Acta Mechanica Sinica

, Volume 33, Issue 1, pp 148–158 | Cite as

Finite deformation analysis of crack tip fields in plastically compressible hardening–softening–hardening solids

Research Paper
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Abstract

Crack tip fields are calculated under plane strain small scale yielding conditions. The material is characterized by a finite strain elastic–viscoplastic constitutive relation with various hardening–softening–hardening hardness functions. Both plastically compressible and plastically incompressible solids are considered. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The initial crack is taken to be a semi-circular notch and symmetry about the crack plane is imposed. Plastic compressibility is found to give an increased crack opening displacement for a given value of the applied loading. The plastic zone size and shape are found to depend on the plastic compressibility, but not much on whether material softening occurs near the crack tip. On the other hand, the near crack tip stress and deformation fields depend sensitively on whether or not material softening occurs. The combination of plastic compressibility and softening (or softening–hardening) has a particularly strong effect on the near crack tip stress and deformation fields.

Keywords

Plasticity Crack tip fields Fracture Compressible solids Material softening 

References

  1. 1.
    Hutchens, S.B., Needleman, A., Greer, J.R.: A microstructurally motivated description of the deformation of vertically alligned carbon nanotube structures. Appl. Phys. Lett. 100, 121910 (2012)Google Scholar
  2. 2.
    Mohan, N., Cheng, J., Greer, J.R., et al.: Uniaxial tension of a class of compressible solids with plastic non-normality. J. Appl. Mech. 80, 040912 (2013)Google Scholar
  3. 3.
    Hwang, K.C., Luo, X.F.: Near-tip fields for cracks growing steadily in elastic-perfectly-plastic compressible material. In: IUTAM Symposium on Recent Advances in Nonlinear Fracture Mechanics, Pasadena (1988)Google Scholar
  4. 4.
    Li, F.Z., Pan, J.: Plane-strain crack-tip fields for pressure-sensitive dilatant materials. J. Appl. Mech. 57, 40–49 (1990)CrossRefGoogle Scholar
  5. 5.
    Yuan, H., Lin, G.: Elastoplastic crack analysis for pressure-sensitive dilatant materials, part I: higher-order solutions and two-parameter characterization. Int. J. Fract. 61, 295–330 (1993)CrossRefGoogle Scholar
  6. 6.
    Yuan, H.: Elastoplastic crack analysis for pressure-sensitive dilatant materials, part II: interface cracks. Int. J. Fract. 69, 167–187 (1994)CrossRefGoogle Scholar
  7. 7.
    Chang, W.J., Kim, M., Pan, J.: Quasi-statically growing crack-tip fields in elastic perfectly plastic pressure-sensitive materials under plane strain conditions. Int. J. Fract. 84, 203–228 (1997)Google Scholar
  8. 8.
    Lai, J., Van der Giessen, E.: A numerical study of crack-tip plasticity in glassy polymers. Mech. Mater. 25, 183–197 (1997)CrossRefGoogle Scholar
  9. 9.
    McMeeking, R.M.: Finite deformation analysis of crack tip opening in elastic-plastic materials and implications for fracture. J. Mech. Phys. Solids 25, 357–381 (1977)CrossRefGoogle Scholar
  10. 10.
    Gearing, B.P., Anand, L.: Notch-sensitive fracture of polycarbonate. Int. J. Solids Struct. 41, 827–845 (2004)CrossRefMATHGoogle Scholar
  11. 11.
    Long, R., Hui, C.-Y.: Crack tip fields in soft elastic solids subjected to large quasi-static deformation–a review. Extrem. Mech. Lett. 4, 131–155 (2015)CrossRefGoogle Scholar
  12. 12.
    Hutchens, S.B., Needleman, A., Greer, J.R.: Analysis of uniaxial compression of vertically aligned carbon nanotubes. J. Mech. Phys. Solids 59, 2227–2237 (2011)CrossRefMATHGoogle Scholar
  13. 13.
    Rice, J.R.: A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 90, 379–386 (1968)CrossRefGoogle Scholar
  14. 14.
    Needleman, A., Tvergaard, V., van der Giessen, E.: Indentation of elastically soft and plastically compressible solids. Acta Mech. Sin. 31, 473–480 (2015)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Needleman, A., Hutchens, S.B., Mohan, N., et al.: Deformation of plastically compressible hardening-softening-hardening solids. Acta Mech. Sin. 28, 1115–1124 (2012)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Deshpande, V.A., Fleck, N.A.: Isotropic constitutive models for metallic foams. J. Mech. Phys. Solids 48, 1253–1283 (2000)CrossRefMATHGoogle Scholar
  17. 17.
    Peirce, D., Shih, C.F., Needleman, A.: A tangent modulus method for rate dependent solids. Compos. Struct. 18, 875–887 (1984)CrossRefMATHGoogle Scholar
  18. 18.
    Shih, C.F.: Relationships between the J-integral and the crack opening displacement for stationary and extending cracks. J. Mech. Phys. Solids 29, 305–326 (1981)CrossRefMATHGoogle Scholar
  19. 19.
    Hutchinson, J.W.: Singular behavior at the end of a tensile crack in a hardening material. J. Mech. Phys. Solids 16, 337–347 (1968)CrossRefMATHGoogle Scholar
  20. 20.
    Rice, J.R., Rosengren, G.F.: Plane strain deformation near a crack tip in a power law hardening material. J. Mech. Phys. Solids 16, 1–12 (1968)CrossRefMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Mechanical Engineering Department, Indian Institute of TechnologyBanaras Hindu UniversityVaranasiIndia
  2. 2.Department of Materials Science & EngineeringTexas A&M UniversityCollege StationUSA

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