Summary
An estimation is found for the energy release due to fragmentation of a brittle inhomogeneity of ellipsoidal shape embedded in a ductile matrix under remote static loading. In the state of completed fragmentation the inhomogeneity is replaced by a void with zero stiffness. Thus, the problem of estimating the energy release reduces to the eigenstrain problem solved by Eshelby. The energy release calculated for prolate spheroidal inhomogeneities is used in the balance of energy to determine the crack density. The application to the geological system of garnet inhomogeneities embedded in a quartz matrix is considered.
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Valentino, A.J.;Sclar, C.B.: Parting in giant garnets as indicator of late brittle deformation at Gore Mountain, Warren Country, NY. Geophys Res Lett 8 (1981) 883–885
Prior, D.J.: Sub-critical fracture and associated retrogression of garnet during mylonitic deformation. Contrib Mineral Petrol 113 (1993) 545–556
Wendt, A.S.;D'Arco, P.;Goffe, B.;Oberhänsli, R.: Radical cracks around a quartz inclusions in almandine: Constraints on the metamorphic history of the Oman mountains. Earth Planetary Sci Lett 114 (1993) 449–461
Ji, S.;Zhao, P.;Saruwatari, K.: Fracturing of garnet crystals in anisotropic metamorphic rocks during uplift. J Struct Geol 19 (1997) 603–620
Trepmann, C.A.;Stöckhert, B.: Cataclastic deformation of garnet: a record of synseismic loading and postseismic creep. J Struct Geol 24 (2002) 1845–1856
Cox, H.L.: The elasticity and strength of paper and other fibrous materials. Br J Appl Phys 3 (1952) 72–79
Zhao, P.;Ji, S.: Refinements of shear-lag model and its applications. Tectonophysics. 279 (1997) 37–53
Mandal, N.;Chakraborty, C.;Samanta, S.K.: Controls of the failure mode of brittle inclusions hosted in a ductile matrix. J Struct Geol 23 (2001) 51–66
Grady, D.E.: Local intertial effects in dynamic fragmentation. J Appl Phys 53 (1982) 322–325
Glenn, L.A.;Chudnowsky, A.: Srrain-energy effects on dynamic fragmentation. J Appl Phys 59 (1986) 1379–1380.
Grady, D.E.;Kipp, M.E.: Geometric statistics and dynamic fragmentation. J Appl Phys 58 (1985) 1210–1222
Grady, D.E.: Pratical size statistics in dynamic fragmentation. J Appl Phys 68 (1990) 6099–6105
Xu, X.P.;Needleman, A.Z.: Numerical simulation of fast crack growth in brittle solids. J Mech Phys Solids 42 (1994) 1397–1434.
Camacho, G.T.;Ortiz, M.: Computational modeling of impact damage in brittle materials. Int J Solids Struct 33 (1996) 2899–2938
Miller, O.;Freund, L.B.;Needleman, A.: Modeling and simulation of dynamic fragmentation in brittle materials. Int J Fracture 96 (1999) 101–125
Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc (London) A241 (1957) 376–396
Mura, T.: Micromechanics of Defects in Solids (Kluwer Academic Publishers, Oxford) 1987.
Le, K.C.: Variational principles of the nonlinear theory of brittle fracture. Appl Math Mech (PMM). 54 (1980) 658–665
Le, K.C.: Variational problems of crack equilibrium and crack propagation. In del Piero G. and Owen D., (eds.) Multiscale Modelling in Continuum Mechanics and Structured Deformations, Springer Verlag, Berlin 2004, pp. 52–81
Gebrande, H.: Elastic wave velocities and constants of rocks and rock forming minerals. In Angeheister G., (ed.) Landolt-Börnstein: Zahlenwerte und Funktionen aus Naturwissenschaft und Technik Vol. 1b 1982 Berlin Springer Verlag
pardavi-Horvath, M.: Microhardness and brittle fracture of garnet single crystals. J Mater Sci 19 (1984) 1159–1170
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Le, K.C., Korobeinik, M. & Hackl, K. Estimation of crack density due to fragmentation of brittle ellipsoidal inhomogeneities embedded in a ductile matrix. Arch. Appl. Mech. 74, 439–448 (2005). https://doi.org/10.1007/BF02637041
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DOI: https://doi.org/10.1007/BF02637041