《复合材料 Composites》课程教学资源（学习资料）第五章陶瓷基复合材料_mechanism.pdf_大学文库

Acta Mechanica Solida Sinica. Vol. 20. No. 2. June 2007 ISSN08949166 Published by AMSS Press, Wuhan, China. DOI: 10.1007/ s10338-007-0717-x FRACTURAL PROCESS AND TOUGHENING MECHANISM OF LAMINATED CERAMIC COMPOSITES *x Zhang Yafang Faculty of Civil Engineering, Guangzhou University, Guangzhou 510006, China) Tang Chun'an2,3 Zhang Yongbin Liang Zhenzao2 School of Civil and Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China) (Research Center for Numerical Test on Material Failure, Dalian University, Dalian 116622, China) Received 9 December 2006: revision received 13 June 2007 ABSTRACT Based on the model of multi-layer beam and the assumption of micro-inhomogeneity of material, the 3D fractural characteristics of laminated ceramic composites have been studie with numerical simulation. Under three-point bending load, crack initiation, coalescence, propa- gation, tuning off in the weak interface and final rupture have been simulated. The spatial distri- bution and evolution process of acoustic emission are also presented in the paper. The simulation verifies the primary mechanism of the weak interface inducing the crack to expand along there and absorbing the fractural energy. The disciplinary significance of the effect of strength and prop- erties of material on the toughness and strength of laminated ceramic composites is, therefore, discussed in this paper KEY WORDS laminated ceramic composite, toughening, numerical simulation I INTRODUCTION Ceramic composites are now widely applied in aeronautical and space engineering, metallurgy, civil engineering and automotive manufacturing due to the advantages such as high strength, high stiffness, good endurance of high temperature and corrosion, etc. However, the most critical obstructs on such applications is brittleness. How to strengthen and toughen the ceramic composite is a hot topic in recent Soft layers are combined with ceramic's brittle structure, so the laminated ceramic composites could be treated as a bionic structure, similar to that of shelves and bones in nature. Traditionally, the ap- proaches to improving toughness could be simply summarized as faults elimination. However, toughening mechanism of the laminated ce different and particular. Since Clegg et al. L published their work in Nature, many studies have been carried out in material preparation, fractural characteristics mechanical characteristics and toughening mechanism in this field(2-5 In these studies, some researchers, like Chang[6 and Guol7l tried to apply numerical methods to this field. Up to date, however, most of these studies were two-dimensional ones. If a three-dimensional CorrespondingauthorE-mail:zhangyafang2004@163.com unding by: S&T Project No. 2006B14601004 gong Province: S&T Project No. 62047, Educational Bureau, Guanzhou City and Fund of Natural Science, Guangdong Province(No. 05001885)

Published by AMSS Press, Wuhan, China. DOI: 10.1007/s10338-007-0717-x Acta Mechanica Solida Sinica, Vol. 20, No. 2, June, 2007 ISSN 0894-9166 FRACTURAL PROCESS AND TOUGHENING MECHANISM OF LAMINATED CERAMIC COMPOSITES Zhang Yafang1 ( 1Faculty of Civil Engineering, Guangzhou University, Guangzhou 510006, China) Tang Chun’an2,3 Zhang Yongbin3 Liang Zhenzao2 ( 2School of Civil and Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China) ( 3Research Center for Numerical Test on Material Failure, Dalian University, Dalian 116622, China) Received 9 December 2006; revision received 13 June 2007. ABSTRACT Based on the model of multi-layer beam and the assumption of micro-inhomogeneity of material, the 3D fractural characteristics of laminated ceramic composites have been studied with numerical simulation. Under three-point bending load, crack initiation, coalescence, propagation, tuning off in the weak interface and final rupture have been simulated. The spatial distribution and evolution process of acoustic emission are also presented in the paper. The simulation verifies the primary mechanism of the weak interface inducing the crack to expand along there and absorbing the fractural energy. The disciplinary significance of the effect of strength and properties of material on the toughness and strength of laminated ceramic composites is, therefore, discussed in this paper. KEY WORDS laminated ceramic composite, toughening, numerical simulation I. INTRODUCTION Ceramic composites are now widely applied in aeronautical and space engineering, metallurgy, civil engineering and automotive manufacturing due to the advantages such as high strength, high stiffness, good endurance of high temperature and corrosion, etc. However, the most critical obstructs on such applications is brittleness. How to strengthen and toughen the ceramic composite is a hot topic in recent years. Soft layers are combined with ceramic’s brittle structure, so the laminated ceramic composites could be treated as a bionic structure, similar to that of shelves and bones in nature. Traditionally, the approaches to improving toughness could be simply summarized as faults elimination. However, toughening mechanism of the laminated ceramic is different and particular. Since Clegg et al.[1] published their work in ‘Nature’, many studies have been carried out in material preparation, fractural characteristics, mechanical characteristics and toughening mechanism in this field[2–5]. In these studies, some researchers, like Chang[6] and Guo[7] tried to apply numerical methods to this field. Up to date, however, most of these studies were two-dimensional ones. If a three-dimensional Corresponding author. E-mail: zhangyafang2004@163.com Funding by: S&T Project No.2006B14601004, Guangdong Province; S&T Project No.62047, Educational Bureau, Guanzhou City and Fund of Natural Science, Guangdong Province (No.05001885).

ACTA MECHANICA SOLIDA SINICA model could be developed, the spatial distribution of crack initiation, coalescence, propagation, and thus a real fractural process in composite could be studied which is of great importance and significance for understanding of the mechanism of the fractural process and toughening of composite ceramics IL. NUMERICAL MODELING Solid material is always heterogeneous because of the presence of micro- weakness or fault in meso- scale. Thus the heterogeneity of material is essential to model verification. Compared to the traditional numerical method, where laminated composite ceramic is usually treated as homogeneous material by many researchers, great improvement has been made with a code named RFPA3D(3D Realistic Failure Process Analysis The ceramic matrix here is divided into cells of a hexahedron, and the heterogeneity of mechanical features is represented with a two parameters Weibull distribution. The probability distribution function can be described as follow f(a) e(ayao)m where a stands for mechanical characteristic parameters, such as Youngs modulus, strength, the P( sons ratio, etc. ao is the mean value of a, m is the shape factor of Weibull, defined as the homogeneity index of material The choice of a proper fracture criterion is crucial to cracking simulation. A Coulomb criterion[ 8 envelope with a tensile cut-off is adopted in this paper for brittle materials. The tensile failure will occur when the principal stress in an element is greater than its tensile strength, see formula(2). Meanwhile to simulate the shear failure. the second valve criterion as formula (3) is also used 01≥ 1+sin o > where o is the frictional angle, o1 and o3 are the maximum and minimum principal stresses, respectively, ot and c are the uniaxial tensile and compression strength of an element, respectively. After a displacement vector is applied to the model, stress and deformation in each element are then computed. When the fracture criterion is met in an element, the element is considered to be weak or failed. The failed element has been applied a very low elastic modulus instead of being removed from the mesh. The stress and the deformation distribution throughout the model are adjusted instantaneously after each element ruptures in an equilibrium state. In the areas with increased stress due to stress redistribution, the stress may exceed the critical value so that further ruptures will occur. The process would be repeated until no more elements exceed the fracture criterion under the same load. Then, the calculation would move to the next step by a small increment and the procedure can be repeated until the whole specimen fractures In this calculation, the stress and strain can be obtained by introducing a damage factor D E(1-D)E0 Fig. 1. Three-dimensional numerical model of laminated ceramic

· 142 · ACTA MECHANICA SOLIDA SINICA 2007 model could be developed, the spatial distribution of crack initiation, coalescence, propagation, and thus a real fractural process in composite could be studied, which is of great importance and significance for understanding of the mechanism of the fractural process and toughening of composite ceramics. II. NUMERICAL MODELING Solid material is always heterogeneous because of the presence of micro-weakness or fault in mesoscale. Thus the heterogeneity of material is essential to model verification. Compared to the traditional numerical method, where laminated composite ceramic is usually treated as homogeneous material by many researchers, great improvement has been made with a code named RFPA3D (3D Realistic Failure Process Analysis). The ceramic matrix here is divided into cells of a hexahedron, and the heterogeneity of mechanical features is represented with a two parameters Weibull distribution. The probability distribution function can be described as follows: f (α) = m α0 · α α0 m−1 · e−(α/α0)m (1) where α stands for mechanical characteristic parameters, such as Young’s modulus, strength, the Poisson’s ratio, etc. α0 is the mean value of α, m is the shape factor of Weibull, defined as the homogeneity index of material. The choice of a proper fracture criterion is crucial to cracking simulation. A Coulomb criterion[8] envelope with a tensile cut-off is adopted in this paper for brittle materials. The tensile failure will occur when the principal stress in an element is greater than its tensile strength, see formula (2). Meanwhile, to simulate the shear failure, the second valve criterion as formula (3) is also used. σ1 ≥ σt (2) and/or 1 + sin φ 1 − sin φσ1 − σ3 ≥ σc (3) where φ is the frictional angle, σ1 and σ3 are the maximum and minimum principal stresses, respectively, σt and σc are the uniaxial tensile and compression strength of an element, respectively. After a displacement vector is applied to the model, stress and deformation in each element are then computed. When the fracture criterion is met in an element, the element is considered to be weak or failed. The failed element has been applied a very low elastic modulus instead of being removed from the mesh. The stress and the deformation distribution throughout the model are adjusted instantaneously after each element ruptures in an equilibrium state. In the areas with increased stress due to stress redistribution, the stress may exceed the critical value so that further ruptures will occur. The process would be repeated until no more elements exceed the fracture criterion under the same load. Then, the calculation would move to the next step by a small increment and the procedure can be repeated until the whole specimen fractures. In this calculation, the stress and strain can be obtained by introducing a damage factor D. ε = σ E = σ (1 − D)E0 (4) Fig. 1. Three-dimensional numerical model of laminated ceramic.

yol. 20, No. 2 Zhang Yafang et al. Fractural Process and Toughening Mechanism of Composites where Eo and E are Young's moduli for the initial stage and damaged stage, respectively. For damage factor D, when no damage happens in the cell, D=0, and when the cell is completely damaged, D= l Corresponding to a given damage status, D is in the range of 0 and 1,i.e0<D<l The beam model under the three-point bending load adopted in this paper is presented in Fig. 1. An ideal interface is applied between the soft and the hard layers to ignore the effect of the real interface The beam with dimensions of0×250×30 mm comprises a total number of50×250×30=375000 cells. a notch with dimensions of 5x2x 30 mm is in the central bottom of the beam for each soft and hard layer, the ratios to the thickness, Young's modulus, and the strength are 1: 10, 1: 10 and 1: 8, respectively. This calculation was completed on a parallel computer system. IIL THE FRACTURAL PROCESS AND TOUGHENING MECHANISM The load-displacement curve of a laminated ce- ramic is presented in Fig. 2, comparing a curve of a block ceramic block. From the figure, the strength of the laminated ceramic is higher than that of the ceramic 2 200 block. Simultaneously, the fractural work increases 3150 122%. Here the fractural work K is defined as the area the load-displacement curve envelopes divided by the cross section of the beame. An explanation of such a phenomenon can be obtained from the failure 50100150200250300350400450500550 displacement(x1.0E-3 mm) process of the specimen, which will be discussed in the following text Fig 2 Load-displacement curves of laminated ceramic. For a ceramic block, when load is applied, the maximum tensile stress zone first appears near the tip of the notch. The micro cracks will initiate near this tip due to the stress concentration. with an increase in the load, the crack will coalesce in this area and propagate upwards until the upper boundary of the beam is reached. Figure 2 also shows that for the block the curve has only one peak point which illustrates that the fracture is a one-off event; and the development of the crack is rapid while the residual stress is small The fractural process of laminated ceramic specimen is presented in Fig 3 through the images of modulus and maximum principal stress From Fig 3(a), i.e. the modulus images, it can be found that the crack propagates upwards first and then deflects into the soft layer when the soft-hard interface is met. After that the crack develops horizontally within the soft layer. With the increase of the load, the crack turns back and develops vertically This procedure is repeated at each soft layer, so vertical and horizontal cracks appear alternately until the beam finally fractures As a result, the fracture is no longer a rapid process but a layer by layer one Moreover, from Fig 3(b), the maximum principal stress images, the crack appears first near the tip f the notch due to stress concentration. Then the main crack develops upwards. When the first soft layer is met, a 3D stress field is changed to a 2D field 1o, 11. A dummy plastic zone' appears near the tip of crack and a so-called passivation will release the stress concentration in this zone, as a result the vertical trend of the cracking is restrained and the crack develops horizontally. In this procedure, the soft layer acts as a shield After the crack traverses at a distance within the soft layer, some new vertical cracks appear with the increase of the load. As more energy is needed for this crack initiation, the strength of laminated ceramic is in general higher than that of the ceramic block. Figure 3 also illustrates that the crack is no longer a straight line but in a zigzag shape or a brick shape. This phenomenon is also observed in the description of a similar test by Guo[121. The conclusion drawn in this section is also in agreement ith the laboratory tests carried out by Cail13 and Tan(14 Images of acoustic emission(AE) for both block and laminated ceramic are presented in Fig 4,where a circle represents an AE event. The radius is directly proportional to the energy dissipated from the damaged cell. For the ceramic block, Fig 4(a) shows that most AE events are located in a narrow belt developing along the load direction, and almost no horizontal events present. This illustrates that cracks

Vol. 20, No. 2 Zhang Yafang et al.: Fractural Process and Toughening Mechanism of Composites · 143 · and/or σ = E0(1 − D)ε (5) where E0 and E are Young’s moduli for the initial stage and damaged stage, respectively. For damage factor D, when no damage happens in the cell, D = 0, and when the cell is completely damaged, D = 1. Corresponding to a given damage status, D is in the range of 0 and 1, i.e. 0 <D< 1. The beam model under the three-point bending load adopted in this paper is presented in Fig.1. An ideal interface is applied between the soft and the hard layers to ignore the effect of the real interface. The beam with dimensions of 50 × 250 × 30 mm comprises a total number of 50 × 250 × 30 = 375000 cells. A notch with dimensions of 5 × 2 × 30 mm is in the central bottom of the beam. For each soft and hard layer, the ratios to the thickness, Young’s modulus, and the strength are 1 : 10, 1 : 10 and 1 : 8, respectively. This calculation was completed on a parallel computer system. III. THE FRACTURAL PROCESS AND TOUGHENING MECHANISM The load-displacement curve of a laminated ceramic is presented in Fig.2, comparing a curve of a ceramic block. From the figure, the strength of the laminated ceramic is higher than that of the ceramic block. Simultaneously, the fractural work increases 122%. Here the fractural work K is defined as the area the load-displacement curve envelopes divided by the cross section of the beam[9]. An explanation of such a phenomenon can be obtained from the failure process of the specimen, which will be discussed in the following text. Fig. 2 Load-displacement curves of laminated ceramic. For a ceramic block, when load is applied, the maximum tensile stress zone first appears near the tip of the notch. The micro cracks will initiate near this tip due to the stress concentration. With an increase in the load, the crack will coalesce in this area and propagate upwards until the upper boundary of the beam is reached. Figure 2 also shows that for the block the curve has only one peak point which illustrates that the fracture is a one-off event; and the development of the crack is rapid while the residual stress is small. The fractural process of laminated ceramic specimen is presented in Fig.3 through the images of modulus and maximum principal stress. From Fig.3(a), i.e. the modulus images, it can be found that the crack propagates upwards first and then deflects into the soft layer when the soft-hard interface is met. After that the crack develops horizontally within the soft layer. With the increase of the load, the crack turns back and develops vertically again. This procedure is repeated at each soft layer, so vertical and horizontal cracks appear alternately until the beam finally fractures. As a result, the fracture is no longer a rapid process but a layer by layer one. Moreover, from Fig.3(b), the maximum principal stress images, the crack appears first near the tip of the notch due to stress concentration. Then the main crack develops upwards. When the first soft layer is met, a 3D stress field is changed to a 2D field[10, 11]. A ‘dummy plastic zone’ appears near the tip of crack and a so-called passivation will release the stress concentration in this zone, as a result the vertical trend of the cracking is restrained and the crack develops horizontally. In this procedure, the soft layer acts as a shield. After the crack traverses at a distance within the soft layer, some new vertical cracks appear with the increase of the load. As more energy is needed for this crack initiation, the strength of laminated ceramic is in general higher than that of the ceramic block. Figure 3 also illustrates that the crack is no longer a straight line but in a zigzag shape or a brick shape. This phenomenon is also observed in the description of a similar test by Guo[12]. The conclusion drawn in this section is also in agreement with the laboratory tests carried out by Cai[13] and Tan[14]. Images of acoustic emission (AE) for both block and laminated ceramic are presented in Fig.4, where a circle represents an AE event. The radius is directly proportional to the energy dissipated from the damaged cell. For the ceramic block, Fig.4(a) shows that most AE events are located in a narrow belt developing along the load direction, and almost no horizontal events present. This illustrates that cracks

20. No. 2 Zhang Yafang et al. Fractural Process and Toughening Mechanism of Composites acoustic emission step 40-0) acoustic emission step 46(0) (a)ceramic block structure (b)laminated composite ceramic Fig. 4. Numerical simulation of AE in laminated model IV. THE EFFECT OF STRENGTH OF SOFT LAYERS To investigate the effect of strength of soft layers using the same beam models presented in the previous section(Fig. 1), numerical simulation on a group of eight specimens with different strengths of the soft layer has been conducted. The strength ratios of soft layers to hard layers are set to be 0. 12, 0.16, 0.2, 0.24, 0.28, 0.32, 0.36 and 0.4 for each specimen, while other features remain unchange The results of the simulation are presented in Fig. 5, where the curves of fractural work K and th peak load versus strength ratio are plotted as Fig. 5(a) and 5(b), respectively. From these figures, it is clear that the fractural work K and the peak load P decrease while the strength of the soft layers increases In particular, when the strength ratio is in the range 0. 24-0.28, both K and P decrease rapidly This implies that if the strength of the soft layer is very high, the deflection and the softening of the crack tips can hardly happen. Meanwhile, if the strength of the soft layer is very low, it will not be advisable to improve the mechanical characteristics of the composite ceramic. In fact, a specimen with strength ratio of 0.08 is also tested, and it is found that all the fractures occur along the soft layer, so that no crack initiates or propagates vertical 3410 0080.120.160.200.240.280.320360.400.44 080.120.160200240.280.320.360.400.44 strength ratio of soft and hard layers strength ratio of soft and hard layers Fig. 5. Curves of fracture energy and peak load of the laminated models versus the strength of soft layer The explanation about this effect can be deduced from Fig. 6, where the fractural process is presented for each specimen. For the specimens No. 1 to 4 with relatively low strength soft layers, an obvious crack deflection can be observed. First the cracks initiate near the tip of the notch, and then propagate vertically along the load direction. Passivation on the crack tips happens when a soft layer is met and the crack deflects along the horizontal direction, i.e. along the soft layer. The lower the strength of the soft layer is, the longer distance the crack goes over horizontally and more energy is dissipated in the cracking process. On the other hand, for the specimens No 5 to 8 with relatively high strength soft layers, the cracks develop upwards quickly but over a shorter distance horizontally. Compared with the cases in previous specimens, less deflection happens and less energy is dissipated. So the toughening effect is not manifest and the laminated ceramic has nearly similar fractural work K as the ceramic block, i. e, no critical improvement has been made on the toughness of the ceramic. Based on the previous discussion, the strength of the soft layers is crucial to the attempt at improving the toughness of the laminated ceramic material. Only those soft layers of adequate strength can increase

Vol. 20, No. 2 Zhang Yafang et al.: Fractural Process and Toughening Mechanism of Composites · 145 · Fig. 4. Numerical simulation of AE in laminated model. IV. THE EFFECT OF STRENGTH OF SOFT LAYERS To investigate the effect of strength of soft layers using the same beam models presented in the previous section (Fig.1), numerical simulation on a group of eight specimens with different strengths of the soft layer has been conducted. The strength ratios of soft layers to hard layers are set to be 0.12, 0.16, 0.2, 0.24, 0.28, 0.32, 0.36 and 0.4 for each specimen, while other features remain unchanged. The results of the simulation are presented in Fig.5, where the curves of fractural work K and the peak load versus strength ratio are plotted as Fig.5(a) and 5(b), respectively. From these figures, it is clear that the fractural work K and the peak load P decrease while the strength of the soft layers increases. In particular, when the strength ratio is in the range 0.24-0.28, both K and P decrease rapidly. This implies that if the strength of the soft layer is very high, the deflection and the softening of the crack tips can hardly happen. Meanwhile, if the strength of the soft layer is very low, it will not be advisable to improve the mechanical characteristics of the composite ceramic. In fact, a specimen with strength ratio of 0.08 is also tested, and it is found that all the fractures occur along the soft layer, so that no crack initiates or propagates vertically. Fig. 5. Curves of fracture energy and peak load of the laminated models versus the strength of soft layer. The explanation about this effect can be deduced from Fig.6, where the fractural process is presented for each specimen. For the specimens No.1 to 4 with relatively low strength soft layers, an obvious crack deflection can be observed. First the cracks initiate near the tip of the notch, and then propagate vertically along the load direction. Passivation on the crack tips happens when a soft layer is met and the crack deflects along the horizontal direction, i.e. along the soft layer. The lower the strength of the soft layer is, the longer distance the crack goes over horizontally and more energy is dissipated in the cracking process. On the other hand, for the specimens No.5 to 8 with relatively high strength soft layers, the cracks develop upwards quickly but over a shorter distance horizontally. Compared with the cases in previous specimens, less deflection happens and less energy is dissipated. So the toughening effect is not manifest and the laminated ceramic has nearly similar fractural work K as the ceramic block, i.e., no critical improvement has been made on the toughness of the ceramic. Based on the previous discussion, the strength of the soft layers is crucial to the attempt at improving the toughness of the laminated ceramic material. Only those soft layers of adequate strength can increase

20. No. 2 Zhang Yafang et al. Fractural Process and Toughening Mechanism of Composites elastic modulus(MPa)step 86(0) acoustic emission step 86(0) elastic modulus(MPa)step 80(0) acoustic emission step 80(0) elastic modulus(MPa)step 90(0) acoustic emission step 90-(0 (a)modulus Fig 6 Curves of fracture energy and peak load of the laminated models versus the strength of soft layer. of crack propagation, the crack will change direction when a soft layer is met. After propagating in the soft layer a certain distance, the crack will turn back to the load direction again, where the distance is determined by the strength of the layer. With such a cyclic procedure, the fracture path is much longer toughness better than that of the brittle ceramic material anism. therefore, gives laminated ceramic a than that in a ceramic block. The energy dissipation mecha Furthermore, the effect of the strength of soft layers has been investigated in details. Extremely high and low strength of the soft layers is not good at improving the toughness of the laminated composite eramic. So, the strength of the soft layer should be designed propert Finally, as the fractural process and the location of cracks is difficult to be observed in laboratory tests, this simulation is helpful for further optimization to improve the characteristics of composite materials References [1 Clegg W.J., Kendall K, Alford N M, A simple way to make tough ceramics. Nature, 1990, 347(10):445-44 2] Portu G, Micele L, Pezzotti G, Laminated ceramic structures from oxide systems. Composites: Part B,2006,37:556-567 3 Pinho S.T., Robinson P, Iannucci L, Fracture toughness of the tensile and compressive fibers failure modes laminated composite. Composites Science and Technology, 2006, 66: 2069-2079 de Portu G. Micele L. Guicciardi S. etc.. Effect of residual stresses on the fracture behavior of notched laminated composites loaded in flexural geometry. Composites Science and Technology, 2005, 65: 1501-1506 5 Yuan Xu-xuan, Jia De-chang, Study on fracture behavior of BN-SiC laminated composite ceramics. Material Science E Technologg, 2005, 13(4): 378-380 [6 Chang X, Tang, C.A. and Zhang, H.Q. Numerical Simulation on Toughening Mechanism of Laminated Composite Ceramic. J Inorganic Materials, 2005, 20(2): 459-464 7 Guo X.H., Hu L and Cai Q.H., Numerical Simulation and Laboratory Test on Toughening of Ceramic Nappe. J. Chinese Ceramic Society, 2000, 28(3): 234-239 [8 Tang C.A., Wang S.H. and Fu Y.F., Numerical Test on Rock Failure Process. Beijing: Sci. Tech. Publisher, 2003:42-43

Vol. 20, No. 2 Zhang Yafang et al.: Fractural Process and Toughening Mechanism of Composites · 147 · Fig. 6. Curves of fracture energy and peak load of the laminated models versus the strength of soft layer. of crack propagation, the crack will change direction when a soft layer is met. After propagating in the soft layer a certain distance, the crack will turn back to the load direction again, where the distance is determined by the strength of the layer. With such a cyclic procedure, the fracture path is much longer than that in a ceramic block. The energy dissipation mechanism, therefore, gives laminated ceramic a toughness better than that of the brittle ceramic material. Furthermore, the effect of the strength of soft layers has been investigated in details. Extremely high and low strength of the soft layers is not good at improving the toughness of the laminated composite ceramic. So, the strength of the soft layer should be designed property. Finally, as the fractural process and the location of cracks is difficult to be observed in laboratory tests, this simulation is helpful for further optimization to improve the characteristics of composite materials. References [1] Clegg W.J., Kendall K., Alford N.M., A simple way to make tough ceramics. Nature, 1990, 347(10): 445-447. [2] de Portu G., Micele L., Pezzotti G., Laminated ceramic structures from oxide systems. Composites: Part B, 2006, 37: 556-567. [3] Pinho S.T., Robinson P., Iannucci L., Fracture toughness of the tensile and compressive fibers failure modes in laminated composite. Composites Science and Technology, 2006, 66: 2069-2079. [4] de Portu G., Micele L., Guicciardi S., etc., Effect of residual stresses on the fracture behavior of notched laminated composites loaded in flexural geometry. Composites Science and Technology, 2005, 65: 1501-1506. [5] Yuan Xu-xuan, Jia De-chang, Study on fracture behavior of BN-SiC laminated composite ceramics. Material Science & Technology, 2005, 13(4): 378-380. [6] Chang X., Tang, C.A. and Zhang, H.Q.. Numerical Simulation on Toughening Mechanism of Laminated Composite Ceramic. J. Inorganic Materials, 2005, 20(2): 459-464. [7] Guo X.H., Hu L. and Cai Q.H., Numerical Simulation and Laboratory Test on Toughening of Ceramic Nappe. J. Chinese Ceramic Society, 2000, 28(3): 234-239. [8] Tang C.A., Wang S.H. and Fu Y.F., Numerical Test on Rock Failure Process. Beijing: Sci. & Tech. Publisher, 2003: 42-43

《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_mechanism

《复合材料 Composites》课程教学资源（学习资料）第五章陶瓷基复合材料_mechanism