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Effect of crack tip shape on near-tip deformation and fields in plastically compressible solids

  • Md Intaf Alam
  • Debashis KhanEmail author
  • Yash Mittal
  • Sandeep Kumar
Technical Paper
  • 72 Downloads

Abstract

In the present study, the crack tip shape effect on near-tip deformation and fields is numerically investigated for a mode I crack under plane strain and small-scale yielding conditions. We explore here the quasi-static deformations of solids characterized by finite strain elastic–viscoplastic material model with bilinear hardening and hardening–softening–hardening hardness functions. For comparative analyses, both plastically incompressible and plastically compressible solids have been considered. It has been observed that the crack tip shape can have great consequence on the near-tip deformation and plastic fields. As the crack tip radius is increased, the plastic strain and stresses advance more to the tip of a crack as compared to the crack surface. It has also been revealed that the combination of crack tip curvature radius, material softening and plastic compressibility provides some useful and fundamental information for the near-tip deformation and plastic fields.

Keywords

Mode I crack Crack tip shape Finite deformation Compressible solid Plasticity 

List of symbols

a

Semi-major axis of the elliptical crack tip

b

Semi-minor axis of the elliptical crack tip

Δa

Crack tip extension

d

Rate of deformation tensor

de

Elastic part of rate of deformation tensor

dp

Plastic part of rate of deformation tensor

E

Young’s modulus

F

Deformation gradient

g

Hardness function

h1, h2, h3

Slopes of the tri-linear hardness function

I

Identity tensor

J

Jacobian

Japp

Applied J-integral

KI

Mode I stress intensity factor

L

Tensor of elastic moduli

m

Hardening exponent

p

Deviatoric part of Kirchhoff stress tensor

R0

Outer radius of the semicircular geometry

t

Time

VACNTs

Vertically aligned carbon nanotubes

yi

Convected coordinates

Greek symbols

α

Plastic compressibility

σ

Cauchy stress tensor

\(\varvec{\tau}\)

Kirchhoff stress

v

Poisson’s ratio

\({\hat{\mathbf{\tau }}}\)

Jaumann rate of Kirchhoff stress

εp

Plastic strain

\({\dot{\epsilon}}_{\text{p}}\)

Plastic strain rate

\(\dot{\varepsilon }_{0}\)

Reference strain rate

σe

Effective stress

σ0

Reference stress

σxx, σyy

Normal stresses in x and y directions, respectively

σxy

Shear stress

σh

Hydrostatic stress

σe

Equivalent stress

Notes

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of Technology (BHU) VaranasiVaranasiIndia

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