Thermal shock fracture of a cylinder with a penny-shaped crack based on hyperbolic heat conduction

2015 ◽  
Vol 91 ◽  
pp. 235-245 ◽  
Author(s):  
S.L. Guo ◽  
B.L. Wang
Keyword(s):  
Heat Conduction ◽  
Thermal Shock ◽  
Hyperbolic Heat Conduction ◽  
Penny Shaped Crack ◽  
Shaped Crack

Hyperbolic Heat Conduction for a Layered Medium of Finite Thickness with an Interface Crack

2012 ◽  
Vol 271-272 ◽  
pp. 1312-1316
Author(s):  
B. Wang
Keyword(s):  
Heat Conduction ◽  
Interface Crack ◽  
Layered Medium ◽  
Finite Thickness ◽  
Crack Problem ◽  
Homogeneous Medium ◽  
Hyperbolic Heat Conduction ◽  
Thermal Flow ◽  
Penny Shaped Crack ◽  
Shaped Crack

This paper studies the thermal flow concentration near an interface crack in a layered medium. Solution method for the thermal flow intensity factor is established. Both the Griffith crack and the penny-shaped crack are studied. Limiting cases of the current problem include (1) the solution of crack problem associated with classical Fourier heat conduction, (2) the solution of an interface crack in an infinite layered medium, and (3) the solution of a crack in a homogeneous medium.

Transient Thermoelastic Fields in a Transversely Isotropic Infinite Solid With a Penny-Shaped Crack

1987 ◽  
Vol 54 (4) ◽  
pp. 854-860 ◽  
Author(s):  
N. Noda ◽  
F. Ashida
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Transient Heat Conduction ◽  
Thermoelastic Problem ◽  
Conduction Equation ◽  
Thermal Stress Field ◽  
Penny Shaped Crack ◽  
Shaped Crack

The present paper deals with a transient thermoelastic problem for an axisymmetric transversely isotropic infinite solid with a penny-shaped crack. A finite difference formulation based on the time variable alone is proposed to solve a three-dimensional transient heat conduction equation in an orthotropic medium. Using this formulation, the heat conduction equation reduces to a differential equation with respect to the spatial variables. This formulation is applied to attack the transient thermoelastic problem for an axisymmetric transversely isotropic infinite solid containing a penny-shaped crack subjected to heat absorption and heat exchange through the crack surface. Thus, the thermal stress field is analyzed by means of the transversely isotropic potential function method.

scholarly journals Thermal shock resistance of solids associated with hyperbolic heat conduction theory

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120754 ◽  
Author(s):  
B. L. Wang ◽  
J. E. Li
Keyword(s):  
Heat Conduction ◽  
Thermal Stress ◽  
Stress Intensity ◽  
Thermal Shock ◽  
Thermal Shock Resistance ◽  
Closed Form Solution ◽  
Hyperbolic Heat Conduction ◽  
Conduction Model ◽  
Fourier Heat Conduction ◽  
Shock Resistance

The thermal shock resistance of solids is analysed for a plate subjected to a sudden temperature change under the framework of hyperbolic, non-Fourier heat conduction. The closed form solution for the temperature field and the associated thermal stress are obtained for the plate without cracking. The transient thermal stress intensity factors are obtained through a weight function method. The maximum thermal shock temperature that the plate can sustain without catastrophic failure is obtained according to the two distinct criteria: (i) maximum local tensile stress criterion and (ii) maximum stress intensity factor criterion. The difference between the non-Fourier solutions and the classical Fourier solution is discussed. The traditional Fourier heat conduction considerably overestimates the thermal shock resistance of the solid. This confirms the fact that introduction of the non-Fourier heat conduction model is essential in the evaluation of thermal shock resistance of solids.

Fractional thermoelasticity problem for an infinite solid with a penny-shaped crack under prescribed heat flux across its surfaces

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190289 ◽  
Author(s):  
Y. Povstenko ◽  
T. Kyrylych
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Stress Field ◽  
Fractional Calculus ◽  
Heat Conduction Equation ◽  
Thermoelasticity Problem ◽  
Conduction Equation ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Fractional Heat Conduction

The time-nonlocal generalization of the Fourier law with the ‘long-tail’ power kernel can be interpreted in terms of fractional calculus and leads to the time-fractional heat conduction equation with the Caputo derivative. The theory of thermal stresses based on this equation was proposed by the first author ( J. Therm. Stresses 28 , 83–102, 2005 ( doi:10.1080/014957390523741 )). In the present paper, the fractional heat conduction equation is solved for an infinite solid with a penny-shaped crack in the case of axial symmetry under the prescribed heat flux loading at its surfaces. The Laplace, Hankel and cos-Fourier integral transforms are used. The solution for temperature is obtained in the form of integral with integrands being the generalized Mittag-Leffler function in two parameters. The associated thermoelasticity problem is solved using the displacement potential and Love’s biharmonic function. To calculate the additional stress field which allows satisfying the boundary conditions at the crack surfaces, the dual integral equation is solved. The thermal stress field is calculated, and the stress intensity factor is presented for different values of the order of the Caputo time-fractional derivative. A graphical representation of numerical results is given. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

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