O.N. Grigoriev et al./Composites: Part B 37(2006)530-541 删斗 多缓汤0 多多 b多多 Fig. 1. Bending configuration(a)and structure of the cross-section of the specimen(b)(sizes in mm) Simultaneous introduction of 5% BC and 12% TiB, results in should follow from the Eshelby model. There are the edge an increase of strength up to 408 MPa(Table 2)and up to effects of redistribution of stresses, inhomogeneity of a stress 650 MPa at TiB 2 content of 20-25%0 The ceramics TiB2-B4C distribution across the thickness of layers. In particular, the has the strength of 415 MPa with a grain size of 5-10 um and extensive zone with tension stresses directed perpendicular to practically no porosity. The results of a detailed study of the the layers plane(ou>0) which are located near the edges. structure and mechanical behavior of Sic-TiB2-B4C ceramic Within this zone the delamination may occur. Moreover, system are presented in [9-10 various types of fracture and microcracking in composites may take place under the joint effect of both thermal and applied 3. 2. Laminated composites stresses Usually we know the parameters of materials for stress 3.2.1. Distribution of the internal stresses calculation with insufficient accuracy and calculated results At the first stage of work we studied the layered composites have only a qualitative nature. There is the need for with the maximum thermal expansion misfit between layers. experimental measurement of the stress fields in layered These systems have the highest probability of uncontrollable composites. Traditionally the tasks of the stress-strain fracture under the influence of thermal stresses measurements are performed by the diffraction methods, and In the temperature range 20-1500C the effective coeffi- first by XRD. These methods are well developed and universal cients of thermal expansion are 5.8 and 8.9/C for Sic in many cases. However, they usually require long measure- and TiB2, respectively, [25]. Within the framework of Eshelby ments and have other problems caused by the low intensity of model, there are the average stresses in a plane of layers [ 22I= X-ray peak lo331=1.4 GPa, tension of TiB2 and compression of Sic Also there is a problem of internal stress determination in According to accepted orientation of axes, the components microcrystals or between layers in layered composites, when 022 and 033 of principal stresses are in a plane of layers, the thickness of alternating layers is made from several microns whereas the au- component is perpendicular to the plane of up to 100s of microns. Therefore search and development of layers. As one can see, for TiB2-SiC laminates calculated alternative methods for determination of internal stresses is residual thermal stresses exceed a possible level of strength and should result in fracture. In practice, the level of thermal Table 2 stresses will be lower as a result of the viscoelastic relaxation Compositions and mechan due to the segregation of impurities on layer's boundaries, reinforced composites cal properties of monolithic ceramics and particles especially in composites based on the a-SiC powders, and also due to presence of the phase(B4C) with intermediate No. Composition of coefficient of thermal expansion (a=6.05X10/C in the ceramics(vol o) (SD, MPa) factor(%) temperature range of 20-1000C [251). l10(5 Finite element methods give more accurate estimation of 3 thermal stresses and the character of their distribution 26. The 4 M5+10%B4C calculations of the residual stresses in this work were done for 5 a- Siculo5+10%BC306(56 five-layer ABCBA symmetric configuration, where A-C are 6 a-SICUFO5+12% layers of ceramics: SiC, SiC +20% TiB2 and TiB2, respect- TiB, +5% B C TiB2+42% BC 415(53) ively(Fig. 2). The stress distribution is more complex, so itSimultaneous introduction of 5% B4C and 12% TiB2 results in an increase of strength up to 408 MPa (Table 2) and up to 650 MPa at TiB2 content of 20–25%. The ceramics TiB2–B4C has the strength of 415 MPa with a grain size of 5–10 mm and practically no porosity. The results of a detailed study of the structure and mechanical behavior of SiC–TiB2–B4C ceramic system are presented in [9–10]. 3.2. Laminated composites 3.2.1. Distribution of the internal stresses At the first stage of work we studied the layered composites with the maximum thermal expansion misfit between layers. These systems have the highest probability of uncontrollable fracture under the influence of thermal stresses. In the temperature range 20–1500 8C the effective coeffi- cients of thermal expansion are 5.8 and 8.9!10K6 /8C for SiC and TiB2, respectively, [25]. Within the framework of Eshelby model, there are the average stresses in a plane of layers js22jZ js33jy1.4 GPa, tension of TiB2 and compression of SiC. According to accepted orientation of axes, the components s22 and s33 of principal stresses are in a plane of layers, whereas the s11-component is perpendicular to the plane of layers. As one can see, for TiB2–SiC laminates calculated residual thermal stresses exceed a possible level of strength and should result in fracture. In practice, the level of thermal stresses will be lower as a result of the viscoelastic relaxation due to the segregation of impurities on layer’s boundaries, especially in composites based on the a-SiC powders, and also due to presence of the phase (B4C) with intermediate coefficient of thermal expansion (aZ6.05!10K6 /8C in the temperature range of 20–1000 8C [25]). Finite element methods give more accurate estimation of thermal stresses and the character of their distribution [26]. The calculations of the residual stresses in this work were done for five-layer ABCBA symmetric configuration, where A–C are layers of ceramics: SiC, SiCC20% TiB2 and TiB2, respect￾ively (Fig. 2). The stress distribution is more complex, so it should follow from the Eshelby model. There are the edge effects of redistribution of stresses, inhomogeneity of a stress distribution across the thickness of layers. In particular, the extensive zone with tension stresses directed perpendicular to the layers plane (s11O0) which are located near the edges. Within this zone the delamination may occur. Moreover, various types of fracture and microcracking in composites may take place under the joint effect of both thermal and applied stresses. Usually we know the parameters of materials for stress calculation with insufficient accuracy and calculated results have only a qualitative nature. There is the need for experimental measurement of the stress fields in layered composites. Traditionally the tasks of the stress–strain measurements are performed by the diffraction methods, and first by XRD. These methods are well developed and universal in many cases. However, they usually require long measure￾ments and have other problems caused by the low intensity of X-ray peaks. Also there is a problem of internal stress determination in microcrystals or between layers in layered composites, when the thickness of alternating layers is made from several microns up to 100s of microns. Therefore search and development of alternative methods for determination of internal stresses is Fig. 1. Bending configuration (a) and structure of the cross-section of the specimen (b) (sizes in mm). Table 2 Compositions and mechanical properties of monolithic ceramics and particles reinforced composites No. Composition of ceramics (vol%) Bending strength (SD, MPa) Fluctuation factor (%) 1 b-SiC 190(40) 21 2 a-SiCM5 110(57) 52 3 a-SiCUF05 170(48) 28 4 a-SiCM5C10% B4C 372(71) 19 5 a-SiCUF05C10% B4C 306(56) 18 6 a-SiCUF05C12% TiB2C5% B4C 408(64) 17 7 TiB2C42% B4C 415(53) 13 532 O.N. Grigoriev et al. / Composites: Part B 37 (2006) 530–541