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Microcracking in polycrystalline ceramics: Elastic isotropy and thermal anisotropy. (English) Zbl 0705.73169
Summary: A hexagonal grain array model is used to study grain boundary microcracking of a polycristalline aggregate due to residual stress. Each grain is assumed to be elastically isotropic but thermally anisotropic. The axes of thermal anisotropy for each grain are arbitrary. An explicit analytic solution is obtained for the entire residual stress field. This solution is used to give a detailed description of the grain boundary stress fields. Further, explicit algebraic formulae are given for stress intensity factors associated with grain boundary microcracks. The results are used to predict the critical grain size for the occurrence of spontaneous microcracking. Agreement between theory and experiment is good.

MSC:
74R99 Fracture and damage
74G70 Stress concentrations, singularities in solid mechanics
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[1] Clarke, F.J.P., Acta metall., 12, 139, (1964)
[2] Cleveland, J.J.; Bradt, R.C., J. am. ceram. soc., 61, 478, (1978)
[3] Davidge, R.W., Acta metall., 29, 1965, (1981)
[4] Eshelby, J.D., (), Ch. 3
[5] Evans, A.G., Acta metall., 26, 1845, (1978)
[6] Fredrich, J.T.; Wong, T.-F.; Fredrich, J.T.; Wong, T.-F., J. geophys. res., J. geophys. res., 91, 743, (1986)
[7] Fu, Y.; Evans, A.G., Acta metall., 30, 1619, (1982)
[8] Fu, Y.; Evans, A.G., Acta metall., 33, 1515, (1985)
[9] Kuszyk, J.A.; Bradt, R.C., J. am. ceram. soc., 56, 420, (1973)
[10] Laws, N., J. mech. phys. solids, 21, 9, (1973)
[11] Ohya, Y.; Nakagawa, Z.; Hamano, K., J. am. ceram. soc., 70, c-184, (1987)
[12] Rice, R.W.; Pohanka, R.C., J. am. ceram. soc., 62, 559, (1979)
[13] Tvergaard, V.; Hutchinson, J.W., J. am. ceram. soc., 71, 157, (1988)
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