O.N. Grigoriev et aL./Composites: Part B 37(2006)530-541 Table 4 Compositions and strength of laminated composites based on SiCUPos powders Bending strength(SD MPa) Fluctuation factor (%) = +42%B4C UFo5+12% TiB2+5% BC a-SiCUFO5+12% TiB 2+5% BC (1)a-SiCu05+10%B4C 397(19) (2)a-SiCUFO5+12% TiB2+5% BC 5 shown in Fig. 8, where the curve obtained by calculation of a corresponding to the portion of the F-w curve up to a loading multilayer beam with the initial moduli is superimposed on the level of F=50 N is presented in Fig. 9, by approximating the experimental F-w diagram. At a loading level of F=50N, equation of the diagram which corresponds to the first significant step on the diagram The obtained Eeff values give no way of determining real (this step is assumed to characterize the initial structural stress distributions across the thickness of the specimen changes of the composite), the deflection w by linear approach accounting for the elastic moduli of the layers would be equal to wc=4.941 um at an experimental value We=7.850 um, i.e. we/w=1.588. The calculated stress in the upper layer (Fig. 1b)is 0.=85.3 MPa. Since experimental 3.3.3. Stress-strain curves for the materials of the layers strains and corresponding stresses were not determined In connection with the above, the object of the second stage because of technical reasons, they should be estimated is to plot a-E curves for each layer of the material. This process theoretically from nonlinear specimen deformation patterns can be divided into two sub stages. First, several assumptions for the behavior of the specimen upon loading(change of physicomechanical and geometrical characteristics, longitudi 3.3.2. Plotting of the nonlinear a-E curve for a quasi nal strain distribution patterns across the thickness of the cross- homogeneous specimen section, etc )are introduced; thus the first approximation a-E At the first stage of theoretical investigations, the effective diagrams for each layer may be plotted. Second, the stress- a-e curve for the composite specimen as some quasi- strain state of th e laminated spec is determined from the homogeneous material should be plotted. From this curve, obtained a-E diagrams for successive loading points.Then the known relations of applied mechanics, for determining the accordance with experimental data, and the stress-strain state is determined points of the beam [22], the effective elastic modulus is found To plot a-E curves for each layer, let us following E (1) 1. The ratio EB/EA=m is maintained in each loading point up where l is the length of the specimen, 1=0.04 m, and In2 is the to the largest experimental value of F=50N distance between the support points, 12=0.02 m If experimental deflections we that correspond to certain loading levels are taken as w and the cross-section is considered to be uniform. with the moment of inertia I= bh/12, we obtain the final equation for the effective elastic modulus (secant modulus) (2) where b is the width of the specimen, b=6.21 m, and h is the thickness of the specimen, h=3. 1X10m From this equation, moduli values summarized in Table 5 are calculated. Let us determine the bending moment and maximum stresses M/W=3F/2bh in each loading point with account of the corresponding effective elastic Deflection w,um noduli. As a result, strains Emax=0max/Ey are obtained. This Fig 8 Experimental load F--deflection w curve()and curve derived from data is also summarized in Table 5, and the a-e diagram initial elastic moduli (2).shown in Fig. 8, where the curve obtained by calculation of a multilayer beam with the initial moduli is superimposed on the experimental F–w diagram. At a loading level of FZ50 N, which corresponds to the first significant step on the diagram (this step is assumed to characterize the initial structural changes of the composite), the deflection w by linear approach would be equal to wcZ4.941 mm at an experimental value weZ7.850 mm, i.e. we/wcZ1.588. The calculated stress in the upper layer (Fig. 1b) is scZ85.3 MPa. Since experimental strains and corresponding stresses were not determined because of technical reasons, they should be estimated theoretically from nonlinear specimen deformation patterns. 3.3.2. Plotting of the nonlinear s–3 curve for a quasi￾homogeneous specimen At the first stage of theoretical investigations, the effective s–3 curve for the composite specimen as some quasi￾homogeneous material should be plotted. From this curve, effective elastic moduli can be obtained. In accordance with known relations of applied mechanics, for determining the deflection in the middle of the span relative to the support points of the beam [22], the effective elastic modulus is found wmax Z Fl3 128Ey3 I 0Ey3 Z Fl3 128wmaxI ; (1) where l is the length of the specimen, lZ0.04 m, and l/2 is the distance between the support points, l/2Z0.02 m. If experimental deflections we that correspond to certain loading levels are taken as wmax and the cross-section is considered to be uniform, with the moment of inertia IZ bh3 /12, we obtain the final equation for the effective elastic modulus (secant modulus) Ey3 Z 3Fl3 32webh3 (2) where b is the width of the specimen, bZ6.21!10K3 m, and h is the thickness of the specimen, hZ3.1!10K3 m. From this equation, moduli values summarized in Table 5 are calculated. Let us determine the bending moment and maximum stresses smaxZM=WZ3Fl=2bh2 in each loading point with account of the corresponding effective elastic moduli. As a result, strains 3maxZsmax=Ey3 are obtained. This data is also summarized in Table 5, and the s–3 diagram corresponding to the portion of the F–w curve up to a loading level of FZ50 N is presented in Fig. 9, by approximating the equation of the diagram. The obtained Eeff values give no way of determining real stress distributions across the thickness of the specimen accounting for the elastic moduli of the layers. 3.3.3. Stress–strain curves for the materials of the layers In connection with the above, the object of the second stage is to plot s–3 curves for each layer of the material. This process can be divided into two sub stages. First, several assumptions for the behavior of the specimen upon loading (change of physicomechanical and geometrical characteristics, longitudi￾nal strain distribution patterns across the thickness of the cross￾section, etc.) are introduced; thus the first approximation s–3 diagrams for each layer may be plotted. Second, the stress– strain state of the laminated specimen is determined from the obtained s–3 diagrams for successive loading points. Then the initial diagrams are corrected by several iterations in accordance with experimental data, and the stress–strain state is determined. To plot s–3 curves for each layer, let us assume the following: 1. The ratio EB/EAZm is maintained in each loading point up to the largest experimental value of FZ50 N. Table 4 Compositions and strength of laminated composites based on SiCUF05 powders No. Compositions of layers (vol%) Bending strength (SD MPa) Fluctuation factor (%) 1 (1) a-SiCUF05 65(13) 20 (2) TiB2C42% B4C 2 (1) a-SiCUF05C12% TiB2C5% B4C 61(6) 10 (2) TiB2C42% B4C 3 b-SiC 314(20) 6 a-SiCUF05C12% TiB2C5% B4C 4 (1) a-SiCUF05C10% B4C 397(19) (2) a-SiCUF05C12% TiB2C5% B4C 5 Fig. 8. Experimental load F—deflection w curve (1) and curve derived from initial elastic moduli (2). O.N. Grigoriev et al. / Composites: Part B 37 (2006) 530–541 537