Skip to main content
SpringerLink
Log in

Merging Experimental Evidence and Molecular Dynamics Theory to Develop Efficient Models of Solids Fracture

  • Conference paper
  • First Online:
Mechanics of Composite and Multi-functional Materials, Volume 7

  • 1240 Accesses

Abstract

Causes of failure mechanisms can only be found at the level of the dynamics of atoms and molecules. However, the subject of dynamics at the level of atomic structure is very complex, especially in terms of modeling and computations. An interesting way to better understand relationships between macro world and atomic realm is to develop Experimental Mechanics techniques that can provide a verification of developed models at the nanometric and subnanometric levels, guiding the derivation of comprehensive but manageable models. This paper will describe how to apply classical EM methods to establish a bridge between classical continuum mechanics variables and the atomistic analysis of solid mechanics. In particular, we analyze the role of the Cauchy-Born rule as standard tool applied in theoretical and numerical methods to describe the continuum utilizing atomistic arguments. Experimental evidence of the validity of the Cauchy-Born rule will be discussed for the case of SiC crystal including dislocations. Likewise, we will examine how to handle the onsets of plasticity and fracture.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Wagner, G.J., Liu, W.K.: Coupling of atomistic and continuum simulations using a bridging scale decomposition. J. Comput. Phys. 190(1), 249–274 (2003)

    Article  MATH  Google Scholar 

  2. Tadmor, E.B., Philips, R., Ortiz, M.: Hierarchical modeling in the mechanics of materials. Int. J. Solids Struct. 37(1–2), 379–389 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Steinmann, P., Elizondo, A., Sunyk, R.: Studies of validity of the Cauchy Born rule by direct comparison of continuum and atomistic modeling. Model. Simul. Mater. Sci. Eng. 15(1), 271–283 (2007)

    Article  Google Scholar 

  4. Shenoy, V.D., Miller, R., Tadmor, E.B., Rodney, D., Philips, R., Ortiz, M.: An adaptive finite element approach to atomic-scale mechanics-the quasicontinuum model. J. Mech. Phys. Solids 47(3), 611–642 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. Arroyo, M., Belytschko, T.: An atomistic-based finite deformation membrane for single layer crystalline films. J. Mech. Phys. Solids 50(9), 1941–1977 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. Clayton, J.D., Chung, P.W.: An atomistic-to-continuum framework for nonlinear crystal mechanics based on asymptotic homogenization. J. Mech. Phys. Solids 54(8), 1604–1639 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Philips, R.: Crystals, defects and microstructures. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

  8. Gray, H.B.: Chemical bonds, 2nd edn. University Science Book, Sausalito (1996)

    Google Scholar 

  9. Lennard-Jones, J.E.: On the determination of molecular fields—Part II. From the equation of state of a gas. Proc. R. Soc. London A 106(738), 463–477 (1924)

    Article  Google Scholar 

  10. Frenkel, D., Smit, B.: Understanding molecular simulation, 2nd edn. Academic, London (2002)

    MATH  Google Scholar 

  11. Mie, G.: Zur kinetischen theorie der einatomigen körper. Ann. Phys. 316(8), 657–697 (1903)

    Article  MATH  Google Scholar 

  12. Morse, P.M.: Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys. Rev. 34, 57–64 (1929)

    Article  MATH  Google Scholar 

  13. Le Roy, R.J., Huang, Y., Jary, C.: An accurate analytic potential function for ground-state N2 from a direct-potential-fit analysis of spectroscopic data. J. Chem. Phys. 125(16), 164310 (2006)

    Article  Google Scholar 

  14. Cauchy, A.L.: De la pression ou tension dans un système des points matériels. Sur le équilibre et le mouvement d’un système de points matériels sollicités par des forces d’attraction ou de répulsion mutuelle. Sur l’équilibre et le mouvement intérieur des corps considérés comme masses continues. In: Cauchy Augustin-Louis, Ouvres Complétés, Tomes 20-21. Gauthier-Villars et fils, Paris (1882–1974)

    Google Scholar 

  15. Born, M.: Atomtheorie Des Festen Zustandes [Dynamik der Kristallgitter]. In: Taubner, G.B. (ed.), Fortschritte der Mathematischen Wessenschaften, Berlin (1923)

    Google Scholar 

  16. Cheung, R.: Silicon carbide microelectromechanical systems for harsh environments. Imperial College Press, London (2006)

    Book  Google Scholar 

  17. Kelly, J.F., Fisher, P., Barnes, P.: Correlation between layer thickness and periodicity of long polytypes in silicon carbide. Mater. Res. Bull. 40(2), 249–255 (2005)

    Article  Google Scholar 

  18. Sciammarella, C.A., Lamberti, L., Sciammarella, F.M.: Measurement of deformations at the sub-nanometric level. In: Proceedings of the NANOMEC06 Symposium on Materials Science and Materials Mechanics at the Nanoscale, Bari, 19–23 Nov 2006

    Google Scholar 

  19. Sciammarella, F.M., Sciammarella, C.A., Lamberti, L.: Processing of a HRTEM image pattern to analyze an edge dislocation. In: Gdoutos, E.E. (ed.) Experimental Analysis of Nano and Engineering Materials and Structures. Springer, Rotterdam (2007)

    Google Scholar 

  20. Sciammarella, F.M., Sciammarella, C.A., Lamberti, L.: Experimental nanomechanics: a look at edge dislocations in 4HSiC crystals. In: Proceedings of the Materials Science and Technology Conference and Exhibition (MS&T’07), Detroit, Sept 2007

    Google Scholar 

  21. Ha, S.Y., Nuhfer, N.T., De Graef, M., Rohrer, G.S., Skowronski, M.: Origin of threading dislocation arrays in SiC boules grown by PVT. Mater. Sci. Forum 338–342, 477–480 (2000)

    Article  Google Scholar 

  22. Williams, D.R., Barry Carter, C.: Transmission electron microscopy, a textbook for materials science, 2nd edn. Springer, New York (2009)

    Google Scholar 

  23. Sciammarella, C.A., Sciammarella, F.M.: Experimental mechanics of solids. Wiley, Chichester (2012)

    Book  MATH  Google Scholar 

  24. Boreman, G.D.: Modulation transfer function in optical and electro-optical systems. SPIE, Bellingham (2001)

    Book  Google Scholar 

  25. JEOL USA: Transmission electron microscopes. http://www.jeolusa.com

  26. General Stress Optics Inc.: Holo-Moiré Strain Analyzer Software HoloStrain, Version 2.0. General Stress Optics Inc., Chicago. www.stressoptics.com

  27. Subramaniam, A., Balani, K.: Materials Science and Engineering (MSE). Chapter 5b: Crystal imperfections dislocations. Indian Institute of Technology, Kanpur. http://home.iitk.ac.in/~anandh/E-book (2013). Accessed 5 Mar 2016

  28. Sciammarella, C.A.: Positron annihilation spectroscopy for life assessment of super alloys. In: Viswathnathan, R. (ed.) Proceedings for the NDE for Damage Assessment Workshop, EPRI TR-110291 (1998)

    Google Scholar 

  29. Yoshida, S., Muchiar, I., Muhamad, R., Widiastuti, R., Kusnowo, A.: Optical interferometric technique for deformation analysis. Opt. Express 2(13), 516–530 (1998)

    Article  Google Scholar 

  30. Panin, V.E.: Wave nature of plastic deformation in solids. Sov. Phys. J. 33(2), 99–110 (1990)

    Article  Google Scholar 

  31. Yoshida, S., Siahaan, B., Pardede, M.H., Sijabat, N., Simangunsong, H., Simbolon, T., Kusnowo, A.: Observation of plastic deformation wave in a tensile-loaded aluminum alloy. Phys. Lett. A 251(1), 54–60 (1999)

    Article  Google Scholar 

  32. Yoshida, S.: Consideration on fracture of solid-state materials. Phys. Lett. A 270(6), 320–325 (2000)

    Article  Google Scholar 

  33. Yoshida, S.: Physical mesomechanics as a field theory. Phys. Mesomech. 8(5–6), 15–20 (2005)

    Google Scholar 

  34. Yoshida, S.: Dynamics of plastic deformation on restoring and energy dissipative mechanisms in plasticity. Phys. Mesomech. 11(3–4), 137–143 (2008)

    Article  Google Scholar 

  35. Yoshida, S., Rourks, R.L., Mita, T., Ichinose, K.: Physical mesomechanical criteria of plastic deformation and fracture. Phys. Mesomech. 12(5–6), 249–253 (2009)

    Article  Google Scholar 

  36. Yoshida, S.: Deformation and fracture of solid-state materials, field theoretical approach and engineering applications. Springer, New York (2015)

    Google Scholar 

  37. Sirelson, V.G., Ozerov, R.P.: Electron density and bonding in crystals: Principles, theory and X-ray diffraction experiments in solid state physics and chemistry. Taylor and Francis, Abingdon (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, 10 SW 32nd Street, Chicago, IL, 60616, USA

    C. A. Sciammarella

  2. Department of Mechanical Engineering, College of Engineering and Engineering Technology, Northern Illinois University, 590 Garden Road, DeKalb, IL, 60115, USA

    C. A. Sciammarella & F. M. Sciammarella

  3. Dipartimento Meccanica, Matematica e Management, Politecnico di Bari, Viale Japigia 182, Bari, 70126, Italy

    L. Lamberti

Authors
  1. C. A. Sciammarella
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. M. Sciammarella
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. Lamberti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. A. Sciammarella .

Editor information

Editors and Affiliations

  1. Southern Research , Birmingham, Alabama, USA

    W. Carter Ralph

  2. Oklahoma State University , Tulsa, Oklahoma, USA

    Raman Singh

  3. University of Dayton Research Institute , Dayton, Ohio, USA

    Gyaneshwar Tandon

  4. The Dow Chemical Company , Midland, Michigan, USA

    Piyush R. Thakre

  5. Purdue University , West Lafayette, Indiana, USA

    Pablo Zavattieri

  6. North Carolina State Universiity, Raleigh, North Carolina, USA

    Yong Zhu

Rights and permissions

Reprints and permissions

Copyright information

© 2017 The Society for Experimental Mechanics, Inc.

About this paper

Cite this paper

Sciammarella, C.A., Sciammarella, F.M., Lamberti, L. (2017). Merging Experimental Evidence and Molecular Dynamics Theory to Develop Efficient Models of Solids Fracture. In: Ralph, W., Singh, R., Tandon, G., Thakre, P., Zavattieri, P., Zhu, Y. (eds) Mechanics of Composite and Multi-functional Materials, Volume 7 . Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-41766-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-41766-0_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41765-3

  • Online ISBN: 978-3-319-41766-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation