Abstract
The elastodynamic stress field around a penny-shaped crack running at a constant speed in an infinite solid is obtained as the sum of the associated static solutions and the wave-effect terms. The results include the stress field in the plane of the running crack and the associated static solutions as special solutions.
The crack-tip circumferential stress, πθθ, is studied in detail as a function of the crack speed,V, the shear wave speed,c 2, Poisson's ratio, ν, and the angle, θ, between the crack plane and a crack-tip radial line. The theory predicts that the running crack may start to bifurcate at the critical speed of 0.665c 2 in the direction θ=41° for ν=0.25. The bifurcation angle predicted is compared to an experimental observation.
Zusammenfassung
Das elastodynamische Spannungsgebiet um einen pfennigförmigen Bruchriss, der mit konstanter Geschwindigkeit in einem unendlichen Körper läuft, wird als Summe der verbundenen statischen Lösung und der Wellenwirkungsterme aufgefasst. Die Ergebnisse schliessen das Spannungsgebiet im Bereich des laufenden Bruchrisses und die zugehörigen statischen Lösungen als Sonderlösungen ein.
Die Ringspannung der Risspitze, πθθ wird als Funktion der RissgeschwindigkietV, der Geschwindigkeit der Scherungswellec 2, der Poissonzahl ν und des Winkels θ zwischen der Bruchebene und einer Radiallinie von der Risspitze aus ausführlich studiert. Die Theorie sagt aus, dass der laufende Riss bei der kritischen Geschwindigkeit von 0.665c 2 in der Richtung θ=41° für ν=0.25 zu gabeln anfangen kann. Der vorausgesagte Gabelungswinkel wird mit Versuchserfahrungen verglichen.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. H. Yoffe,The Moving Griffith Crack, Phil Mag.,42, 739–750, 1951.
Y. M. Tsai,Dynamic Stress Distribution Around the Tip of a Running Crack, Eng. Fract. Mech.6, 509–522, 1974.
A. A. Wells andD. Post,The Dynamic Stress Distribution Surrounding a Running Crack, Proc. Soc. Exp. Stress Anal.16, No. 1, 69–92, 1958.
D. Rader,On the Dynamics of Crack Growth in Glass, Exp. Mech.7, 160–167, 1967.
J. P. Lee andH. Kolsky,Fractures Produced by Longitudinal and Flexural Stress Pulses and Stress Pulses Produced by Brittle Fractures, Brown University Tech. Rep. No. 10, 1970.
I. N. Sneddon,Fourier Transforms, McGraw-Hill, New York, 1951.
Y. M. Tsai,Exact Stress Distribution, Crack Shape and Energy for a Running Penny-Shaped Crack in an Infinite Elastic Solid, Int. J. Fract.9, 1973.
Y. M. Tsai,Stress Waves Produced by Impact on the Surface of a Plastic Medium, J. Franklin Inst.285, No. 3, 204–221, 1968.
G. N. Watson,A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1944.
Y. M. Tsai,Stress Distribution, Crack Shape, and Energy for a Penny-Shaped Crack in a Plate of Finite Thickness, Eng. Fract. Mech.4, 155–169, 1972.
Y. M. Tsai,Propagation of a Brittle Crack at Constant and Accelerating Speeds, Int. J. Solids Struct.9, 625–642, 1973.
G. R. Irwin,Basic Concepts for Dynamic Fracture Testing, J. Basic Eng.91, 519–524, 1969.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tsai, Y.M. Elastodynamic stress field and bifurcation of a running penny-shaped crack. Journal of Applied Mathematics and Physics (ZAMP) 27, 791–800 (1976). https://doi.org/10.1007/BF01595130
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01595130