1874 K Goda/Composites Science and Technology 59(1999)1871-1879 the material constants used in the simulation. Some of These results imply that the more cumulative fiber break the material constants, i.e. the Weibull parameters of pattern increases the composite strength. Such stress/ the fiber strength, the Youngs modulus and tensile strain behavior and strengths are closely related with the strength of the matrix, were determined in experiment degrees of matrix and interfacial damages following [16], in which boron fibers with a diameter of 142 um fiber breaks. In the next session the relation between produced by AVCO and an epoxy resin (Araldite the damage type and fiber stress distribution around a CY230/hardner HY2967) supplied by Ciba-Geigy Co. broken fiber is described were used as the test materials, a shear modulus of the interface element is supposed to be equal to that of the 2400 matrix, because the interface layer does not exist as an 日v=117MPa appreciable thickness and is used as a model to express 2300 -O t, =20. 4 MPa nterfacial debonding. It is also assumed that the width of 4 =35.0 MPa the interface element corresponds to the width of pro- 32200& jection of the fiber, i.e. the fiber diameter. For simplicity the thickness of the interface element was set to be a 1/100 of the fiber diameter. According to the material constants shown in table l. the fiber volume fraction of 态2000 the composite is relatively low, approximately 0.1 1900 However, the distance between fibers used here gives the fiber volume fraction of 0.53 if the fibers are distributed Fiber element order next to broken element in hexagonal array (a) Stress concentration on fiber elements perpendicular to fiber axis 3. Results a1500 一t,=117MPa 3. 1. Stress/ strain curve 1000v=350MPa Fig. 3 shows typical stress/strain diagrams of the simulation results. In the computation, interfacial shear strengths, t, of 11.7, 20.4 and 35.0 MPa were used 500 under the same set of random fiber strengths. The stress levels at the first fiber break are therefore all the same but the behavior following the break is completely dif- ferent. Fig. 3(a) shows a similar fracture process to that of a bundle consisting of small number of fibers. That is Distance from broken point along fiber axis mm the first fiber break indicates the maximum stress and (b)Stress recovery of broken fiber element along fiber axis is followed by the other individual fiber breaks. In Fig.3(b)the level of the second peak is higher than the Fig. 4. Fiber stress distributions around a broken fiber element the fiber axis. shows that the stress level drops rapidly after the first Reprinted with permission from Trans JSME 1997: 63A: 445-452 peak, though recovering slightly around 0.8% strain. C 1999 The Japan Society of Mechanical Engineers [16] 400 400 d300 d300 的200 0204060.81.0 002040.60.81.0 0.20.40.60.81.0 Strain Fig 3. Simulated stress/strain diagrams of a boron/epoxy composite (a)tr=11.7 MPa(b)tr=20.4 MPa(c)I,=350 MPa. Reprinted with pe mission from Trans JSME 1997: 63A: 445-452.@ 1999 The Japan Society of Mechanical Engineers [16]the material constants used in the simulation. Some of the material constants, i.e. the Weibull parameters of the ®ber strength, the Young's modulus and tensile strength of the matrix, were determined in experiment [16], in which boron ®bers with a diameter of 142 mm produced by AVCO and an epoxy resin (Araldite CY230/hardner HY2967) supplied by Ciba-Geigy Co. were used as the test materials. A shear modulus of the interface element is supposed to be equal to that of the matrix, because the interface layer does not exist as an appreciable thickness and is used as a model to express interfacial debonding. It is also assumed that the width of the interface element corresponds to the width of pro￾jection of the ®ber, i.e. the ®ber diameter. For simplicity the thickness of the interface element was set to be a 1/100 of the ®ber diameter. According to the material constants shown in Table 1, the ®ber volume fraction of the composite is relatively low, approximately 0.1. However, the distance between ®bers used here gives the ®ber volume fraction of 0.53 if the ®bers are distributed in hexagonal array. 3. Results 3.1. Stress/strain curve Fig. 3 shows typical stress/strain diagrams of the simulation results. In the computation, interfacial shear strengths, I, of 11.7, 20.4 and 35.0 MPa were used under the same set of random ®ber strengths. The stress levels at the ®rst ®ber break are therefore all the same, but the behavior following the break is completely dif￾ferent. Fig. 3(a) shows a similar fracture process to that of a bundle consisting of small number of ®bers. That is, the ®rst ®ber break indicates the maximum stress and is followed by the other individual ®ber breaks. In Fig. 3(b) the level of the second peak is higher than the ®rst level and indicates the maximum stress. Fig. 3(c) shows that the stress level drops rapidly after the ®rst peak, though recovering slightly around 0.8% strain. These results imply that the more cumulative ®ber break pattern increases the composite strength. Such stress/ strain behavior and strengths are closely related with the degrees of matrix and interfacial damages following ®ber breaks. In the next session the relation between the damage type and ®ber stress distribution around a broken ®ber is described. Fig. 3. Simulated stress/strain diagrams of a boron/epoxy composite. (a) I ˆ 11:7MPa (b) I ˆ 20:4MPa (c) I ˆ 35:0 MPa. Reprinted with per￾mission from Trans JSME 1997;63A:445±452. # 1999 The Japan Society of Mechanical Engineers [16]. Fig. 4. Fiber stress distributions around a broken ®ber element: (a) stress concentration on ®ber elements perpendicular to the ®ber axis; (b) stress recovery of broken ®ber element along the ®ber axis. Reprinted with permission from Trans JSME 1997;63A:445±452. # 1999 The Japan Society of Mechanical Engineers [16]. 1874 K. Goda / Composites Science and Technology 59 (1999) 1871±1879