On Problems of Fracture of Materials in Compression along Two Internal Parallel Cracks

A. N. Guz; V. M. Nazarenko; Ⅰ. P. Starodubtsev

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1997 > 18(6): 483-494

A. N. Guz, V. M. Nazarenko, Ⅰ. P. Starodubtsev. On Problems of Fracture of Materials in Compression along Two Internal Parallel Cracks[J]. Applied Mathematics and Mechanics, 1997, 18(6): 483-494.

Citation:

A. N. Guz, V. M. Nazarenko, Ⅰ. P. Starodubtsev. On Problems of Fracture of Materials in Compression along Two Internal Parallel Cracks[J]. Applied Mathematics and Mechanics, 1997, 18(6): 483-494.

Citation:

A. N. Guz, V. M. Nazarenko, Ⅰ. P. Starodubtsev. On Problems of Fracture of Materials in Compression along Two Internal Parallel Cracks[J]. Applied Mathematics and Mechanics, 1997, 18(6): 483-494.

PDF( 2872 KB)

On Problems of Fracture of Materials in Compression along Two Internal Parallel Cracks

Institute of Mechanics of the National Academy of Sciences of Ukraine, Ulitsa Nesterova 3, Kiev, 252057, Ukraine

Received Date: 1996-11-17
Publish Date: 1997-06-15

Abstract

Abstract

The frqcture of materials under the action of compressive forces, directed along cracks which are parallel in plere cannot be described within the framework of the linear fracture mechanics. The criteria of fracture of the Griffith-Irvin or COC type,used in classical linear fracture mechanics, are not applicable in this problem, since these forces have no influence on stress intensity coefficients and on values of cracks opening[1,2].The problems of such a class may be described only by using new approaches.One of possible approaches is presented by the first author, which involves using linearized relations, derived from exact non-linear equations of deformable solid body mechanics[3, 4, 5]. It should be remarked here that this approach has been widely used inproblems of deformable bodies stability. As a criterion of the initiation of fracture the criterion of local instability near defects of the crack type is used. In these cases the process of loss of stability initiates the fracture process.
- fracture,
- internal parallel crack,
- criterion of the initiation of fracture

FullText(HTML)

References(18)

References

[1]	G.P.Chevepanov,Mechanics of Brittle Fracture,Nauka,Moscow (1974).
[2]	M.K.Kassir and G.C.Sih,Mechanics of Fracture,Three-Dimensional Crack Problems,Vol.2,Noordhoff Leiden (1975).
[3]	A.N.Guz,Mechanics of Brittle Fracture of Materials with Initial Stresses,Naukova Dumka,Kiev (1983).
[4]	A.N.Guz,Foundations of Three-Dimensional Theoly of Deformable Bodies Stability,Vyshcha Shkola,Kiev(1986).
[5]	A.N.Guz,Foundation of mechanics of brittle fracture of materials with initial stresses,Adv.Fract.Rec.Proc.6th Int.Conf (ICF6),New Delhi,4~10 Dec.,1984,Vol.2(1984),1223~1230.
[6]	A.N.Guz,V.M.Nazarenko and I.P.Starodubtsev,Plane problem of fracture of materials with two parallel cracks in compression along the cracks,Problems of Mechanics of Deformable Solid Body,University of Kalinin,Kalinin (1986),138~151.(inRussian)
[7]	I.P.Starodubtsev,Fracture of the body in compression along two parallel cracks in plane deformation condition Prikl.Mechanika,24,6 (1988),79~84.
[8]	A.N.Guz and V.M,Nazarenko,Symmetric failure of the half space with penny-shaped cracks in compression,Theor.Appl.Fract.Mech.,3,3 (1985),233~245.
[9]	V.V.Bolotin,Defects of the delamination type in structures of composite materials,Mechanics of Composite Materials,2 (1984).239~255.
[10]	A.N.Guz,Mechanics of Composite Materials and Structures Elements,Vol.1,Naukova Dumka,Kiev (1982).
[11]	A.M.Mikhailov,Some problems of cracks theory in beam approximation,J.Appl.Mech.and Techni.Fizi.,5 (1967),128~133.
[12]	A.N.Polilov and Yu.N.Rabotnov,Development of delaminations in compression of composites,Izv.,AN SSSR,Mechanika Tverdogo Tela,4 (1983),166~171.
[13]	L.I.Slepyan,Mechanics of Cracks,Leningrad (1981).
[14]	W.L.Yin,Axisymmetric buckling and growth of a circular delamination in compressed laminate,In t.J.Solids Struct.,21,5 (1985),503~514.
[15]	S.G.Mikhlin and Kh.L.Smolitsky,Approximate Methods of Solutions of Differential and Intengral Eqeuations,Nauka,Moscow (1965)..
[16]	B.P.Maslov,Investigation of stochastic composites with nonlinear and anisotropic properties of components,Dissertation for Doctor Degree,Kiev (1983).
[17]	D.Kolarov,A.Baltov and N.Boncheva,Mechanics of Plastic Media,Mir,Moscow (1979).
[18]	A.N.Guz,V.I.Knukh and V.M.Nazarenko,Compressive failure of materials with two parallel cracks: small and large deformation,Theor.Appl.Fracture Mech.,11 (1989),213~223.