THE TEMPERATURE FIELDS AROUND THE TIP OF A FAST RUNNING CRACK

Abstract

Abstract: 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 comparedwith other theories and experimental results.

Key words: stenosis, degree of anisotropy, trapping bolus, free tube, tethered tube

Wang Mao-hua. THE TEMPERATURE FIELDS AROUND THE TIP OF A FAST RUNNING CRACK. Applied Mathematics and Mechanics (English Edition), 1984, 5(6): 1853-1858.

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References

(1) Andersson, H., A finite-element representation of stable crack-growth, J. Mech. Phys. Solids, 21, 5(1973) , 337-356.
(2) Andersson, H., Finite element treatment of a uniformly moving elastic-plastic crack tip, J. Mech. Phys. Solids, 22, 4(1974) , 285-308.
(3) Weichert, R., On the temperature rise at the tip of a fast running crack, J. Mech. Phys. Solids, 22, 2(1974) , 127-133.
(4) Bergkuit, Hans., The motion of a brittle crack, J. Mech. Phys. Solids, 21, 4(1974) , 17-26.
(5) Rice, J.R., Limitations to the small scale yielding approximation for crack tip plasticity, J. Mech. Phys. Solids, 22, 1(1974) , 17-26.
(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.
(7) Hill, R., The Mathematical Theory of Plasticity, Oxford(1950).
(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.
(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).
(10) Watson, G.N., A Tratise on the Theory of Bessel Function, (Second Edition) Combridge University Press, London (1944).
(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 Metha-crylate), J. Polymer Sci., A-2, 4, 3(1966) , 359-363.
(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.
(13) Touloukian, Y.S., Thermophysical Properties of High Temperature Solids Material , 4(1967).
(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 Sooiety A341, 1672 (1975) , 537-557.
(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.

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