A Dislocation Green’s Function for the Analysis of Multiple Coplanar Cracks or Cracks With Nonuniform Crack Fronts

1990 ◽  
Vol 57 (3) ◽  
pp. 589-595 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Mixed Boundary ◽  
Crack Opening ◽  
Symmetry Plane ◽  
Mode I ◽  
Opening Displacement ◽  
External Crack ◽  
Present Solution ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Coplanar Cracks

This analysis considers the interaction between a penny-shaped crack or a circular external crack and a mode I “opening” point dislocation. The dislocation is taken to lie on the plane of the crack. Symmetry considerations allow the reduction to a mixed boundary value problem for a half space which is solved by well-known methods from potential theory. Closed-form expressions are obtained for the crack opening displacement, stress on the symmetry plane, and the mode I stress intensity factor around the internal or external crack. The use of the present solution for the accurate numerical treatment of cracks with large amplitude variations in the crack front curvature as well as cases of multiple coplanar cracks is outlined.

A mode I crack with multiple islands of ideal contact between the crack faces: An asymptotic model

2021 ◽  
pp. 108128652110214
Author(s):  
Ivan Argatov
Keyword(s):  
Crack Opening ◽  
Reduction Factor ◽  
Mode I ◽  
Asymptotic Model ◽  
Mode I Crack ◽  
Opening Displacement ◽  
Multiple Contacts ◽  
Scaling Hypothesis ◽  
Penny Shaped Crack ◽  
Crack Faces

The problem of a mode I crack having multiple contacts between the crack faces is considered. In the case of small contact islands of arbitrary shapes, which are arbitrarily located inside the crack, the first-order asymptotic model for the crack opening displacement is constructed using the method of matched asymptotic expansions. The case of a penny-shaped crack has been studied in detail. A scaling hypothesis for the compliance reduction factor is formulated.

Scattering by a horizontal subsurface penny-shaped crack

1986 ◽  
Vol 408 (1835) ◽  
pp. 277-294 ◽  
Keyword(s):  
Crack Opening ◽  
Resonance Phenomenon ◽  
Polar Coordinates ◽  
Axially Symmetric ◽  
Opening Displacement ◽  
Time Harmonic ◽  
Wave Resonance ◽  
Penny Shaped Crack ◽  
Rectangular Coordinates ◽  
Shaped Crack

The scattering by a horizontal subsurface penny-shaped crack subjected to axially symmetric loading is investigated. The formulation begins with deriving the response of a time harmonic point force in rectangular coordinates. Then, the integral representation and integral equations are converted into polar coordinates by applying the condition of axial symmetry. The results contain crack opening displacement (COD), stress intensity factors, scattered pattern and the frequency spectrum of the Rayleigh wave and the back-scattered longitudinal wave. Resonance phenomenon is compared with the plane strain case solved in an earlier paper.

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.

Sudden Twisting of a Penny-Shaped Crack

1972 ◽  
Vol 39 (2) ◽  
pp. 395-400 ◽  
Author(s):  
G. C. Sih ◽  
G. T. Embley
Keyword(s):  
Integral Transform ◽  
Crack Opening ◽  
Dynamic Crack ◽  
Static Case ◽  
Opening Displacement ◽  
Transient Problems ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Sudden Appearance ◽  
Square Root Singularity

A transient stress analysis for the problem of a torque applied suddenly to the surface of a penny-shaped crack in an infinite elastic body is carried out. The singular solution is equivalent to that of the sudden appearance of a crack in a body under torsion. Using an integral transform technique developed for this class of transient problems, the dynamic stresses near the periphery of the crack are found to have the same angular distribution and inverse square root singularity as in the static case. This character of the local solution prevails for all time only in a toroidal region extremely close to the crack border. Within this region, the stress intensity is found to vary with time, reaching a peak greater than the static value and subsequently oscillating about that value with decreasing amplitude. The dynamic crack-opening displacement field is also given for any instant of time after loading.

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.

Determination of cohesive laws in wood bonded joints under mode I loading using the DCB test

Holzforschung ◽  
2013 ◽  
Vol 67 (8) ◽  
pp. 913-922 ◽  
Author(s):  
Filipe G.A. Silva ◽  
Jose Xavier ◽  
Fábio A.M. Pereira ◽  
José J.L. Morais ◽  
Nuno Dourado ◽  
...  
Keyword(s):  
Strain Energy ◽  
Inverse Method ◽  
Strain Energy Release Rate ◽  
Direct Method ◽  
Crack Opening ◽  
Strain Energy Release ◽  
Mode I ◽  
Bonded Joints ◽  
Opening Displacement ◽  
Cohesive Laws

Abstract The cohesive laws (CLs) have been investigated by means of direct and inverse methods concerning wood bonded joints under pure mode I. The experimental results were obtained by tests with double cantilever beam. The direct method is based on the differentiation of the relation between strain energy release rate and crack opening displacement at the crack tip. An equivalent crack method was used to evaluate the strain energy release rate in the course of the test without monitoring the crack length, which is difficult to observe exactly. The crack opening displacement was determined by postprocessing local displacements measured by digital image correlation. The inverse method requires a previous assumption of the CL shape, and as such, a trilinear law with bilinear softening relationship was selected. The cohesive parameters were identified by an optimization procedure involving a developed genetic algorithm. The idea is to minimize an objective function that quantifies the difference between the experimental and the numerical load-displacement curves resulting from the application of a given law. A validation procedure was performed based on a numerical analysis with finite elements. Both methods in focus provided good agreement with the experimental data. It was observed that CLs adopted by the inverse method are consistent with the ones obtained with the direct method.

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