Transient Thermoelastic Problem in an Infinite Body Containing a Penny-Shaped Crack Due to Time and Position Dependent Temperature Condition

1986 ◽  
Vol 66 (6) ◽  
pp. 233-239 ◽  
Author(s):  
N. Noda ◽  
Y. Matsunaga
Keyword(s):  
Thermoelastic Problem ◽  
Infinite Body ◽  
Penny Shaped Crack ◽  
Shaped Crack

scholarly journals The Penny-Shaped Crack and the Plane Strain Crack in an Infinite Body of Power-Law Material

1981 ◽  
Vol 48 (4) ◽  
pp. 830-840 ◽  
Author(s):  
M. Y. He ◽  
J. W. Hutchinson
Keyword(s):  
Plane Strain ◽  
Power Law ◽  
Deformation Theory ◽  
Small Strain ◽  
Stress And Strain ◽  
Infinite Body ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Remote Stress ◽  
Plane Strain Crack

A study is carried out of the problem of a penny-shaped crack in an infinite body of power-law material subject to general remote axisymmetric stressing conditions. The plane strain version of the problem is also examined. The material is incompressible and is characterized by small strain deformation theory with a pure power relation between stress and strain. The solutions presented also apply to power-law creeping materials and to a class of strain-rate sensitive hardening materials. Both numerical and analytical procedures are employed to obtain the main results. A perturbation solution obtained by expanding about the trivial state in which the stress is everywhere parallel to the crack leads to simple formulas which are highly accurate even when the remote stress is perpendicular to the crack.

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 A note on the thermoelastic problem for a penny-shaped crack

1969 ◽  
Vol 10 (2) ◽  
pp. 169-172 ◽  
Author(s):  
John Tweed
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Normal Component ◽  
Surface Displacement ◽  
The State ◽  
Thermoelastic Problem ◽  
State Of Stress ◽  
Penny Shaped Crack ◽  
Shaped Crack

1. The problem of determining the state of stress in the vicinity of a penny-shaped crack which is opened by thermal means has been considered by Olesiak and Sneddon [1]. In that paper no simple closed expressions were given either for the stress-intensity factor at the tip of the crack or for the normal component of the surface displacement. The purpose of this note is to show how such expressions may be derived.

Analysis of Three-Dimensional Cracks with Independent Crack Mesh

2006 ◽  
Vol 110 ◽  
pp. 55-62
Author(s):  
Tae Soon Kim ◽  
Jai Hak Park ◽  
June Soo Park ◽  
Jong Sung Kim ◽  
Tae Eun Jin
Keyword(s):  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Surface Crack ◽  
Three Dimensional ◽  
Fatigue Loading ◽  
Infinite Body ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Galerkin Boundary Element Method

In order to simulate the growth of arbitrarily shaped three-dimensional cracks, the finite element alternating method is extended. As the required solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear is used. In the study, a crack is modeled as distribution of displacement discontinuities, and the governing equation is formulated as singularity-reduced integral equations. With the proposed method several example problems, such as a penny-shaped crack, an elliptical crack in an infinite solid and a semi-elliptical surface crack in an elbow are solved. And their growth under fatigue loading is also considered and the accuracy and efficiency of the method are demonstrated.

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