SUN and SINGH: MULTIPLE MATRIX CRACKING Table 1. Mechanical properties of SiC fiber and F glass Materials Elastic modulus(GPa) Strength(GPa) Failure strain (% SCS-6 SiC fibre 0.8-1.0 423[21 F glass+ 0.056 ta is the coefficient of thermal expansion(25-500.C). +The composition for F glass is 76% Sioz-16% B203-8%K2O, obtained from Corning Glass Works, Corning. NY Fig. 4. From the load-displacement curve, the debond initiation point (point A in Fig. 4), the peak load (point B)at which the interfacial debond ing has propagated through the sample thickness, and the load drop (point C) corresponding to the beginning of a steady-state interfacial sliding can be measured. The debond initiation stress ad at point A was about 55 MPa [22]. The frictional sliding stress tr determined from the load value at point C was about 30 MPa [22]. The debond energy Ia can then be obtained from equations(12)and(16) vided that ad and tr are available. Therefore the interfacial properties of these Sic fiber-reinforced 1 00um borosilicate glass composites, as listed in Table 2, were determined in this way from the fiber pushout Fig.3. A cross section of the SiC fiber reinforced glass load-displacement curves composite displaying uniformly distributed fibers 3.3. Matrix cracking and debond length measurement The sample had a surface dimension of techniques 50mm x 3.3 mm and a thickness of about 1.4 mm. The sample was stressed using an Instron testing Figure 3 shows the well-distributed fibers from the machine in the four point flexure mode. The outer ross section of a composite. The material par- span was 40 mm and the inner span was 20 mm meters and mechanical properties of composite are For the purpose of finding the evolution of multiple listed in Table 2 matrix cracks and interfacial debonding, the sample as loaded to several different levels of stress/load 3. 2. Measurement of interfacial properties t a crosshead speed of 0.2 mm/min and then unloaded. The loading curves during a typical test are shown in Fig. 5. The changes in the light trans- debond initiation stress and frictional sliding stress mission pattern(white band) on either side of a were measured using the fiber pushout technique. matrix crack were observed. It was believed that the Fiber pushout tests were conducted using a Micro white band was caused by the light scattering and Measure Machine(Process Equipment Company, absorption at the debonded portion of the fiber OH)at a loading rate of 10 N/min. The pushout matrix interface. The change in the white band was probe, made of tungsten carbide, was about 100 Am attributed to the process of relative displacement by pushing a fully dense bulk alumina plate of 5mm in thickness. The real fiber displacement uring a pushout test was obtained after subtracting the machine compliance. A typical load-displace- Thickne t curve for a fibi per pushout test is shown in Table 2. Parameters and properties for SCS-6 fiber reinforced Fiber volume fraction, Vr 0.12 modulus of composite. Ec(GPa) 2 Matrix)(MPa/m) 0.77D2 First matrix cracking stress, FMc (MPa) d o/m) 1.2±0.3[22] Debond initiation stress, ad(MPa) 55+5122 Fig. 4. A typical load-displacement curve during a fiber cAlculated by rule of mixtureThe sample had a surface dimension of 50 mm 3.3 mm and a thickness of about 1.4 mm. Figure 3 shows the well-distributed ®bers from the cross section of a composite. The material par￾ameters and mechanical properties of composite are listed in Table 2. 3.2. Measurement of interfacial properties The interfacial properties such as interfacial debond initiation stress and frictional sliding stress were measured using the ®ber pushout technique. Fiber pushout tests were conducted using a Micro Measure Machine (Process Equipment Company, OH) at a loading rate of 10 N/min. The pushout probe, made of tungsten carbide, was about 100 mm in diameter. The machine compliance was measured by pushing a fully dense bulk alumina plate of 5 mm in thickness. The real ®ber displacement during a pushout test was obtained after subtracting the machine compliance. A typical load±displace￾ment curve for a ®ber pushout test is shown in Fig. 4. From the load±displacement curve, the debond initiation point (point A in Fig. 4), the peak load (point B) at which the interfacial debond￾ing has propagated through the sample thickness, and the load drop (point C) corresponding to the beginning of a steady-state interfacial sliding can be measured. The debond initiation stress sd at point A was about 55 MPa [22]. The frictional sliding stress tf determined from the load value at point C was about 30 MPa [22]. The debond energy Gd can then be obtained from equations (12) and (16) pro￾vided that sd and tf are available. Therefore, the interfacial properties of these SiC ®ber-reinforced borosilicate glass composites, as listed in Table 2, were determined in this way from the ®ber pushout load±displacement curves. 3.3. Matrix cracking and debond length measurement techniques The sample was stressed using an Instron testing machine in the four point ¯exure mode. The outer span was 40 mm and the inner span was 20 mm. For the purpose of ®nding the evolution of multiple matrix cracks and interfacial debonding, the sample was loaded to several di€erent levels of stress/load at a crosshead speed of 0.2 mm/min and then unloaded. The loading curves during a typical test are shown in Fig. 5. The changes in the light trans￾mission pattern (white band) on either side of a matrix crack were observed. It was believed that the white band was caused by the light scattering and absorption at the debonded portion of the ®ber± matrix interface. The change in the white band was attributed to the process of relative displacement Table 1. Mechanical properties of SiC ®ber and F glass Materials Elastic modulus (GPa) Strength (GPa) Failure strain (%) a$ (10ÿ6 /8C) SCS-6 SiC ®bre 400 3.4 0.8±1.0 4.23 [21] F glass% 56 0.056 0.1 4.25 $a is the coecient of thermal expansion (25±5008C). %The composition for F glass is 76% SiO2±16% B2O3±8% K2O, obtained from Corning Glass Works, Corning, NY Fig. 3. A cross section of the SiC ®ber reinforced glass composite displaying uniformly distributed ®bers. Table 2. Parameters and properties for SCS-6 ®ber reinforced borosilicate glass composite Fiber volume fraction, Vf 0.12 Elastic modulus of composite, Ec (GPa) 97.3$ Matrix porosity (%) 1±2 [1] KIc (Matrix) (MPa/Zm) 0.77 [21] First matrix cracking stress, sFMC (MPa) 90 [1] Ultimate strength (composite), scu (MPa) 440 [1] Interfacial frictional stress, tf (MPa) 3023 [22] Interfacial debonding energy, Gd (J/m2 ) 1.220.3 [22] Debond initiation stress, sd (MPa) 5525 [22] $Calculated by rule of mixture Fig. 4. A typical load±displacement curve during a ®ber pushout test. SUN and SINGH: MULTIPLE MATRIX CRACKING 1661