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IssuesArchive of Issues2012-4pp.400-414

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R.V. Goldstein and M.N. Perelmuter, "Kinetics of Crack Formation and Growth on the Material Interface," Mech. Solids. 47 (4), 400-414 (2012)
Year 2012 Volume 47 Number 4 Pages 400-414
DOI 10.3103/S002565441204005X
Title Kinetics of Crack Formation and Growth on the Material Interface
Author(s) R.V. Goldstein (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo†101, str.†1, Moscow, 119526 Russia,
M.N. Perelmuter (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo†101, str.†1, Moscow, 119526 Russia,
Abstract A model of thermal fluctuation crack formation in a weakened bond region on a material interface is proposed. The weakened bond region is modeled by a bridged crack whose properties vary in time according to the thermal fluctuation mechanism. It is assumed that at least one of the materials is a polymer and the crack part occupied by bridges (the end region) is not small compared with the crack length. The stresses in the bridges and the kinetic dependence of the bond density in the crack end region are determined by solving a system of singular integrodifferential equations. The condition for the crack-defect nucleation is the decrease to the critical value of the average bond density on the corresponding part of the weakened bond region. Numerical results permitting one to estimate the crack nucleation time and the typical levels of external loads for the chosen material parameters are presented.
Keywords crack formation and growth, end region, thermal fluctuation fracture, durability, integrodifferential equations
1.  R. V. Goldstein and M. N. Perelmuter, "An Interface Crack with Bonds between the Surfaces," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 94-112 (2001) [Mech. Solids (Engl. Transl.) 36 (1), 77-92 (2001)].
2.  M. N. Perelmuter, "A Criterion for the Growth of Cracks with Bonds in the End Zone," Prikl. Mat. Mekh. 71 (1), 152-171 (2007) [J. Appl. Math. Mech. (Engl. Transl.) 71 (1), 137-153 (2007)].
3.  R.V. Goldstein and M. N. Perelmuter, "Modeling of Crack Resistance of Composite Materials," Vych. Mekh. Sploshn. Sred 2 (2), 22-39 (2009).
4.  L. M. Kachanov, "On the Kinetics of Crack Growth," Prikl. Mat. Mekh. 25 (3), 498-502 (1961) [J. Appl. Math. Mech. (Engl. Transl.) 25 (3), 739-745 (1961)].
5.  B. I. Kostrov, L. V. Nikitin, and L. M. Flitman, "Crack Propagation in Elastoviscous Bodies," Fiz. Zemli, No. 7, 20-35 (1970).
6.  V. M. Entov and R. L. Salganik, "Prandtl Crack in a Viscoelastic Body. Stationary Crack Propagation," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 6, 41-60 (1969) [Mech. Solids (Engl. Transl.)].
7.  R. A. Schapery, "A Theory of Crack Initiation and Growth in Viscoelastic Media. Part I. Theoretical Developments," Int. J. Fract. 11 (1), 141-159 (1975); "A Theory of Crack Initiation and Growth in Viscoelastic Media. Part II. Approximate Methods of Analysis," Int. J. Fract. 11 (3), 369-388 (1975).
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14.  H. Kausch, Fracture of Polymers (Springer, Berlin, 1978; Mir, Moscow, 1981).
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17.  G. I. Barenblatt, V. M. Entov, and R. L. Salganik, "On the Kinetics of Crack Propagation. General Concepts. Cracks Close to Equilibrium," Inzh. Zh. Mekh. Tverd. Tela, No. 5, 82-92 (1966) [Mech. Solids (Engl. Transl.) 1 (5), 53-59 (1966)].
18.  G. I. Barenblatt, V. M. Entov, and R. L. Salganik, "On the Kinetics of Cracks Propagation. Fluctuational Fracture," Inzh. Zh. Mekh. Tverd. Tela, No. 1, 122-128 (1967) [Mech. Solids (Engl. Transl.)].
19.  R. L. Salganik, L. Rapoport, and V. A. Gotlib, "Effect of Structure on Environmentally Assisted Subcritical Crack Growth in Brittle Materials," Int. J. Fract. 87, 21-46 (1997).
20.  R. L. Salganik, "The Adhesive Joint Fracture due to Crack Propagation Affected by Heat and Active Agent Concentration," Int. J. Fract. 65, 141-159 (1994).
21.  I. Narisova, Strength of Polymer Materials (Khimiya, Moscow, 1987) [in Russian].
22.  A. Tobolskii, Properties and Structure of Polymers (Khimiya, Moscow, 1964) [in Russian].
23.  M. N. Perelmuter, "Boundary Element Analysis of Structures with Nonclassical Bridged Cracks," in Proceedings of the Symposium of International Association for Boundary Element Methods (IABEM2011), Italy, 2011, pp. 253-258.
24.  L. I. Slepyan, Mechanics of Cracks (Sudostroenie, Leningrad, 1981) [in Russian].
25.  J. R. Rice and G. C. Sih, "Plane Problems of Cracks in Dissimilar Media," Trans. ASME J. Appl. Mech. 32, 218-224 (1965).
26.  M. N. Perelmuter, "An Interface Crack with Non-Linear Bonds in a Bridged Zone," Prikl. Mat. Mekh. 75 (1), 152-171 (2011) [J. Appl. Math. Mech. (Engl. Transl.) 75 (1), 106-118 (2011)].
27.  V. K. Khanna, "Adhesion-Delamination Phenomena at the Surfaces and Interfaces in Microelectronics and MEMS Structures and Packaged Devices," J. Phys. D: Appl. Phys. 44, 1-19 (2011).
28.  R. V. Goldstein, V. F. Bakirov, and M. N. Perelmuter "Modeling of Adhesion Strength and Fracture Kinetics of the Microelectronic Package Polymer-Polymer Joints," in Proc. Inst. Phys. Technol., Russian Acad. Sci., Vol. 13: Modeling and Simulation of Submicron Technology and Devices (1997), pp. 115-125.
Received 30 November 2011
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