Takeda, M. Kiriyama/Composites: Part A 30(1999)593-59 using specimens with parallel micro-lines printed on the heoretical Prediction urfaces. Interfacial debonding was found to grow intermit △口 tently as the applied stress increased. The debonding length distribution depended on the number of 90 plies as well as the type of damage modes. Based on the above microscopic observation, an analytical model for damage growth was proposed using the energy balance calculation based on Kuo and Chou [101, with the modification of including the effects of the interaction between different damage modes as well as the Poisson contraction in debonded regions. The 0100200300 predicted damage sequence agreed reasonably well with the experimental one, although further improvement is neces Applied Stress(MPa) sary for better prediction Fig. 7. Comparison between predicted and experimental overall crack References predicted evolution of matrix cracks for each laminate configuration. The initial crack was always in mode 1 [1 Marshall DB, Evans AG. Failure mechanisms in ceramic-fiber/o followed by several cracks at the earlier loading mic-matrix composites. J Am Ceram Soc 1985: 68(5): 225-231 [2] Prewo KM. Tension and flexural strength of silicon carbide fibre- stage. The following damage evolution depended on the reinforced glass ceramics. J Mater Sci 1986; 21: 3590-3600 type of laminate configuration, although the final saturated 3] Prewo KM. Carbon fibre reinforced glass matrix composite: tension crack density was similar. As expected in the microscopic and flexural properties. J Mater Sci 1988 23: 2745-2752 observations that revealed the interfacial debonding always 4 Budiansky B, Hutchinson JW occurred when cracks appear in 0 plies, the present analysis reinforced ceramics. J Mech Phys Solids 1986, 34(2): 167-18 5] Marshall DB, Oliver wC. Measurement of interfacial mechanical predicted only modes 1, 3, and 5 could occur in the present properties in fiber-reinforced ceramic composites. J Am Ceram So material system 987;70(8:542-548. Fig. 7 shows the overall crack density as a function of the [6 Hsueh CH. Matrix cracking with frictional bridging fibres in contin- applied stress. The theoretical prediction agrees well with ic composites. Part 2: Cracking due to residual stres- the experimental results, although the former provides steeper ses. J Mater sci199530:4793-4800. [7 Ahn BK, Curtin WA. Strain and hysteresis by stochastic matrix crack increase than the latter in the large crack density region ing in ceramic matrix composites. J Mech Phys Solids 1997; 45: 177- 8]Kuo wS Damage of multi-directionally reinforced ceramic-matrix 5 Conclusions Matrix crack evolution was studied for SiC fiber-rein 9 Karandikar P, Chou Tw. Characterization and forced glass matrix composite [0, 90,031(m=1, 2, 3) acking and elastic moduli changes in Nicalon-CAS composites Compos Sci Technol 1993: 46: 253-264 cross-ply laminates. Characteristic damage patterns were (10) Kuo wS, Chou TW. Multiple cracking of unidirectinal and cross-ply matrix cracks generating in both 0 and 90 plies Matrix ceramic matrix composites. J Am Ceram Soc 1995: 78(3):745-755 cracks penetrating into both 0 and 90 plies were dominant [11] Takeda N, Nizuma H, Ogihama S, Kobayashi A. Application of in[03/901/03]laminates, while matrix cracks only existing in micro-line/grid methods to temperature-dependent microscopic 0 plies were also observed more often from the earlier deformation and damage in CFRP laminates. Exp Mech ading stage as the number of 90 plies increased. A 1997;37(2:182-187 novel in situ sem observation was conducted to measure [12] Takeda N, Kiriyama M. Modeling of microscopic damage sequence in SiC fiber reinforced glass matrix cross-ply laminates, 1998 the fiber/matrix interfacial debonding and sliding in 0 pli (submitted)predicted evolution of matrix cracks for each laminate configuration. The initial crack was always in mode 1, followed by several mode 1 cracks at the earlier loading stage. The following damage evolution depended on the type of laminate configuration, although the final saturated crack density was similar. As expected in the microscopic observations that revealed the interfacial debonding always occurred when cracks appear in 08 plies, the present analysis predicted only modes 1, 3, and 5 could occur in the present material system. Fig. 7 shows the overall crack density as a function of the applied stress. The theoretical prediction agrees well with the experimental results, although the former provides steeper increase than the latter in the large crack density region. 5. Conclusions Matrix crack evolution was studied for SiC fiber-rein￾forced glass matrix composite [03/90m/03] (m ˆ 1, 2, 3) cross-ply laminates. Characteristic damage patterns were matrix cracks generating in both 08 and 908 plies. Matrix cracks penetrating into both 08 and 908 plies were dominant in [03/901/03] laminates, while matrix cracks only existing in 08 plies were also observed more often from the earlier loading stage as the number of 908 plies increased. A novel in situ SEM observation was conducted to measure the fiber/matrix interfacial debonding and sliding in 08 plies using specimens with parallel micro-lines printed on the surfaces. Interfacial debonding was found to grow intermit￾tently as the applied stress increased. The debonding length distribution depended on the number of 908 plies as well as the type of damage modes. Based on the above microscopic observation, an analytical model for damage growth was proposed using the energy balance calculation based on Kuo and Chou [10], with the modification of including the effects of the interaction between different damage modes as well as the Poisson contraction in debonded regions. The predicted damage sequence agreed reasonably well with the experimental one, although further improvement is neces￾sary for better prediction. References [1] Marshall DB, Evans AG. Failure mechanisms in ceramic–fiber/cera￾mic–matrix composites. J Am Ceram Soc 1985;68(5):225–231. [2] Prewo KM. Tension and flexural strength of silicon carbide fibre￾reinforced glass ceramics. J Mater Sci 1986;21:3590–3600. [3] Prewo KM. Carbon fibre reinforced glass matrix composite: tension and flexural properties. J Mater Sci 1988;23:2745–2752. [4] Budiansky B, Hutchinson JW, Evans AG. Matrix fracture in fiber￾reinforced ceramics. J Mech Phys Solids 1986;34(2):167–189. [5] Marshall DB, Oliver WC. Measurement of interfacial mechanical properties in fiber-reinforced ceramic composites. J Am Ceram Soc 1987;70(8):542–548. [6] Hsueh CH. Matrix cracking with frictional bridging fibres in contin￾uous fibre ceramic composites. Part 2: Cracking due to residual stres￾ses. J Mater Sci 1995;30:4793–4800. [7] Ahn BK, Curtin WA. Strain and hysteresis by stochastic matrix crack￾ing in ceramic matrix composites. J Mech Phys Solids 1997;45:177– 209. [8] Kuo WS. Damage of multi-directionally reinforced ceramic–matrix composites. PhD Dissertation, University of Delaware, Newark, DE, 1992. [9] Karandikar P, Chou TW. Characterization and modeling of micro￾cracking and elastic moduli changes in Nicalon-CAS composites. Compos Sci Technol 1993;46:253–264. [10] Kuo WS, Chou TW. Multiple cracking of unidirectinal and cross-ply ceramic matrix composites. J Am Ceram Soc 1995;78(3):745–755. [11] Takeda N, Niizuma H, Ogihama S, Kobayashi A. Application of micro-line/grid methods to temperature-dependent microscopic deformation and damage in CFRP laminates. Exp Mech 1997;37(2):182–187. [12] Takeda N, Kiriyama M. Modeling of microscopic damage sequence in SiC fiber reinforced glass matrix cross-ply laminates, 1998 (submitted). N. Takeda, M. Kiriyama / Composites: Part A 30 (1999) 593–597 597 Fig. 7. Comparison between predicted and experimental overall crack densities