scholarly journals Thermal Stresses in an Elastic Circular Cylinder Containing an Oblate Spheroidal Cavity or a Penny-shaped Crack under Uniform Heat Flow

1986 ◽  
Vol 29 (253) ◽  
pp. 2007-2014 ◽  
Author(s):  
Toyomi UCHlYAMA ◽  
Eiichiro TSUCHIDA
Keyword(s):  
Heat Flow ◽  
Circular Cylinder ◽  
Thermal Stresses ◽  
Oblate Spheroidal ◽  
Uniform Heat ◽  
Spheroidal Cavity ◽  
Penny Shaped Crack ◽  
Shaped Crack

The Penny-Shaped Interface Crack With Heat Flow, Part 1: Perfect Contact

1983 ◽  
Vol 50 (1) ◽  
pp. 29-36 ◽  
Author(s):  
C. J. Martin-Moran ◽  
J. R. Barber ◽  
M. Comninou
Keyword(s):  
Heat Flux ◽  
Heat Flow ◽  
Thermal Stresses ◽  
Contact Region ◽  
Thermal Contact ◽  
Dissimilar Materials ◽  
Contact Radius ◽  
Crack Face ◽  
Penny Shaped Crack ◽  
Shaped Crack

A solution is given for the thermal stresses due to a penny-shaped crack at the interface between dissimilar materials loaded in tension for the case where the heat flux is into the material with higher distortivity. Regions of separation and perfect thermal contact are developed at the crack faces. A harmonic potential function representation is used to reduce the problem to a three-part boundary value problem which is formulated as a pair of coupled Abel integral equations using the method of Green and Collins. These equations are further reduced to a single Fredholm equation which is solved numerically. Results are presented illustrating the effect of heat flux and applied tractions on the contact radius and the stress intensity factors for various combinations of material constants. The effect of heat flux is profoundly influenced by the relative signs of Dundurs constant β and a constant γ describing the mismatch of distortivities. If the more distortive material is also the more rigid, the contact region at the crack face is reduced by heat flow; otherwise it is increased. In the latter case, solutions involving separation are obtained even for applied compressive tractions if the latter is within a certain range. The solution also exhibits nonuniqueness in this range.

Steady-state thermal stresses in an elastic solid containing an insulated penny-shaped crack

1975 ◽  
Vol 10 (1) ◽  
pp. 19-24 ◽  
Author(s):  
J R Barber
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Heat Flow ◽  
Thermal Stresses ◽  
Mixed Boundary ◽  
Elastic Solid ◽  
Mixed Boundary Value Problem ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Axisymmetric Problems

A solution is given for the steady-state thermal stress and displacement field in an infinite elastic solid containing an insulated penny-shaped crack. The problem is reduced to a mixed-boundary-value problem for the half-space, making use of Green's isothermal solution for the thick elastic plate in complex harmonic potentials and a particular thermoelastic solution due to Williams. In the axisymmetric case, the complex potential reduces to the real harmonic function used by Shail in his solution for the external crack. To illustrate the use of the method in both axisymmetric and non-axisymmetric problems, complete solutionsare given for (1) a uniform heat flow and (2) a linearly varying heat flow disturbed by an insulated penny-shaped crack.

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