Abstract
This article investigates the dynamic problem for moving cracks in materials with initial stresses, considering previous publications by the author on this subject. Stresses and displacements in the linearized theory are represented as analytical functions of complex variables for dynamic problems. Exact solutions are obtained for the general case of unequal roots for the basic equation. New mechanical effects of the considered dynamic problems (the wedge problem) are analyzed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. I. Barenblatt and G. P. Cherepanov, “Wedge-splitting of a brittle body,”Prikl. Matem. Mekh.,24 No. 4, 662–682 (1960).
G. I. Barenblatt and G. P. Cherepanov, “Equilibrium and propagation of cracks in an anisotropic medium,”Prikl. Matem. Mekh.,25, No. 1, 46–55 (1961).
L. A. Galin,Contact Problems in Elasticity Theory [in Russian], Fizmatgiz, Moscow (1953).
A. N. Guz', “Theory of cracks in elastic bodies with initial stresses (wedge problems),”Prikl. Mekh.,17, No. 5, 3–12 (1981).
A. N. Guz',Mechanics of Brittle Fracture for Materials with Initial Stresses [in Russian], Nauk. Dumka, Kiev (1983).
A. N. Guz', “Order of singularity at the crack tip in material with initial stresses,”Dokl. Akad. Nauk SSSR,289, No. 2, 310–312 (1986).
A. N. Guz',Nonclassical problems in Fracture Mechanics. In Four Volumes (in Five Books). Vol. 2. Brittle Fracture of Materials with Initial Stresses [in Russian; A. N. Guz', general editor], Nauk. Dumka, Kiev (1991).
A. N. Guz', “Order of singularity in problems of the mechanics of brittle fracture of materials with initial stresses,”Prikl. Mekh.,34, No. 2, 3–8 (1998).
A. N. Guz', “Dynamic problems in the mechanics of brittle fracture of materials with initial stresses for moving cracks. 1. Formulation of problems, general relations,”Prikl. Mekh.,34, No. 12, 3–15 (1998).
A. N. Guz', “Dynamic problems in the mechanics of brittle fracture of materials with initial stresses for moving cracks. 2. Normal tear cracks (Mode I),”Prikl. Mekh.,35, No. 1, 3–16 (1999).
A. N. Guz', “Dynamic problems in the mechanics of brittle fracture of materials with initial stresses for moving cracks. 3. Transverse shear (Mode II) and longitudinal shear (Mode III) cracks,”Prikl. Mekh.,35, No. 2, 3–14 (1999).
G. P. Cherepanov,Brittle Fracture Mechanics [in Russian], Nauka, Moscow (1974).
J. W. Craggs, “On the propagation of a crack in an elastic-brittle material,”J. Mech. Phys. Solids,8, No. 1, 66–75 (1960).
E. Yoffe, “The moving Griffith crack,”Phil. Mag.,42, No. 330, 739–750 (1951).
Additional information
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 12–21, March, 1999.
Rights and permissions
About this article
Cite this article
Guz', A.N. Dynamic problems of the mechanics of brittle fracture of materials with initial stresses for moving cracks 4. Wedge problems. Int Appl Mech 35, 225–232 (1999). https://doi.org/10.1007/BF02682116
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02682116