of the IF method. Residual stresses in alumina and silicon nitride ceramics, which are machined under different grinding conditions, are estimated by using the proposed method. The estimated results are also verified by comparison with residual stresses measured by the X-ray method. Finally, the bending strength is correlated with the estimated residual stress, and the discussion is made on the obtained relation between them. ESTIMATION PROCEDURE OF RESIDUAL STRESS Estimation Principle by IF Method At a critical level for equilibrium crack growth in an indented ceramic material with a residual stress, the net stress intensity factor Knet remains constant as follows [9]. Knet = KCA + KR = KIC , (1) where KIC is the fracture toughness and KR is a residual stress intensity factor associated with the residual stress field. In Eqn. 1, KCA is a fracture toughness evaluated by using an IF method. It is noted that KCA is an apparent fracture toughness affected by the residual stress. The evaluation procedures for KCA and KR are described in the following. Several formulae to evaluate the fracture toughness KC of ceramics by using the IF method have been proposed [ex. 13], though the following equation recommended in the Japanese Industrial Standard (JIS) R 1607 [14] is adopted in this work. KC = 3/2 1/2 [ ] ( /2) a E P d α , (2) where α, E and P are an empirical coefficient, the Young's modulus of an indented material and the indentation peak load set in a Vickers hardness tester, respectively. The coefficient α in Eqn. 2 is given as 0.026 in JIS R 1607. Other dimensions d and a are the diagonal length of a Vickers impression and the half surface-length of a crack well-developed after indentation, respectively. The measured crack length a is affected by a residual stress field as illustrated in Fig. 1. In this case, the toughness KC calculated by Eqn. 2 should be interpreted as an apparent fracture toughness KCA. Since the growth of an indentation-induced crack is restrained under a compressive stress field, the crack length acom under a compressive stress is expected to be shorter than the length ao in no residual stress field. On the contrary, it is anticipated that the crack length aten observed under a tensile stress is longer than the length ao. ～ ～ ～ ～ Compressive stress field Tensile stress field No stress field Vickers impression Induced crack 2 ao ao acom aten Figure 1: Illustration of indentation-induced crack A grinding-induced residual stress σR is generally known to be compressive. In experimental studies [4-6, 15],
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