SUN and SINGH: MULTIPLE MATRIX CRACKING B5651 B58 1502 100 B5-18 0 0.2 0.6 0.8 Displacement(mm) Fig. 5. The load-displacement curves for a composite loaded to different stress levels(for example, B5 18 denotes the sample B5 loaded at 18 N). between the fiber and matrix at the interface which 4. RESULTS AND DISCUSSION led to debonding as shown in Fig. 6. Each white band corresponds to a fiber-matrix interfacial 4. 1. Development of multiple matrix cracks and debonding with a matrix crack running across in the crack saturation middle of the band. The debond length was thus Four-point flexure tests were performed on the measured as half of the length of the white band. Sic fiber-reinforced transparent borosilicate glass After each load-unload cycle, the number and pos- composites. The first matrix crack occurs at a stress ition of matrix cracks, and debond length around of 85 MPa. A close look at the matrix under an each crack surface were recorded and measured by optical microscope revealed that more than one photographing and video recording method. The crack was generated which also included an incom- agnification of the pictures in Fig. 6 was about 16. letely propagated crack. This behavior was also We did not observe any time dependent growth observed by Dutton [21]. Therefore, an evidence of of the debond crack within a short time of our ex- first load drop in the load-displacement curve may periments in which specimens were loaded to a pre- not represent the real FMC point. After FMC, the determined level of stress and then immediately stress distribution along the fiber length but in the unloaded for measuring the debond length. No matrix phase varied from zero at the matrix crack change in the debond length was observed as a surfaces to a new pre-crack value. Subsequent for function of time after unloading. We understand mation of new cracks always occurred at progress- that glasses are prone to stress corrosion cracking ively higher stress levels because the flaw size is but we have not seen any growth of the debond smaller than that for the previous matrix cracks length during our experiments and therefore have This preference of crack for a larger flaw demon- not considered in the model calculations strated that the matrix cracking stress can vary over Although the continuity of the composite is dis- a range of values, which was also discussed by rupted by the multiple matrix cracks, the externally Zok [7] and Curtin [9]. The stiffness of the compo- applied stress is still calculated as the stress on the site which is indicated by the slope of the linear outermost tension surface of a rectangular specimen portion of each curve in Fig. 5 decreased with the suming that the elastic beam theory for the generation of additional new matrix cracks flexure model(MIL-STD-1942A)is valid Figure 7 shows the sequence and position of the Experiments were conducted on a total of 10 matrix cracks generated because of the increasing samples of the same fiber volume fraction. Debond load. The numbers on the dashed lines from I to 16 length measurement techniques were applied to in Fig. 7 indicate the sequence of matrix crack gen- only five of them. All of them showed a similar eration. The magnitude of the load/stress, written behavior. These data on the number of cracks and horizontally along the various crack numbers, indi- crack spacing from the 10 samples were used for cates the load/ stress at which these cracks were cre- the statistical distribution of crack density and ated. For example, the first three cracks 1, 2 and 3 crack spacing were detected at a load of 18 N( 85 MPa,corre-between the ®ber and matrix at the interface which led to debonding as shown in Fig. 6. Each white band corresponds to a ®ber±matrix interfacial debonding with a matrix crack running across in the middle of the band. The debond length was thus measured as half of the length of the white band. After each load±unload cycle, the number and pos￾ition of matrix cracks, and debond length around each crack surface were recorded and measured by photographing and video recording method. The magni®cation of the pictures in Fig. 6 was about 16. We did not observe any time dependent growth of the debond crack within a short time of our ex￾periments in which specimens were loaded to a pre￾determined level of stress and then immediately unloaded for measuring the debond length. No change in the debond length was observed as a function of time after unloading. We understand that glasses are prone to stress corrosion cracking but we have not seen any growth of the debond length during our experiments and therefore have not considered in the model calculations. Although the continuity of the composite is dis￾rupted by the multiple matrix cracks, the externally applied stress is still calculated as the stress on the outermost tension surface of a rectangular specimen assuming that the elastic beam theory for the ¯exure model (MIL-STD-1942A) is valid. Experiments were conducted on a total of 10 samples of the same ®ber volume fraction. Debond length measurement techniques were applied to only ®ve of them. All of them showed a similar behavior. These data on the number of cracks and crack spacing from the 10 samples were used for the statistical distribution of crack density and crack spacing. 4. RESULTS AND DISCUSSION 4.1. Development of multiple matrix cracks and crack saturation Four-point ¯exure tests were performed on the SiC ®ber-reinforced transparent borosilicate glass composites. The ®rst matrix crack occurs at a stress of 85 MPa. A close look at the matrix under an optical microscope revealed that more than one crack was generated which also included an incom￾pletely propagated crack. This behavior was also observed by Dutton [21]. Therefore, an evidence of ®rst load drop in the load±displacement curve may not represent the real FMC point. After FMC, the stress distribution along the ®ber length but in the matrix phase varied from zero at the matrix crack surfaces to a new pre-crack value. Subsequent for￾mation of new cracks always occurred at progress￾ively higher stress levels because the ¯aw size is smaller than that for the previous matrix cracks. This preference of crack for a larger ¯aw demon￾strated that the matrix cracking stress can vary over a range of values, which was also discussed by Zok [7] and Curtin [9]. The sti€ness of the compo￾site which is indicated by the slope of the linear portion of each curve in Fig. 5 decreased with the generation of additional new matrix cracks. Figure 7 shows the sequence and position of the matrix cracks generated because of the increasing load. The numbers on the dashed lines from 1 to 16 in Fig. 7 indicate the sequence of matrix crack gen￾eration. The magnitude of the load/stress, written horizontally along the various crack numbers, indi￾cates the load/stress at which these cracks were cre￾ated. For example, the ®rst three cracks 1, 2 and 3 were detected at a load of 18 N (85 MPa, corre￾Fig. 5. The load±displacement curves for a composite loaded to di€erent stress levels (for example, B5- 18 denotes the sample B5 loaded at 18 N). 1662 SUN and SINGH: MULTIPLE MATRIX CRACKING