On the stress singularity in steady-state transonic shear crack propagation

Georgiadis, H.G.

doi:10.1007/bf00019775

Cited by 20 publications

(7 citation statements)

References 18 publications

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“…if contact is giving way to separation--the strength of the singularity will be equal to or stronger than square-root, being described by the multiplier (x -b)-1/2-~. We note that an expanding crack [30,31] is equivalent to a receding contact region and therefore has the same asymptotic behaviour 3.…”

Section: Discussionmentioning

confidence: 86%

On the super-Rayleigh/subseismic elastodynamic indentation problem

Georgiadis

Barber

1993

J Elasticity

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Section: Discussionmentioning

confidence: 86%

On the super-Rayleigh/subseismic elastodynamic indentation problem

Georgiadis

Barber

1993

J Elasticity

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“…In the course of this investigation, an integral equation formulation was developed for the steady-state problem of an indenter moving over a half-plane at constant speed, using the classical solution of Cole and Huth (1958) as a Green's function. However, the resulting equation exhibited different asymptotic behavior at the ends of the contact zone from other published solutions to elastodynamic crack and contact problems (see, e.g., Brock, 1977;Freund, 1979;Burridge et al, 1979;Georgiadis, 1986;Robinson and Thompson, 1974). Further investigation showed that this inconsistency was attributable to an error in the Cole/Huth solution in the transonic range.…”

Section: Introductionmentioning

confidence: 58%

Steady-State Transonic Motion of a Line Load Over an Elastic Half-Space: The Corrected Cole/Huth Solution

Georgiadis

Barber

1993

Journal of Applied Mechanics

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Similarly, the boundary condition is free from applied stress and the media are £ = 0.2,-n = 0.8. By truncating the infinite algebraic Eq. (3.16) to n = s = 3 for K a a = 0.1 and n = 5 = 4 for K a a = 1.0, 2.0, we find the coefficients A". Figures 2 and 3 show the results of stress concentration factors of calculation. Now, we conclude this paper with the following discussions: (a) From the numerical results indicated above, we can see that the effect of anisotropy on dynamic stress concentration is quite significant in engineering sense. (b) The convergence of Eq. (3.16) depends on wave number K a a and on cavity shapes. For low K a a, a few terms of the series are sufficient; while for high K a a, the convergence is rather slow. So, in this case, the number of terms needed becomes large in order to get reasonably good results. (c) For the square cavity case, the mapping function (4.2) maps the unit circle only to "nearly square cavity" with corners as shown in the figure attached. Such shape of course misses the character of sharp corners. This is the weak point of the method of mapping as noted universally in static case. Increasing the number of terms of the mapping functions is a way to make the corners of the figure rather sharp.

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“…Fung, 1965;Georgiadis, 1986;Barber, 1996;Brock and Rodgers, 1997) according to which a steady stress and displacement field is created in the medium w.r.t. an observer situated in a frame of reference attached to the moving load, if this source has been moving steadily for a sufficiently long time.…”

Section: à1 (K)mentioning

confidence: 99%

The three-dimensional steady-state thermo-elastodynamic problem of moving sources over a half space

Lykotrafitis

Georgiadis

2003

International Journal of Solids and Structures

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A procedure based on the Radon transform and elements of distribution theory is developed to obtain fundamental thermoelastic three-dimensional (3D) solutions for thermal and/or mechanical point sources moving steadily over the surface of a half space. A concentrated heat flux is taken as the thermal source, whereas the mechanical source consists of normal and tangential concentrated loads. It is assumed that the sources move with a constant velocity along a fixed direction. The solutions obtained are exact within the bounds of BiotÕs coupled thermo-elastodynamic theory, and results for surface displacements are obtained over the entire speed range (i.e. for sub-Rayleigh, super-Rayleigh/subsonic, transonic and supersonic source speeds). This problem has relevance to situations in Contact Mechanics, Tribology and Dynamic Fracture, and is especially related to the well-known heat checking problem (thermo-mechanical cracking in an unflawed half-space material from high-speed asperity excitations). Our solution technique fully exploits as auxiliary solutions the ones for the corresponding plane-strain and anti-plane shear problems by reducing the original 3D problem to two separate 2D problems. These problems are uncoupled from each other, with the first problem being thermoelastic and the second one pure elastic. In particular, the auxiliary plane-strain problem is completely analogous to the original problem, not only with regard to the field equations but also with regard to the boundary conditions. This makes the technique employed here more advantageous than other techniques, which require the prior determination of a fictitious auxiliary plane-strain problem through solving an integral equation.

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On the stress singularity in steady-state transonic shear crack propagation

Cited by 20 publications

References 18 publications

On the super-Rayleigh/subseismic elastodynamic indentation problem

On the super-Rayleigh/subseismic elastodynamic indentation problem

Steady-State Transonic Motion of a Line Load Over an Elastic Half-Space: The Corrected Cole/Huth Solution

The three-dimensional steady-state thermo-elastodynamic problem of moving sources over a half space

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