foiles, “Surface step effects on nanoindentation,”
*Phys. Rev. Lett.*, 8716, art. no.-l65507, 2001.Google Scholar - [19]G.S. Smith, E.B. Tadmor, N. Bernstein, and E. Kaxiras, “Multiscale simulations of silicon nanoindentation,”
*Acta Mater.*, 49, 4089–4101, 2001.CrossRefGoogle Scholar - [20]K.J. VanVliet, J. Li, T. Zhu, S. Yip, and S. Suresh, “Quantifying the early stages of plasticity through nanoscale experiments and simulations,”
*Phys. Rev. B*, 67, 2003.Google Scholar - [21]V. Vitek, “Core structure of screw dislocations in body-centred cubic metals: relation to symmetry and interatomic bonding,”
*Philos. Mag.*, 84, 415–428, 2004.CrossRefADSGoogle Scholar - [22]H. Koizumi, Y Kamimura, and T. Suzuki, “Core structure of a screw dislocation in a diamond-like structure,”
*Philos. Mag. A*, 80, 609–620, 2000.CrossRefADSGoogle Scholar - [23]C. Woodward and S.I. Rao, “Ab
*initio*simulation of (a/2) ¡ 110] screw dislocations in gamma-TiAl,”*Philos. Mag.*, 84, 401–413, 2004.CrossRefADSGoogle Scholar - [24]W. Cai, V.V. Bulatob, J.P. Chang, J. Li, and S. Yip, “Periodic image effects in dislocation modelling,”
*Philos. Mag.*, 83, 539–567, 2003.CrossRefADSGoogle Scholar - [25]J. Li, C.-Z. Wang, J.-P. Chang, W. Cai, V.V. Bulatov, K.-M. Ho, and S. Yip, “Core energy and peierls stress of screw dislocation in bcc molybdenum: a periodic cell tight-binding study,”
*Phys. Rev. B*, (in print). See http://164.107.79.177/Archive/Papers/04/Li04c.pdf, 2004. - [26]H.C. Huang, G.H. Gilmer, and T.D. de laRubia, “An atomistic simulator for thin film deposition in three dimensions,”
*J. Appl. Phys.*, 84, 3636–3649, 1998.CrossRefADSGoogle Scholar - [27]L. Dong, J. Schnitker, R.W. Smith, and D.J. Srolovitz, “Stress relaxation and misfit dislocation nucleation in the growth of misfitting films: molecular dynamics simulation study,”
*J. Appl. Phys.*, 83, 217–227, 1998.CrossRefADSGoogle Scholar - [28]D. Holland and M. Marder, “Ideal brittle fracture of silicon studied with molecular dynamics,”
*Phys. Rev. Lett.*, 80, 746–749, 1998.CrossRefADSGoogle Scholar - [29]M.J. Buehler, F.F. Abraham, and H.J. Gao, “Hyperelasticity governs dynamic fracture at a critical length scale,”
*Nature*, 426, 141–146, 2003.CrossRefADSGoogle Scholar - [30]R. Perez and P. Gumbsch, “Directional anisotropy in the cleavage fracture of silicon,”
*Phys. Rev. Lett.*, 84, 5347–5350, 2000.CrossRefADSGoogle Scholar - [31]N. Bernstein and D.W. Hess, “Lattice trapping barriers to brittle fracture,”
*Phys. Rev. Lett.*, 91, art. no.-025501, 2003.Google Scholar - [32]S.J. Zhou, D.M. Beazley, P.S. Lomdahl, and B.L. Holian, “Large-scale molecular dynamics simulations of three-dimensional ductile failure,”
*Phys. Rev. Lett.*, 78, 479–482, 1997.CrossRefADSGoogle Scholar - [33]P. Keblinski, D. Wolf, S.R. Phillpot, and H. Gleiter, “Structure of grain boundaries in nanocrystalline palladium by molecular dynamics simulation,”
*Scr. Mater.*, 41, 631–636, 1999.CrossRefGoogle Scholar - [34]M. Mrovec, T. Ochs, C. Elsasser, V. Vitek, D. Nguyen-Manh, and D.G. Pettifor, “Never ending saga of a simple boundary,”
*Z. Metallk.*, 94, 244–249, 2003.Google Scholar - [35]M.L. Falk and J.S. Langer, “Dynamics of viscoplastic deformation in amorphous solids,”
*Phys. Rev. E*, 57, 7192–7205, 1998.CrossRefADSGoogle Scholar - [36]G. Henkelman and H. Jonsson,“Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points,”
*J. Chem. Phys.*, 113, 9978–9985, 2000.CrossRefADSGoogle Scholar - [37]T. Vegge and W. Jacobsen, “Atomistic simulations of dislocation processes in copper,”
*J. Phys.-Condes. Matter*, 14, 2929–2956, 2002.CrossRefADSGoogle Scholar - [38]V.V. Bulatov, S. Yip, and A.S. Argon, “Atomic modes of dislocation mobility in silicon,”
*Philos. Mag. A*, 72, 453–496, 1995.CrossRefADSGoogle Scholar - [39]M. Wen and A.H.W. Ngan, “Atomistic simulation of kink-pairs of screw dislocations in body-centred cubic iron,”
*Acta Mater.*, 48, 4255–4265, 2000.CrossRefGoogle Scholar - [40]B.D. Wirth, G.R. Odette, D. Maroudas, and G.E. Lucas, “Energetics of formation and migration of self-interstitials and self-interstitial clusters in alpha-iron,”
*J. Nucl. Mater.*, 244, 185–194, 1997.CrossRefADSGoogle Scholar - [41]T.D. de laRubia, H.M. Zbib, T.A. Khraishi, B.D. Wirth, M. Victoria, and M.J. Caturia, “Multiscale modelling of plastic flow localization in irradiated materials,”
*Nature*, 406, 871–874, 2000.CrossRefADSGoogle Scholar - [42]R. Devanathan, W.J. Weber, and F. Gao, “Atomic scale simulation of defect production in irradiated 3CSiC,”
*J. Appl. Phys.*, 90, 2303–2309, 2001.CrossRefADSGoogle Scholar - [43]E.B. Tadmor, M. Ortiz, and R. Phillips, “Quasicontinuum analysis of defects in solids,”
*Philos. Mag. A*, 73, 1529–1563, 1996.CrossRefADSGoogle Scholar - [44]V. Bulatov, F.F. Abraham, L. Kubin, B. Devincre, and S. Yip, “Connecting atomistic and mesoscale simulations of crystal plasticity,”
*Nature*, 391, 669–672, 1998.CrossRefADSGoogle Scholar - [45]V.B. Shenoy, R. Miller, E.B. Tadmor, D. Rodney, R. Phillips, and M. Ortiz, “An adaptive finite element approach to atomic-scale mechanics — the quasicontinuum method,”
*J. Mech. Phys. Solids*, 47, 611–642, 1999.MATHCrossRefMathSciNetADSGoogle Scholar - [46]R. Madec, B. Devincre, L. Kubin, T. Hoc, and D. Rodney, “The role of collinear interaction in dislocation-induced hardening,”
*Science*, 301, 1879–1882, 2003.CrossRefADSGoogle Scholar - [47]J.H. Wang, J. Li, S. Yip, S. Phillpot, and D. Wolf, “Mechanical instabilities of homogeneous crystals,”
*Phys. Rev. B*, 52, 12627–12635, 1995.CrossRefADSGoogle Scholar - [48]I.S. Sokolnikoff,
*Tensor Analysis, Theory and Applications to Geometry and Mechanics of Continua.*, 2nd edn., Wiley, New York, 1964.Google Scholar - [49]S.C. Hunter,
*Mechanics of Continuous Media*, 2nd edn., E. Horwood, Chichester, 1983.MATHGoogle Scholar - [50]J.F. Lutsko, “Stress and elastic-constants in anisotropic solids — molecular dynamics techniques,”
*J. Appl. Phys.*, 64, 1152–1154, 1988.CrossRefADSGoogle Scholar - [51]J.F. Lutsko, “Generalized expressions for the calculation of elastic constants by computer-simulation,”
*J. Appl. Phys.*, 65, 2991–2997, 1989.CrossRefADSGoogle Scholar - [52]J.F. Ray, “Elastic-constants and statistical ensembles in moleculardynamics,”
*Comput. Phys. Rep.*, 8, 111–151, 1988.CrossRefADSGoogle Scholar - [53]T. Cagin and J.R. Ray, “Elastic-constants of sodium from molecular-dynamics,”
*Phys. Rev. B*, 37, 699–705, 1988.CrossRefADSGoogle Scholar - [54]W. Cai, V.V. Bulatov, J.P. Chang, J. Li, and S. Yip, “Anisotropic elastic interactions of a periodic dislocation array,”
*Phys. Rev. Lett.*, 86, 5727–5730, 2001.CrossRefADSGoogle Scholar - [55]A. Stroh, “Steady state problems in anisotropic elasticity,”
*J. Math. Phys.*, 41, 77–103, 1962.MATHMathSciNetGoogle Scholar - [56]J. Hirth and J. Lothe,
*Theory of Dislocations*, 2nd edn., Wiley, New York, 1982.Google Scholar - [57]M.W. Finnis and J.E. Sinclair, “A simple empirical n-body potential for transition metals,”
*Philos. Mag. A*, 50, 45–55, 1984.CrossRefADSGoogle Scholar - [58]V. Vitek, “Theory of core structures of dislocations in body-centered cubic metals,”
*Cryst Lattice Defects*, 5, 1–34, 1974.Google Scholar - [59]J. Knap and K. Sieradzki, “Crack tip dislocation nucleation in FCC solids,”
*Phys. Rev. Lett.*, 82, 1700–1703, 1999.CrossRefADSGoogle Scholar - [60]J. Schiotz and A.E. Carlsson, “The influence of surface stress on dislocation emission from sharp and blunt cracks in fcc metals,”
*Philos. Mag. A*, 80, 69–82, 2000.CrossRefADSGoogle Scholar - [61]P. Gumbsch, J. Riedle, A. Hartmaier, and H.F. Fischmeister, “Controlling factors for the brittle-to-ductile transition in tungsten single crystals,”
*Science*, 282, 1293–1295, 1998.CrossRefADSGoogle Scholar - [62]J.R. Rice and G.E. Beltz, “The activation-energy for dislocation nucleation at a crack,”
*J. Mech. Phys. Solids*, 42, 333–360, 1994.MATHCrossRefADSGoogle Scholar - [63]G. Xu, A.S. Argon, and M. Oritz, “Critical configurations for dislocation nucleation from crack tips,”
*Philos. Mag. A*, 75, 341–367, 1997.CrossRefADSGoogle Scholar - [64]Y. Mishin, M.J. Mehl, D.A. Papaconstantopoulos, A.F. Voter, and J.D. Kress, “Structural stability and lattice defects in copper:
*ab initio*, tight-binding, and embeddedatom calculations,”*Phys. Rev. B*, 6322, art. no.-224106, 2001.Google Scholar - [65]A. Stroh, “Dislocations and cracks in anisotropic elasticity,”
*Phil. Mag.*, 7, 625, 1958.CrossRefMathSciNetADSGoogle Scholar - [66]J. Li, “Atomeye: an efficient atomistic configuration viewer,”
*Model. Simul. Mater. Sci. Eng.*, 11, 173–177, 2003.MATHCrossRefADSGoogle Scholar