Engineering Transactions, 18, 2, pp. 327–350, 1970

Zniszczenie Pełzające w Ośrodka Sprężysto-Lepko-Plastycznych

M. Wnuk
South Dakota State University
United States

In the paper are considered progresses dependent on the time and path of load, which take place in the vicinity of the edge of an axially-symmetrical fissure before the occurrence of cracking. In order to obtain an idea of the nonlinear behaviour of plastics in the regions of large stresses and to describe the rheological properties of the material around the fissure we postulate a model which assumes the existence of narrow plastic zones of the Dugdale type, while we assume that the material far from the fissure behaves as a linear visco-clastic medium.
In accordance with this model, the limit of plasticity varies with time, as is suggested by Crochet’s equation. This signifies a higher flow pressure with a more rapid load, and conversely. In view of such an assumption, it is possible to describe the first phase of deformations preceding the destruction – namely, the forming of a craze, i.e. a region in which irreversible changes of the mechanical properties and of optical properties occur. This region is formed around the edge of the fissure.
Several cases of creeping destruction are considered with different load histories. In particular, the universal equation p0/pG=[K(0)/K(t*)]1/2 is introduced with relates the material strength p0 on the time of duration of the load t*. The characteristic material properties and the length of the fissure are determined by the critical Griffith stress pG, whereas the function K (t) describes the rheological features of plastic. This equation holds for both the three and two-dimensional problems if the ration of the load to the initial yield stress is small. Attention is drawn to the considerable similarity between the universal equation and that derived by Williams for the spherical defect under hydrostatic tension.
In  the limiting case, both the theories of fracture – i.e., Griffith’s and Irwins-Orowan’s – results from the theory presented here.

Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


T. C. BAKER, F. W. PRESTON, Fatigue of glass under static load, J. Appl. Phys., 17 (1946), 170.

J. P. BERRY, Fracture processes in polymeric materials, J. Polymer Sci., 50 (1961), 153.

F. BUECHE, Tensile strength of plastic above the glass temperature, J. Appl. Phys., 9, 26 (1955), 1133.

L. C.CESSNA, S. S. STERNSTEIN, Viscoelasticity and plasticity considerations in the fracture of glasslike high polymers, fundamental phenomena in the materials sciences, Plenum Press, 4 (1967), 45.

M. J. CROCHET, Symmetric deformations of viscoelastic-platic cylinders, J. Appl. Mech., 2, 33 (1966), 327.

J. N. GOODIER, F. A. FIELD, Plastic energy dissipation in crack propagation, Fracture of solids, Proc. Int. Conf. in Maple Valley, Interscience Publishers, 1962, 103.

S. A. C. GRAHAM, Two extending crack problems in linear viscoelasticity theory, Report No. PSR-47/3, Notrh Carolina State University, 1966.

R. A. HELLER, R. D. STOLL, A. M. FREUDENTHAL, An Elastic-Plastic Behaviour of a Filled Elastomer, Columbia University Teport, June 1962.

R. P. KAMBOUR, The role of crazing in the mechanism of fracture of glassy polumers, Report No. 67-C-085, General Electric, March 1967.

W. G. KNAUSS, The time-dependent fracture of viscoelastic materials, Proceeding, First International Conference on Fracture, 2 (1965), 1139.

J. R. LOW, Jr., Microstructural aspect of fracture, Fracture of Solids, Metallurgical Society Conferences, Maple Valley, Wasjington, August 21-24, 1962, 20, John Wiley and Sons, New York, 197-236.

S. A. F. MURREL, The theory of the propagation of elliptical Griffith cracks under various conditions of plane strain or plane stress, Brit. J. Appl. Phys., 15 (1964), 1195.

H. K. MUELLER, W. G. KNAUSS, The Mechanical Characterization of Solithane 113 in the Swollen and Unswollen State, GALCIT SM 67-8, California Institute of Technology, December 1967.

Z. OLESIAK, M. P. WNUK, Plastic energy disspation due to a penny-shaped crack, Int. Journal of Fracture Mechanics, 4, 4 (1968), 383. Polish Complete Text: Rozpr. Inż. 3, 14 (1966), 411.

M. POLANYI, Uber die Natur des Zerreissvorganges, Z. Physik, 7 (1921), 323. And: Uver eine. Art Gitterstorung die einen Kristall plastisch Machen konnte, ibid., 89 (1934), 660.

J. R. RICE, An Explanation of the Fracture Mechanics Energy Balance from the Point of View of Continuum Mechanics, Int. Conf. Fracture, Sendai, Japan, 1965.

R. A. SCHAPERY, Irreversible Thermodynamics and Variational Principles with Applications to Viscoelasticity, California Institute of Technology, ARL 62-418, August 1962.

R. A. SCHAPPERY, M. L. WILLIAMS, On the Acceleration of Cracs in Viscoelastic Media, GALCIT SM 62-39, California Institute of Technology, September 1962.

T. L. SMITH, Dependence of the ultimate properties of a G-R-S rubber on strain rate and temperature, J. Polymer Sci. 32 (1958), 99.

N. W. TAYLOR, Mechanism of fracture of glass and similar brittle solids, J. Appl. Phys., 18 (1947), 943.

M. L. WILLIAMS, The fracture of viscoelastic material, Fracture of Solids, Proceedings Int. Con. In Maple Valley, 1962, Interscience Publishers, 1963.

M. I. WILLIAMS, Fracture in Viscoelastic Media, Report Presented at the Ilikon Corp. Symposium, 1966.

M. P. WNUK, Nature of fracture in relation to total potential energy, Brit. J. Appl. Physics, Ser. 2, 1 (1968), 217-236.