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Research Papers: Heat and Mass Transfer

Heat Conduction and Thermo-Elastic Stress Field Disturbed by a Thermal-Medium Crack Propagating in Orthotropic Materials Characterized by Real or Complex Eigenvalues

[+] Author and Article Information
Yue-Ting Zhou

School of Aerospace Engineering
and Applied Mechanics,
Tongji University,
Shanghai 200092, China

Tae-Won Kim

School of Mechanical Engineering,
Hanyang University,
Seoul 133-791, South Korea
e-mail: twkim@hanyang.ac.kr

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 4, 2016; final manuscript received May 27, 2017; published online July 6, 2017. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 139(12), 122005 (Jul 06, 2017) (10 pages) Paper No: HT-16-1118; doi: 10.1115/1.4036981 History: Received March 04, 2016; Revised May 27, 2017

A dynamic, partially permeable crack model for orthotropic materials is established with the crack full of thermal medium. Besides external thermal and elastic loadings, the heat flux generated by the crack interior full of a medium also contributes to the crack boundary conditions, which is dependent on the crack opening displacement. Thus, the heat conduction is dependent on elastic field. First, the heat conduction equation is solved exactly in terms of unknown heat flux of the crack interior. Then, the elastic field is presented for real or complex eigenvalue cases on the basis of the operator theory. Finally, the thermal and elastic fields are presented analytically, and the heat flux of the crack interior is determined explicitly. Numerical results are offered to show the influences of the thermal conductivity coefficient, normal and shear loadings and crack velocity on the distributions of the heat flux, temperature difference across the crack surfaces, and thermal stress intensity factor. Figures illustrate that increasing the crack velocity leads to a more thermally impermeable crack and produces a bigger temperature difference across the crack surfaces.

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Figures

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Fig. 1

The distribution of the normalized heat flux qm/qp versus the ration ηm/η2 with different values of the crack velocity Vr, when (a) σp=10 MPa and (b) σp=100 MPa

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Fig. 2

The distribution of the normalized heat flux qm/qp versus the crack velocity Vr with different values of the ration ηm/η2, when (a) σp=10 MPa and (b) σp=100 MPa

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Fig. 3

The effect of the crack velocity Vr on the normalized temperature distribution T(X,0)/T0, when (a) ηm/η2=0.05 and (b) ηm/η2=0.5

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Fig. 4

Normalized thermal stress intensity factor Fs/F0 versus the crack velocity Vr with different values of the ration ηm/η2

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Fig. 5

Normalized thermal stress intensity factor Fs/F0 versus the shear loading σs with different values of σp

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