0. Zan et al. Ceramics International 30(2004)441-446 mIcs can be interpreted in terms of the effect of layer number(N)of a specimen with fixed thickness(3 mm). strength decreases with the layer number increasing. But the extent of decrease is very small(no more than 100 MPa), and with the layer number exceeding more than about 30, the curve tends to level off. For work of frac- Fig. 5. The illustration of the flexure test ture of the multilayer materials, a maximum is observed atN≈30 Similar to the analysis of the effect of thickness ratio width and span of the specimen are H, B and 2L in four on mechanical properties, the results above are also point bending, respectively. And some hypotheses are easily understood. Because the thickness of specimen is described as follows: (a) H/L<0. 2;(b) The ratio of fixed, the increase of layer number means the thickne flexibility [w(x)]and the curvature radius [p(x)] is far less decrease of both matrix-layer and interlayer. Obviously, than 1, i.e. w(x)lp(x)<<l;(c)h<<h2 this will reduce the strength of the materials. It is well The number of the matrix-layer (m) is odd, i.e known that work of fracture is determined by both dis- m= 2n-1, then H=mh-hy. Hence, the maximum ten tance and times of crack deflection [3]. With an increase sile stress and the maximum shear stress can be expres of layer number, the thickness of interlayers is deduced, sed a nd the following crack deflection distance is reduced At the same time. the crack deflection times are (mh-h) increased obviously because of the interlayer number is increasing. These two factors influence the work of fracture together, and will lead to an optimal value in various numbers of layers, which was determined to be about 30 in this experiment where M is the bending moment in the segment with the stress of pure bending, 2 is the equivalent bending 4. Analysis and Discussions rigidity, O is the shear stress, and S-max is the maximum equivalent static moment 4.1. Mechanical model of the Si3N4/ BN multilayer materials in bendt H/2 WB1 In order to simplify the calculation process, a for point bending test is used to analyze the stress of the multilayer ceramics, which is illustrated in Fig. 5. The BEc)ydy cimen possessed the following parameters: layer hickness(h1, h2), Youngs modulus(E, e2), and Pois- sons ratio(u1, U2), and the total thickness of a couple of matrix-layer and interlayer h=h1+hz. Total thickness, Sz.max= E(v)ydA EB E2-E1 (m2-1) 4.2. Bending strength analysis In the flexural test with the crosshead speed of 0 mm/min, the specimen will fracture by way of shear lapse or bending lapse due to the maximum shear stress (Tmax)or the m tensile stress(omax), respectively. The latter is more familiar to the Si3 N4/BN multilayer ceramics, when the expression below is satisfied: Fig 4. Bending strength and work of fractmics can be interpreted in terms of the effect of layer number (N) of a specimen with fixed thickness (3 mm). According to Fig. 4, it is found that the bending strength decreases with the layer number increasing. But the extent of decrease is very small (no more than 100 MPa), and with the layer number exceeding more than about 30, the curve tends to level off. For work of frac￾ture of the multilayer materials, a maximum is observed at N
30. Similar to the analysis of the effect of thickness ratio on mechanical properties, the results above are also easily understood. Because the thickness of specimen is fixed, the increase of layer number means the thickness decrease of both matrix-layer and interlayer. Obviously, this will reduce the strength of the materials. It is well known that work of fracture is determined by both dis￾tance and times of crack deflection [3]. With an increase of layer number, the thickness of interlayers is deduced, and the following crack deflection distance is reduced. At the same time, the crack deflection times are increased obviously because of the interlayer number is increasing. These two factors influence the work of fracture together, and will lead to an optimal value in various numbers of layers, which was determined to be about 30 in this experiment. 4. Analysis and Discussions 4.1. Mechanical model of the Si3N4/BN multilayer materials in bending In order to simplify the calculation process, a four￾point bending test is used to analyze the stress of the multilayer ceramics, which is illustrated in Fig. 5. The specimen possessed the following parameters: layer thickness (h1, h2), Young’s modulus (E1, E2), and Pois￾son’s ratio (
1,
2), and the total thickness of a couple of matrix-layer and interlayer h=h1+h2. Total thickness, width and span of the specimen are H, B and 2L in four￾point bending, respectively. And some hypotheses are described as follows: (a) H/2L40.2; (b) The ratio of flexibility [w(x)] and the curvature radius [(x)] is far less than 1, i.e. w(x)/(x)< <1; (c) h1< <h2. The number of the matrix-layer (m) is odd, i.e. m=2n1, then H=mhh1. Hence, the maximum ten￾sile stress and the maximum shear stress can be expres￾sed as: max ¼ E2M 2S ð Þ mh  h1 ð1Þ max ¼ Q BS SZ;max ð2Þ where M is the bending moment in the segment with the stress of pure bending,  is the equivalent bending rigidity, Q is the shear stress, and Sz,max is the maximum equivalent static moment: M ¼ ðH=2 H=2 WBy2 dy ð3Þ S ¼ ðH=2 H=2 BE yð Þy2 dy ð4Þ SZ;max ¼ ð A E yð ÞydA ¼ E2B 8 H2  h2 2  E2  E1 8 Bhh1 m2  1 ð5Þ 4.2. Bending strength analysis In the flexural test with the crosshead speed of 0.5 mm/min, the specimen will fracture by way of shear lapse or bending lapse due to the maximum shear stress (max) or the maximum tensile stress (max), respectively. The latter is more familiar to the Si3N4/BN multilayer ceramics, when the expression below is satisfied: max max 5 b i ð6Þ Fig. 4. Bending strength and work of fracture with a various number of layers (- - - bending strength; ––– work of fracture). Fig. 5. The illustration of the flexure test. 444 Q. Zan et al. / Ceramics International 30 (2004) 441–446