coefficient of ith layer at temperature T, and To and Ti are actual and "joining"temperature, respectively. During cooling of the sample the deformation difference, due to the different thermal expansion coefficients, is accommodated by creep as long as the temperature is high enough. Below a certain temperature, called the "joining temperature, the different components become bonded together and internal stresses appear. The "joining temperature is usually the value that is known only approximately. In practice, T is generally accepted to lie somewhat below the sintering temperature. If Bi(T)is a linear function, Ei sPi >AT, where AT=T-To 阝(70)+B1(T) is the average value of the thermal expansion coefficient in the temperature range from To Using the condition of crack growth(K1=Klc, where K,l is the fracture toughness of material) and(1), (10), we obtain K Ic (17) Using Eq.(13)the first integral in(17) can be expressed for a layered material as o(a,a,(r)dx=-Onwy2 6(21-102) where n is the number of layers broken by the crack (or notch) completely(Fig. 2). Using Eq(15), the second integral in(17) for a layered material takes the form Kr=h-, a o, (r)dx E#1J42,a|ua/4-120+(Jo-10x (19) Here, K is the stress intensity due to the residual stresses The following formula is given for the stress intensity of an edge crack in the specimen under bending as being accurate to +0. 2% in the range a=0 to 1 [15] f0(), where fo(a) is a nondimensional stress intensity factor given by the following expression [15] 1.5a2[1.99-0(1-0)(215-3930+270 fo(0)= +2x)(1-a)32 (21) Taking into account Eqs. (12),(21), expression(20) can be transformed to the form KI=Y(a)o a12 (22)coefficient of ith layer at temperature T, and T0 and T j are actual and “joining” temperature, respectively. During cooling of the sample the deformation difference, due to the different thermal expansion coefficients, is accommodated by creep as long as the temperature is high enough. Below a certain temperature, called the “joining” temperature, the different components become bonded together and internal stresses appear. The “joining” temperature is usually the value that is known only approximately. In practice, T j is generally accepted to lie somewhat below the sintering temperature. If βi ( ) T is a linear function, ~ε β i i ≤ >∆T, where ∆TT T = −j 0 , < ≥ + β β β i i ij () () T T 0 2 is the average value of the thermal expansion coefficient in the temperature range from T0 to T j . Using the condition of crack growth (K K 1 1 = c , where K1c is the fracture toughness of material) and (1), (10), we obtain: K h x a x dx h x a x dx c a a a 1 r 0 0 = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ∫ ∫ , () , () . ασ ασ (17) Using Eq. (13) the first integral in (17) can be expressed for a layered material as h x a x dx w I II E h x a a a m L L L n , () ( ) α σ , σ α ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = − ′ ∫ + 0 2 1 2 0 2 1 6 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − + ′ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − − [ ] ,[ ] I x I dx E h x a I x I dx LL i LL x x i 01 01 1 α i n i n x a ∫ ∑ ∫ = ⎧ ⎨ ⎪ ⎩ ⎪ ⎫ ⎬ ⎪ ⎭ 1 ⎪ , (18) where n is the number of layers broken by the crack (or notch) completely (Fig. 2). Using Eq. (15), the second integral in (17) for a layered material takes the form: K h x a x dx I II E h x a r a r L L L = n ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = − ′ ⎛ ⎝ ⎜ ∫ + , () , ασ α 0 1 2 0 2 1 1 ⎞ ⎠ ⎟ ⎧ ⎨ ⎪ ⎩ ⎪ −+ − ∫ x a LL L L LL L L n [ ( )] I J I J I J I J x dx 11 2 0 10 01 + ′ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −+ − − ∑ ∫ = E h x a IJ I J IJ i x x i n LL L L LL i i ,[ ( α 1 1 11 2 0 10 I J x dx L L 0 1 )] . ⎫ ⎬ ⎪ ⎭ ⎪ (19) Here, Kr is the stress intensity due to the residual stresses. The following formula is given for the stress intensity of an edge crack in the specimen under bending as being accurate to ±0.2% in the range α = 0 to 1 [15]: K Ps bw f 1 3 2 = 0 ( ), α (20) where f 0 ( ) α is a nondimensional stress intensity factor given by the following expression [15]: f 0 12 2 1 5 1 99 1 2 15 3 93 2 7 1 2 ( ) . [ . ( )( . . . )] ( )( α α αα α α α = −− − + + 1 3 2 − α) . (21) Taking into account Eqs. (12), (21), expression (20) can be transformed to the form: KY a 1 m 1 2 = () , α σ (22) 296