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Numerical Implementation of an Interfacial Edge Dislocation Solution in a Multi-Layered Medium
Authors: Aditya Khanna, Andrei Kotousov
Abstract:
A novel method is presented for obtaining the stress field induced by an edge dislocation in a multilayered composite. To demonstrate the applications of the obtained solution, we consider the problem of an interfacial crack in a periodically layered bimaterial medium. The crack is modelled as a continuous distribution of edge dislocations and the Distributed Dislocation Technique (DDT) is utilized to obtain numerical results for the energy release rate (ERR). The numerical implementation of the dislocation solution in MATLAB is also provided.Keywords: Distributed dislocation technique, Edge dislocation, Elastic field, Interfacial crack, Multi-layered composite.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1338353
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[1] J. L. Sackman, J. M. Kelly and A. E. Javid “A layered notch filter for high-frequency dynamic isolation,” J. Pressure Vessel Technol., vol. 111, no.1, pp. 17-24, 1989.
[2] H. Holleck, M. Lahres and P. Woll, “Multilayer coatings – influence of fabrication parameters on constitution and properties,” Surf. Coat. Technol., vol. 41, pp. 179-190, 1990.
[3] B.A. Roeder C.T. Sun, “Dynamic penetration of Alumina/aluminium laminates: experiments and modelling,” Int. J. Impact Eng., vol. 25, no. 2, pp. 169-185, 2001.
[4] L. Chen and M. J. Pindera, “Plane analysis of finite multilayered media with multiple aligned cracks - Part I: theory,” J. Appl. Mech., vol. 74, no. 1, pp. 128-143, 2006.
[5] A. Khanna and A. Kotousov, “Stress analysis of a crack in a fiberreinforced layered composite,” Compos. Struct., vol. 118, pp. 139-148, 2014.
[6] I. Sellinger, P. M. Weiss, A. Nguyen, Y. Lu, R. A. Assink, W. Gong and C.J. Brinker, “Continuous self-assembly of organic–inorganic nanocomposite coatings that mimic nacre,” Nature, vol. 394 , pp. 256- 260, 1998.
[7] H. Gao, B. Ji, I. L. Jäger, E. Arzt and P. Fratzl, “Materials become insensitive to flaws at nanoscale: Lessons from nature,” Proc. Natl. Acad. Sci. USA, vol. 100, no. 10, pp. 5597-5600, 2003.
[8] A. A. Daneshy, “Hydraulic Fracture Propagation in Layered Formations,” SPE J., vol. 18, no.1, pp. 33-41, 1978.
[9] A. Gudmundsson, T. H. Simmenes, B. Larsen and S. L. Philipp, “Effects of internal structure and local stresses on fracture propagation, deflection, and arrest in fault zones,” J. Struct. Geol., vol. 32, pp. 1643- 1655, 2010.
[10] A. Khanna and A. Kotousov, “Controlling the Height of Multiple Hydraulic Fractures in Layered Media,” SPE J. SPE-176017-PA, 2015.
[11] A. Khanna, A. Kotousov, J. Sobey and P. Weller, “Conductivity of narrow fractures filled with a proppant monolayer,” J. Petrol. Sci. Eng., vol. 100, pp 9-13, 2012.
[12] A. Khanna, A. Keshavarz, K. Mobbs, M. Davis and P. Bedrikovetsky, “Stimulation of the natural fracture system by graded proppant injection,” J. Petrol. Sci. Eng., vol. 111, pp. 71-77, 2013.
[13] V.V. Bolotin, “Delaminations in composite structures: its origin, buckling, growth and stability,” Compos. Part B – Eng., vol. 27, no.2, pp. 129-145, 1996.
[14] A.C. Garg, “Delamination - a damage mode in composite structures,” Eng. Fract. Mech., vol. 29, no. 5, pp. 557-584, 1988.
[15] J. Cook, J.E. Gordon, C.C. Evans and D.M. Marsh, “A mechanism for the control of crack propagation in all-brittle systems,” P. Roy. Soc. Lond. A – Mat., vol. 282, no. 1391, pp. 508-520, 1964.
[16] M-Y. He and J.W. Hutchinson, “Crack deflection at an interface between dissimilar elastic materials,” Int. J. Solids. Struct., vol. 25, no. 9, pp. 1053-1067, 1989.
[17] V. Gupta, A.S. Argon and Z. Suo, “Crack deflection at an interface between two orthotopic media,” J. Appl. Mech. vol. 59, no. 2S, pp. S79- S87, 1992.
[18] J. Li, “Debonding of the interface as ‘crack arrestor’,” Int. J. Fract., vol. 105, no. 1, pp. 57-79, 2000.
[19] K. Okumura and P-G. de Gennes, “Why is nacre strong? Elastic theory and fracture mechanics for biocomposites with stratified structures,” Eur. Phys. J. – E, vol. 4, no. 1, pp. 121-127, 2001.
[20] M.P. Cleary, “Primary factors governing hydraulic fractures in heterogeneous stratified porous formations,” No. UCRL-13884; CONF- 781112-10 (Massachusetts Inst. of Tech., Cambridge, USA 1978).
[21] B. Bilby and J. Eshelby, “Dislocations and the theory of fracture,” in: Fracture: an advanced treatise, vol. 1., H. Liebowitz, Ed. New York, USA: Academic Press, 1968.
[22] A. Kotousov, L. Bortolan Neto and A. Khanna, “On a rigid inclusion pressed between two elastic half spaces,” Mech. Mater. vol. 68, pp. 38- 44, 2014.
[23] L. Bortolan Neto and A. Khanna, “The performance of hydraulic fractures partially filled with compressible proppant,” Aust. J. Multidisciplinary Eng., vol. 10, no. 2, pp. 185, 2013.
[24] A. Khanna, L. Bortolan Neto and A. Kotousov, “Effect of residual opening on the inflow performance of a hydraulic fracture,” Int. J. Eng. Sci. vol. 74, pp. 80-90, 2014.
[25] L. Bortolan Neto, A. Khanna and A. Kotousov, “Conductivity and performance of hydraulic fractures partially filled with compressible proppant packs,” Int. J. Rock Mech. Min. Sci., vol. 74, pp. 1-9, 2015.
[26] F. Erdogan G. Gupta, “The stress analysis of multi-layered composites with a flaw,” Int. J. Solids Struct., vol. 7, no. 1, pp. 39-61, 1971.
[27] F. Erdogan G.D. Gupta, “Layered composites with an interface flaw,” Int. J. Solids Struct., vol. 7, no. 8, pp. 1089-1107, 1971.
[28] F. Erdogan, “Fracture problems in composite materials,” Eng. Fract. Mech. vol. 4, no. 4, pp. 811-840, 1972.
[29] L. Kucherov, Delamination in periodically layered bi-material composites. Delamination in periodically layered bi-material composites (Ph.D. Thesis, Tel Aviv University, Israel 2003).
[30] L. Kucherov and M. Ryvkin, “Interface crack in periodically layered bimaterial composite,” Int. J. Fract., vol. 117, no. 2, pp. 175-194, 2002.
[31] P.A. Kelly, J.J. O’Connor and D.A. Hills, “Stress field due to a dislocation in layered media,” J. Phys. D – Appl. Phys. vol. 28, no. 3, pp. 530-534, 1995.
[32] N.A. Fleck, J.W. Hutchinson and Z. Suo, “Crack path selection in a brittle adhesive layer,” Int. J. Solids Struct., vol. 27, no. 13, pp. 1683- 1703, 1991.
[33] C-H. Kuo, “Elastic field due to an edge dislocation in a multi-layered composite,” Int. J. Solids Struct., vol. 51, pp. 1421-1433, 2014.
[34] N.L. Muskhelishvili, Some Basic Problems of Mathematical Theory of Elasticity. Groningen, The Netherlands: P. Noordhoff, 1958.
[35] T-Y. Zhang and J.C.M. Li, “Interaction of an edge dislocation with an interfacial crack,” J. Appl. Phys., vol. 72, no. 6, pp. 2215-2226, 1992.
[36] C-Y. Hui and D.C. Lagoudas, “Stress fields of interface dislocations,” J. Appl. Mech. vol. 57, no. 1, pp. 247-248, 1990.
[37] A.P.S. Selvadurai, Partial Differential Equations in Mechanics 2: The Biharmonic Equation, Poisson's Equation. Springer Science & Business Media, 2000.
[38] D.A. Hills, P.A. Kelly, D.N. Dai and A.M. Korsunsky, Solution of crack problems: the distributed dislocation technique. Dordrecht, The Netherlands: Kluwer Academic Publishers, 1996.
[39] J.R. Rice, “Plane problems of cracks in dissimilar media,” J. Appl. Mech., vol. 55, no. 1, pp. 98-103, 1988.