Takeda, M. Kiriyama/Composites: Part A 30(1999)593-59 595 0.4 0.4 y-a-173.6(MPa) 0.3 -195.2(MPa) 日 o213.1(MPa) V…2473(MPa) 10010 x(um) 0 o…z0=0.1725(mm) Fig. 3. Relative interfacial displacement as a function of distance from 0.1 crack tip at0°90° interface(O90y03]) fiber/matrix interface. The region of fiber/matrix debonding 20-1001020 is found at the interface where Ax=0 ig. 3 shows some representative results of Ar as func- Fig. 4. Distribution of relative interfacial displacement at different tions of x and the stress level at the o%/90% interface in stances =o in the thickness direction from 0/90interface(0y/903/03 903/03] specimens. For the sequence of debonding and slid Ocp=183.9 MPa).(a)Crack penetrating both 0 and 90 plies, (b) Isolated ing at x <o, La was almost the same, even when the applied crack in o plies. stress g increased from 173.6 to 195.2 MPa. while the rela tive displacement or sliding, Ax, increased especially near interaction between different modes [8, 10]. Shear-lag the crack tip. Approximately 3 um increase in Ly was found analysis was used to obtain the stress transfer both at the by the stress level of 213.1 MPa, but no increase was 0/90 interfaces and fiber/matrix interfaces in 0 plies. In observed at 230. 1 MPa, while Ar increased near the crack this study, the stress distribution is modified, considering the tip. A remarkable increase in Ld was found again at Poisson contraction in debonded regions in 0 plies as noted 247.3 MPa. In summary, it can be concluded that the in the Ar measurement. Thus, in debonded regions, the stress increases. The derivative of A xlx increases near the axial stress in a fiber or is given by shear stress To and the dobonding tip with increasing applied stress. This is due to the relaxation in residual thermal stress as well as the dor __ 2To (2) decrease in interfacial friction Fig 4 shows the distribution of Ax at several distances =o where ro is the fiber radius. To is determined assuming the from the 0/90 interface in the thickness direction. Fig 4a is Coulomb friction as for matrix cracks penetrating into both 0 and 90 plies, and Fig 4b for cracks only existing in 0 plies In the case of Fig T0=-(+吓) (3) 4a, both Ly and Ax decrease with increasing =o, except near where u is the coefficient of friction, and o and pare the 07 /90 interface. This is presumably due to fiber misa normal stresses in the radial direction at the interface due ignment and interlaminar shear stress. In the case of Fig. to thermal expansion mismatch and Poisson contraction b, on the other hand, both Ld and x are almost independent effects, respectively. the friction occurs when oc+ap<o on =0. In both cases, Ax is almost zero at the specimen The debonding length Ld in modes 3 and 5 was predicted surface (E0=0.6 mm) suming that the shear stress distribution in the thickness in 0 plies is linear. Displacements of fibers and matrix in debonded regions in 0 plies(uf and um) were related with 4. Theoretical approach the average displacements in 0 and 90 plies which were calculated from the shear-lag analysis, assuming a proper 4. 1. Stress analysis and debonding length prediction geometric similarity rule. The details of the stress analysis and debonding length prediction are found in Ref [121 Kuo [8 classified the cracking states in a cross-ply laminate into five damage modes, as shown in Fig. 5, and 4.2. Energy balance criterion for matrix crack evolution theoretically derived the critical stress for each mode based on the energy balance criterion, without considering the The observed damages were classified into 13 patterns,fiber/matrix interface. The region of fiber/matrix debonding is found at the interface where Dx ± 0. Fig. 3 shows some representative results of Dx as func￾tions of x and the stress level at the 08/908 interface in [03/ 903/03] specimens. For the sequence of debonding and slid￾ing at x , 0, Ld was almost the same, even when the applied stress s increased from 173.6 to 195.2 MPa, while the rela￾tive displacement or sliding, Dx, increased especially near the crack tip. Approximately 3 mm increase in Ld was found by the stress level of 213.1 MPa, but no increase was observed at 230.1 MPa, while Dx increased near the crack tip. A remarkable increase in Ld was found again at 247.3 MPa. In summary, it can be concluded that the debonding grows intermittently, not gradually as the applied stress increases. The derivative of Dx/x increases near the dobonding tip with increasing applied stress. This is due to the relaxation in residual thermal stress as well as the decrease in interfacial friction. Fig. 4 shows the distribution of Dx at several distances z0 from the 08/908 interface in the thickness direction. Fig. 4a is for matrix cracks penetrating into both 08 and 908 plies, and Fig. 4b for cracks only existing in 08 plies. In the case of Fig. 4a, both Ld and Dx decrease with increasing z0, except near the 08/908 interface. This is presumably due to fiber misa￾lignment and interlaminar shear stress. In the case of Fig. 4b, on the other hand, both Ld and x are almost independent on z0. In both cases, Dx is almost zero at the specimen surface (z0 ˆ 0.6 mm). 4. Theoretical approach 4.1. Stress analysis and debonding length prediction Kuo [8] classified the cracking states in a cross-ply laminate into five damage modes, as shown in Fig. 5, and theoretically derived the critical stress for each mode based on the energy balance criterion, without considering the interaction between different modes [8,10]. Shear-lag analysis was used to obtain the stress transfer both at the 08/908 interfaces and fiber/matrix interfaces in 08 plies. In this study, the stress distribution is modified, considering the Poisson contraction in debonded regions in 08 plies as noted in the Dx measurement. Thus, in debonded regions, the relationship between the interfacial shear stress t 0 and the axial stress in a fiber sf is given by dsf dx ˆ 2 2t0 r0 …2† where r0 is the fiber radius. t 0 is determined assuming the Coulomb friction as t0 ˆ 2m…sc 1 sp† …3† where m is the coefficient of friction, and sc and sp are normal stresses in the radial direction at the interface due to thermal expansion mismatch and Poisson contraction effects, respectively. the friction occurs when sc 1 sp , 0. The debonding length Ld in modes 3 and 5 was predicted assuming that the shear stress distribution in the thickness in 08 plies is linear. Displacements of fibers and matrix in debonded regions in 08 plies (uf and um) were related with the average displacements in 08 and 908 plies which were calculated from the shear-lag analysis, assuming a proper geometric similarity rule. The details of the stress analysis and debonding length prediction are found in Ref. [12]. 4.2. Energy balance criterion for matrix crack evolution The observed damages were classified into 13 patterns, N. Takeda, M. Kiriyama / Composites: Part A 30 (1999) 593–597 595 Fig. 3. Relative interfacial displacement as a function of distance from crack tip at 08/908 interface ([03/903/03]). Fig. 4. Distribution of relative interfacial displacement at different distances z0 in the thickness direction from 08/908 interface. ([03/903/03], s CP ˆ 183.9 MPa). (a) Crack penetrating both 08 and 908 plies, (b) Isolated crack in 08 plies