A Survey of Macro-Microcrack Interaction Problems

2000 ◽  
Vol 53 (5) ◽  
pp. 117-146 ◽  
Author(s):  
Vera Petrova ◽  
Vitauts Tamuzs ◽  
Natalia Romalis
Keyword(s):  
Three Dimensional ◽  
Elastic Solid ◽  
Singular Integral Equations ◽  
Crack Location ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Microcrack Interaction ◽  
The Impact ◽  
The Continuum ◽  
Model Approach

The results obtained on the problem of the interaction between a large crack and an array of microcracks or other microdefects are reviewed. The following problems are considered: interaction of main crack with microcracks in the two-dimensional case at tensile, shear or combined stress state; a closure of macro or microcracks as a result of their interaction, and the influence of this phenomenon on the stress intensity factor; the thermal cracking of an elastic solid caused by the macro-microcracks interaction and cracks closure; the interaction of a crack with an array of small pores or rigid inclusions; three-dimensional problems of the interaction of a penny-shaped crack with small penny-shaped microcracks. Discussed analytical results are based on the asymptotic analysis and the series solution to systems of singular integral equations describing the interaction of the macrocrack and microdefects. The series solutions were obtained with respect to the small parameter representing the ratio of micro- to macrocrack sizes. Throughout the review, the known solutions on the crack interaction are surveyed. The comparison with solutions to other relevant problems such as an interaction of semi-infinite crack with an array of finite cracks is given. The impact of a close crack location, and a comparison with relevant results of the continuum model approach are discussed. This review article includes 332 references.

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.

Three-Dimensional Analysis of Cracking in a Multilayered Composite

1995 ◽  
Vol 62 (2) ◽  
pp. 273-281 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Integral Equations ◽  
Stiffness Matrix ◽  
Crack Opening ◽  
Crack Problem ◽  
Three Dimensional ◽  
Single Layer ◽  
Singular Integral Equations ◽  
Material System ◽  
Multilayered Composite ◽  
Penny Shaped Crack

The three-dimensional problem of a multilayered composite containing an arbitrarily oriented crack is considered in this paper. The crack problem is analyzed by the equivalent body force method, which reduces the problem to a set of singular integral equations. To compute the kernels of the integral equations, the stiffness matrix for the layered medium is formulated in the Hankel transformed domain. The transformed components of the Green’s functions and derivatives are determined by solving the stiffness matrix equations, and the kernels are evaluated by performing the inverse Hankel transform. The crack-opening displacements and the three modes of the stress intensity factor at the crack front are obtained by numerically solving the integral equations. Examples are given for a penny-shaped crack in a bimaterial and a three-material system, and for a semicircular crack in a single layer adhered to an elastic half-space.

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