Elastic Wave Scattering from an Interface Crack: Antiplane Strain

1987 ◽  
Vol 54 (3) ◽  
pp. 503-508 ◽  
Author(s):  
A. Bostro¨m
Keyword(s):  
Interface Crack ◽  
Crack Opening ◽  
Plane Waves ◽  
Integral Equation Method ◽  
Far Field ◽  
Antiplane Strain ◽  
Opening Displacement ◽  
Direct Integral ◽  
The Matrix ◽  
Scattering Of Elastic Waves

The two-dimensional scalar problem of scattering of elastic waves under antiplane strain from an interface crack between two elastic half-spaces is considered. The method used is a direct integral equation method with the crack-opening displacement as the unknown. Chebyshev polynomials are used as expansion functions and the matrix in the resulting equations is simplified by contour integration techniques. The scattered far field is expressed explicitly in simple functions and the expansion coefficients. The consequences of energy conservation are explored and are used as a check in the numerical implementation. For incoming plane waves numerical results are given for the total scattered energy and the far field amplitude.

Elastic wave scattering by a circular crack

1982 ◽  
Vol 308 (1502) ◽  
pp. 167-198 ◽  
Keyword(s):  
Cross Sections ◽  
Circular Crack ◽  
Integral Equation Method ◽  
Infinite Matrix ◽  
Far Field ◽  
Direct Integral ◽  
Elastic Wave Scattering ◽  
The Matrix ◽  
Expansion Coefficients ◽  
Scattering Cross Sections

The scattering of waves by a circular crack in an elastic medium is solved by a direct integral equation method. The solution method is based on expansion of stresses and displacements on the crack surface in terms of trigonometric functions and orthogonal polynomials. The expansion coefficients are related through an infinite matrix, and by contour integration the matrix elements are expressed in terms of finite integrals. The scattered far field is expressed explicitly in terms of simple functions and the displacement expansion coefficients. The system of equations is solved numerically, and extensive results are given both in the form of maps of the scattered far field and as scattering cross sections. Neither the method nor the specific results are restricted by any assumptions of symmetry.

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.

Review of hypersingular integral equation method for crack scattering and application to modeling of ultrasonic nondestructive evaluation

2003 ◽  
Vol 56 (4) ◽  
pp. 383-405 ◽  
Author(s):  
Anders Bostro¨m
Keyword(s):  
Integral Equation ◽  
Nondestructive Testing ◽  
Crack Opening ◽  
Integral Equation Method ◽  
Boundary Element Methods ◽  
Hypersingular Integral Equation ◽  
Ultrasonic Nondestructive Testing ◽  
Opening Displacement ◽  
Hypersingular Integral ◽  
Integral Equation Methods

The scattering of elastic waves by cracks in isotropic and anisotropic solids has important applications in various areas of mechanical engineering and geophysics, in particular in ultrasonic nondestructive testing and evaluation. The scattering by cracks can be investigated by integral equation methods, eg, boundary element methods, but here we are particularly concerned with more analytically oriented hypersingular integral equation methods. In these methods, which are only applicable to very simple crack shapes, the unknown crack opening displacement in the integral equation is expanded in a set of Chebyshev functions, or the like, and the integral equation is projected onto the same set of functions. This procedure automatically takes care of the hypersingularity in the integral equation. The methods can be applied to cracks in 2D and 3D, and to isotropic or anisotropic media. The crack can be situated in an unbounded space or in a layered structure, including the case with an interface crack. Also, problems with more than one crack can be treated. We show how the crack scattering procedures can be combined with models for transmitting and receiving ultrasonic probes to yield a complete model of ultrasonic nondestructive testing. We give a few numerical examples showing typical results that can be obtained, also comparing with some experimental results. This review article cites 78 references.    

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.

Matrix Cracking In Brittle-Matrix Composites with Tailored Interfaces

1994 ◽  
Vol 365 ◽  
Author(s):  
Sawai Danchaivijit ◽  
L-Y. Chao ◽  
D. K. Shetfty
Keyword(s):  
Steady State ◽  
Crack Length ◽  
Uniaxial Tension ◽  
Sliding Friction ◽  
Crack Opening ◽  
State Theory ◽  
Matrix Cracking ◽  
Opening Displacement ◽  
The Matrix ◽  
Cracking Stress

ABSTRACTMatrix cracking from controlled through cracks with bridging filaments was studied in a model unidirectional composite of SiC filaments in an epoxy-bonded alumina matrix. An unbonded, frictional interface was produced by moderating the curing shrinkage of the epoxy with the alumina filler and coating the filaments with a releasing agent. Uniaxial tension test specimens (2.5 × 25 × 125 mm) with filament-bridged through cracks were fabricated by a novel two-step casting technique involving casting, precracking and joining of cracked and uncracked sections. Distinct matrix-cracking stresses, corresponding to the extension of the filamentbridged cracks, were measured in uniaxial tension tests using a high-sensitivity extensometer. The crack-length dependence of the matrix-cracking stress was found to be in good agreement with the prediction of a fracture-mechanics analysis that employed a new crack-closure force - crack-opening displacement relation in the calculation of the stress intensity for fiber-bridged cracks. The prediction was based on independent experimental measurements of the matrix fracture toughness (Kcm), the interfacial sliding friction stress (τ) and the residual stress in the matrix (σmI). The matrix-cracking stress for crack lengths (2a) greater than 3 mm was independent of the crack length and agreed with the prediction of the steady-state theory of Budiansky, Hutchinson and Evans[2]. Tests on specimens without the deliberately introduced cracks indicated a matrix-cracking stress significantly higher than the steady-state stress.

Fiber Pullout Characteristics Under Dynamic Loading Conditions

2001 ◽  
Author(s):  
N. Sridhar ◽  
Q. D. Yang ◽  
B. N. Cox
Keyword(s):  
Shear Stress ◽  
Crack Opening ◽  
Interfacial Shear Stress ◽  
Friction Stress ◽  
Crack Plane ◽  
Opening Displacement ◽  
Fiber Pullout ◽  
Dynamic Propagation ◽  
Dependent Relationship ◽  
The Matrix

Abstract Inertial effects in the mechanism of fiber pullout during dynamic propagation of a bridged crack are critically examined. By reposing simple shear lag models of pullout as problems of dynamic wave propagation, the effect of frictional coupling between the fiber and the matrix is accounted for in a fairly straightforward way. The frictional sliding between the fiber and the matrix is described by a constant interfacial friction stress, the sign of which depends on the relative particle velocity of the fiber and the matrix. Analytical solutions are derived when the load or bridging traction on the fiber in the crack plane increases linearly in time. The results show that when the wave speed of the matrix exceeds a critical value, the frictional fiber pullout behavior transitions from a state of pure slip to a state where part of the sliding zone slips and the remaining sticks. When stick occurs, the fiber and the matrix within the stick zone slide past each other with an interfacial shear stress less than the shear stress required for slipping. Regions of slip and stick propagate and increase with time and influence the time-dependent relationship between the crack opening displacement and the bridging tractions.

Micromechanical Dynamic Influence of Rigid Disk-Shaped Inclusion on Neighboring Crack in 3D Elastic Matrix

2007 ◽  
Vol 567-568 ◽  
pp. 133-136 ◽  
Author(s):  
Victor V. Mykhas'kiv ◽  
O. Khay ◽  
Jan Sladek ◽  
Vladimir Sladek ◽  
Chuan Zeng Zhang
Keyword(s):  
Boundary Integral Equations ◽  
Crack Opening ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Elastic Matrix ◽  
Opening Displacement ◽  
Rigid Disk ◽  
Time Harmonic ◽  
Penny Shaped Crack ◽  
Shaped Inclusion

A 3D time-harmonic problem for an infinite elastic matrix with an arbitrarily located interacting rigid disk-shaped inclusion and a penny-shaped crack is analyzed by the boundary integral equation method. Perfect bonding between the matrix and the moving inclusion is assumed. The crack faces are subjected to time-harmonic loading. The boundary integral equations (BIEs) obtained are solved numerically by the implementation of regularization and discretization procedures. Numerical calculations are carried out for a crack under tensile loading of constant amplitude, where an interacting inclusion is perpendicular to the crack and has the same radius. Both the normal crack-opening-displacement and the mode-I stress intensity factor are investigated for different wave numbers and distances between the crack and the inclusion.

scholarly journals Criteria For Progressive Interfacial Debonding With Friction In Fiber-Reinforced Ceramic Composites

1995 ◽  
Vol 409 ◽  
Author(s):  
Chun-Hway Hsueh
Keyword(s):  
Axial Strain ◽  
Crack Opening ◽  
Ceramic Composites ◽  
Interfacial Debonding ◽  
Fiber Reinforced ◽  
Opening Displacement ◽  
Strain Criterion ◽  
Mismatch Strain ◽  
The Matrix ◽  
Debonded Interface

AbstractCriteria for progressive debonding at the fiber/matrix interface with friction along the debonded interface are considered for fiber-reinforced ceramic composites. The energy-based criterion is adopted to analyze the debond length, the crack-opening displacement, and the displacement of the composite due to interfacial debonding. The analytical solutions are identical to those obtained from the mismatch-strain criterion, in which interfacial debonding is assumed to occur when the mismatch in the axial strain between the fiber and the matrix reaches a critical value. Furthermore, the mismatch-strain criterion is found to bear the same physical meaning as the strength-based criterion.

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