Lugory et al. Acta Materialia 53(2005)289-296 Table I Geometrical characteristics of Si3 N/Si,N 30 wt% TiN layered materials Layer imens of type 2 Composition Layer thickness Residual stress tion Layer thickness Residual stress MPa) 752 Si3Na30 wt%TIN 852 30 wt% TiN 618 l86 142 23456789 l81 -225.7 sssss Si3Na30 wt%TIN 6l1 Si3Na-30 wt% TIN 1844 145 -227.3 Si3Na30 wt%TIN 6l1 Si3Na-30 wt% TIN 626 182.7 143 -228.8 Si3Na30 wt%TIN 616 47.1 Si3Na-30 wt% TIN 620 14 230.9 Si3Na-30 wt% TiN 733 Thickness(um) 45 4000 The average residual stress in layer. phere at a pressure of 10 Pa to avoid oxidation and disso- toughness Klc calculations because of a significant sim- ciation of the materials. An analysis of the macrostructure plification of the procedure. The most appropriate coor of the specimens was made with an optical microscope. dinate origin is on the tensile surface of the sample 3. Measurements of the CTes, the Ei and the ke of monolithic ceramics The values of the thermal expansion coefficient B of the si3 N4 and Si3Na-30 wt% TiN monolithic ceramics a function of temperature are presented in Fig. 2. The CTEs of both compositions are a linear function of the temperature, and the Cte of the Si3N4-30 wt% TiN is higher than the Cte of the Si,N4 over all investi- gated temperature ranges. The temperature dependence B [K be asB×10° 101+3.62797×10-3 T and B×10°=1.979406+302463 x 10-'Tfor the Si3N4 and the Si3 N4-30 wt%TiN, respec tively. The accuracy of such measurements is about 15%. Surface under tension Si3N4-30 TiN monolithic samples were measured to be 308 and (b) 323 GPa, respectively. Mean values of the intrinsic frac x ture toughness of monolith materials, measured by SEVNB, are approximately the same for both the Si3N4 and the Si3 N4- 30 wt% TiN compositions, about 4+ 1 MPa m".These measured values of CTEs, E and K(o were used in all calculations 4. Calculation of the apparent fracture toughness A weight function analysis has been used to estimate the apparent fracture toughness in laminates with resid- ual stresses [3, 13, 17, 18]. A schematic presentation of a two-componen Fig. 1(a), where ti is the thickness of a ith layer, w is Surface under tension the total thickness of the specimen, b is the width, and Fig 1. Scheme of a two-component multilayer specimen: (a)n Nis the total number of layers. The choice of coordinate of layers and layer boundary coordinates: (b) an analyzed system is of great importance to the apparent fracture location in a layered samplephere at a pressure of 10 Pa to avoid oxidation and disso￾ciation of the materials. An analysis of the macrostructure of the specimens was made with an optical microscope. 3. Measurements of the CTEs, the Ei and the K1c (i) of monolithic ceramics The values of the thermal expansion coefficient b of the Si3N4 and Si3N4–30 wt% TiN monolithic ceramics as a function of temperature are presented in Fig. 2. The CTEs of both compositions are a linear function of the temperature, and the CTE of the Si3N4–30 wt% TiN is higher than the CTE of the Si3N4 over all investi￾gated temperature ranges. The temperature dependence of b [K1 ] can be presented as b · 106 = 1.09274 · 101 + 3.62797 · 103 T and b · 106 = 1.979406 + 3.02463 · 103 T for the Si3N4 and the Si3N4–30 wt% TiN, respec￾tively. The accuracy of such measurements is about 15%. Young
s moduli of the Si3N4 and the Si3N4–30 wt% TiN monolithic samples were measured to be 308 and 323 GPa, respectively. Mean values of the intrinsic frac￾ture toughness of monolith materials, measured by SEVNB, are approximately the same for both the Si3N4 and the Si3N4–30 wt% TiN compositions, about 4 ± 1 MPa m1/2. These measured values of CTEs, Ei and KðiÞ 1c were used in all calculations. 4. Calculation of the apparent fracture toughness A weight function analysis has been used to estimate the apparent fracture toughness in laminates with resid￾ual stresses [3,13,17,18]. A schematic presentation of a two-component multilayered sample is shown in Fig. 1(a), where ti is the thickness of a ith layer, w is the total thickness of the specimen, b is the width, and N is the total number of layers. The choice of coordinate system is of great importance to the apparent fracture toughness K1c calculations because of a significant sim￾plification of the procedure. The most appropriate coor￾dinate origin is on the tensile surface of the sample Fig. 1. Scheme of a two-component multilayer specimen: (a) numbers of layers and layer boundary coordinates; (b) an analyzed crack location in a layered sample. Table 1 Geometrical characteristics of Si3N4/Si3N4–30 wt% TiN layered materials Layer # Specimens of type 1 Specimens of type 2 Composition Layer thickness (lm) Residual stress (MPa)a Composition Layer thickness (lm) Residual stress (MPa)a 1 Si3N4 752 223.6 Si3N4–30 wt% TiN 852 42.3 2 Si3N4–30 wt% TiN 618 186 Si3N4 142 274 3 Si3N4 181 225.7 Si3N4–30 wt% TiN 611 44.1 4 Si3N4–30 wt% TiN 625 184.4 Si3N4 145 272.5 5 Si3N4 176 227.3 Si3N4–30 wt% TiN 611 45.6 6 Si3N4–30 wt% TiN 626 182.7 Si3N4 143 271.1 7 Si3N4 176 228.8 Si3N4–30 wt% TiN 616 47.1 8 Si3N4–30 wt% TiN 620 181.1 Si3N4 143 269.6 9 Si3N4 726 230.9 Si3N4–30 wt% TiN 733 48.7 Thickness (lm) 4500 4000 a The average residual stress in layer. M. Lugovy et al. / Acta Materialia 53 (2005) 289–296 291