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


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.


Plasticity Crack tip fields Fracture Compressible solids Material softening 


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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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