Mechanics of Solids (about journal) Mechanics of Solids
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in January 1966
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IssuesArchive of Issues2002-6pp.98-104

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E. S. Sibgatullin, "On the universality of a fracture criterion," Mech. Solids. 37 (6), 98-104 (2002)
Year 2002 Volume 37 Number 6 Pages 98-104
Title On the universality of a fracture criterion
Author(s) E. S. Sibgatullin (Naberezhnye Chelny)
Abstract We consider quasi-brittle fracture of an isotropic body with a macro-crack. It is shown that if "exact" criteria of fracture are used, the limiting load for a body with a crack can be determined independently of the direction of the crack growth. When approximate fracture criteria are used, the limiting load and the direction of the crack growth are proposed to be determined by finding extremal values of external load parameters (the corresponding functional relations are provided by the fracture criterion), with subsequent analysis of the stress-strain state in the directions away from the crack tip corresponding to those extremal values. The investigation utilizes two "exact" fracture criteria, similar to the well known σθ- criterion and the S-criterion (proposed by Sih). The efficiency of our method is demonstrated by an example.

As mentioned in [1], a fracture criterion for a body with a crack, in general, should be supplemented with a criterion for finding the direction of crack propagation, i.e., conditions of local fracture near the crack front consist of two equations related to one another but each having its own meaning. Thus, one often has to utilize some additional hypothesis (formulated on the basis of experimental data) for the preliminary identification of the direction of crack propagation, which can be subsequently used for finding the limiting load for the body with a crack. This approach has become traditional in applications of many fracture criteria (see, for instance, [1]). However, in some cases, this approach entails certain difficulties (for example, when finding the bearing capacity of an anisotropic body with a macro-crack, in general). In the present paper, it is shown that by suitably passing from the stresses σij (i,j=x,y,z) to the stress intensity factor KI, KII, KIII in the limiting load condition for the material (based on one or another strength hypothesis), one can obtain exact fracture criteria which are self-sufficient as regards the determination of the bearing capacity of a body with a crack, i.e., there is no need to determine beforehand the direction of the crack growth. However, in this situation, there is another problem related to the uncertainty of dimensions of the region of the material destruction near the crack tip (this region becomes known if the limiting load is known). We propose a method for overcoming this difficulty. The essential points of this method can be formulated as follows:

1. Choose a suitable approximation for the exact fracture criterion.

2. Single out the function p(θ) involved in the approximate fracture criterion, where p is the external load parameter (the origin O of the system of the polar coordinates r, θ coincides with the crack tip, and the polar axis r0 coincides with the initial direction of the crack).

3. Determine the extrema of the function p(θ) and the corresponding critical values of the argument θ.

4. Investigate the stress-strain state in the directions corresponding to the critical values of the argument θ.

5. On the basis of the fracture mechanism most probable for a given material, choose the crack growth direction θ* among the critical values of the angle θ, and find the limiting load p*=p*).

Note that the approach proposed here requires no additional criterion for the preliminary determination of the crack growth direction.
1.  V. V. Panasiuk, A. E. Andreikiv, and V. Z. Parton, Fracture Mechanics and Material Strength. Volume 1. Fundamentals of Materials Fracture Mechanics [in Russian], Naukova Dumka, Kiev, 1988.
2.  M. P. Svaruk, Fracture Mechanics and Material Strength. Volume 2. Stress Intensity Factors for Bodies with Cracks [in Russian], Naukova Dumka, Kiev, 1988.
3.  V. N. Shlyannikov, "Strain energy density and the zone of the fracture process. Part 1. Theoretical Prerequisites," Problemy Prochnosti, No. 10, pp. 3-17, 1995.
4.  E. S. Sibgatullin and I. G. Teregulov, "A new version of the σθ-criterion in fracture mechanics," Applied Problems of Strength and Plasticity. Numerical Simulation of Physical-Mechanical Processes [in Russian], pp. 52-55, TNI KMK, Moscow, 1999.
5.  G. C. Sih, "Some basic problems in fracture mechanics and new concepts," Eng. Fract. Mech., Vol. 5, No. 2, pp. 365-377, 1973.
6.  I. G. Teregulov, Strength of Materials and Basic Principles of Elasticity and Plasticity [in Russian], Vyssh. Shkola, Moscow, 1984.
7.  E. M. Wu, "Strength and fracture of composites," in L. J. Broutman and R. H. Krock (Editors), Composite Materials. Fracture and Fatigue. Volume 5 [Russian translation], pp. 206-266, Mir, Moscow, 1970.
8.  S. E. Kovchik and E. M. Morozov, Fracture Mechanics and Material Strength. Volume 3. Characteristics of Short-Term Crack Resistance and Methods of their Determination, Kiev, Naukova Dumka, 1988.
9.  S. Murakami, Stress Intensity Factors Handbook. Volume 2 [Russian translation], Mir, Moscow, 1990.
Received 3 April 2000
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