Y. Kagawa, K Goto/ Materials Science and Engineering 4250(1998)285-290 Fiber Ill, K exhibits a slightly smaller value than the critical 9000 stress intensity factor of the matrix, K 显40 O PMMA The 3D crack-fibre interaction in the composite studied is divided into three stages: elastic constraint stage(stage D), matrix crack bowing stage(stage II)and Normalized crack length c/r crack bridging stage(stage mechanism for fracture resistance of the composite Fig.9. Applied stress versus crack length of pure PMMA and the within this experiment is the elastic constraint effect by Fiber The interface partial debonding phenomena decide he termination of the stages: the first partial debonding n front of the crack tip gives the end of stage I. The formation of the cylindrical debonding gives the end of stage II. To have an efficient toughening effect gener ated from the fibre. the fibre-matrix interface must bond until the crack reaches the fibre. on the other hand. after the crack reaches the fibre. the interface must debond before the crack penetrates into the fibr Normalized crack length, c/r Fig. 10. Strain gauge reading versus crack length of pure PMMA and the composite References Fiber [1 M.W. Barsoum, P. Kangutkar, A.S.D. Wang, Compos. Sci Technol.44(1992)257-269 2A.S.D. Wang, X.G. Huang, M.w. Barsoum, Compos. Sci. Tech nol.44(1992)271-282 BIRY. Kim, N.J. Pagano, J. Am. Ceram. Soc. 74(5)(1991) [4 N.J. Pagano, R.Y. Kim, Mech. Compos Mater. Struct. 1(1994) [R.E. Dutton, N.J. Pagano, R.Y. Kim, J. Am. Ceram Soc. 79(4) (1996)865-872 Normalized crack length, c/r [6 Y. Kagawa, K. Goto, Ceram. (1995)247-251 [ K. Goto, Y. Kagawa, Mater A176(1994)357-361 Fig. Il Normalised stress intensity factor, K/Kc, versus normalised 8K. Goto, Y. Kagawa, Ceram. (1995)253-258 crack length, c/r, of the composite and pure PMMA(K/Km=l) 9 K Goto, Y. Kagawa, K. Nojima, H. Iba, Mater. Sci. Eng. A212 0]K J. Jpn. Ceram. Soc. 100(1993)6 increase of the normalised crack length, c/r. At stage L, []Y Mater. Sci. Eng. A221(1996)163-172. K is 1.2 times as large as the value for pure [12] T M A.S. Argon, Mech. Mater. 19(1995)343- PMMA. This behaviour is explained by the elastic [3]AF58 M. Ortiz, J. Mech. Phys. Solids 39(6)(1991) constraint effect; i.e. that the stress at the crack tip is [14 Toshiba Ceramics Catalogue, 1995 reduced by the stiffer fibre, since Er< Em [7, 8]. As (15 Mitsubishi Rayon Catalogue, 1994 mentioned before, the applied stresses on the composite [16]H. Poritsky, Physics 5(12)(1934)406-411 at stages II and Ill with the same crack length were [17 C. Jansen, Specimen for fracture mechanics studies on glass. The maller than that of pure PMMA. After the crack front Ceramic Society of Japan, 10th Inter. Cong on Glass, Kyoto Japan, July, 1974 reached the fibre-matrix interface, i. e, in stages II and [18]J. Cook, J.E. Gordon, Proc. R Soc. A282(1964)508290 Y. Kagawa, K. Goto / Materials Science and Engineering A250 (1998) 285–290 Fig. 9. Applied stress versus crack length of pure PMMA and the composite. Fig. 10. Strain gauge reading versus crack length of pure PMMA and the composite. Fig. 11. Normalised stress intensity factor, K/Kc m, versus normalised crack length, c/r, of the composite and pure PMMA (K/Kc m=1). III, K exhibits a slightly smaller value than the critical stress intensity factor of the matrix, Kc m. 4. Summary The 3D crack–fibre interaction in the composite studied is divided into three stages: elastic constraint stage (stage I), matrix crack bowing stage (stage II) and crack bridging stage (stage III). The most effective mechanism for fracture resistance of the composite within this experiment is the elastic constraint effect by a stiffer fibre. The interface partial debonding phenomena decide the termination of the stages: the first partial debonding in front of the crack tip gives the end of stage I. The formation of the cylindrical debonding gives the end of stage II. To have an efficient toughening effect gener￾ated from the fibre, the fibre–matrix interface must bond until the crack reaches the fibre. On the other hand, after the crack reaches the fibre, the interface must debond before the crack penetrates into the fibre. References [1] M.W. Barsoum, P. Kangutkar, A.S.D. Wang, Compos. Sci. Technol. 44 (1992) 257–269. [2] A.S.D. Wang, X.G. Huang, M.W. Barsoum, Compos. Sci. Tech￾nol. 44 (1992) 271–282. [3] R.Y. Kim, N.J. Pagano, J. Am. Ceram. Soc. 74 (5) (1991) 1082–1090. [4] N.J. Pagano, R.Y. Kim, Mech. Compos. Mater. Struct. 1 (1994) 3–29. [5] R.E. Dutton, N.J. Pagano, R.Y. Kim, J. Am. Ceram. Soc. 79 (4) (1996) 865–872. [6] Y. Kagawa, K. Goto, Ceram. Trans. 57 (1995) 247–251. [7] K. Goto, Y. Kagawa, Mater. Sci. Eng. A176 (1994) 357–361. [8] K. Goto, Y. Kagawa, Ceram. Trans. 57 (1995) 253–258. [9] K. Goto, Y. Kagawa, K. Nojima, H. Iba, Mater. Sci. Eng. A212 (1996) 69–74. [10] K. Sekine, Y. Kagawa, J. Jpn. Ceram. Soc. 100 (1993) 621–625. [11] Y. Kagawa, K. Sekine, Mater. Sci. Eng. A221 (1996) 163–172. [12] T.M. Mower, A.S. Argon, Mech. Mater. 19 (1995) 343–364. [13] A.F. Bower, M. Ortiz, J. Mech. Phys. Solids 39 (6) (1991) 815–858. [14] Toshiba Ceramics Catalogue, 1995. [15] Mitsubishi Rayon Catalogue, 1994. [16] H. Poritsky, Physics 5 (12) (1934) 406–411. [17] C. Jansen, Specimen for fracture mechanics studies on glass, The Ceramic Society of Japan, 10th Inter. Cong. on Glass, Kyoto, Japan, July, 1974. [18] J. Cook, J.E. Gordon, Proc. R. Soc. A282 (1964) 508. increase of the normalised crack length, c/r. At stage I, K is :1.2 times as large as the value for pure PMMA. This behaviour is explained by the elastic constraint effect; i.e. that the stress at the crack tip is reduced by the stiffer fibre, since EfEm [7,8]. As mentioned before, the applied stresses on the composite at stages II and III with the same crack length were smaller than that of pure PMMA. After the crack front reached the fibre–matrix interface, i.e., in stages II and