Advertisement

Local Stress and Damage Response of Polycrystal Materials to Light Shock Loading Conditions via Soft Scale-Coupling

  • C. A. BronkhorstEmail author
  • P. W. Marcy
  • S. A. Vander Wiel
  • H. Cho
  • V. Livescu
  • G. T. Gray III
Chapter
  • 55 Downloads

Abstract

Accurately representing the process of porosity-based ductile damage in polycrystalline metallic materials via computational simulation remains a significant challenge. The heterogeneity of deformation in this class of materials due to the anisotropy of deformation of individual single crystals creates the conditions for the formation of a damage field. The work reported upon here is interested in the formation of porosity in the body-centered cubic metal tantalum. This chapter reports on the soft-coupled linkage between a macroscale damage model and mesoscale calculations of a suite of polycrystal realizations of tantalum. The macroscale model is used to represent a tantalum on tantalum plate impact experiment and predict the point in time in the loading profile when porosity is likely to initiate. The 3D loading history from the macroscale calculation is then used to define the probable loading history profile experienced within the experimental sample. Tantalum displays non-Schmid behavior in the motion of the dominant screw dislocations during deformation. This introduces directionality in the magnitude of stress required to propagate glide of these screw dislocations. A model is presented which provides representation of non-Schmid effects in tantalum. This model is employed in performing of meso-scale calculations of statistically equivalent microstructures of the tantalum material to provide local-scale stress condition at the time of the loading profile where initiation of porosity is anticipated. The results of these simulations suggest that non-Schmid effects significantly impact the local stress conditions within the microstructure and are very important to represent. The results also suggest that vonMises stress conditions at grain boundaries and grain boundary triple lines are highly variable close to those features but the variability is reduced with distance to the grain center. The computational results also suggest that the stress traction conditions at the grain boundary are a strong function of the orientation of each boundary with respect to the shock direction. Grain boundaries whose surface normal is parallel to the shock direction have a significantly higher normal tensile traction than other grain boundaries. Grain boundaries whose normal is at 45 or 135 degrees to the shock direction have relatively higher magnitudes of shear stress.

Keywords

Ductile damage Crystal plasticity Shock loading Porosity Metals Grain boundary Statistics Defects Nucleation Non-schmid effect Scale-coupling Dislocations 

Notes

Acknowledgments

This work was performed at Los Alamos National Laboratory and funded through the Laboratory Directed Research and Development program via projects 20170033DR and 20150594ER. The authors also wish to acknowledge the assistance provided by Dr. M. Ardeljan in constructing the SVEs used in this study.

References

  1. 1.
    F.L. Addessio, J.N. Johnson, Rate-dependent ductile failure model. J. Appl. Phys. 74, 1640–1648 (1993)CrossRefGoogle Scholar
  2. 2.
    C. Alleman, S. Ghosh, D.J. Luscher, C.A. Bronkhorst, Evaluating the effects of loading parameters on single crystal slip in tantalum using molecular mechanics. Phil. Mag. 94, 92–116 (2013)CrossRefGoogle Scholar
  3. 3.
    C. Alleman, D.J. Luscher, C.A. Bronkhorst, S. Ghosh, Distributed-enhanced homogenization framework and model for heterogeneous elasto-plastic problems. J. Mech. Phys. Solids 85, 176–202 (2015)CrossRefGoogle Scholar
  4. 4.
    L. Anand, Single-crystal elasto-viscoplasticity: application to texture evolution in polycrystalline metals at large strains. Comput. Methods Appl. Mech. Eng. 193, 5359–5383 (2004)CrossRefGoogle Scholar
  5. 5.
    R.J. Asaro, J.R. Rice, Strain localization in ductile single crystals. J. Mech. Phys. Solids 25, 309–338 (1977)CrossRefGoogle Scholar
  6. 6.
    A. Acharya, A.J. Beaudoin, Grain size effect in viscoplastic polycrystal at moderate strains. J. Mech. Phys. Solids 48, 2213–2230 (2000)CrossRefGoogle Scholar
  7. 7.
    R. Becker, Ring fragmentation predictions using the Gurson model with material stability conditions as failure criteria. Int. J. Sol. Struct. 39, 3555–3580 (2002)CrossRefGoogle Scholar
  8. 8.
    R. Becker, Effects of crystal plasticity on materials loaded at high pressures and strain rates. Int. J. Plasticity 20, 1983–2006 (2004)CrossRefGoogle Scholar
  9. 9.
    C.A. Bronkhorst, S.R. Kalidindi, L. Anand, Polycrystal plasticity and the evolution of crystallographic texture in FCC metals. Phil. Trans. R. Soc. Lond. A 341, 443–477 (1992)CrossRefGoogle Scholar
  10. 10.
    C.A. Bronkhorst, G.T. Gray III, F.L. Addessio, V. Livescu, N.K. Bourne, S.A. MacDonald, P.J. Withers, Response and representation of ductile damage under varying shock loading conditions in tantalum. J. Appl. Phys. 119, 085103 (2016)CrossRefGoogle Scholar
  11. 11.
    C.A. Bronkhorst, E.K. Cerreta, Q. Xue, P.J. Maudlin, T.A. Mason, G.T. Gray III, An experimental and numerical study of the localization behavior of tantalum and stainless steel. Int. J. Plasticity 22, 1304–1335 (2006)CrossRefGoogle Scholar
  12. 12.
    C.A. Bronkhorst, B.L. Hansen, E.K. Cerreta, J.F. Bingert, Modeling the microstructural evolution of metallic polycrystal materials under localization conditions. J. Mech. Phys. Solids 55, 2351–2383 (2007)CrossRefGoogle Scholar
  13. 13.
    E.P. Busso, Cyclic deformation of monocrystalline nickel aluminide and high temperature coatings, Ph.D. Thesis, MIT, 1990Google Scholar
  14. 14.
    E.P. Busso, F.A. McClintock, A dislocation mechanics-based crystallographic model of a B2-type intermetallic alloy. Int. J. Plasticity 12, 1–28 (1996)CrossRefGoogle Scholar
  15. 15.
    S.R. Chen, G.T. Gray III, Constitutive behavior of tantalum and tantalum-tungsten alloys. Met. Mat. Trans. A 27A, 2994–3006 (1996)CrossRefGoogle Scholar
  16. 16.
    H. Cho, C.A. Bronkhorst, H.M. Mourad, J.R. Mayeur, D.J. Luscher, Anomalous plasticity of body-centered-cubic crystals with non-Schmid effects. Int. J. Solids Struct. 139–140, 138–149 (2018)CrossRefGoogle Scholar
  17. 17.
    Dream.3D version 4.2, BlueQuartz Software, Springboro OH, USA, 2013Google Scholar
  18. 18.
    P.S. Follansbee, U.F. Kocks, A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable. Acta Metall. 36, 81–93 (1988)CrossRefGoogle Scholar
  19. 19.
    G.T. Gray III, Shock wave testing of ductile materials, in ASM Handbook, (ASM International, Materials Park, 2000)Google Scholar
  20. 20.
    G.T. Gray III, High-strain-rate deformation: mechanical behavior and deformation substructures induced. Annu. Rev. Mater. Res. 42, 285–303 (2012)CrossRefGoogle Scholar
  21. 21.
    G.T. Gray III, K.S. Vecchio, Influence of peak pressure and temperature on the structure/property response of shock-loaded Ta and Ta-10W. Met. Mat. Trans. A 26, 2555–2563 (1995)CrossRefGoogle Scholar
  22. 22.
    G.T. Gray III, N.K. Bourne, J.C.F. Millett, Shock response of tantalum: Lateral stress and shear strength through the front. J. Appl. Phys. 94, 6430–6436 (2003)CrossRefGoogle Scholar
  23. 23.
    G.T. Gray III, N.K. Bourne, K.S. Vecchio, J.C.F. Millett, Influence of anisotropy (crystallographic and microstructural) on spallation in Zr, Ta, HY-100 steel, and 1080 eutectoid steel. Int. J. Fract. 163, 243–258 (2010)CrossRefGoogle Scholar
  24. 24.
    G.T. Gray III, N.K. Bourne, V. Livescu, C.P. Trujillo, S. MacDonald, P. Withers. The influence of shock-loading path on the spallation response of Ta. in Proceedings of APS Topical Group of Shock Compression of Condensed Matter, Seattle, 7–12 July 2013Google Scholar
  25. 25.
    M. Groeber, S. Ghosh, M.D. Uchic, D.M. Dimiduk, A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 2: Synthetic structure generation. Acta Mat. 56, 1274–1287 (2008)CrossRefGoogle Scholar
  26. 26.
    A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part 1 – Yield criteria and flow rules for porous ductile media. J. Eng. Mat. Tech. 99, 2–15 (1977)CrossRefGoogle Scholar
  27. 27.
    M.E. Gurtin, On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J. Mech. Phys. Solids 48, 989–1036 (2000)CrossRefGoogle Scholar
  28. 28.
    M.E. Gurtin, E. Fried, L. Anand, The Mechanics and Thermodynamics of Continua (Cambridge University Press, Cambridge, 2010)CrossRefGoogle Scholar
  29. 29.
    J.W. Hancock, A.C. Mackenzie, On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. J. Mech. Phys. Solids 24, 147–169 (1976)CrossRefGoogle Scholar
  30. 30.
    G.R. Johnson, S.R. Beissel, C.A. Gerlach, R.A. Stryk, T.J. Holmquist, A.A. Johnson, S.E. Ray, J.J. Arata, User Instructions for the 2006 Version of the EPIC Code (Network Computing Services Inc., Minneapolis, 2006)Google Scholar
  31. 31.
    J.N. Johnson, Dynamic fracture and spallation in ductile solids. J. Appl. Phys. 52, 2812 (1981)CrossRefGoogle Scholar
  32. 32.
    J.N. Johnson, F.L. Addessio, Tensile plasticity and ductile fracture. J. Appl. Phys. 64, 6699 (1988)CrossRefGoogle Scholar
  33. 33.
    J.N. Johnson, G.T. Gray III, N.K. Bourne, Effect of pulse duration and strain rate on incipient spall fracture in copper. J. Appl. Phys. 86, 4892 (1999)CrossRefGoogle Scholar
  34. 34.
    S.R. Kalidindi, C.A. Bronkhorst, L. Anand, Crystallographic texture evolution in bulk deformation processing of FCC metals. J. Mech. Phys. Solids 40, 537–569 (1992)CrossRefGoogle Scholar
  35. 35.
    M. Knezevic, B. Drach, M. Ardeljan, I.J. Beyerlein, Three dimensional predictions of grain scale plasticity and grain boundaries using crystal plasticity finite element models. Comput. Methods Appl. Mech. Eng. 277, 239–259 (2014)CrossRefGoogle Scholar
  36. 36.
    U.F. Kocks, A.S. Argon, M.F. Ashby, Thermodynamics and Kinetics of Slip. Progress in Materials Science (Pergamon, Oxford, 1975)Google Scholar
  37. 37.
    U.F. Kocks, Laws for work-hardening and low-temperature creep. J. Eng. Mater. Technol. 98, 76–85 (1976)CrossRefGoogle Scholar
  38. 38.
    M. Kothari, L. Anand, Elasto-viscoplastic constitutive equations for polycrystalline metals: application to tantalum. J. Mech. Phys. Solids 46, 51–83 (1998)CrossRefGoogle Scholar
  39. 39.
    P.J. Maudlin, J.F. Bingert, J.W. House, S.R. Chen, On the modeling of the Taylor cylinder impact test for orthotropic texture materials: experiments and simulations. Int. J. Plasticity 15, 139–166 (1999)CrossRefGoogle Scholar
  40. 40.
    P.J. Maudlin, E.N. Harstad, T.A. Mason, Q.H. Zuo, F.L. Addessio. TEPLA-a: coupled anisotropic elastoplasticity and damage, the Joint DoD/DOE Munitions Technology Program progress report, LA-UR-14015-PR (2003)Google Scholar
  41. 41.
    S. Nemat-Nasser, J.B. Isaacs, Direct measurement of isothermal flow stress of metals at elevated temperatures and high strain rates with application to Ta and Ta-W alloys. Acta Mater. 45, 907–919 (1997)CrossRefGoogle Scholar
  42. 42.
    D.J. Savage, I.J. Beyerlein, M. Knezevic, Coupled texture and non-Schmid effects on yield surfaces on body-centered cubic polycrystals predicted by a crystal plasticity finite element approach. Int. J. Solids Struct. 109, 22–32 (2017)CrossRefGoogle Scholar
  43. 43.
    P. Shanthraj, M.A. Zikry, Dislocation-density mechanisms for void interactions in crystalline materials. Int. J. Plasticity 34, 154–163 (2012)CrossRefGoogle Scholar
  44. 44.
    V. Tvergaard, A. Needleman, Analysis of the cup-cone fracture in a round tensile bar. Acta Metall. 32, 157–169 (1984)CrossRefGoogle Scholar
  45. 45.
    Y.P. Varshni, Temperature dependence of the elastic constants. Phys. Rev. B 2, 3952–3958 (1970)CrossRefGoogle Scholar
  46. 46.
    D. Versino, C.A. Bronkhorst, A computationally efficient ductile damage model accounting for micro-inertia. Comp. Meth. Appl. Mech. Engr. 333, 395–420 (2018)CrossRefGoogle Scholar
  47. 47.
    Q. Wu, M.A. Zikry, Dynamic fracture predictions of microstructural mechanisms and characteristics in martensitic steels. Eng. Frac. Mech. 145, 54–66 (2014)CrossRefGoogle Scholar
  48. 48.
    Q.H. Zuo, J.R. Rice, An implicit algorithm for a rate-dependent ductile failure model. J. Appl. Phys. 104, 083526 (2008)CrossRefGoogle Scholar
  49. 49.
    Q.H. Zuo, Modified formulation of a rate-dependent damage model for ductile materials. J. Appl. Phys. 107, 053513 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • C. A. Bronkhorst
    • 1
    • 2
    Email author
  • P. W. Marcy
    • 3
  • S. A. Vander Wiel
    • 3
  • H. Cho
    • 4
  • V. Livescu
    • 5
  • G. T. Gray III
    • 5
  1. 1.Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Department of Engineering PhysicsUniversity of WisconsinMadisonUSA
  3. 3.Computer, Computational, and Statistical Sciences DivisionLos Alamos National LaboratoryLos AlamosUSA
  4. 4.School of Mechanical and Aerospace EngineeringKorea Advanced Institute of Science and TechnologyDaejeonRepublic of Korea
  5. 5.Materials Science and Technology DivisionLos Alamos National LaboratoryLos AlamosUSA

Personalised recommendations