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.

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.

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.

scholarly journals Transient Elasto-Dynamic Response of a Circular Crack in a Thick Plate Under Torsion

1979 ◽  
Vol 101 (3) ◽  
pp. 207-209 ◽  
Author(s):  
E. P. Chen
Keyword(s):  
Dynamic Response ◽  
Thick Plate ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Circular Crack ◽  
Dual Integral Equations ◽  
Numerical Laplace Inversion ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Sudden Appearance

The elasto-dynamic response of a thick plate under torsion is considered in this study. A penny-shaped crack is assumed to exist in the center of the plate such that the problem is axisymmetric in nature. The crack is pressurized suddenly along its surfaces resulting in transient conditions. This problem is also equivalent to that of sudden appearance of a crack in the loaded plate. Hankel and Laplace transforms are used to reduce the problem to the solution of a pair of dual integral equations. A numerical Laplace inversion routine is used to recover the time dependence of the solution. The dynamic stress intensity factor is determined and its dependence on time and geometry is discussed.

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.

An Axisymmetric Crack in Bonded Materials With a Nonhomogeneous Interfacial Zone Under Torsion

1995 ◽  
Vol 62 (1) ◽  
pp. 116-125 ◽  
Author(s):  
M. Ozturk ◽  
F. Erdogan
Keyword(s):  
Crack Opening ◽  
Crack Problem ◽  
Strain Energy Release ◽  
Interfacial Region ◽  
Interfacial Zone ◽  
Mode Iii ◽  
Shear Moduli ◽  
Penny Shaped Crack ◽  
Energy Release Rates ◽  
Shaped Crack

In this study the mode III axisymmetric crack problem for two dissimilar homogeneous materials bonded through a thin layer of nonhomogeneous interfacial region is considered. The shear modulus of the interfacial layer is assumed to be μ2(z) = μ1 exp (αz). It is also assumed that μ3 = μ1 exp (αh), h being the thickness of the layer and μ1 and μ3 the shear moduli of the adherents. The main results of the study are the stress intensity factors, the strain energy release rates and, to a limited extent, the crack-opening displacements obtained as functions of the two primary variables h/a and μ3/μ1 under various loading conditions, where a is the radius of the crack. Some results are also presented for a penny-shaped crack in an unbounded nonhomogeneous medium.

Dynamic crack-opening displacement of a mode III edge crack in a semi-infinite piezoceramic strip under electric excitation

2007 ◽  
Vol 221 (9) ◽  
pp. 1009-1017
Author(s):  
X-F Li ◽  
Kang Yong Lee
Keyword(s):  
Crack Opening Displacement ◽  
Edge Crack ◽  
Crack Opening ◽  
Transversely Isotropic ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Dynamic Crack ◽  
Mode Iii ◽  
Opening Displacement ◽  
Electric Excitation

The transient response of a semi-infinite transversely isotropic piezoceramic strip containing an edge crack is analysed for the case where electric excitation is suddenly exerted at the material end surface. The crack is assumed to be impermeable to electric field. Ahypersingular integral equation for crack-opening displacement (COD) is derived via solving the associated mixed initial-boundary-value problem and solved numerically based on a collocation technique. By performing a numerical inversion of Laplace transform, dynamic CODs are determined and illustrated graphically.

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