Analysis of a penny-shaped crack with semi-permeable boundary conditions across crack face in a 3D thermal piezoelectric semiconductor

2021 ◽  
Vol 131 ◽  
pp. 76-85
Author(s):  
ChangHai Yang ◽  
MingHao Zhao ◽  
Chunsheng Lu ◽  
QiaoYun Zhang
Keyword(s):  
Boundary Conditions ◽  
Crack Face ◽  
Piezoelectric Semiconductor ◽  
Penny Shaped Crack ◽  
Shaped Crack

The Penny-Shaped Interface Crack With Heat Flow, Part 2: Imperfect Contact

1983 ◽  
Vol 50 (4a) ◽  
pp. 770-776 ◽  
Author(s):  
J. R. Barber ◽  
Maria Comninou
Keyword(s):  
Heat Flux ◽  
Thermal Contact ◽  
Closed Form Solution ◽  
Integral Equation Method ◽  
Form Solution ◽  
Heat Fluxes ◽  
Crack Face ◽  
Imperfect Contact ◽  
Penny Shaped Crack ◽  
Shaped Crack

The penny-shaped crack with heat flux is investigated for the case in which the heat flux is into the material with the lower distortivity. A harmonic potential function representation is used to reduce the problem to a boundary value problem which is solved by an integral equation method. If a sufficiently high tensile traction is applied, a solution is obtained involving a central circle of separation and surrounding annuli of imperfect and perfect thermal contact. For lower tractions, or higher heat fluxes, the crack closes completely and a closed-form solution is obtained in which the division of the crack face into imperfect and perfect contact regions is unaffected by further changes in heat flux or traction. Multiple solutions are obtained in an intermediate range.

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.

Scattering by two penny-shaped cracks with spring boundary conditions

1993 ◽  
Vol 443 (1917) ◽  
pp. 183-201 ◽  
Keyword(s):  
Boundary Conditions ◽  
Crack Opening ◽  
Integral Equation Method ◽  
Neumann Series ◽  
Single Crack ◽  
Opening Displacement ◽  
Direct Integral ◽  
Spherical Waves ◽  
Penny Shaped Crack ◽  
Shaped Crack

The elastodynamic scattering by a penny-shaped crack with spring boundary conditions is investigated. The transition ( T ) matrix of the crack is determined and the usefulness of this is illustrated by considering also the scattering by two cracks. The T matrix of a single crack is first determined by a direct integral equation method which gives the crack-opening displacement and the integral representation which subsequently gives the scattered field expanded in spherical waves. Two cracks are considered by a multi-centred T matrix approach where matrix inverses are expanded in Neumann series. Rotation matrices are employed so that the cracks may have an arbitrary orientation. The back-scattered longitudinal far field amplitude is computed both in the frequency and time domain in a few cases and the effects due to multiple scattering are in particular explored.

A penny-shaped crack in a transversely isotropic piezoelectric layer

2001 ◽  
Vol 20 (6) ◽  
pp. 997-1005 ◽  
Author(s):  
Bao-Lin Wang ◽  
Naotake Noda ◽  
Jie-Cai Han ◽  
Shan-Yi Du
Keyword(s):  
Piezoelectric Layer ◽  
Transversely Isotropic ◽  
Penny Shaped Crack ◽  
Shaped Crack
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