Abstract
Both growth and branching of sharp cracks in perfect single crystals are studied. Strength and deformation criteria of sharp crack branching are proposed. These criteria describe brittle, quasi-brittle, and ductile material behavior under fracture propagation. For inner cracks, simple relations have been obtained that describe crack branching when curves of Kolumb-Mohr type theoretical strength for the generalized deformation mode are known. Multiple crack branching, associated with a multiplicity of eigenvalues when the system is buckled, is discussed. It has been ascertained that the principle of local symmetry in the vicinity of a crack tip is valid for perfect single crystals if the symmetry axis of a crystal is in line with the crack axis. When asymmetric perturbations of an atomic lattice occur in the vicinity of a crack tip or the symmetry axis of a single crystal is inconsistent with the crack axis, the principle of local symmetry fails. Solids with a hierarchy of regular structures that are typical for Macro-, Micro- and Nano-scales are studied in the same way. The curves of theoretical strength (Kolumb-Mohr type) of every structural level of material are considered to be known for the generalized stress state.
Similar content being viewed by others
References
Argatov, I.I. and Nasarov, S.A. (2002). Energy release at crack kinking in a plane anisotropic solid. Prikl, Matem. Mekhan. [in Russian], 66(3), 502-514.
Goldstein, R.V. and Salganik, R.L. (1974). Brittle fracture of solids with arbitrary crack. Int. J. Fract. 10, 507-523.
Gumbsch, P. (1995). An atomistic study of brittle fracture: Toward explicit failure criteria from atomistic modeling. J. Mater. Res. 10(11), 2897-2907.
Kelly, A., Tyson, W.R. and Cottrell, A.H. (1967). Ductile and brittle crystals. The Philos. Mag. 15, 567-586.
Knott, J.F. (1983). Mechanics of fracture. In: Atomistics of Fracture (Edited by R. Latanision and J.R. Pickens), Plenum Press, New York, 209-235.
Kornev, V.M. (1996). Integral criteria for the brittle strength of cracked bodies with defects in the presence of vacancies at the tip of a crack. Strength of compacted ceramic-type bodies. J. Appl. Mech. and Techn. Phys. 37(5), 756-764.
Kornev, V.M. (2000). Hierarchy of strength criteria of structured brittle media. Satellite initiation of microcracks. J. Appl. Mech. and Techn. Phys. 41(2), 367-375.
Kornev, V.M. and Kurguzov, V.D. (1999). A discrete-integral strength criterion for complicated stress states. Fatigue and Fracture of Engineering Materials and Structures 22(11), 989-995.
Kornev, V.M. and Kurguzov, V.D. (2000). Modeling of an edge dislocation and estimate of the dislocation core for a closed-packed atomic layer. J. Appl. Mech. and Techn. Phys. 41(5), 211-216.
Kornev, V.M. and Kurguzov, V.D. (2000a). The discrete-integral strength criterion for complicated stress state. Izv. RAN, Mekhan. Tverd. Tela [in Russian], No. 6, 99-106.
Kornev, V.M. and Kurguzov, V.D. (2001). The discrete-integral strength criterion for complicated stress state at the presence of foreign atoms, In: Dinamica Sploshnoi Sredy, RAN Siberian Branch [in Russian], Institute of Hydrodynamics 119, 62-67.
Kornev, V.M. and Tikhomirov, Yu.V. (2000). Loss of stability of on atomic chain region in the presence of impurity. Strength reduction of cracked brittle solids. J. Appl. Mech. and Techn. Phys. 37(3), 433-443.
Macmillan, N.H. (1983). The ideal strength of solids. In: Atomistics of Fracture (Edited by R. Latanision and J.R. Pickens), Plenum Press, New York, 95-164.
Paul, B. (1968). Macroscopic criteria for plastic flow and brittle fracture, Fracture. An Avanced Treatise. (Edited by H. Liebowitz) Vol. II. Mathematical Fundamentals, Academic Press, New York, London, 313-496.
Rauchs, G., Munz, D. and Fett, T. (2002). Calculation of crack tip phase transformation zones in TZP with the weight function method, Fracture Mechanics of Ceramics. (Edited by R.C. Bradt and all), Vol. 13. Crack-Microstructure Interaction, R-Curve Behavior, Environmental Effects in Fracture, and Standardization, Kluwer Academic/Plenum Pulishers, New York, Boston, Dordrecht, London, Moscow, 1-8.
Rice, J.R. (1992). Dislocation nucleation from a crack tip: an analysis based on the Peierls concept. J. Mech. Phys. Solids. 40(2), 239-271.
Rice, J. and Thomson, R. (1974). Ductile versus brittle behaviour of crystals. The Philos. Mag. 29, 73-97.
Savruk, M.P. (1988). Fracture mechanics and strength of materials, Vol. 2: Stress-intensity factor in cracked bodies [in Russian], Naukova Dumka, Kiev.
Schmitt-Thomas, K.G. (1989). Metallkunde fur das Maschinenwesen, Springer-Verlag, Berlin, Heidelberg, New York.
Thomson, R. (1983). Physics of fracture. In: Atomistics in Fracture. (Edited by R. Latanision and J.R. Pickens), Plenum Press, New York, 167-204.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kornev, V. Rupture crack branching in solids with structural hierarchy. International Journal of Fracture 128, 205–213 (2004). https://doi.org/10.1023/B:FRAC.0000040983.88519.55
Issue Date:
DOI: https://doi.org/10.1023/B:FRAC.0000040983.88519.55