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Journal of Elasticity

, Volume 4, Issue 4, pp 293–299 | Cite as

On the uniqueness of plane elastodynamic solutions for running cracks

  • L. B. Freund
  • R. J. Clifton
Article

Summary

Modifications of the linear elastodynamic uniqueness theorem are presented which extend its range of applicability so as to include running crack solutions. First, it is shown that the near tip stress field for running cracks has universal spatial dependence in a coordinate system local to the crack tip. The rate at which energy is absorbed by the running crack can then be calculated in terms of the crack motion and the scalar stress intensity factors. The fact that this rate of energy absorption is positive for any running crack plays a central role in the subsequent proof of the uniqueness theorem. The results apply for arbitrary motion of a curved crack, provided that the crack tip speed is less than the Rayleigh wave speed of the material.

Keywords

Stress Intensity Intensity Factor Stress Intensity Factor Energy Absorption Spatial Dependence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Résumé

Le théorème d'unicité de solution en élastodynamique linéaire reçoit des modifications le rendant applicable à l'étude de la propagation d'une fissure. Il est démontré premièrement que si l'on emploie des coördonées entrainées par la fissure le champ élastique en fond de fissure propagée est independant de la forme géometrique du corps ainsi que des éfforts qu'il subit. D'autre part la rapidité avec laquelle l'énergie est absorbée par la fissure propagée peut être calculée sous forme du mouvement de la fissure et des facteurs d'intensité des contraintes. Le fait qu'une fissure se propageant d'une façon quelconque reçoit toujours de l'énergie de son entourage joue un role central à la preuve du théorème d'unicité. Les resultats sont applicable a un mouvement quelconque d'une fissure courbe si la vitesse de propagation de la fissure ne dépasse pas la vitesse d'onde de Rayleigh.

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References

  1. [1]
    Achenbach, J. D., Wave Propagation in Elastic Solids. North-Holland, 1973, p. 80.Google Scholar
  2. [2]
    Wheeler, L. T. and Sternberg, E., Some Theorems in Classical Elastodynamics, Arch. Rat. Mech. Anal. 31 (1968) 51Google Scholar
  3. [3]
    Friedlander, F. G., Sound Pulses. Cambridge University Press 1958, p. 20Google Scholar
  4. [4]
    Freund, L. B., Energy Flux into the Tip of an Extending Crack in an Elastic Solid. J. Elasticity 2 (1972) 341Google Scholar
  5. [5]
    Rice, J. R., Mathematical Analysis in the Mechanics of Fracture, in Fracture, Vol. II, ed. by H. Liebowitz, Academic Press, 1968, p. 191Google Scholar
  6. [6]
    Freund, L. B., Crack Propagation in an Elastic Solid Subjected to General Loading—IV. Obliquely Incident Stress Pulse. J. Mech. Phys. Solids 22 (1974) 137Google Scholar

Copyright information

© Noordhoff International Publishing 1974

Authors and Affiliations

  • L. B. Freund
    • 1
  • R. J. Clifton
    • 1
  1. 1.Division of EngineeringBrown UniversityProvidenceU.S.A.

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