Interaction between a rigid line inclusion and an elastic circular inclusion

1997 ◽  
Vol 18 (5) ◽  
pp. 441-448 ◽  
Author(s):  
Tang Renji ◽  
Tao Fangming ◽  
Zhang Minghuan
Keyword(s):  
Circular Inclusion ◽  
Rigid Line Inclusion ◽  
Rigid Line ◽  
Elastic Circular Inclusion ◽  
Line Inclusion

Anisotropic Media with a Crack or a Rigid Line Inclusion,

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Crack Opening Displacement ◽  
Crack Opening ◽  
Null Vector ◽  
Opening Displacement ◽  
Rigid Line Inclusion ◽  
Rigid Line ◽  
The Matrix ◽  
Structural Failures ◽  
The Right ◽  
Line Inclusion

A crack, or cracks, in a material is perhaps one of the most studied problems in solid mechanics. This is due to the fact that many structural failures are related to the presence of a crack in the material. The knowledge of stress distribution near a crack tip is indispensable in a fracture mechanics analysis (Rice, 1968; Sih and Liebowitz, 1968; Sih and Chen, 1981; Kanninen and Popelar, 1985; K. C. Wu, 1989a). A crack is represented by a slit cut whose surfaces are assumed traction-free. This is a mathematical idealization. For a composite material that consists of stiff short fibers or whiskers in the matrix, we have rigid line inclusions. A rigid line inclusion is the counterpart of a crack. It is sometimes called an anticrack. The displacement at a rigid line inclusion either vanishes or has a rigid body translation and rotation. One of the puzzling problems for a crack is the one when it is located on the x1-axis that is an interface between two dissimilar materials. The displacement of the crack surfaces near the crack tips may oscillate, creating a physically unacceptable phenomenon of interpenetration of two materials. The bimaterial tensor Š introduced in Section 8.8 plays a key role in the analysis. If Š vanishes identically, there is no oscillation. If Š is nonzero, we may decompose the tractions applied on the crack surfaces into two components, one along the right null vector of Š denoted by to and the other on the right eigenplane of Š denoted by tγ . The solution associated with to is not oscillatory. It has the property that the traction on the interface x2=0 is polarized along the right null vector of Š while the crack opening displacement is polarized along the left null vector of Š. The solution associated with tγ is oscillatory. It has the property that the traction on the interface x2=0 is polarized on the right eigenplane of Š while the crack opening displacement is polarized on the left eigenplane of Š.

Green's Function for a Point Heat Source in an Anisotropic Body Containing an Elliptic Hole or a Rigid Inclusion

1999 ◽  
Vol 15 (3) ◽  
pp. 89-95
Author(s):  
Chung-Hao Wang ◽  
Ching-Kong Chao
Keyword(s):  
Heat Source ◽  
Rigid Inclusion ◽  
Elliptic Hole ◽  
Anisotropic Body ◽  
Point Heat Source ◽  
Intensity Factors ◽  
Rigid Line Inclusion ◽  
Rigid Line ◽  
Stress Functions ◽  
Line Inclusion

AbstractThe thermoelastic problem associated with a point heat source embedded in an anisotropic body containing an elliptic hole or a rigid inclusion is considered in this paper. By using the formalism of Stroh [1], the approach of analytic function continuation and the technique of conformal mapping, the expression for the temperature, displacements and stress functions is expressed in explicit matrix form. The present derived solutions are also valid for some special problems such as a crack or a rigid line inclusion if one lets the minor axis of the ellipse approach to zero. The stress intensity factors induced by a point heat source are also obtained.

Thermoelastic Problem of Dissimilar Anisotropic Solids With a Rigid Line Inclusion

1994 ◽  
Vol 61 (4) ◽  
pp. 978-980 ◽  
Author(s):  
C. K. Chao ◽  
R. C. Chang
Keyword(s):  
Thermal Stresses ◽  
Elastic Problem ◽  
Analytical Continuation ◽  
Thermoelastic Problem ◽  
Special Technique ◽  
Rigid Line Inclusion ◽  
Rigid Line ◽  
Variable Representation ◽  
Line Inclusion ◽  
Plane Elastic Problem

A general solution to the thermoelastic problem of an interface rigid line inclusion between anisotropic dissimilar media is presented. The complex variable representation of plane elastic problem developed by Lekhnitskii is extended into anisotropic thermoelasticity, and a special technique of analytical continuation is introduced to deal with the dissimilar media problem. It is indicated that singularities of the thermal stresses induced by a rigid line inclusion are similar to the case of a slit crack. A numerical example for zirconia bonded to titanium composite under remote heat flux is also examined.

On the Changing Order of Singularity at a Crack Tip

1977 ◽  
Vol 44 (4) ◽  
pp. 625-630 ◽  
Author(s):  
R. J. Nuismer ◽  
G. P. Sendeckyj
Keyword(s):  
Closed Form ◽  
Stress Singularity ◽  
Closed Form Solution ◽  
Crack Tip ◽  
Form Solution ◽  
Square Root ◽  
Rigid Line Inclusion ◽  
Rigid Line ◽  
Line Inclusion ◽  
Crack Tip Stress

The nature of the transition in the crack tip stress singularity from an inverse square root to an inverse fractional power as a crack tip reaches a phase boundary or a geometrical discontinuity for interface cracks is examined. This is done by analyzing the simple closed-form solution to the problem of a rigid line inclusion with one side partially debonded for the case of antiplane deformation. For this example, the crack tip stress singularity changes from an inverse square root to an inverse three-quarters power as the crack tips approach the inclusion tips (i.e., when one face of the rigid line inclusion is completely debonded). A detailed analysis, based on series expansions of the closed-form solution, is used to show how the singularity transition occurs. Moreover, the expansions indicate difficulties that may be encountered when solving such problems by approximate methods.

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