Residual strain energy in composites containing particles
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Residual strain energy in composites containing particles Toshiaki Mizutani R&D Center, Toshiba Corporation, 1, Komukai Toshiba-cho, Saiwai-ku, Kawasaki-shi 210, Japan (Received 27 June 1995; accepted 25 July 1995)
Selsing’s formula for radial tension at the particle-matrix interface is extended into a general formula which includes the effects of the amount of dispersed particles. A relationship is derived between individual volumes of strained unit cells in the crystal lattices of the particles and of the surrounding matrix. These relationships are used to predict the effect of the particles (2H–TiB2 , 2H–ZrB2 , and t–WB) on their unit cells and on the unit cell of the surrounding 6H–SiC matrix. The precision of these predictions was 7.1% or better. Hence, in principle, it is possible to investigate the distributions of residual bulk stress/strain. Estimates of characterizing values of the three composite systems are attempted on the rough basis of the elastic constants of the SiC matrix, confirming the physical validity of this approach as a first approximation. Further, the residual bulk strain energies of the particles and the matrix are discussed in connection with the elastic term involved in the fracture energy of such composites.
I. INTRODUCTION
Several experimental reports have confirmed that a dispersion of TiB2 or ZrB2 particles toughens SiC ceramics sintered with boron aid and carbon aid, (B and C aids).1–5 The toughness K1C is related to Young’s modulus EC and the fracture energy GC of the composite, namely K1C s2EC GC d1/2 . The fracture energy GC can be treated as a primitive term GO (the surface energies of component materials) plus additional terms GE and GN (the elastic and nonelastic energies in the composite), namely GC GO 1 GE 1 GN . However, no major mechanism has yet been verified for the toughening phenomenon of such composites. The various proposed mechanisms have little in common because they are based on different mechanical models (such as microcracking, deflection, bowing, blunting, pinning, and bridging), and also because they involve different parameters (such as surface energies, thermal expansion coefficients, elastic constants, and residual stresses).6–16 Most of these mechanisms seem to be concerned with GN . However, as far as physical analysis is concerned, this term should be third in priority. The author et al. have previously examined the lattice constants using x-ray diffraction (XRD) in two forms of such composite systems: sintered blocks and the corresponding pulverized powders.17 Volumetric deformations of unit cells were observed in the crystal lattices of 6H–SiC matrix (compressive) and dispersed 2H–MeB2 particles (expansive). Further, it appeared that the compressive deformation intensified and the Presented in part at the 6th fall symposium of the Japan Ceramics Society, Kita-Kyushu-shi, Japan, Oct. 7, 1993 (High Temperature and High Strength Ceramics Division, Paper No. 2-2C21). J. Mater. Res., Vol. 11, No. 2, Feb
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