Advertisement

Modelling shock waves in composite materials using generalised orthotropic pressure

  • M. K. Mohd NorEmail author
  • C. S. Ho
  • N. Ma’at
  • M. F. Kamarulzaman
Original Article
  • 12 Downloads

Abstract

Excellent mechanical properties of composite materials have numerous engineering applications, especially in aerospace structures. The main characteristics are due to their strength-to-weight ratio and low cost of manufacturing. Therefore, the understanding and an ability to predict the formation and propagation of shock waves in such materials are important. This paper investigates the ability of the constitutive model generalised for orthotropic materials to predict a complex elastoplastic deformation behaviour which involves very high pressures and shockwaves in composite materials. The formulation consists of a stress tensor formulated based on the combination between Mandel stress tensor and a new pressure generalised for orthotropic materials. The formulation is further combined with a shock equation of state (EOS) to define a new orthotropic EOS. The implementation of this newly orthotropic EOS in the Laboratory (LLNL)-DYNA3D code of UTHM’s version is presented in this paper for potential implementation in the other hydrocode. The formulation is then tested against plate impact test data of carbon fibre-reinforced epoxy composites along the through-thickness and longitudinal directions including the results obtained by Vignjevic’s model (Vignjevic et al. in J Appl Phys 104(4):044904, 2008). A good agreement is obtained in each test.

Keywords

Shock wave propagation Plate impact test Carbon fibre-reinforced epoxy composites Orthotropic pressure 

Notes

Acknowledgements

Authors wish to convey sincere gratitude to Universiti Tun Hussein Onn Malaysia (UTHM) for providing the financial means during the preparation to complete this work under Geran Penyelidikan Pascasiswazah (GPPS), Vot U746 and UTHM Contract Research Grant, Vot H276.

References

  1. 1.
    Anderson, C.E., Cox, P.A., Johnson, G.R., Maudlin, P.J.: A constitutive model for anisotropic materials suitable for wave propagation computer program-II. Comput. Mech. 15, 201–223 (1994)zbMATHCrossRefGoogle Scholar
  2. 2.
    Asay, J.R., Shahinpoor, M.: High-Pressure Shock Compression of Solids. Springer, New York (1993)zbMATHCrossRefGoogle Scholar
  3. 3.
    Colvin, J.D., Minich, R.W., Kalantar, D.H.: A model for plasticity kinetics and its role in simulating the dynamic behaviour of Fe at high strain rates. Int. J. Plast. 25(4), 603–611 (2009)zbMATHCrossRefGoogle Scholar
  4. 4.
    Davison, L., Graham, R.A.: Shock compression of solids. Phys. Rep. 55, 255–379 (1979)ADSCrossRefGoogle Scholar
  5. 5.
    Eliezer, S., Ghatak, A., Hora, H., Teller, E.: An Introduction to Equations of State, Theory and Applications. Cambridge University Press, Cambridge (1986)Google Scholar
  6. 6.
    Furnish, M.D., Chhabildas, L.C.: Alumina strength degradation in the elastic regime. AIP Conf. Proc. 429(1), 501–504 (1998)ADSCrossRefGoogle Scholar
  7. 7.
    Gray, G.T., Bourne, N.K., Millett, J.C.F.: Shock response of tantalum: lateral stress and shear strength through the front. J. Appl. Phys. 94(10), 6430–6436 (2003)ADSCrossRefGoogle Scholar
  8. 8.
    Gruneisen, E.: The State of Solid Body. NASA R19542 (1959)Google Scholar
  9. 9.
    Itskov, M.: On the application of the additive decomposition of generalized strain measures in large strain plasticity. Mech. Res. Commun. 31, 507–517 (2004)zbMATHCrossRefGoogle Scholar
  10. 10.
    Itskov, M., Aksel, N.: A constitutive model for orthotropic elasto-plasticity at large strains. Arch. Appl. Mech. 74, 75–91 (2004)ADSzbMATHCrossRefGoogle Scholar
  11. 11.
    Kanel, G.I., Zaretsky, E.B., Rajendran, A.M., Razorenov, S.V., Savinykh, A.S., Paris, V.: Search for conditions of compressive fracture of hard brittle ceramics at impact loading. Int. J. Plast. 25(4), 649–670 (2009)zbMATHCrossRefGoogle Scholar
  12. 12.
    Khan, A.S., Kazmi, R., Farrokh, B.: Multiaxial and non-proportional loading responses, anisotropy and modeling of Ti–6Al–4V titanium alloy over wide ranges of strain rates and temperatures. Int. J. Plast. 23(6), 931–950 (2007a)zbMATHCrossRefGoogle Scholar
  13. 13.
    Khan, A.S., Kazmi, R., Farrokh, B., Zupan, M.: Effect of oxygen content and microstructure on the thermo-mechanical response of three Ti–6Al–4V alloys: experiments and modeling over a wide range of strain-rates and temperatures. Int. J. Plast. 23(7), 1105–1125 (2007b)zbMATHCrossRefGoogle Scholar
  14. 14.
    Khan, A.S., Kazmi, R., Pandey, A., Stoughton, T.: Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part-I: a very low work hardening aluminum alloy (Al6061-T6511). Int. J. Plast 25(9), 1611–1625 (2009)CrossRefGoogle Scholar
  15. 15.
    Khan, A.S., Meredith, C.S.: Thermo-mechanical response of Al 6061 with and without equal channel angular pressing (ECAP). Int. J. Plast. 26(2), 189–203 (2010)zbMATHCrossRefGoogle Scholar
  16. 16.
    Ma’at, N., Mohd Nor, M.K., Ho, C.S., Abdul Latif, N., Ismail, A.E., Kamarudin, K.A., Jamian, S., Ibrahim Tamrin, M.N., Awang, M.K.: Effects of temperature and strain rates on the mechanical behaviour of commercial aluminium alloy AA6061. J. Adv. Res. Fluid Mech. Therm. Sci. 54(1), 21–26 (2019)Google Scholar
  17. 17.
    Malvern, L.E.: Introduction to the Mechanics of a Continuous Medium. Prentice-Hall Inc, Englewood Cliffs (1969)Google Scholar
  18. 18.
    Mandel, J.: Plasticité Classiqueet Viscoplastié’. CISM Lecture Notes. Springer, Wien (1972)Google Scholar
  19. 19.
    Meredith, C.S., Khan, A.S.: Texture evolution and anisotropy in the thermo-mechanical response of UFG Ti processed via equal channel angular pressing. Int. J. Plast. 30–31, 202–217 (2012)CrossRefGoogle Scholar
  20. 20.
    Meyers, M.A.: Dynamic Behaviour of Materials. Wiley Inc, New York (1994)zbMATHCrossRefGoogle Scholar
  21. 21.
    Millett, J.C.F., Bourne, N.K., Meziere, Y.J.E., Vignjevic, R., Lukyanov, A.: The effect of orientation on the shock response of a carbon fibre-epoxy composite. Comput. Sci. Technol. 67, 3253–60 (2007)CrossRefGoogle Scholar
  22. 22.
    Minich, R., Cazamias, J., Kumar, M., Schwartz, A.: Effect of microstructural length scales on spall behaviour of copper. Metall. Mater. Trans. A 35(9), 2663–2673 (2004)CrossRefGoogle Scholar
  23. 23.
    Mohd Nor, M.K., Vignjevic, R., Campbell, J.: Modelling of shockwave propagation in orthotropic materials. Appl. Mech. Mater. 315, 557–561 (2013a)CrossRefGoogle Scholar
  24. 24.
    Mohd Nor, M.K., Vignjevic, R., Campbell, J.: Plane-stress analysis of the new stress tensor decomposition. Appl. Mech. Mater. 315, 635–639 (2013b)CrossRefGoogle Scholar
  25. 25.
    Mohd Nor, M.K., Mohamad Suhaimi, I.: Effects of temperature and strain rate on commercial aluminum alloy AA5083. Appl. Mech. Mater. 660, 332–336 (2014)CrossRefGoogle Scholar
  26. 26.
    Mohd Nor, M.K.: The development of unique orthogonal rotation tensor algorithm in the LLNL-DYNA3D for orthotropic materials constitutive model. Aust. J. Basic Appl. Sci. 9(37), 22–27 (2015)Google Scholar
  27. 27.
    Mohd Nor, M.K.: Modelling inelastic behaviour of orthotropic metals in a unique alignment of deviatoric plane within the stress space. Int. J. Non-Linear Mech. 87, 43–57 (2016a)ADSCrossRefGoogle Scholar
  28. 28.
    Mohd Nor, M.K.: Modeling of constitutive model to predict the deformation behaviour of commercial aluminum alloy AA7010 subjected to high velocity impacts. ARPN J. Eng. Appl. Sci. 11(4), 2349–2353 (2016b)Google Scholar
  29. 29.
    Mohd Nor, M.K., Ma’at, N.: Simplified approach to validate constitutive formulation of orthotropic materials undergoing finite strain deformation. J. Eng. Appl. Sci. 11(10), 2146–2154 (2016)Google Scholar
  30. 30.
    Mohd Nor, M.K., Ma’at, N., Kamarudin, K.A., Ismail, A.E.: Implementation of finite strain-based constitutive formulation in LLNL-DYNA3D to predict shockwave propagation in commercial aluminum alloys AA7010. IOP Conf. Ser. Mater. Sci. Eng. 160, 012023 (2016)CrossRefGoogle Scholar
  31. 31.
    Mohd Nor, M.K., Ma’at, N., Ho, C.S.: An anisotropic elastoplastic constitutive formulation generalised for orthotropic materials. Contin. Mech. Thermodyn. 30(4), 825–860 (2018).  https://doi.org/10.1007/s00161-018-0645-7 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Nakamachi, E., Tam, N.N., Morimoto, H.: Multi-scale finite element analyses of sheet metals by using SEM-EBSD measured crystallographic RVE models. Int. J. Plast. 23(3), 450–489 (2007)zbMATHCrossRefGoogle Scholar
  33. 33.
    Reinhardt, W.D., Dubey, R.N.: An Eulerian-based approach to elastic–plastic decomposition. Acta Mech. 131, 111–119 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Sinha, S., Ghosh, S.: Modeling cyclic ratcheting based fatigue life of HSLA steels using crystal plasticity FEM simulations and experiments. Int. J. Fatigue 28(12), 1690–1704 (2006)CrossRefGoogle Scholar
  35. 35.
    Sitko, M., Skoczeń, B., Wróblewski, A.: FCC-BCC phase transformation in rectangular beams subjected to plastic straining at cryogenic temperatures. Int. J. Mech. Sci. 52(7), 993–1007 (2010)CrossRefGoogle Scholar
  36. 36.
    Sitnikova, E., Guan, Z.W., Schleyer, G.K., Cantwell, W.J.: Modelling of perforation failure in fibre metal laminates subjected to high impulsive blast loading. Int. J. Solids Struct. 51, 3135–3146 (2014)CrossRefGoogle Scholar
  37. 37.
    Smallman, R.E.: Modern Physical Metallurgy, 4th edn. Butterworths, London (1985)Google Scholar
  38. 38.
    Steinberg, D.J.: Equation of State and Strength Properties of Selected Materials. Report No. UCRL-MA-106439, Lawrence Livermore National Laboratory, Livermore, CA (1991)Google Scholar
  39. 39.
    Vignjevic, R., Bourne, N.K., Millett, J.C.F., De Vuyst, T.: Effects of orientation on the strength of the aluminum alloy 7010–T6 during shock loading: experiment and simulation. J. Appl. Phys. 92(8), 4342–4348 (2002)ADSCrossRefGoogle Scholar
  40. 40.
    Vignjevic, R., Campbell, J., Bourne, N. K., Djordjevic, N.: Modelling Shock Waves in Orthotropic Elastic Materials. In: Conference on Shock Compression of Condensed Matter, Hawaii (2007)Google Scholar
  41. 41.
    Vignjevic, R., Campbell, J., Bourne, N.K., Djordjevic, N.: Modelling shock waves in orthotropic elastic materials. J. Appl. Phys. 104(4), 044904 (2008)ADSCrossRefGoogle Scholar
  42. 42.
    Vignjevic, R., Millett, J.C.F., Bourne, N.K., Meziere, Y., Lukyanov, A.: The behaviour of a carbon-fibre epoxy composite under shock loading. In: Furnish, M.D., Elert, M.L., Russell, T.P., White, C.T. (eds.) Shock Compression of Condensed Matter 2005, pp. 825–828. American Institute of Physics, Melville, NY (2006)Google Scholar
  43. 43.
    Wackerle, J.: Shock-wave compression of quartz. J. Appl. Phys. 33, 922–937 (1962)ADSCrossRefGoogle Scholar
  44. 44.
    Zaretsky, E.B., Kanel, G.I.: Plastic flow in shock-loaded silver at strain rates from 10[sup 4]s[sup - 1] to 10[sup 7]s[sup - 1] and temperatures from 296 K to 1233 K. J. Appl. Phys. 110(7), 073502 (2011)ADSCrossRefGoogle Scholar
  45. 45.
    Zel’dovich, Y.B., Raizer, Y.P.: Physics of Shock Waves and High-temperature Hydrodynamic Phenomena, vols. 1 and 2. Academic Press, New York (1966)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Crashworthiness and Collisions Research Group (COLORED) Mechanical Failure Prevention and Reliability Research Centre (MPROVE), Faculty of Mechanical and Manufacturing EngineeringUniversiti Tun Hussein Onn MalaysiaParit RajaMalaysia

Personalised recommendations