3734 HENAGER et al. SUBCRITICAL CRACK GROWTH: PART I Table 5. Hi-Nicalon fiber creep investigations Person/group Result for ((/mol) Remarks Rugg and Tressler [621 423±74 nle in argon Bodet 200-300 Di Carlo et al.[34] 600(*600=348) nsile in air, transient creep observed placement observed at 1373 K expected for this more approximate equivalence between our blunt notch and creep-resistant fiber. This is seen clearly(Fig. 4) a sharp crack in bending when the Hi-C data are compared to the set of data Estimates of the damage zone(plastic zone)size, for the CG-C materials at 1373 K. Here the Hi-C Ip can be made using the relation [54] for a mode- material at 1423 K deforms at the same rate as the I crack CG-C materials at 1373 K, a 50 K shift. The pub- lished creep parameters for Nicalon-CG and Hi-Nica lon fibers in air [34] predict about 100 K temperature differential to reach 1% creep strain in 300 h for an ()=2rG)o)3-2cose(6 applied stress of 500 MPa 4. 2. Damage zone morpholog where KMC is the mode-I stress intensity factor at Optical microscopy of cracked and sectioned speci- which matrix cracking occurs and o,y is set to the ens, where the test was interrupted before final fail- matrix cracking stress. For the CG-C materials,we ure and the specimen was unloaded at temperature, observed the onset of matrix cracking(nonlinea reveals a multiply cracked damage zone(Fig. 6a). load-displacement onset) at applied loads of 325 N The damage zone width, estimated number of cracks which corresponds to a K MCI of 5.0 MPa m/2. The in the zone, and mean-crack spacings are shown in maximum extent of the damage zone, 2ry is equal to Table 3. The accumulated specimen displacements 1.2x10- m using a value for o, of 100 MPa, which are shown in Table 2 and a representative load-dis- is in good agreement with our observed damage zone lacement curve in Fig 5a. Stresses above the matrix widths. A contour plot of equation(6) is shown in cracking stress cause multiple cracking at the speci- Fig. 6b, showing the contour of constant o,, of 100 men notch. The notch acts as a stress concentration, MPa ahead of the notch. and the damage is contained within a zone appro A careful study of the damage zone mately 1.25 mm in width, which is about twice the reveals little or no fiber breakage, even at the notch notch width. The stress concentration factor of the root where the crack-opening displacements are larg- notch, Yn, is given by st. This supports the hypothesis that fiber creep acts to unload the bridging fibers and allow crack propa- gation without fiber fracture [55 A mean-crack Vip (4) ing of 1. 4x10- m(140 um)obtains in the CG-C materials at 1373 K for the initial cracking from the notch while this spacing increases to 3.0x10- m(300 um) after substantial crack growth and crack shed ding. Calculated crack spacings, using parameters for where a is the notch depth and p is the notch radius our CG-C materials(Table 1)and assuming a matrix I Our notch geometries vary slightly but the notch cracking stress of 100 MPa, range from 1. 5x10-to lepth, a, is typically 1x10-3m and p is 2. 5x10-m, 3. 1x10-4 m(150 to 300 um). Crack spacings are which gives a value for Yn of 4.4. Adjusting this value about 3.6x10- m(360 um) in the Hi-C material at for a finite width specimen, where a/W was 0. 18, we 1448 K. The initial loading causes matrix cracking at have that Yn is equal to 4.0 [52]. Using the relation the notch root in a manner that is consistent with stress redistribution processes of these materials, (5)termed class II CMCs by others [56], and the cracks appear to be distributed according to multiple crack ing theory. where o is the bending stress we find that the notch However, the damage zone is more complex than mode-I stress intensity factor, KI, equal to a simple system of relatively straight, multipl O MPa which compares to that for a such as those observed in unidirectional co composites. sharp crack (SENB specimen [53]) of Repeated sectioning and optical microscopy of the KI=5.9x10-20 MPa m 2. We see that there damage zones reveals that the cracking patterns are3734 HENAGER et al.: SUBCRITICAL CRACK GROWTH: PART I Table 5. Hi-Nicalon fiber creep investigations Person/group Result for Q (kJ/mol) Remarks Rugg and Tressler [62] 423±74 Load control tensile in argon Chollon et al. [63] 220±17 (1273–1523 K) Tensile in argon, 1 GPa; steady-state creep observed 700±30 (1523–1673 K) below 1673 K Bodet et al. [64] 340–420 argon Dead weight tensile in argon and air; 150–700 MPa; 200–300 air steady state observed DiCarlo et al. [34] 600 (p*600=348) 1273–1673 K tensile in air; transient creep observed below 1% strain placement observed at 1373 K expected for this more creep-resistant fiber. This is seen clearly (Fig. 4) when the Hi-C data are compared to the set of data for the CG-C materials at 1373 K. Here the Hi-C material at 1423 K deforms at the same rate as the CG-C materials at 1373 K, a 50 K shift. The pub￾lished creep parameters for Nicalon-CG and Hi-Nica￾lon fibers in air [34] predict about 100 K temperature differential to reach 1% creep strain in 300 h for an applied stress of 500 MPa. 4.2. Damage zone morphology Optical microscopy of cracked and sectioned speci￾mens, where the test was interrupted before final fail￾ure and the specimen was unloaded at temperature, reveals a multiply cracked damage zone (Fig. 6a). The damage zone width, estimated number of cracks in the zone, and mean-crack spacings are shown in Table 3. The accumulated specimen displacements are shown in Table 2 and a representative load–dis￾placement curve in Fig. 5a. Stresses above the matrix cracking stress cause multiple cracking at the speci￾men notch. The notch acts as a stress concentration, and the damage is contained within a zone approxi￾mately 1.25 mm in width, which is about twice the notch width. The stress concentration factor of the notch, Yn, is given by Yn 3 a 2r
1  4 2  a 2r (4) where a is the notch depth and r is the notch radius [51]. Our notch geometries vary slightly but the notch depth, a, is typically 1×10
3 m and r is 2.5×10
4 m, which gives a value for Yn of 4.4. Adjusting this value for a finite width specimen, where a/W was 0.18, we have that Yn is equal to 4.0 [52]. Using the relation Kn sYn√r (5) where s is the bending stress we find that the notch has a mode-I stress intensity factor, KI, equal to 6.4×10
2 s MPa m1/2 which compares to that for a sharp crack (SENB specimen [53]) of KI = 5.9×10
2 s MPa m1/2. We see that there is an approximate equivalence between our blunt notch and a sharp crack in bending. Estimates of the damage zone (plastic zone) size, ry, can be made using the relation [54] for a mode￾I crack ry(q) 1 2p
KMC I syy 2 [cos
q 2 6 (3
2 cos q) 2 ] (6) where KMCI is the mode-I stress intensity factor at which matrix cracking occurs and syy is set to the matrix cracking stress. For the CG-C materials, we observed the onset of matrix cracking (nonlinear load–displacement onset) at applied loads of 325 N, which corresponds to a KMCI of 5.0 MPa m1/2. The maximum extent of the damage zone, 2ry, is equal to 1.2×10
3 m using a value for sc of 100 MPa, which is in good agreement with our observed damage zone widths. A contour plot of equation (6) is shown in Fig. 6b, showing the contour of constant syy of 100 MPa ahead of the notch. A careful study of the damage zone and cracking reveals little or no fiber breakage, even at the notch root where the crack-opening displacements are larg￾est. This supports the hypothesis that fiber creep acts to unload the bridging fibers and allow crack propa￾gation without fiber fracture [55]. A mean-crack spac￾ing of 1.4×10
4 m (140 µm) obtains in the CG-C materials at 1373 K for the initial cracking from the notch while this spacing increases to 3.0×10
4 m (300 µm) after substantial crack growth and crack shed￾ding. Calculated crack spacings, using parameters for our CG-C materials (Table 1) and assuming a matrix cracking stress of 100 MPa, range from 1.5×10
4 to 3.1×10
4 m (150 to 300 µm). Crack spacings are about 3.6×10
4 m (360 µm) in the Hi-C material at 1448 K. The initial loading causes matrix cracking at the notch root in a manner that is consistent with stress redistribution processes of these materials, termed class II CMCs by others [56], and the cracks appear to be distributed according to multiple crack￾ing theory. However, the damage zone is more complex than a simple system of relatively straight, multiple cracks, such as those observed in unidirectional composites. Repeated sectioning and optical microscopy of the damage zones reveals that the cracking patterns are