  Mechanics of Solids A Journal of Russian Academy of Sciences   Founded
in January 1966
Issued 6 times a year
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E. S. Sibgatullin, "On the universality of a fracture criterion," Mech. Solids. 37 (6), 98104 (2002) 
Year 
2002 
Volume 
37 
Number 
6 
Pages 
98104 
Title 
On the universality of a fracture criterion 
Author(s) 
E. S. Sibgatullin (Naberezhnye Chelny) 
Abstract 
We consider quasibrittle fracture of an isotropic body with a macrocrack.
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
stressstrain 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 σ_{θ} criterion and the
Scriterion (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 macrocrack, in general).
In the present paper, it is shown that by suitably passing from the
stresses σ_{ij} (i,j=x,y,z) to the stress intensity factor
K_{I}, K_{II}, K_{III} in the limiting load condition for the
material (based on one or another strength hypothesis), one can obtain
exact fracture criteria which are selfsufficient 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 r_{0} 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 stressstrain 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(θ_{*}).
Note that the approach proposed here requires no additional criterion for
the preliminary determination of the crack growth direction. 
References 
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. 317, 1995. 
4.  E. S. Sibgatullin and I. G. Teregulov,
"A new version of the σ_{θ}criterion in fracture mechanics,"
Applied Problems of Strength and Plasticity. Numerical Simulation of
PhysicalMechanical Processes [in Russian], pp. 5255, 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. 365377, 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. 206266,
Mir, Moscow, 1970. 
8.  S. E. Kovchik and E. M. Morozov, Fracture Mechanics and Material
Strength. Volume 3. Characteristics of ShortTerm 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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