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Interaction between heat dipole and circular interfacial crack

  • Wan-shen Xiao (肖万伸)Email author
  • Chao Xie (谢超)
  • You-wen Liu (刘又文)
Article

Abstract

The heat dipole consists of a heat source and a heat sink. The problem of an interfacial crack of a composite containing a circular inclusion under a heat dipole is investigated by using the analytical extension technique, the generalized Liouville theorem, and the Muskhelishvili boundary value theory. Temperature and stress fields are formulated. The effects of the temperature field and the inhomogeneity on the interfacial fracture are analyzed. As a numerical illustration, the thermal stress intensity factors of the interfacial crack are presented for various material combinations and different positions of the heat dipole. The characteristics of the interfacial crack depend on the elasticity, the thermal property of the composite, and the condition of the dipole.

Key words

thermoelasticity heat dipole interfacial crack circular inclusion inhomogeneity 

Nomenclature

R

inclusion radius

L′

interfacial crack arc

L

interface arc

S+, S

inclusion domain and matrix domain

I, II

material numbers for inclusion and matrix

μj, κj

elasticity constants of the jth material

ρ

polar radius of heat dipole center location

θ

polar angle of heat dipole center location

r

half span length of heat dipole

z1, z2

coordinates of heat source and heat sink

ϕ

angle between the span line and the x-axis

α

half of the central angle of the crack arc

T(·)

temperature field function

Re(·)

real part of a complex variable or a complex function

i

imaginary unit

\( \overline {( \cdot )} \)

conjugate value of a complex parameter

g(·)

the real part of its differential is the complex function for temperature

q

heat flux

Q

total heat transfer rate

κt

the coefficient of heat conductivity

σ

normal stress

τ

shear stress

ϕ(·), ψ(·)

complex potential functions for stress

Φ(·), Ψ(·)

differential function of complex potential for stress

β

heat expansion coefficient

u, υ

displacements

e, f, K, W, σ, S, J, N, O

constants

Kj, Kjl

stress intensity factors of crack tip

Y (·)

Plemelj function

ω(·)

transform function

Chinese Library Classification

TB381 O343.7 

2000 Mathematics Subject Classification

74R10 74F05 

References

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Copyright information

© Shanghai University and Springer Berlin Heidelberg 2009

Authors and Affiliations

  • Wan-shen Xiao (肖万伸)
    • 1
    Email author
  • Chao Xie (谢超)
    • 1
  • You-wen Liu (刘又文)
    • 1
  1. 1.College of Mechanics and AerospaceHunan UniversityChangshaP. R. China

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