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 cracksVol. 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 ce￾ramic 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