Applied Mathematics and Mechanics

, Volume 5, Issue 6, pp 1853–1858 | Cite as

The temperature fields around the tip of a fast running crack

  • Wang Mao-hua


When a crack is running, the temperature rise is a quite important actual problem, which not only depends on some material constants, but also the propagation velocity and the distribution of the heat resource density. In this paper, the shape of plastic zone around the crack tip and the density of heat resource have been discussed and the model of the temperature fields has been proposed. The numerical results with PMMA are given and compared with other theories and experimental results


Mathematical Modeling PMMA Temperature Field Temperature Rise Industrial Mathematic 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. (1).
    Andersson, H., A finite-element representation of stable crack-growth, J. Mech. Phys. Solids, 21, 5(1973), 337–356.CrossRefGoogle Scholar
  2. (2).
    Andersson, H., Finite element treatment of a uniformly moving elastic-plastic crack tip, J. Mech. Phys. Solids, 22, 4(1974), 285–308.CrossRefGoogle Scholar
  3. (3).
    Weichert, R., On the temperature rise at the tip of a fast running crack, J. Mech. Phys. Solids, 22, 2(1974), 127–133.CrossRefGoogle Scholar
  4. (4).
    Bergkuit, Hans., The motion of a brittle crack, J. Mech. Phys. Solids, 21, 4(1974), 17–26.Google Scholar
  5. (5).
    Rice, J.R., Limitations to the small scale yielding approximation for crack tip plasticity, J. Mech. Phys. Solids, 22, 1(1974), 17–26.CrossRefGoogle Scholar
  6. (6).
    Ritchie, R.Q., J.F. Knotl and J.R. Rice, On the relation-ship between critical tensile stress and fracture toghness in mild steel, J. Mech. Phys. Solids, 21, 6(1973), 395–410.CrossRefGoogle Scholar
  7. (7).
    Hill, R., The Mathematical Theory of Plasticity, oxford (1950).Google Scholar
  8. (8).
    Lasson, S.G. and A.J. Carlsson, Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials, J. Mech. Phys. Solids, 21, 4(1973), 263–277.CrossRefGoogle Scholar
  9. (9).
    Vetvebkee, B.M., V.V. Bencuk and A.J. Jaremei, The deformations and the failure criteria around the tip of gracks. Translations of Mechanics, No. 2, 3, (1974). (Chinese version)Google Scholar
  10. (10).
    Watson, G.N., A Tratise on the Theory of Bessel Function, (Second Edition) Combridge University Press, London (1944).Google Scholar
  11. (11).
    Kambour, R.P. and R.E. Barker, Mechanism of fracture is glassy polymers: IV Temperature rise at the tip of propagating crack in poly (Methyl Methacrylate), J. Polymer Sci., A-2, 4, 3(1966), 359–363.Google Scholar
  12. (12).
    Levy, N. and J.R. Rice, In Physics of Strength and Plasticity (Ed. A. S. Argon), Combridge Mass: M. I. T. Press (1969), 277.Google Scholar
  13. (13).
    Touloukian, Y.S., Thermophysical Properties of High Temperature Solids Material, 4(1967).Google Scholar
  14. (14).
    Fuller, K.N.G., G. Fox and J.E. Field, The temperature rise at the tip of fast-moving cracks in glassy polymers, Proceeding of the Koyal Society A341, 1672 (1975), 537–557.Google Scholar
  15. (15).
    Rosenthal, D., The theory of moving sources of heat and its application to metal treatments, Trans. A. S. M. E., 68, 8(1946), 849–866.Google Scholar

Copyright information

© HUST Press 1984

Authors and Affiliations

  • Wang Mao-hua
    • 1
  1. 1.Beijing Institute of Aeronautical EngineeringBeijing

Personalised recommendations