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.

Thermal Stress in a Finitely Deformed Incompressible Elastic Medium Containing a Penny-Shaped Crack

2003 ◽  
Vol 19 (1) ◽  
pp. 143-147
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity Factor ◽  
Thermal Stress ◽  
Stress Intensity ◽  
Thermal Stresses ◽  
Elastic Solid ◽  
Crack Plane ◽  
Lateral Stress ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Small Deformations

ABSTRACTThe thermal stress for a penny-shaped crack contained in an infinite isotropic elastic solid initially subjected to an axisymmetrical tension of any amount at infinity is investigated using the techniques of Hankel transforms and multiplying factors. The effect that the lateral normal stress has on the thermal stresses is studied on the basis of the theory of small deformations superposed on finite deformation. Symmetrical thermal loadings are applied over the crack surfaces. For the case of constant temperature over the crack surfaces, expressions for the crack shape and thermal stresses in the crack plane are obtained in closed forms. The stress intensity factor is also obtained and shown to be dependent on the lateral stress.

Longitudinal wave propagation in an infinite isotropic elastic plate with a penny-shaped crack

1969 ◽  
Vol 66 (2) ◽  
pp. 439-442
Author(s):  
H. S. Paul
Keyword(s):  
Longitudinal Wave ◽  
Elastic Plate ◽  
Mixed Boundary ◽  
Elastic Solid ◽  
Vertical Displacement ◽  
Dual Integral Equation ◽  
Positive Direction ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Plane Longitudinal Wave

The stress distribution, subject to a constant pressure over the entire surface of a penny-shaped crack is discussed by Sneddon(4). Recently, Robertson (3) has considered the diffraction of a plane longitudinal wave by a penny-shaped crack on a semi-infinite elastic solid. In the present analysis, the propagation of longitudinal wave in an infinite isotropic elastic plate with a penny-shaped crack in the middle has been investigated. The plane longitudinal wave is moving in the positive direction of z-azis and is impinging on the surface of the penny-shaped crack. The dual integral equation technique of Noble(l) is utilized to solve the mixed boundary-value problem. The analysis closely follows the method used in the author's previous paper (2). The vertical displacement is analysed numerically.

Thermal Stresses in Transversely Isotropic Semi-Infinite Elastic Solids

1958 ◽  
Vol 25 (1) ◽  
pp. 86-88
Author(s):  
Brahmadev Sharma
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Thermal Stresses ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Elastic Solids ◽  
Stress Problem ◽  
Method Of Solution ◽  
General Method

Abstract A general method of solution of the steady-state thermal-stress problem of a transversely isotropic semi-infinite elastic solid is given in this paper.

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.

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