laminated ceramics [8]. There have also been a number material are [19 of experimental studies of laminated ceramics that were conducted using these models, attempting to maximize f2(ar2-ar1)△T the mechanical properti CrI EIfi+ E2f2 Silicon nitride is the most promising and well- developed ceramics for structural application because and of its outstanding mechanical properties as well as its superior wear resistance [9]. The addition of Tin to E1fi(ar1-ar2)△T Si3N4 leads to an increase of Youngs modulus, electri Or2= ELfi+ E2f2 cal conductivity, and CTE of Si3N4 ceramics [10]. B varying the amount of TiN in silicon nitride ceramics we can increase the Cte/Youngs modulus mismatch where E/=E/(1-v),fi="*Dm, f2="2. and develop composites with compressive and tensile E and V: is the elastic modulus and Poissons ratio of j-th component respectively, II and l2 are the thickness stresses in alternative layers. This may further improve of layers for the first and second component, aTI and the mechanical properties of laminates [11-13]. B Si3N4 belongs to the space group C 6h(P63/m) and T2 are the thermal expansion coefficients(CTE)of the first and second components respectively, AT is the irreducible representation for the optical phonons the difference between the joining temperature and the en re ported[ 14-17] current temperature, and h is the total thickness of the specimen Topic= 4Ag+ 2Au 3Bg+ 4Bu+ 2Elg 5E2g The choice of composition for Si3N4-based ceramic laminates is dependent on the coefficient of thermal 4Elu+ 2E expansion and Youngs modulus of the compound Four compositions of composite layers were used: where Ag, Elg and E2g modes are Raman active and a 1. Si3 N4-5 wt %Y203-2 wt% AlO3 and Elu are infrared active Raman and infrared active bands are mutually excluded since the crystal structure 2. TIN. 3. Si3N4(5 wt%Y2O3-2 wt %Al,O3)-20 wt %TIN; has a center of symmetry. The goal of this work is to study the interrelation 4. Si3 N4(5 wt %Y2O3-2 wt% Al2O3)-50 wt %TiN. etween structure, residual stresses, mechanical prop- The residual stresses in each laver of the erties, and fracture behavior of complex particulate layered Si3N4/Si3N4-TiN based composites Si3 N4/Si3 N4-20%TiN, Si3 N4/Si3 N4-50%Tin, and Si3N4/Tin laminates, each sample having different numbers of layers and known layer thickness, were calculated using Equations I and 2 [19]. The joining temperature, used to determine the residual stresses. 2. Analysis of residual stresses was assumed to be 1200Crather than the hot pressing In this work, two-component brittle layered compos- temperature of 1800C. It was found that these ites with symmetric macrostructure are considered. The materials are sufficiently soft at the temperature above lyers consisting of different components alternate one 1200C to have a zero stress state due to ductile glassy after another, but the external layers consist of the same phases at the grain boundaries. Youngs moduli and omponent. Thus, the total number of layers N in such a CTE's of the components were calculated by the rule composite sample is odd. The layers of the first compo- of mixture and are presented in Table L Results of the nent including two extermal(top)layers are designated residual stress calculations are shown in Table II by index 10=1), and the layers of the second compo- nent(internal)are designated by index 2(=2). The number of layers designated by index I is(N+1)/2 and 3. Experimental the number of layers designated by index 2 is(N-1)/2. a-Si3N4(dso= l um) and Tin (dso=3 um)was used The layer of each component has some constant thick- formixture preparation Grinding of mixtures of certain ness,and the layers of same component have identical compositions was done in the ball mill for 5 h. After grinding, the plastification and rolling of thin tapes was There are effective residual stresses in the lay ayers of ach component in the layered ceramic composite dur- ing cooling the difference in deformation due to th TABLE I Youngs moduli and CTE of the components different thermal factors of the componen Composition CTE. 1/K is accommodated by creep as long as the temperature is high enough. Below a certain temperature, which Si3Na-5 wt% Y203-2 wt%320 3×10-6 called the"joining"temperature, the different com- A1,O 935×10-6 ponents become bonded together and internal stresses SigN4(5 wt%Y2 03 335.62 3.826×10-6 appear. In each layer, the total strain after sintering is 2 wt%Al203)-20 wt. the sum of an elastic component and a thermal com ponent [18]. In the case of a perfectly rigid bondin Si3N4(5wt%Y2O3-2w%364.93 5378×10-6 the residual stresses in the layers of a two-component AlO3)-50 wt%TIN 5444laminated ceramics [8]. There have also been a number of experimental studies of laminated ceramics that were conducted using these models, attempting to maximize the mechanical properties. Silicon nitride is the most promising and well￾developed ceramics for structural application because of its outstanding mechanical properties as well as its superior wear resistance [9]. The addition of TiN to Si3N4 leads to an increase of Young’s modulus, electri￾cal conductivity, and CTE of Si3N4 ceramics [10]. By varying the amount of TiN in silicon nitride ceramics, we can increase the CTE/Young’s modulus mismatch and develop composites with compressive and tensile stresses in alternative layers. This may further improve the mechanical properties of laminates [11–13]. β- Si3N4 belongs to the space group C2 6h (P63/m) and the irreducible representation for the optical phonons has been reported [14–17] optic = 4Ag + 2Au + 3Bg + 4Bu + 2E1g + 5E2g + 4E1u + 2E2u where Ag, E1g and E2g modes are Raman active and Au and E1u are infrared active. Raman and infrared active bands are mutually excluded since the crystal structure has a center of symmetry. The goal of this work is to study the interrelation between structure, residual stresses, mechanical prop￾erties, and fracture behavior of complex particulate￾layered Si3N4/Si3N4-TiN based composites. 2. Analysis of residual stresses In this work, two-component brittle layered compos￾ites with symmetric macrostructure are considered. The layers consisting of different components alternate one after another, but the external layers consist of the same component. Thus, the total number of layers N in such a composite sample is odd. The layers of the first compo￾nent including two external (top) layers are designated by index 1 (j = 1), and the layers of the second compo￾nent (internal) are designated by index 2 (j = 2). The number of layers designated by index 1 is (N+1)/2 and the number of layers designated by index 2 is (N−1)/2 . The layer of each component has some constant thick￾ness, and the layers of same component have identical thickness. There are effective residual stresses in the layers of each component in the layered ceramic composite. Dur￾ing cooling, the difference in deformation due to the different thermal expansion factors of the components is accommodated by creep as long as the temperature is high enough. Below a certain temperature, which is called the “joining” temperature, the different com￾ponents become bonded together and internal stresses appear. In each layer, the total strain after sintering is the sum of an elastic component and a thermal com￾ponent [18]. In the case of a perfectly rigid bonding, the residual stresses in the layers of a two-component material are [19]: σr1 = E 1E 2 f2(αT 2 − αT 1)T E 1 f1 + E 2 f2 (1) and σr2 = E 2E 1 f1(αT 1 − αT 2)T E 1 f1 + E 2 f2 (2) where Ej = Ej/(1 − νj), f1 = (N+1)l1 2h , f2 = (N−1)l2 2h , Ej and Vj is the elastic modulus and Poisson’s ratio of j-th component respectively, l1 and l2 are the thickness of layers for the first and second component, αT1 and αT2 are the thermal expansion coefficients (CTE) of the first and second components respectively, T is the difference between the joining temperature and the current temperature, and h is the total thickness of the specimen. The choice of composition for Si3N4-based ceramic laminates is dependent on the coefficient of thermal expansion and Young’s modulus of the compounds. Four compositions of composite layers were used: 1. Si3N4-5 wt.% Y2O3-2 wt.% Al2O3; 2. TiN; 3. Si3N4 (5 wt.%Y2O3-2 wt.%Al2O3)-20 wt.%TiN; 4. Si3N4 (5 wt.% Y2O3-2 wt.% Al2O3)-50 wt.%TiN. The residual stresses in each layer of the Si3N4/Si3N4-20%TiN, Si3N4/Si3N4-50%TiN, and Si3N4/TiN laminates, each sample having different numbers of layers and known layer thickness, were calculated using Equations 1 and 2 [19]. The joining temperature, used to determine the residual stresses, was assumed to be 1200 ◦C rather than the hot pressing temperature of 1800 ◦C. It was found that these materials are sufficiently soft at the temperature above 1200 ◦C to have a zero stress state due to ductile glassy phases at the grain boundaries. Young’s moduli and CTE’s of the components were calculated by the rule of mixture and are presented in Table I. Results of the residual stress calculations are shown in Table II. 3. Experimental α-Si3N4 (d50 = 1 µm) and TiN (d50 = 3 µm) was used for mixture preparation. Grinding of mixtures of certain compositions was done in the ball mill for 5 h. After grinding, the plastification and rolling of thin tapes was T AB L E I Young’s moduli and CTE of the components Composition E, GPa CTE, 1/K Si3N4-5 wt.% Y2O3-2 wt.% Al2O3 320 3 × 10−6 TiN 440 9.35 × 10−6 Si3N4(5 wt.% Y2O3- 2 wt.%Al2O3)-20 wt.% TiN 335.62 3.826 × 10−6 Si3N4(5 wt.% Y2O3-2 wt.% Al2O3)-50 wt.%TiN 364.93 5.378 × 10−6 5444