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Multiscale modeling of intergranular fracture in metals

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Applied Computational Materials Modeling
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Abstract

Multiscale modeling methods for the analysis of fracture in metallic microstructures are discussed. Molecular dynamics models are used to analyze grain-boundary sliding and fracture in an aluminum bicrystal model. A bilinear traction-displacement relationship that may be embedded into cohesive zone finite elements for microscale problems is extracted from the nanoscale molecular dynamics results.

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References

  1. J. Q. Broughton, F. F. Abraham, N. Bernstein and E. Kaxiras, Concurrent coupling of length scale: methodology and application, Phys. Rev. B 60, 2391–2403 (1999).

    Article  CAS  Google Scholar 

  2. F. F. Abraham, N. Bernstein, J. Q. Broughton and D. Hess, Dynamic fracture of silicon: concurrent simulation of quantum electrons, classical atoms, and the continuum solid, Mater. Res. Soc. Bull. 25, 27–32 (2000).

    CAS  Google Scholar 

  3. N. M. Ghoniem and K. Cho, The emerging role of multiscale modeling in nano-and micro-mechanics of materials, CMES: Comp. Model. Eng. Sci 3, 147–173 (2002).

    Google Scholar 

  4. E. B. Tadmor, M. Ortiz and R. Phillips, Quasicontinuum analysis of defects in solids, Phil. Mag. A 73, 1529–1563 (1996).

    Article  Google Scholar 

  5. R. E. Miller and E. B. Tadmor, The quasicontinuum method: overview, applications, and current direction, J. Comp. Aided Mat. Design 9, 203–239 (2002).

    Article  CAS  Google Scholar 

  6. S. Shen and S. N. Atluri, Multiscale simulation based on the meshless local petrovgalerkin (MLPG) method, CMES: Comp. Model. Eng. Sci. 5, 235–255 (2004).

    Google Scholar 

  7. V. Tvergaard and J. W. Hutchinson, The relation between crack growth resistance and fracture process parameters in elastic-plastic solids, J. Mech. Phys. Solids 40, 1377–1397 (1992).

    Article  Google Scholar 

  8. G. T. Camacho and M. Ortiz, Computational modeling of impact damage in brittle materials, Int. J. Solids Struct. 33, 2899–2938 (1996).

    Article  Google Scholar 

  9. P. Klein and H. Gao, Crack nucleation and growth as strain localization in a virtual-bond continuum, Eng. Fract. Mech. 61, 21–48 (1998).

    Article  Google Scholar 

  10. E. Iesulauro, A. R. Ingraffea, S. Arwade, and P. A. Wawrzynek, Simulation of grain boundary decohesion and crack initiation in aluminum microstructure models, in Fatigue and Fracture Mechanics: 33 rd Volume, ASTM STP 1417, (W. G. Reuter and R. S. Piascik, Eds, American Society for Testing and Materials, West Conshohocken, PA, 2002).

    Google Scholar 

  11. V. Tvergaard and J. W. Hutchinson, The influence of plasticity on mixed-mode interface toughness, J. Mech. Phys. Solids 41, 1119–1135 (1993).

    Article  Google Scholar 

  12. J. C. J. Schellekens and R. de Borst, On the numerical integration of interface elements, Int. J. Numer. Meth. Enng. 36, 43–66 (1992).

    Article  Google Scholar 

  13. P. P. Camanho and C. G. Davila, Mixed-mode decohesion finite elements for the simulation of delamination in composite materials, NASA/TM-2002-211737.

    Google Scholar 

  14. A. Turon and C. G. Davila, An engineering solution for using coarse meshes in the simulation of delamination using cohesive zone models, NASA/TM-2005, (to be published).

    Google Scholar 

  15. D. Raabe, Computational Materials Science: The Simulation of Materials Microstructures and Properties, (Wiley-VCH, Weinheim, 1998).

    Google Scholar 

  16. M. S. Daw, S. M. Foiles and M. I. Baskes, The embedded-atom method: a review of theory and applications, Mat. Sci. Reports 9, 251–310 (1992).

    Article  Google Scholar 

  17. J. Schiotz and K. W. Jacobsen, A maximum in the strength of nanocrystalline copper, Science 300, 1357–1359 (2003).

    Article  Google Scholar 

  18. F. F. Abraham, The atomic dynamics of fracture, J. Mech. Phys. Solids 49, 2095–2111 (2001).

    Article  Google Scholar 

  19. Y. Mishin, D. Farkas, M. J. Mehl and D. A. Papaconstantopoulos, Interatomic potentials for monoatomic metals from experimental data and ab initio calculations, Phys. Rev. B. 59, 3393–3407 (1999).

    Article  CAS  Google Scholar 

  20. D. Wolf, Structure-energy correlation for grain boundaries in fcc metals — III. Symmetrical tilt boundaries, Acta Metal. 38, 781–790 (1990).

    Article  CAS  Google Scholar 

  21. U. Dahmen, J. D. Hetherington, M. A. O’Keefe, K. H. Westmacott, M. J. Mills, M. S. Daw and V. Vitek, Atomic structure of a Σ99 grain boundary in A1: a comparison between atomic-resolution observation and pair-potential and embedded-atom simulations, Phil. Mag. Lettrs. 62, 327–335 (1990).

    Article  Google Scholar 

  22. V. Yamakov, D. Wolf, S. R. Phillpot, A. K. Mukherjee and H. Gleiter, Dislocation processes in the deformation of nanocrystalline A1 by molecular-dynamics simulation, Nature Materials 1, 45–48 (2002).

    Article  CAS  Google Scholar 

  23. V. Yamakov, D. Wolf, S. R. Phillpot and H. Gleiter, Dislocation-discolation and dislocation-twin reactions in nanocrystalline al by molecular-dynamics simulation, Acta Mater. 51, 4135–4147 (2003).

    Article  CAS  Google Scholar 

  24. P. Gumbsch, S. J. Zhou and B. L. Holian, Molecular dynamics investigation of dynamic crack stability, Phys. Rev. B 55, 3445–3455 (1997).

    Article  CAS  Google Scholar 

  25. C. G. Dávila, Mixed-mode decohesion elements for analysis of progressive delamination. 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, Seattle, WA April, 16–19 2001, article: AIAA-01-1486.

    Google Scholar 

  26. J. D. Honeycutt and H. C. Andersen, Molecular dynamics study of melting and freezing of small Lennard-Jones clusters, J. Phys. Chem. 91, 4950–4963 (1987).

    Article  CAS  Google Scholar 

  27. E. B. Tadmor and S. Hai, A Peierls criterion for the onset of deformation twinning at a crack tip, J. Mech. Phys. Solids 51, 765–793 (2003).

    Article  CAS  Google Scholar 

  28. M. Parrinello and A. Rahman, Polymorphic transitions in single crystals; a new molecular dynamics method, J. Appl. Phys. 52, 7182–7190 (1981).

    Article  CAS  Google Scholar 

  29. J. A. Zimmerman, R. E. Jones, P. A. Klein, D. J. Bammann, E. B. Webb III and J. J. Hoyt, Continuum definitions for stress in atomistic simulation, SAND Report, SAND2002-8608.

    Google Scholar 

  30. P. D. Zavattieri, P. V. Raghuram and H. D. Espinosa, A computational model of ceramic microstructures subjected to multi-axial dynamic loading, J. Mech. Phys. Solids 49, 27–68 (2001).

    Article  Google Scholar 

  31. P. D. Zavattieri and H. D. Espinosa, An examination of the competition between bulk behavior and interfacial behavior of ceramics subjected to dynamic pressure-shear loading, J. Mech. Phys. Solids 51, 607–635 (2003).

    Article  Google Scholar 

  32. Y. J. Wei and L. Anand Grain-boundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metals, J. Mech. Phys. Solids 52, 2587–2616 (2004).

    Article  CAS  Google Scholar 

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Yamakov, V., Phillips, D.R., Saether, E., Glaessgen, E.H. (2007). Multiscale modeling of intergranular fracture in metals. In: Bozzolo, G., Noebe, R.D., Abel, P.B., Vij, D. (eds) Applied Computational Materials Modeling. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-34565-9_10

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