Near-Tip Fields for Penny-Shaped Cracks in Magnetoelectroelastic Media

2006 ◽  
Vol 312 ◽  
pp. 41-46 ◽  
Author(s):  
Bao Lin Wang ◽  
Yiu Wing Mai
Keyword(s):  
Closed Form ◽  
Transversely Isotropic ◽  
Crack Plane ◽  
Axially Symmetric ◽  
Crack Configuration ◽  
Penny Shaped Crack ◽  
Electric And Magnetic Fields ◽  
Shaped Crack ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids

This paper solves the penny-shaped crack configuration in transversely isotropic solids with coupled magneto-electro-elastic properties. The crack plane is coincident with the plane of symmetry such that the resulting elastic, electric and magnetic fields are axially symmetric. The mechanical, electrical and magnetical loads are considered separately. Closed-form expressions for the stresses, electric displacements, and magnetic inductions near the crack frontier are given.

Further Investigation and Application of the Principle of Correspondence Between Elastic and Piezoelectric Problems

2002 ◽  
Vol 731 ◽  
Author(s):  
Edgar Karapetian ◽  
Larissa Gorbatikh
Keyword(s):  
Transversely Isotropic ◽  
Piezoelectric Medium ◽  
Crack Plane ◽  
Isotropic Materials ◽  
Penny Shaped Crack ◽  
Tangential Forces ◽  
Shaped Crack ◽  
Transversely Isotropic Materials ◽  
Plane Of Isotropy

AbstractIn the present work, the recently established principle of correspondence between the elastic and the piezoelectric problems for the transversely isotropic materials has been applied to obtain the solution of the problem of interaction of two tangential forces and a penny-shaped crack. The problem under consideration is described as follows: a penny-shaped crack in the unbounded piezoelectric medium is interacting with two tangential forces of the same magnitude acting in the same direction and applied arbitrarily but symmetrically with respect to the crack plane, which is a plane of isotropy. Some further investigation of the principle of correspondence is made and the important limiting conditions are stated.

Elastic inclusions and inhomogeneities in transversely isotropic solids

1994 ◽  
Vol 444 (1920) ◽  
pp. 239-252 ◽  
Keyword(s):  
Closed Form ◽  
Elastic Field ◽  
Transversely Isotropic ◽  
Potential Functions ◽  
Closed Form Expression ◽  
Inclusion Problem ◽  
Stress Vector ◽  
Equivalent Inclusion Method ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids

A method that introduces a new stress vector function ( the hexagonal stress vector ) is applied to obtain, in closed form, the elastic fields due to an inclusion in transversely isotropic solids. The solution is an extension of Eshelby’s solution for an ellipsoidal inclusion in isotropic solids. The Green’s functions for double forces and double forces with moment are derived and these are then used to solve the inclusion problem. The elastic field inside the inclusion is expressed in terms of the newtonian and biharmonic potential functions, which are similar to those needed for the solution in isotropic solids. Two more harmonic potential functions are introduced to express the solution outside the inclusion. The constrained strain inside the inclusion is uniform and the relation between the constrained strain and the misfit strain has the same characteristics as those of the Eshelby tensor for isotropic solids, namely, the coefficients coupling an extension to a shear or one shear to another are zero. The explicit closed form expression of this tensor is given. The inhomogeneity problem is then solved by using Eshelby’s equivalent inclusion method. The solution for the thermoelastic displacements due to thermal inhomogeneities is also presented.

Thermal Stress in a Transversely Isotropic Medium Containing a Penny-Shaped Crack

1983 ◽  
Vol 50 (1) ◽  
pp. 24-28 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Thermal Stress ◽  
Material Properties ◽  
Isotropic Medium ◽  
Thermal Stresses ◽  
Transversely Isotropic ◽  
Crack Plane ◽  
Intensity Factors ◽  
Transversely Isotropic Medium ◽  
Penny Shaped Crack ◽  
Shaped Crack

The thermal stress problem for a penny-shaped crack contained in a transversely isotropic medium is investigated using the techniques of Hankel transforms and double integrations. Symmetrical thermal loadings are applied over the crack surfaces. For constant temperature and heat flux over the crack surfaces, expressions for the crack shapes and the thermal stresses in the crack plane are obtained in closed forms. The stress intensity factors are also obtained and shown to be dependent on the material properties.

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

Indentation of a Penny-Shaped Crack by an Oblate Spheroidal Rigid Inclusion in a Transversely Isotropic Medium

1984 ◽  
Vol 51 (4) ◽  
pp. 811-815 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Contact Stress ◽  
Rigid Inclusion ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Penny Shaped Crack ◽  
Shaped Crack

The stress distribution produced by the identation of a penny-shaped crack by an oblate smooth spheroidal rigid inclusion in a transversely isotropic medium is investigated using the method of Hankel transforms. This three-part mixed boundary value problem is solved using the techniques of triple integral equations. The normal contact stress between the crack surface and the indenter is written as the product of the associated half-space contact stress and a nondimensional crack-effect correction function. An exact expression for the stress-intensity is obtained as the product of a dimensional quantity and a nondimensional function. The curves for these nondimensional functions are presented and used to determine the values of the normalized stress-intensity factor and the normalized maximum contact stress. The stress-intensity factor is shown to be dependent on the material constants and increasing with increasing indentation. The stress-intensity factor also increases if the radius of curvature of the indenter surface increases.

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