where 199-a(1-a)(215-3930+270x2) Y() (23) (1+20) /2 It was shown in [3] that Eqs.(20),(22)can be successfully used to determine fracture toughness of ceramic matrix layered materials. However, it should be noted that as applied to inhomogeneous(particularly, layered) materials the equations give the so-called apparent fracture toughness. In bending test, this is the fracture toughness of some effective homogeneous specimen that meets the following conditions: 1)to have the same dimensions as real layered specimen; 2)to have notch depth equal to that of real layered specimen; 3) under the same loading conditions to demonstrate the same critical load as that for real layered specimen. In spite of relativity of this value, it is a useful characteristic allowing contributions of such factors as residual stresses and material inhomogeneity to be accounted for. Thus, experimental value of the apparent fracture toughness of layered specimen can be found using expression Kom =Y(o)om, a/2 (24) It follows from Eqs.(17)(19)and(24)that apparent fracture toughness of layered composite K written as 6(a)2(2-1012)kx(-k,) K a[Lox-lu x where Ki is the fracture toughness of ith layer material. Expression(25)suggests that the higher resistance to fracture is derived from a reduction of the crack driving force rather than from an increase in the intrinsic resistance to crack extension Experimental. The choice of composition for Si3N4 based ceramics laminates is determined by the coefficient of thermal expansion and Young's modulus of the compounds. Three compositions of composite layers were used: 1)Si,N4(MIl, Starck, Germany); 2) Si3N4-20 wt TiN (grade C, Starck, Germany); 3)Si3N--70 wt Tin (grade C, Starck, Germany). Youngs moduli, Poisson ratios, joining temperature T and average values of coefficients of thermal expansion of compositions under study are given in [16]. Mean values of intrinsic fracture toughness of monolith materials are evaluated in the work to be approximately the same for all layer compositions, being 5 MPa. m. Note that the intrinsic fracture toughness corresponds to fracture toughness of layer material Milling of mixtures of certain compositions was done in the ball mill for 5 h. The formation of a thin ceramic layer is of specific importance, as the sizes of residual stress zones(tensile and compressive)are directly connected with the thickness of layers. Green tapes were manufactured with rolling. Rolling permits to control thickness of green layers, to obtain high green density and a rather low amount of solvent and organic additives in comparison with other methods such as a tape casting [17]. However there is a problem to produce thin tapes(<100 um) with a small amount of plasticizer and sufficient strength and elasticity to handle green layers after rolling Crude rubber (4 wt %)was added to the mixture of powders as a plastisizer through a 3% solution in petrol Then the powders were dried up to the 2 wt% residual amount of petrol in the mixture. After sieving powders with 500 um sieve, granulated powders were dried up to the 0.5 wt. residual petrol. A roll mill with 40 mm rolls used for rolling. The velocity of rolling was 1. 5 m/min. Working pressure varied from 10 MPa for the relative density of 64% to 100 MPa for 74% density. The thickness of green tapes was either 0.4-0.5 mm or 0.8-1.0 mm, the width was 60-65 mm. Samples of ceramics were prepared by hot pressing of tapes stacked together. The hot pressi was performed at the temperature 1780-1820%C, with duration of 20 min and under the pressure of 30 MPa Green tapes were stacked together to form desirable layered structure. The graphite dies were used for the hot pressing without protective atmosphere. After hot pressing, the thickness of the Si3N4 layers was 160-960 um, and the thickness of the SiN \ayers with Tin additive varied from 160 to 480Aim In the range ofwhere Y ( ) . ( )( . . . ) ( )( ) α . αα α α α α = −− − + + − 1 99 1 2 15 3 93 2 7 12 1 2 3 2 (23) It was shown in [3] that Eqs. (20), (22) can be successfully used to determine fracture toughness of ceramic matrix layered materials. However, it should be noted that as applied to inhomogeneous (particularly, layered) materials the equations give the so-called apparent fracture toughness. In bending test, this is the fracture toughness of some effective homogeneous specimen that meets the following conditions: 1) to have the same dimensions as real layered specimen; 2) to have notch depth equal to that of real layered specimen; 3) under the same loading conditions to demonstrate the same critical load as that for real layered specimen. In spite of relativity of this value, it is a useful characteristic allowing contributions of such factors as residual stresses and material inhomogeneity to be accounted for. Thus, experimental value of the apparent fracture toughness of layered specimen can be found using expression (22): KY a app m = () . α σ 1 2 (24) It follows from Eqs. (17)–(19) and (24) that apparent fracture toughness of layered composite Kapp can be written as K Y a I II K K wE h x a app L L L c i r n = − − ′ ⎛ + 6 1 2 1 2 0 2 1 2 1 ( ) ( )( ) , ( ) α α ⎝ ⎜ ⎞ ⎠ ⎟ − + ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − = ∫ [ ] ,[ ] I x I dx h ∑ x a I x I dx LL LL i n x a n 01 01 1 α ⎧ ⎨ ⎪ ⎩ ⎪ ⎫ ⎬ ⎪ ⎭ ⎪ , (25) where K c i 1 ( ) is the fracture toughness of ith layer material. Expression (25) suggests that the higher resistance to fracture is derived from a reduction of the crack driving force rather than from an increase in the intrinsic resistance to crack extension. Experimental. The choice of composition for Si3N4 based ceramics laminates is determined by the coefficient of thermal expansion and Young’s modulus of the compounds. Three compositions of composite layers were used: 1) Si3N4 (M11, Starck, Germany); 2) Si3N4–20 wt.% TiN (grade C, Starck, Germany); 3) Si3N4–70 wt.% TiN (grade C, Starck, Germany). Young’s moduli, Poisson ratios, joining temperature T j and average values of coefficients of thermal expansion of compositions under study are given in [16]. Mean values of intrinsic fracture toughness of monolith materials are evaluated in the work to be approximately the same for all layer compositions, being 5 MPa m⋅ 1 2/ . Note that the intrinsic fracture toughness corresponds to fracture toughness of layer material. Milling of mixtures of certain compositions was done in the ball mill for 5 h. The formation of a thin ceramic layer is of specific importance, as the sizes of residual stress zones (tensile and compressive) are directly connected with the thickness of layers. Green tapes were manufactured with rolling. Rolling permits to control thickness of green layers, to obtain high green density and a rather low amount of solvent and organic additives in comparison with other methods such as a tape casting [17]. However there is a problem to produce thin tapes (<100 µm) with a small amount of plasticizer and sufficient strength and elasticity to handle green layers after rolling. Crude rubber (4 wt.%) was added to the mixture of powders as a plastisizer through a 3% solution in petrol. Then the powders were dried up to the 2 wt.% residual amount of petrol in the mixture. After sieving powders with a 500 µm sieve, granulated powders were dried up to the 0.5 wt.% residual petrol. A roll mill with 40 mm rolls was used for rolling. The velocity of rolling was 1.5 m/min. Working pressure varied from 10 MPa for the relative tape density of 64% to 100 MPa for 74% density. The thickness of green tapes was either 0.4–0.5 mm or 0.8–1.0 mm, the width was 60–65 mm. Samples of ceramics were prepared by hot pressing of tapes stacked together. The hot pressing was performed at the temperature 1780–1820°C, with duration of 20 min and under the pressure of 30 MPa. Green tapes were stacked together to form desirable layered structure. The graphite dies were used for the hot pressing without protective atmosphere. After hot pressing, the thickness of the Si3N4 layers was in the range of 160–960 µm, and the thickness of the Si3N4 layers with TiN additive varied from 160 to 480 µm. 297