C Pergamon Acta mater.4902001)3727-3738 www.elsevier.com/locate/actamat SUBCRITICAL CRACK GROWTH IN CVI SIC!SIC COMPOSITES AT ELEVATED TEMPERATURES: EFFECT OF FIBER CREEP RATE C H. HENAGER Jr, C.A. LEWINSOHN+ and R. H. JONES Pacific Northwest National Laboratory,$ Materials Sciences/P8-15, 902 Battelle Blvd, PO box 999, Richland. WA 99352-0999 US Received 3 April 2000, received in revised form 9 July 2001: accepted 9 July 2001) Abstract-Subcritical crack-growth studies in SiC!SiC composites were conduc reinforced with Hi-Nicalon fibers over a broad temperature range materials reinforced with Nicalon-CG fibers. Composites with a 0/90 plain weave and carbon interphase were tested in argon from 1 173 to 1473 K. Crack growth data obtained ronments are onsistent with a proposed fiber-creep-controlled crack-growth mechanism Measured crack-growth activation energies and ti perature exponents in argon agree with fiber creep-activation energies and nonlinear reep equations for both fiber types. Estimates of local strains during crack growth are in reasonable agreement with estimated fiber creep strains for the given times and temperatures. The increased creep resistance of Hi-Nicalon fibers is reflected in reduced crack-growth rates for composites containing those fibers. 200/ Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Ceramics-structural; Composites; Mechanical properties-creep; High temperature; Fracture 1 INTRODUCTION stand critical time-dependent deformation mech- Continuous fiber ceramic matrix composites( CFCCs) anisms are more reliable than unreinforced ceramics [I], but Previous studies(this group and others)have are prone to time-dependent failures from stable crack shown that creep of bridging fibers at elevated tem- [2-71 or from mechanical embrittlement(unstable nation for the observed creep or slow crack growth crack growth)caused by environmental exposure 18, of these continuous-fiber composites where the Sic 9. In particular, we are interested in understanding matrix is more creep resistant than the fibers [2, 3 time-dependent properties for these materials in gas- 3-26]. These results support the hypothesis that cooled advanced fission and fusion reactor environ creeping fibers transfer stress back to the matrix ments [10-12). Such environments are pristine in causing further matrix cracking, a loss of matrix stiff terms of oxygen content, and composites with carbon- ness, and increased loading of the crack-bridging fib- based interphases appear attractive. Since life-predic- ers, ultimately leading to failure. Recent results rel- tion methodologies for these materials would neces- evant to this work include experimental creep or sarily include time-dependent crack growth as an crack-growth tests on SiC/SiC composites [18, 19, important failure mechanism, it is essential to under- 23-26] and models of time-dependent crack growth [27-31]A complete discussion of the models appears in a companion paper [32] and will not be I To whom all correspondence should be addressed E-mail address: chuck. henager(@pnl. gov(C. H. Hen- Evans and Weber [18] documented increased com- pliances due to matrix cracking and also observed supported by Associated Western Univer- fiber sliding stresses at 1473 K that were almost one west Division(AWU NW) under Grant order of magnitude smaller than at room temp rature DE-FC -75522, DE-FG07-93ER-75912, or DE- Wilshire et al. [23] compared composite creep rates AC06-76RLO1830 le to matrix cracking to account for observed com 1359-6454/01/S20.00@ 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. P:S1359-6454(01)00276-2
Acta mater. 49 (2001) 3727–3738 www.elsevier.com/locate/actamat SUBCRITICAL CRACK GROWTH IN CVI SiCf/SiC COMPOSITES AT ELEVATED TEMPERATURES: EFFECT OF FIBER CREEP RATE C. H. HENAGER Jr†, C. A. LEWINSOHN‡ and R. H. JONES Pacific Northwest National Laboratory,§ Materials Sciences/P8-15, 902 Battelle Blvd, PO box 999, Richland, WA 99352-0999, USA ( Received 3 April 2000; received in revised form 9 July 2001; accepted 9 July 2001 ) Abstract—Subcritical crack-growth studies in SiCf/SiC composites were conducted with composites reinforced with Hi-Nicalon fibers over a broad temperature range for comparison to earlier studies on materials reinforced with Nicalon-CG fibers. Composites with a 0/90 plain weave architecture and carbon interphase were tested in argon from 1173 to 1473 K. Crack growth data obtained in inert environments are consistent with a proposed fiber-creep-controlled crack-growth mechanism. Measured crack-growth activation energies and time–temperature exponents in argon agree with fiber creep-activation energies and nonlinear creep equations for both fiber types. Estimates of local strains during crack growth are in reasonable agreement with estimated fiber creep strains for the given times and temperatures. The increased creep resistance of Hi-Nicalon fibers is reflected in reduced crack-growth rates for composites containing those fibers. 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Ceramics—structural; Composites; Mechanical properties—creep; High temperature; Fracture & fracture toughness 1. INTRODUCTION Continuous fiber ceramic matrix composites (CFCCs) are more reliable than unreinforced ceramics [1], but are prone to time-dependent failures from stable crack growth occurring in inert and oxidizing environments [2–7] or from mechanical embrittlement (unstable crack growth) caused by environmental exposure [8, 9]. In particular, we are interested in understanding time-dependent properties for these materials in gascooled advanced fission and fusion reactor environments [10–12]. Such environments are pristine in terms of oxygen content, and composites with carbonbased interphases appear attractive. Since life-prediction methodologies for these materials would necessarily include time-dependent crack growth as an important failure mechanism, it is essential to under- † To whom all correspondence should be addressed. E-mail address: chuck.henager@pnl.gov (C. H. Henager Jr) ‡ Research supported by Associated Western Universities, Inc., Northwest Division (AWU NW) under Grant DE-FG06-89ER-75522, DE-FG07-93ER-75912, or DEFG06-92RL-12451 with the US Department of Energy. § Pacific Northwest National Laboratory is operated for the US Department of Energy by Battelle under Contract DE-AC06-76RLO 1830. 1359-6454/01/$20.00 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6454(01)00276-2 stand critical time-dependent deformation mechanisms. Previous studies (this group and others) have shown that creep of bridging fibers at elevated temperatures in inert environments is one possible explanation for the observed creep or slow crack growth of these continuous-fiber composites where the SiC matrix is more creep resistant than the fibers [2, 3, 13–26]. These results support the hypothesis that creeping fibers transfer stress back to the matrix, causing further matrix cracking, a loss of matrix stiffness, and increased loading of the crack-bridging fibers, ultimately leading to failure. Recent results relevant to this work include experimental creep or crack-growth tests on SiCf/SiC composites [18, 19, 23–26] and models of time-dependent crack growth [27–31]. A more complete discussion of the models appears in a companion paper [32] and will not be included here. Evans and Weber [18] documented increased compliances due to matrix cracking and also observed fiber sliding stresses at 1473 K that were almost one order of magnitude smaller than at room temperature. Wilshire et al. [23] compared composite creep rates at 1573 K to fiber creep rates to demonstrate the degree of load transfer to the fibers that must occur due to matrix cracking to account for observed com-
3728 HENAGER et al. SUBCRITICAL CRACK GROWTH: PART I posite creep rates. They observed extensive matrix exponents if the understanding produced by the pre- cracking due to fiber creep and pointed out that this vious studies is correct. present authors have observed [4, 33). Zhu et al. [2 performed creep tests in air and argon at 1573 K on 2. EXPERIMENTAL APPROACH Hi-Nicalon-fiber SiC/SiC and Nicalon-CG-fiber The experimental approach has been described SiC/siC and made many of the same observations. more detail elsewhere [3] and will only be summar They did measure a slower creep rate and longer ized here. Subcritical crack growth was obtained by time-to-rupture for the Hi-Nicalon-fiber composite loading single-edge-notched beam(SENB)specimens attributed to a greater creep resistance of Hi-Nicalon (typically 50x55x4 mm)in 1/4 four-point bending in fibers compared to Nicalon-CG fibers [34]. Tressler a fully articulated silicon-carbide fixture with an outer al. [26] crept Hi-Nicalon-fiber SiC/SiC microcom- span length of 40 mm. We incorporated the specimen posites at 1473 to 1673 K and demonstrated a model and fixture in a vertically oriented mullite tube con that used explicit fiber and matrix creep data to tained within a high-temperature furnace mounted to account for creep deformation with and without an electromechanically controlled mechanical test matrix cracks. They observed transient creep curves frame. t The SENB specimens contained an initial for all materials and conditions in their study. A rule- notch with a depth-to-width ratio(all) of approxi- of-mixtures creep model was used for the material mately 0. 2. The notch was made by a high-speed dia- without matrix cracks, while a different approach mond saw and was typically 3.9x10-4 m wide at the suitable for a crack bridging fiber in tension was tip of the notch and 5.9x10-4 m wide at the mouth adopted for the cracked microcomposites No attempt was made to sharpen the notch. Speci- However, few studies have compared creep or mens were heated to the test temperature at a rate of crack-growth rates in materials with similar com- about 0. 25 K/s and were allowed to equilibrate for posite architecture but different fibers [13, 25, 35]. 1200 s at temperature. Then a load calculated [38]to Studies by the present authors [2-4, 13] have demon- provide an initial applied stress intensity of 9 to 10 strated that thermal activation energies for crack MPa m 2 was applied to the sample and held for the growth in inert environments are consistent with acti- duration of the test. This stress intensity was chosen vation energies measured for these same fibers in sin- to induce some initial crack extension and crack e-fiber creep or stress relaxation tests [34, 36]. bridging and it falls between that required for matrix However, this strong evidence for a crack growth cracking and the peak load fracture toughness, Ko, mechanism controlled by fiber creep would be bols- reported in Table 1. In addition, we periodically tered by supporting evidence in similar materials with unloaded to 95% of the constant applied load and then different fibers. Additional data would provide an reloaded; at the time of the initial loading and 5, 25 opportunity for testing our ability to model crack and 50 h after the initial loading to generate hysteresis growth in a specific specimen geometry using loops(for the Hi-Nicalon materials only) detailed fiber properties where the fiber type was the The atmosphere inside the mullite tube was con- most significant variable trollable and maintained at atmospheric pressure Moreover, since these composites are being con- (1.01x10 Pa). We used gettered argon, initially sidered for use in high-temperature, gas-cooled reac- 99.999% pure, for testing, with an oxygen content tor concepts [10-12], we are interested in lifetimes in reduced to less than 0.01 Pa by passing the gas ert environments or in low oxygen concentrations. through a titanium-gettering furnace. The deflection Many of the studies discussed above were performed of the specimen midpoint was measured by using ar in air, which is a very degrading environment, parti- alumina pushrod, also containing a thermocouple, cularly for CFCCs with a carbon-based fiber-matrix attached to a strain-gauge extensometer. The dis- interphase. This teaches us little about life prediction placements were corrected for differences between and failure mechanisms in environments where these the load-point and midpoint and for the compliance materials are seriously being considered for use. of the test apparatus 3] Therefore, we began the present study using similar An SiC/SiC CFCC containing Hi-NicalonTM fibers 0/90-woven, chemical vapor infiltration(CVI)-SiC was examined in this study and compared to the matrix CFCCs reinforced with Hi-Nicalon fibers to results of previous studies [2-4, 13] on materials con- compare with the previous Nicalon-CG fiber CFCCs taining "Ceramic-grade" Nicalon TM(Nicalon-CG) 24, 13]. This study is the first to critically compare fibers. Data obtained using the previous Nicalon-CG the effect of fiber creep characteristics on crack- materials were extended over a temperature range growth kinetics and activation energies in an inert from 1173 to 1398 K. The Hi-Nicalon materials were environment. Hi-Nicalon fibers have higher creep fabricated from two-dimensional, plain weave fiber activation energies and a reduced creep rate compared to Nicalon-CG fibers [34, 36, 37]. Composites made with Hi-Nicalon fibers should exhibit crack-growth ates and activation energies consis on fiber creep rates, activation energies, and creep t Instron1125,Instron Corp,Canton,MA,USA
3728 HENAGER et al.: SUBCRITICAL CRACK GROWTH: PART I posite creep rates. They observed extensive matrix cracking due to fiber creep and pointed out that this cracking facilitates environmental ingress, as the present authors have observed [4, 33]. Zhu et al. [25] performed creep tests in air and argon at 1573 K on Hi-Nicalon-fiber SiCf/SiC and Nicalon-CG-fiber SiCf/SiC and made many of the same observations. They did measure a slower creep rate and longer time-to-rupture for the Hi-Nicalon-fiber composite attributed to a greater creep resistance of Hi-Nicalon fibers compared to Nicalon-CG fibers [34]. Tressler et al. [26] crept Hi-Nicalon-fiber SiCf/SiC microcomposites at 1473 to 1673 K and demonstrated a model that used explicit fiber and matrix creep data to account for creep deformation with and without matrix cracks. They observed transient creep curves for all materials and conditions in their study. A ruleof-mixtures creep model was used for the material without matrix cracks, while a different approach suitable for a crack bridging fiber in tension was adopted for the cracked microcomposites. However, few studies have compared creep or crack-growth rates in materials with similar composite architecture but different fibers [13, 25, 35]. Studies by the present authors [2–4, 13] have demonstrated that thermal activation energies for crack growth in inert environments are consistent with activation energies measured for these same fibers in single-fiber creep or stress relaxation tests [34, 36]. However, this strong evidence for a crack growth mechanism controlled by fiber creep would be bolstered by supporting evidence in similar materials with different fibers. Additional data would provide an opportunity for testing our ability to model crack growth in a specific specimen geometry using detailed fiber properties where the fiber type was the most significant variable. Moreover, since these composites are being considered for use in high-temperature, gas-cooled reactor concepts [10–12], we are interested in lifetimes in inert environments or in low oxygen concentrations. Many of the studies discussed above were performed in air, which is a very degrading environment, particularly for CFCCs with a carbon-based fiber-matrix interphase. This teaches us little about life prediction and failure mechanisms in environments where these materials are seriously being considered for use. Therefore, we began the present study using similar 0/90-woven, chemical vapor infiltration (CVI)-SiC matrix CFCCs reinforced with Hi-Nicalon fibers to compare with the previous Nicalon-CG fiber CFCCs [2–4, 13]. This study is the first to critically compare the effect of fiber creep characteristics on crackgrowth kinetics and activation energies in an inert environment. Hi-Nicalon fibers have higher creep activation energies and a reduced creep rate compared to Nicalon-CG fibers [34, 36, 37]. Composites made with Hi-Nicalon fibers should exhibit crack-growth rates and activation energies consistent with Hi-Nicalon fiber creep rates, activation energies, and creep exponents if the understanding produced by the previous studies is correct. 2. EXPERIMENTAL APPROACH The experimental approach has been described in more detail elsewhere [3] and will only be summarized here. Subcritical crack growth was obtained by loading single-edge-notched beam (SENB) specimens (typically 50×5.5×4 mm) in 1/4 four-point bending in a fully articulated silicon-carbide fixture with an outer span length of 40 mm. We incorporated the specimen and fixture in a vertically oriented mullite tube contained within a high-temperature furnace mounted to an electromechanically controlled mechanical test frame.† The SENB specimens contained an initial notch with a depth-to-width ratio (a/W) of approximately 0.2. The notch was made by a high-speed diamond saw and was typically 3.9×104 m wide at the tip of the notch and 5.9×104 m wide at the mouth. No attempt was made to sharpen the notch. Specimens were heated to the test temperature at a rate of about 0.25 K/s and were allowed to equilibrate for 1200 s at temperature. Then a load calculated [38] to provide an initial applied stress intensity of 9 to 10 MPa m1/2 was applied to the sample and held for the duration of the test. This stress intensity was chosen to induce some initial crack extension and crack bridging and it falls between that required for matrix cracking and the peak load fracture toughness, KQ, reported in Table 1. In addition, we periodically unloaded to 95% of the constant applied load and then reloaded; at the time of the initial loading and 5, 25, and 50 h after the initial loading to generate hysteresis loops (for the Hi-Nicalon materials only). The atmosphere inside the mullite tube was controllable and maintained at atmospheric pressure (1.01×105 Pa). We used gettered argon, initially 99.999% pure, for testing, with an oxygen content reduced to less than 0.01 Pa by passing the gas through a titanium-gettering furnace. The deflection of the specimen midpoint was measured by using an alumina pushrod, also containing a thermocouple, attached to a strain-gauge extensometer. The displacements were corrected for differences between the load-point and midpoint and for the compliance of the test apparatus [3]. An SiCf/SiC CFCC containing Hi-Nicalon fibers was examined in this study and compared to the results of previous studies [2–4, 13] on materials containing “Ceramic-grade” Nicalon (Nicalon-CG) fibers. Data obtained using the previous Nicalon-CG materials were extended over a temperature range from 1173 to 1398 K. The Hi-Nicalon materials were fabricated from two-dimensional, plain weave fiber † Instron 1125, Instron Corp., Canton, MA, USA
HENAGER et al. SUBCRITICAL CRACK GROWTH: PART I 3729 Table 1. Physical properties of the materials tested(variability given as 95% confidence intervals) Composite designation CG-C Hi-C Fiber architecture 2D plain weave fiber mats 2D plain weave fiber mats thermal cvi at-1050°C othermal cvi at-1050° eramic-grade nical Fiber vol ameter(um) 14±2.3 ol. fractio Composite coating CVD SIC CVD SIC Modulus (GPa) 122±21 172±23 Fracture toughness, Ko(MPa m")5 nterface sliding stress(MPay 8.4+6.6 72.1±33.5 aWe do not have access to all the processing details for these vendor-supplied materials. However, the processing of these CVI-SiC/SiC The modulus is calculated from the measured from the linear portion of loading during flexural testing of SENB specimens at elevated temperatur ture compliance. "Calculated using peak load as described in ASTM E399 mEasured by fiber push-in test at room temperature as described in [43] mats.t Before matrix infiltration, a 1-um-thick carbon 3. RESULTS interphase layer was deposited on the fibers by chemi- 3. 1. Displacement-time cures each bend-bar were coated with a 2-um-thick layer The displacement-time curve for a representative of silicon carbide, deposited by CVD, to provide oxi- CG-C specimen tested at a constant load of 630 N at dation resistance and to protect the surfaces from 1373 K for 8x10 s in argon is a nonlinear curve( Fig damage. These materials will be abbreviated as"Hi- 1), suggestive of a transient creep curve, but indicate the fiber type and the interphase com- accompanied by subcritical, time-dependent crack position(Table 1) growth in a multiply-cracked damage zone(see The materials studied previously were fabricated in below) that extends from the notch root much as a a similar manner. t The Nicalon-CG fibers were also mode I crack. The data shown in Fig. I are the midp- oated with either a I-um-thick carbon interphase int displacement of the notched bar as a function of layer, a 0. 4-um-thick carbon/boron nitride(C/BN) time, t, and are compared to a functional fit of the interphase layer, or a I-Hm-thick multi-layer form nterphase layer consisting of carbon/boron carbide/boron nitride (C/B,C/BN), with the carbon f= alt exp(-bIDIe layer next to the fiber. These materials will be abbreviated"CG-C. The time-independent mechan- ical properties of the CG-C materials in argon were corresponds to a Sherby-Dorn creep equation entical, within experimental uncertainties, in a,b, and c are independent fitting parameters pendent of the interphase chemistry and thickness Composite properties and identification details are listed in Table 0.004 We tested Hi-C specimens at 1373, 1423, 1448 - fit to data nd 1473 K in argon ed 10 CG-C specimens tested at 1173, 1273, 1298, 1323, 5 1348,1373,and1398K gon. The Hi-C com-§610 sites were tested at temperatures higher than the CG-C materials because Hi-Nicalon fibers have greater thermal stability compared to Nicalon-CG 2I0 8105 t Composite fabrication performed by DuPont Lanxide Fig. 1. Displacement-time curve for a CG-C material(Table Corp, Wilmington, DE, USA 1)at 600 N constant load(corresp Composite fabrication performed by RCL, Whittier, m 2 )test at 1373 K in argon. Experi ve (solid line) CA, USA(RCI is no longer existent). is compared to equation(1)
HENAGER et al.: SUBCRITICAL CRACK GROWTH: PART I 3729 Table 1. Physical properties of the materials testeda (variability given as 95% confidence intervals) Composite designation CG-C Hi-C Fiber architecture 2D plain weave fiber mats 2D plain weave fiber mats Processing conditions Isothermal CVI at 1050°C Isothermal CVI at 1050°C Fiber type Ceramic-grade Nicalon Hi-Nicalon Fiber coating thickness (µm) 1.0±0.1 1.0±0.1 Fibers/tow 420 321 Fiber diameter (µm) 15.0±0.5 14±2.3 Fiber vol. fraction 40 40 Composite coating CVD SiC CVD SiC Porosity 20±5% 6±1.4% Modulus (GPa)b 122±21 172±23 Fracture toughness, KQ (MPa m1/2) c 17.5 22.4±0.1 Interface sliding stress (MPa)d 8.4±6.6 72.1±33.5 a We do not have access to all the processing details for these vendor-supplied materials. However, the processing of these CVI-SiC/SiC materials is rather standardized. b The modulus is calculated from the specimen compliance measured from the linear portion of loading during flexural testing of SENB specimens at elevated temperature and corrected for fixture compliance. c Calculated using peak load as described in ASTM E399. d Measured by fiber push-in test at room temperature as described in [43]. mats.† Before matrix infiltration, a 1-µm-thick carbon interphase layer was deposited on the fibers by chemical vapor deposition (CVD). The outer surfaces of each bend-bar were coated with a 2-µm-thick layer of silicon carbide, deposited by CVD, to provide oxidation resistance and to protect the surfaces from damage. These materials will be abbreviated as “HiC” to indicate the fiber type and the interphase composition (Table 1). The materials studied previously were fabricated in a similar manner.‡ The Nicalon-CG fibers were also coated with either a 1-µm-thick carbon interphase layer, a 0.4-µm-thick carbon/boron nitride (C/BN) interphase layer, or a 1-µm-thick multi-layer interphase layer consisting of carbon/boron carbide/boron nitride (C/B4C/BN), with the carbon layer next to the fiber. These materials will be abbreviated “CG-C.” The time-independent mechanical properties of the CG-C materials in argon were identical, within experimental uncertainties, independent of the interphase chemistry and thickness. Composite properties and identification details are listed in Table 1. We tested Hi-C specimens at 1373, 1423, 1448, and 1473 K in argon and compared the results with CG-C specimens tested at 1173, 1273, 1298, 1323, 1348, 1373, and 1398 K in argon. The Hi-C composites were tested at temperatures higher than the CG-C materials because Hi-Nicalon fibers have greater thermal stability compared to Nicalon-CG fibers. † Composite fabrication performed by DuPont Lanxide Corp., Wilmington, DE, USA. ‡ Composite fabrication performed by RCI, Whittier, CA, USA (RCI is no longer existent). 3. RESULTS 3.1. Displacement–time curves The displacement–time curve for a representative CG-C specimen tested at a constant load of 630 N at 1373 K for 8×105 s in argon is a nonlinear curve (Fig. 1), suggestive of a transient creep curve, but accompanied by subcritical, time-dependent crack growth in a multiply-cracked damage zone (see below) that extends from the notch root much as a mode I crack. The data shown in Fig. 1 are the midpoint displacement of the notched bar as a function of time, t, and are compared to a functional fit of the form: f a[t exp(b/T)]c (1) which corresponds to a Sherby–Dorn creep equation where a, b, and c are independent fitting parameters Fig. 1. Displacement–time curve for a CG-C material (Table 1) at 600 N constant load (corresponding to a Ka = 9.6 MPa m1/2) test at 1373 K in argon. Experimental curve (solid line) is compared to equation (1) (dashed line).
3730 HENAGER et al. SUBCRITICAL CRACK GROWTH: PART I 2.50 0.000l 三 ∠1398K 1473K 2 81 1510 g610 51 2 10 1273K CG-C 1373K 110421043104410451 Fig. 2. Displacement-time curves for a Nicalon-CG (CG-C) Fig 4. Displacement-time curves for identical Hi-C SENI range of 1273 he in 25 K temperature steps for 4XI0- four CG-C specimens tested at 1373 K in argon are included nt-time data were adjusted for each temperat and only the time-depen and T is the temperature in Kelvin. The 630 N load corresponds to an initial applied stress intensity (K) 9.6 MPa m/ at the initial normalized notch length f alW=0. 17(a=0.93 mm). We explored the tem perature dependence of this subcritical cracking for (a) the CFCC materials by performing identical tests over a range of temperatures(Figs 2-4). Initially, one specimen of the CG-C material was tested by taking it to progressively higher temperatures in argon, each exposure lasting for 4x10s(Fig. 2), from 1273 to 2 500 1398 K in 25 K increments and at a constant load of 630 N. The specimen was unloaded during tempera- 4001 ture increases and allowed to come to thermal equilib- rium at the new, higher temperature before it was Total plastic reloaded. Similar temperature-dependent data for the train at zero load CG-C material were obtained by performing identical 1373 K in argon where the specimens were held for elastic. ot tests on three separate specimens at 1 173, 1273, and 1030.000120.0016 longer times at constant loads corresponding to initial (b) K values of 10 MPa m(Fig. 3). The loading dis-70 placements of the samples are not shown--only the hours in Ar: min in O: le-dependent displacements under constant load are plotted in Figs 2-4 400 300 3105 l373K 2105010"21034105 11041.210-41.4104 273K Mid-Point Displacement (m) 1173K Fig. 5.(a)Load-displacement data showing unloading measured in flexure at 0. 5. 25. and 5 10 1105 1.510 2 10 ment on Hi-C material at 1448K in argon. Note that there is essentially no change in the appearance of the loops after 50 Fig. 3. Displacement-time curves for three identical CG-C cated(see Table 2).(b) Similar load-di The data were adjusted so that zero time coincides with th beginning of the time-dependent displacements. The loads on to 202 Pa O,(added each specimen correspond to a K,=10 MPa mn and loop widening, which is attributed to interphase recession
3730 HENAGER et al.: SUBCRITICAL CRACK GROWTH: PART I Fig. 2. Displacement–time curves for a Nicalon-CG (CG-C) SENB specimen tested at 600 N in argon over a temperature range of 1273 to 1398 K in 25 K temperature steps for 4×104 s per step. The displacement–time data were adjusted to zero for each temperature step and only the time-dependent displacements are shown. and T is the temperature in Kelvin. The 630 N load corresponds to an initial applied stress intensity (Ka) of 9.6 MPa m1/2 at the initial normalized notch length of a/W = 0.17 (a = 0.93 mm). We explored the temperature dependence of this subcritical cracking for the CFCC materials by performing identical tests over a range of temperatures (Figs 2–4). Initially, one specimen of the CG-C material was tested by taking it to progressively higher temperatures in argon, each exposure lasting for 4×104 s (Fig. 2), from 1273 to 1398 K in 25 K increments and at a constant load of 630 N. The specimen was unloaded during temperature increases and allowed to come to thermal equilibrium at the new, higher temperature before it was reloaded. Similar temperature-dependent data for the CG-C material were obtained by performing identical tests on three separate specimens at 1173, 1273, and 1373 K in argon where the specimens were held for longer times at constant loads corresponding to initial K values of 10 MPa m1/2 (Fig. 3). The loading displacements of the samples are not shown—only the time-dependent displacements under constant load are plotted in Figs 2–4. Fig. 3. Displacement–time curves for three identical CG-C SENB specimens tested at 1373, 1273, and 1173 K in argon. The data were adjusted so that zero time coincides with the beginning of the time-dependent displacements. The loads on each specimen correspond to a Ka = 10 MPa m1/2. Fig. 4. Displacement–time curves for identical Hi-C SENB specimens tested at 1373 to 1473 K in argon. The curves for four CG-C specimens tested at 1373 K in argon are included for comparison. Fig. 5. (a) Load–displacement data showing unloading– reloading hysteresis loops measured in flexure at 0, 5, 25, and 50 h, respectively, during a subcritical-crack-growth experiment on Hi-C material at 1448 K in argon. Note that there is essentially no change in the appearance of the loops after 50 h of crack growth. Elastic, inelastic, and plastic strains are indicated (see Table 2). (b) Similar load–displacement data showing unloading–reloading hysteresis loops at 0, 5, 25 h in argon at 1448 K but immediately followed by exposure during testing to 202 Pa O2 (added to argon gas feed). Note the slope decrease and loop widening, which is attributed to interphase recession
HENAGER et al: SUBCRITICAL CRACK GROWTH: PART I Table 2. SCG specimens total strain and time data for representative CG-C and Hi-C materials Specimen ID Test temperature(K) Test duration(s) ent Strain at load Strain at unloading displacement"(m) 戀 1.0x10-4 2.0×10-2 1473 12×10 1.82×105 1373 2.73×105 5.6×10 5.5×10-3 ent at load excluding elastic and inelastic loading displacements(Fig. 5a). sing four-point bending relation between outer fiber strain and specimen deflection but allowing the displacement only in the see equation(7)and Table 3). Subcritical-crack-growth (SCG) data for Hi-C immediately followed by naterials are similar to those of the previously tested (pO2=202 Pa) for which the hysteresis loops appear CG-C materials [2-4, 13]. The temperature depen- distinctly different(Fig. 5b). Although the fidelity of dence of cracking in the Hi-C materials was investi- these hysteresis curves lacks the precision required gated by testing separate and identical specimens at to obtain detailed information regarding interface slip 1373, 1423, 1448, and 1473 K(Fig. 4) at constant transfer(because of surrounding elastic unloading of ads corresponding to initial Ka values of 10 MPa the SENB specimen), it is apparent that the interface m. The displacement-time curves for several CG- mechanical properties are unchanged when compared C specimens tested at 1373 K are included for com- to oxidation-induced interface removal mechanism parison with the Hi-C materials 42,43] recoverable, strain during the scG testing (Table 2), 3.2. Subcritical crack growth damage sone both under load and unloaded (for selected The resultant cracking observed under these con- specimens). It was found that the total plastic strain ditions for CG-C materials is shown in Fig. 6a in an under load was equal to the total plastic strain after optical micrograph of a polished SENB cross-section, unloading for the specimens where an accurate value where the section was taken from the center of the for the inelastic loading strain due to matrix cracking SENB bar by cutting the bar lengthwise parallel to the on loading above the matrix cracking stress was crack propagation direction and normal to the plane obtained. In addition, we investigated the possibility containing the cracks. Multiple cracks are seen in the that other inelastic deformation mechanisms were CVI-SiC matrix material. but little fiber breakage is responsible for the observed behavior by qualitatively observed, even at the root of the notch where the analyzing unloading-reloading hysteresis loops that crack opening displacement would be the largest were performed periodically during the crack-growth schematic of the cracked damage zone is shown in experiments on the Hi-C materials(Fig 5a). The load Fig. 6b. A single Hi-C specimen was also sectioned versus displacement data for the hysteresis loops and showed similar multiple cracking (uncorrected for machine compliance) in inert Several specimens were tested, unloaded while at environments exhibited characteristics observed by temperature, cooled with no applied load, and then others [39-41]. In contrast to this, we also show hys- sectioned for optical microscopy of the cracks and of teresis loops for a specimen tested in argon but the damage zone. Data from these nens, In microscopy of sectioned SCG specime emperature Test duration Initial crack Number of cracks"(n) Dam ength(m) length(m) CG-C-I ■睡 Hi-C-2 2.0×105 1,12×10-3 265×10-3 1.45×10-3 3.6×10-4 Initial number emanating from notch and final number at maximum damage zone extent final crack length)
HENAGER et al.: SUBCRITICAL CRACK GROWTH: PART I 3731 Table 2. SCG specimens total strain and time data for representative CG-C and Hi-C materials Specimen ID Test temperature (K) Test duration (s) Total time-dependent Strain at loadb Strain at unloading displacementa (m) CG-C-1 1373 1.16×104 1.32×105 2.6×103 – CG-C-2 1373 7.45×104 2.82×105 5.6×103 – CG-C-3 1373 9.62×104 3.7×105 7.5×103 – CG-C-4 1373 6.22×105 9.2×105 1.85×102 – CG-C-5 1373 7.65×105 1.0×104 2.0×102 – Hi-C-1 1473 1.81×105 1.04×104 1.7×102 – Hi-C-2 1448 2.0×105 7.3×105 1.2×102 1.2×102 Hi-C-3 1423 1.82×105 4.4×105 7.3×103 – Hi-C-4 1373 2.73×105 3.35×105 5.6×103 5.5×103 a Specimen mid-point displacement at load excluding elastic and inelastic loading displacements (Fig. 5a). b Strain computed at notch root using four-point bending relation between outer fiber strain and specimen deflection but allowing the displacement to occur only in the damage zone (see equation (7) and Table 3). Subcritical-crack-growth (SCG) data for Hi-C materials are similar to those of the previously tested CG-C materials [2–4, 13]. The temperature dependence of cracking in the Hi-C materials was investigated by testing separate and identical specimens at 1373, 1423, 1448, and 1473 K (Fig. 4) at constant loads corresponding to initial Ka values of 10 MPa m1/2. The displacement–time curves for several CGC specimens tested at 1373 K are included for comparison with the Hi-C materials. Data were obtained for the total “plastic,” or nonrecoverable, strain during the SCG testing (Table 2), both under load and unloaded (for selected specimens). It was found that the total plastic strain under load was equal to the total plastic strain after unloading for the specimens where an accurate value for the inelastic loading strain due to matrix cracking on loading above the matrix cracking stress was obtained. In addition, we investigated the possibility that other inelastic deformation mechanisms were responsible for the observed behavior by qualitatively analyzing unloading–reloading hysteresis loops that were performed periodically during the crack-growth experiments on the Hi-C materials (Fig. 5a). The load versus displacement data for the hysteresis loops (uncorrected for machine compliance) in inert environments exhibited characteristics observed by others [39–41]. In contrast to this, we also show hysteresis loops for a specimen tested in argon but Table 3. Summary of optical microscopy of sectioned SCG specimens Test Temperature Test duration Initial crack Final crack Number of cracksa (n) Damage zone Mean crack specimen (K) (s) length (m) length (m) width (m) spacing (m) Initial Final CG-C-1 1373 1.16×104 1.0×103 1.18×103 1 – – CG-C-2 1373 7.45×104 0.82×103 1.62×103 9 5 1.24×103 2.5×104 CG-C-3 1373 9.62×104 0.93×103 1.95×103 8 3 1.14×103 3.8×104 CG-C-4 1373 6.22×105 0.76×103 2.44×103 10 4 1.33×103 3.3×104 CG-C-5 1373 7.65×105 0.93×103 2.75×103 10 5 1.24×103 2.5×104 Average –––– 9 4 1.24×103 3.0×104 CG-C Hi-C-2 1448 2.0×105 1.12×103 2.65×103 4 1.45×103 3.6×104 a Initial number emanating from notch and final number at maximum damage zone extent (final crack length). immediately followed by testing in oxygen (pO2 = 202 Pa) for which the hysteresis loops appear distinctly different (Fig. 5b). Although the fidelity of these hysteresis curves lacks the precision required to obtain detailed information regarding interface slip transfer (because of surrounding elastic unloading of the SENB specimen), it is apparent that the interface mechanical properties are unchanged when compared to oxidation-induced interface removal mechanisms [42, 43]. 3.2. Subcritical crack growth damage zone The resultant cracking observed under these conditions for CG-C materials is shown in Fig. 6a in an optical micrograph of a polished SENB cross-section, where the section was taken from the center of the SENB bar by cutting the bar lengthwise parallel to the crack propagation direction and normal to the plane containing the cracks. Multiple cracks are seen in the CVI–SiC matrix material, but little fiber breakage is observed, even at the root of the notch where the crack opening displacement would be the largest. A schematic of the cracked damage zone is shown in Fig. 6b. A single Hi-C specimen was also sectioned and showed similar multiple cracking. Several specimens were tested, unloaded while at temperature, cooled with no applied load, and then sectioned for optical microscopy of the cracks and of the damage zone. Data from these specimens, in
3732 HENAGER et al: SUBCRITICAL CRACK GROWTH: PART I Crack her argon and agree with fiber-creep activation energies for both fiber types. Optical microscopy reveals multiply cracked damage zone, and crack lengths are obtained for comparison with model results. We esti- mate the total plastic strain from the specimen dis- placements and find that these values compare favor A ably with estimates of single-fiber creep strains under Notch S Damage similar conditions. Crack velocities are calculated from the optical measurements of crack lengtH 4.1. Fiber creep properties and activation energies Previous investigations of subcritical crack growth 0.2 mm in CG-C composites by Henager and colleagues [2 4, 13] hypothesized that fiber creep is the rate-con- Cyy =100 MPa trolling deformation mechanism for crack extension cracking stress in an inert environment This is not th case for those materials tested in oxygen-containing environments [4, 33, 42, 44]. However, in inert environments at temperatures above about 1000 K, cracks bridged with fine-grained ceramic fibers width,D extend under applied loads, apparently due to a decrease in crack shielding caused by fiber creep in the crack wake. Both the crack-tip stress intensities and crack-opening displacements are shown to be time dependent because of the relaxation of the crack- wake bridging forces resulting from creep of the bridging fibers [2-4, 13]. Matching the measured Multiple Cracked Damage Zone temperature dependence of the cracking, using an activation-energy analysis, with the activation energy fter 6 2x10 s at 1373 K in argon. (b)Sche. for creep in Nicalon-CG fibers was a significant step micrograph of polished sections of tested zone showing parameters discussed in text in identifying the mechanism that dominates the rate and in ontour of constant o,, of 100 MPa of width of cracking [4]. However, this hypothesis would be 1.2 mm is super this schematic strengthened by including crack-growth rates in materials with other fibers, comparing the results in ms of test time, test temperature, number of cracks terms of published fiber-creep parameters as was done he damage zone and crack are listed in previously [4]. This is useful in understanding the dif Table 3. The cracks were hard to follow from the ferences between crack growth controlled by fiber notch through the 0o-plies, but in several cases, the creep versus other time-dependent relaxation pro- entire set of cracks(in that one plane)could be cesses, such as viscous sliding or oxidative interface maged and measured. Although the cracks were dif. removal mechanisms [4, 5, 45] ficult to image it appears that crack shedding is occur- Previous scg data were presented by computing ring as the cracks propagate away from the notch, crack velocities from displacement-time data using with the number of cracks decreasing by a factor of standard linear-elastic relationships between displace two. The crack length data for the CG-C specimens ments in bending and crack lengths. If our hypothes are more complete since only a single Hi-C specimen Is correct, the time-dependent displacement of the was sectioned specimens is proportional to the creep rate of the fib- ers and the displacement-time curves can be used to determine activation energies for crack growth 4. DISCUSSION AND ANALYSIS OF RESULTS Therefore, measured displacement rates are adequate This paper describes time-dependent crack-growth for this study. The shapes of the displacement-time experiments performed with two types of fibers and curves are similar for the CG-C and Hi-C materials these results are used to explore the effects of fiber and exhibit a power-law form(Figs 1-4). DiCarlo et reep rates on the subcritical-crack-growth behavior al. [34, 36, 37, 4648] have performed the most sig- f SiC/SiC composites. The experimental findings nificant amount of single fiber-creep testing and have support the hypothesis that fiber creep controls the developed an extensive database of creep properties rate of crack extension in these composite materials. and empirical fitting parameters to a Sherby-Dorn Activation energit
3732 HENAGER et al.: SUBCRITICAL CRACK GROWTH: PART I Fig. 6. (a) Optical micrograph of polished sections of tested CG-C specimen after 6.2×105 s at 1373 K in argon. (b) Schematic of damage zone showing parameters discussed in text and in Table 3. Contour of constant syy of 100 MPa of width 1.2 mm is superimposed on this schematic. terms of test time, test temperature, number of cracks in the damage zone, and crack lengths, are listed in Table 3. The cracks were hard to follow from the notch through the 0°-plies, but in several cases, the entire set of cracks (in that one plane) could be imaged and measured. Although the cracks were dif- ficult to image it appears that crack shedding is occurring as the cracks propagate away from the notch, with the number of cracks decreasing by a factor of two. The crack length data for the CG-C specimens are more complete since only a single Hi-C specimen was sectioned. 4. DISCUSSION AND ANALYSIS OF RESULTS This paper describes time-dependent crack-growth experiments performed with two types of fibers and these results are used to explore the effects of fiber creep rates on the subcritical-crack-growth behavior of SiCf/SiC composites. The experimental findings support the hypothesis that fiber creep controls the rate of crack extension in these composite materials. Activation energies are calculated for cracking in argon and agree with fiber-creep activation energies for both fiber types. Optical microscopy reveals a multiply cracked damage zone, and crack lengths are obtained for comparison with model results. We estimate the total plastic strain from the specimen displacements and find that these values compare favorably with estimates of single-fiber creep strains under similar conditions. Crack velocities are calculated from the optical measurements of crack length. 4.1. Fiber creep properties and activation energies Previous investigations of subcritical crack growth in CG-C composites by Henager and colleagues [2– 4, 13] hypothesized that fiber creep is the rate-controlling deformation mechanism for crack extension when these composites are loaded above the matrix cracking stress in an inert environment. This is not the case for those materials tested in oxygen-containing environments [4, 33, 42, 44]. However, in inert environments at temperatures above about 1000 K, cracks bridged with fine-grained ceramic fibers extend under applied loads, apparently due to a decrease in crack shielding caused by fiber creep in the crack wake. Both the crack-tip stress intensities and crack-opening displacements are shown to be time dependent because of the relaxation of the crackwake bridging forces resulting from creep of the bridging fibers [2–4, 13]. Matching the measured temperature dependence of the cracking, using an activation-energy analysis, with the activation energy for creep in Nicalon-CG fibers was a significant step in identifying the mechanism that dominates the rate of cracking [4]. However, this hypothesis would be strengthened by including crack-growth rates in materials with other fibers, comparing the results in terms of published fiber-creep parameters as was done previously [4]. This is useful in understanding the differences between crack growth controlled by fiber creep versus other time-dependent relaxation processes, such as viscous sliding or oxidative interface removal mechanisms [4, 5, 45]. Previous SCG data were presented by computing crack velocities from displacement–time data using standard linear-elastic relationships between displacements in bending and crack lengths. If our hypothesis is correct, the time-dependent displacement of the specimens is proportional to the creep rate of the fibers and the displacement–time curves can be used to determine activation energies for crack growth. Therefore, measured displacement rates are adequate for this study. The shapes of the displacement–time curves are similar for the CG-C and Hi-C materials and exhibit a power-law form (Figs 1–4). DiCarlo et al. [34, 36, 37, 46–48] have performed the most significant amount of single fiber-creep testing and have developed an extensive database of creep properties and empirical fitting parameters to a Sherby–Dorn transient creep expression as:
HENAGER et al. SUBCRITICAL CRACK GROWTH: PART I e. Ao'Pexpl=pgs fiber-creep activation energies for those particular (2)fibers, respectively. The agreement is best for Hi-C and less good for CG-C. Fabrication differences in Nicalon-CG fibers over the years may be one cause In equation(2), E is the creep strain, A is a constant, of this discrepancy. The single fiber-creep data indi- o is the applied stress, n is the stress exponent, t is cate that the d'o term should be significantly differ time, @e is the true activation energy, p is the time- ent for the Nicalon-CG and Hi-Nicalon fibers(Table temperature exponent, and the other symbols have 4), which is also observed in the experimental fits their usual meanings. Values for these parameters are The time-temperature exponent, P, for CG-C and Hi listed in Table 4. DiCarlo et al.[34] report activation C composites is similar in the crack-growth fits. How energies of 600 kJ/mol for Hi-Nicalon fibers and 500 ever, since the observed deformation is transient, and kJ/mol for Nicalon-CG fibers between 1473 to 1673 other parameters are involved, such as the stress K in air, up to 1% strain at stresses ranging from 200 exponent, these comparisons must be done with care to 400 MPa. This activation-energy determination is Nonetheless, the agreement between the activation based on the transient creep analysis of Sherby and energies for fiber creep and subcritical crack growth Don [49], from which one obtains the power-law (or displacement) supports the hypothesis that fiber unctional form used by DiCarlo. This approach avo- creep controls the rate of crack extension in these ids the assumption that the activated process has composites. reached a steady state, which is probably not true for Others have also investigated high-temperature either fiber creep of Hi-Nicalon fibers (Table 5), but the acti- Therefore, our displacement-time data were fit to vation energies shown in Table 5 differ widely. Part of the discrepancy is related to observations regarding apparent steady-state creep versus transient-creep A'σpexp (3)egimes. The analysis for determining activation ener- ies depends greatly on this interpretation [50]. Note that for the Sherby-Dorn analysis, the product of p, the time-temperature exponent, and @c, the true acti- where 8mp is the midpoint displacement of the speci- vation energy, equals the apparent activation energy mens.For the fit, the term a" was treated as a single one would obtain assuming a steady-state creep rate parameter, and the three parameters(Ao" @e, and p) Another explanation is that the creep characteristics were simultaneously determined for each material of Hi-Nicalon fibers are sensitive to oxygen concen- type from the displacement, time, and temperature tration. The differences in values reported by these data. Since all the composite data were obtained at a groups may be a result of variable experimental con- obtained for a stress exponent. The fit parameters in the material propenes o ed ment, or variations gle stress-intensity level, no information was ditions, especially the test enviro rs among separate Table 4)are in good agreement with those obtained manufacturing batches by DiCarlo et al. [34, 36, 37, 4648] using single- The increased creep of the hi-Nicalon data. In particular, measured activation fibers improves the th resistance of the energies for crack growth in composites with either composites [13, 25 displacement-time Hi-Nicalon or Nicalon -CG fibers agree with measured curves for the Hi-C materials reflect the reduced dis- Table 4. Fiber creep data and composite crack growth data Fiber: experimental fit Creep parameters f=Ao"Pexp(-po kn) A(MP asp) P @.(kJ/mol) Nicalon-CG Composite. experimental Displacement-time fit parameters A'ofrexp(-QJkn Ao(m s-p) G-C long-term(Fi CG-C short-term(Fig. 2) 8.2+0.6 430±3 Fitting equation and parameters from DiCarlo et al.[34] b Fitting equation shown, but term Ao treated as a single parameter
HENAGER et al.: SUBCRITICAL CRACK GROWTH: PART I 3733 ec Asn t p exp pQc kT (2) In equation (2), ec is the creep strain, A is a constant, s is the applied stress, n is the stress exponent, t is time, Qc is the true activation energy, p is the time– temperature exponent, and the other symbols have their usual meanings. Values for these parameters are listed in Table 4. DiCarlo et al. [34] report activation energies of 600 kJ/mol for Hi-Nicalon fibers and 500 kJ/mol for Nicalon-CG fibers between 1473 to 1673 K in air, up to 1% strain at stresses ranging from 200 to 400 MPa. This activation-energy determination is based on the transient creep analysis of Sherby and Dorn [49], from which one obtains the power-law functional form used by DiCarlo. This approach avoids the assumption that the activated process has reached a steady state, which is probably not true for either fiber. Therefore, our displacement–time data were fit to the following: dmp Asn t p exp pQ kT (3) where dmp is the midpoint displacement of the specimens. For the fit, the term Asn was treated as a single parameter, and the three parameters (Asn , Qc, and p) were simultaneously determined for each material type from the displacement, time, and temperature data. Since all the composite data were obtained at a single stress-intensity level, no information was obtained for a stress exponent. The fit parameters (Table 4) are in good agreement with those obtained by DiCarlo et al. [34, 36, 37, 46–48] using single- fiber creep data. In particular, measured activation energies for crack growth in composites with either Hi-Nicalon or Nicalon-CG fibers agree with measured Table 4. Fiber creep data and composite crack growth data Fibera : experimental fit Creep parameters e = Asn t p exp(pQc/kT) A (MP an sp ) npQc (kJ/mol) Hi-Nicalon 121 1.8 0.58 600 Nicalon-CG 1.5 1.2 0.40 500 Compositeb : experimental Displacement–time fit parameters fit dmp = Asn [t exp(Qc/kT)]p Asn (m sp ) p Qc (kJ/mol) Hi-C long-term (Fig. 4) 340±60 0.40±0.004 614±8 CG-C long-term (Fig. 3) 0.2±0.03 0.41±0.005 374±6 CG-C short-term (Fig. 2) 8.2±0.6 0.49±0.003 430±3 a Fitting equation and parameters from DiCarlo et al. [34]. b Fitting equation shown, but term Asn treated as a single parameter. fiber-creep activation energies for those particular fibers, respectively. The agreement is best for Hi-C and less good for CG-C. Fabrication differences in Nicalon-CG fibers over the years may be one cause of this discrepancy. The single fiber-creep data indicate that the Asn term should be significantly different for the Nicalon-CG and Hi-Nicalon fibers (Table 4), which is also observed in the experimental fits. The time–temperature exponent, p, for CG-C and HiC composites is similar in the crack-growth fits. However, since the observed deformation is transient, and other parameters are involved, such as the stress exponent, these comparisons must be done with care. Nonetheless, the agreement between the activation energies for fiber creep and subcritical crack growth (or displacement) supports the hypothesis that fiber creep controls the rate of crack extension in these composites. Others have also investigated high-temperature creep of Hi-Nicalon fibers (Table 5), but the activation energies shown in Table 5 differ widely. Part of the discrepancy is related to observations regarding apparent steady-state creep versus transient-creep regimes. The analysis for determining activation energies depends greatly on this interpretation [50]. Note that for the Sherby–Dorn analysis, the product of p, the time–temperature exponent, and Qc, the true activation energy, equals the apparent activation energy one would obtain assuming a steady-state creep rate. Another explanation is that the creep characteristics of Hi-Nicalon fibers are sensitive to oxygen concentration. The differences in values reported by these groups may be a result of variable experimental conditions, especially the test environment, or variations in the material properties of the fibers among separate manufacturing batches. The increased creep resistance of the Hi-Nicalon fibers improves the crack-growth resistance of the composites [13, 25, 35]. The displacement–time curves for the Hi-C materials reflect the reduced dis-
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 are
3734 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 published creep parameters for Nicalon-CG and Hi-Nicalon 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 specimens, where the test was interrupted before final failure 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–displacement curve in Fig. 5a. Stresses above the matrix cracking stress cause multiple cracking at the specimen notch. The notch acts as a stress concentration, and the damage is contained within a zone approximately 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 1×103 m and r is 2.5×104 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 6.4×102 s MPa m1/2 which compares to that for a sharp crack (SENB specimen [53]) of KI = 5.9×102 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 modeI crack ry(q) 1 2p KMC I syy 2 [cos q 2 6 (32 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 1.2×103 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 largest. This supports the hypothesis that fiber creep acts to unload the bridging fibers and allow crack propagation without fiber fracture [55]. A mean-crack spacing of 1.4×104 m (140 µm) obtains in the CG-C materials at 1373 K for the initial cracking from the notch while this spacing increases to 3.0×104 m (300 µm) after substantial crack growth and crack shedding. Calculated crack spacings, using parameters for our CG-C materials (Table 1) and assuming a matrix cracking stress of 100 MPa, range from 1.5×104 to 3.1×104 m (150 to 300 µm). Crack spacings are about 3.6×104 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 cracking 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
HENAGER et al. SUBCRITICAL CRACK GROWTH: PART I 3735 not uniform throughout the thickness of the com- The permanent strain at zero load, ET(o), includes con- posite. We were unable to quantify this finding but tributions from misfit relief and sliding, E6, and per- this would seem to be a consequence of the 2D woven manent plastic strain, eB(O), such that architecture, which results in overlapping 0/90 fiber tows and relatively large volumes of CVI SiC matrix HO=E+ EB() material containing crossover voids 144. We often observe cracking associated with these larger micro- Given that e is recovered on unloading, that eo is structural features. Still, every crack path through approximately equal to es, and that e<ep(o), then these composite materials must be bridged by fibers eP() is essentially equal to EB(), as observed. This in several layers permanent strain, EB() is equated with the damage 43. Accumulated plastic strain zone strain, Epz, calculated in equation (7)and is assumed to be due to fiber creep in the damage zone Our hypothesis also implies that there is a relation- ship between crack growth and the measured perma- and permanent plastic strain is explored in Fig. 7a, nent plastic strain if the crack growth is controlled by where the time-dependent permanent strain(Table 2) fiber creep. We observed that crack propagation is is shown as a function of time-dependent crack length accompanied by permanent specimen deflection, or (Table 3). The relationship is nearly a linear one sug- strain,in proportion to test duration, or crack length, gesting that crack propagation and permanent strai at constant load and temperature Table 2). The per- are related by a common mechanism manent specimen strains are not recovered on Assuming both permanent strain and crack exten- unloading(Fig. 5 and Table 2). We estimate these sion are caused by fiber creep, then these two quan- strains by calculating the strain in the damage zone, tities should reflect similar kinetics to each other and Epz, due to the multiple cracking as follows: to fiber ci ship is explored(Fig. 7b) by plotting crack length and strain as functions of 1152 time and applying the Sherby-Dorn function in a non- where the first bracketed term is the bending formula 0.025 for strain as a function of midpoint displacement, 8n and s is the outer span length. The term(w-ao)cor-002 rects for the notch depth, ao is the initial notch length, a and Epz is then the strain at the notch root. The second 0.015 term corrects for the fact that the strain is assumed tg occur only in the damage zone of width nd, where 3 0.01 Linear Fit the number of cracks (Table 3), and s/2 is the inner span. There is an initial stress concentration due to 0.005 the notch that falls off as the cracks propagate into 0.002 Once the cracks are a distance ao from the blunt notch Crack Length (m) the stress concentration of the notch has decreased from 4.0 to 1. 5 [57] However, this stress concen tration is accounted for by using the experimental dis placement data in Table 2, which reflect crack exten- of the notch. these strains are tabulated in table 2 E using values for nd equal to 1. 24x10-3 m and oo 0.02 Two of the Hi-c tests. where more detailed unloading-reloading tests were performed, show that measured strains at load and after unloading are the 0.001 same. The total specimen strain at load and as a func- 10610 tion of time, E,(O), can be written as the sum of elastic Time(s strain,e, inelastic loading strain due to matrix crack ing and misfit strain relief, es, and time-dependent Fig. 7,(a)Relationship between calculated g strain and plastic) strain, ep(o),as crack length for sectioned CG-C specimens after testing at 73 K(b) Crack length time showing similarities in kinetics and Sherby -Dorn fit (8) (dashed and dotted curves) for CG-C specimens at 1373
HENAGER et al.: SUBCRITICAL CRACK GROWTH: PART I 3735 not uniform throughout the thickness of the composite. We were unable to quantify this finding but this would seem to be a consequence of the 2D woven architecture, which results in overlapping 0/90 fiber tows and relatively large volumes of CVI SiC matrix material containing crossover voids [44]. We often observe cracking associated with these larger microstructural features. Still, every crack path through these composite materials must be bridged by fibers in several layers. 4.3. Accumulated plastic strain Our hypothesis also implies that there is a relationship between crack growth and the measured permanent plastic strain if the crack growth is controlled by fiber creep. We observed that crack propagation is accompanied by permanent specimen deflection, or strain, in proportion to test duration, or crack length, at constant load and temperature (Table 2). The permanent specimen strains are not recovered on unloading (Fig. 5 and Table 2). We estimate these strains by calculating the strain in the damage zone, eDZ, due to the multiple cracking as follows: eDZ 48(wa0)dmp 11s2 s 2nd¯ (7) where the first bracketed term is the bending formula for strain as a function of midpoint displacement, dmp, and s is the outer span length. The term (wa0) corrects for the notch depth, a0 is the initial notch length, and eDZ is then the strain at the notch root. The second term corrects for the fact that the strain is assumed to occur only in the damage zone of width nd¯, where d¯ is the mean crack spacing in the damage zone, n is the number of cracks (Table 3), and s/2 is the inner span. There is an initial stress concentration due to the notch that falls off as the cracks propagate into the uniform bending field of the SENB specimen. Once the cracks are a distance a0 from the blunt notch the stress concentration of the notch has decreased from 4.0 to 1.5 [57]. However, this stress concentration is accounted for by using the experimental displacement data in Table 2, which reflect crack extension and subsequent SENB deflection in the presence of the notch. These strains are tabulated in Table 2 using values for nd¯ equal to 1.24×103 m and 1.45×103 m for CG-C and Hi-C materials, respectively. Two of the Hi-C tests, where more detailed unloading–reloading tests were performed, show that measured strains at load and after unloading are the same. The total specimen strain at load and as a function of time, eT(t), can be written as the sum of elastic strain, ee , inelastic loading strain due to matrix cracking and misfit strain relief, es , and time-dependent (plastic) strain, ep (t), as eT(t) ee es ep (t) (8) The permanent strain at zero load, e0 T(t), includes contributions from misfit relief and sliding, es 0, and permanent plastic strain, ep 0(t), such that e0 T(t) es 0 ep 0(t) (9) Given that ee is recovered on unloading, that es 0 is approximately equal to es , and that es ep (t), then ep (t) is essentially equal to ep 0(t), as observed. This permanent strain, ep 0(t) is equated with the damage zone strain, eDZ, calculated in equation (7) and is assumed to be due to fiber creep in the damage zone only. The relationship between measured crack length and permanent plastic strain is explored in Fig. 7a, where the time-dependent permanent strain (Table 2) is shown as a function of time-dependent crack length (Table 3). The relationship is nearly a linear one suggesting that crack propagation and permanent strain are related by a common mechanism. Assuming both permanent strain and crack extension are caused by fiber creep, then these two quantities should reflect similar kinetics to each other and to fiber creep. This relationship is explored (Fig. 7b) by plotting crack length and strain as functions of time and applying the Sherby–Dorn function in a nonFig. 7. (a) Relationship between calculated bending strain and crack length for sectioned CG-C specimens after testing at 1373 K. (b) Crack length and bending strain as functions of time showing similarities in kinetics and Sherby–Dorn fits (dashed and dotted curves) for CG-C specimens at 1373 K.
3736 HENAGER et al. SUBCRITICAL CRACK GROWTH: PART I linear least squares fit(dashed curves). The fit para- 4.4. Crack velocities meters are in close agreement to the fits obtained fror the displacement-time curves and the fiber creep data, The crack velocity as a function of time is shown ga for the Cg-C materials calculated from th Table 4). Of course, since the specimen strain is pro- crack length as a function of the time curve of fig portional to the specimen displacement, this connec- tion is expected. However, it is not obvious that this 7b. Crack velocities are in the range of 10-9 m/s after would also hold for crack length e further checked the hypothesis short times. This is compared with a calculated crack controlling crack extension and permanent strain in velocity curve using an effective elastic crack nese materials by comparing the permanent strain as odology presented in previous studies [24, 13, 35, 601, based on the use of specimen compliance [61] a function of time(Table 2)with the calculated creep There is no calculable relation between compliance strain of Nicalon-CG and Hi-Nicalon fibers for the and crack length(damage zone extent) without a same time period using equation(2). The result shown in Fig. 8 for Nicalon-CG. This comparison is priori knowledge of the crack density and crack-face forces as a function of time, temperature, and applied approximate, but the observed reasonable agreement load. In general, these are not known. Making the suggests our rough strain calculations are of the cor- rect magnitude. The comparison assumes a uniform appropriate connection between crack length and compliance requires an explicit crack-bridging model good for the single Hi-C data point(Table 2)but is argument. This is particularly true when multiple within a factor of two(5.7x10-3 calculated and cracking occurs. The linear-elastic compliance-crack length relation [3] should underpredict actual crack 2x10-2 for specimen Hi-C-2). Therefore, it seems lengths since the bridging forces stiffen a mode-I reasonable to suggest that the strain in the damage crack relative to an unbridged crack( Fig. 9b).Since zone can be accounted for by fiber creep Finally, we qualitatively analyzed the hysteres this is not observed, we conclude that the multiple loops for changes in loop width. We observed no changes in loop widths as a function of time for any (a) of the specimens for which hysteresis loops were btained, although we note that these loops lack the fidelity of loops from tensile tests. Si Ince loop crack length data(Fig. 7b) width is sensitive to the value of the sliding stres [39-41, 58], we conclude that there is no time-depe dence for the sliding stress in this experiment, with the above caveat. a change in width would sugges pend was operative. Therefore, it is unlikely that any other -- time-dependent mechanism, such as interphase oxi- elastic crack length dation or viscous sliding between the fiber and matrix, is operable in argon [5]. This turns out not to be the ase for those materials tested in argon-oxygen mix- Time(s) tures 14, 42, 59](Fig. 5b) for which loop width changes in bending are readily observed (b) Crack 0.0025 0.015 4105 810 Time(s) 2105 6105 8 10 Fig. 9.(a)Experimental crack velocity, calculated from the privative of the fitted crack length vs. time curve in Fig. 7b compared to an effective elastic-crack calculation 3].(b) Fig 8. Experimental strains(Table 2)compared to calculated Experimental crack length compared to effective elastic creep strain for Nicalon-CG fibers at 1373 K. The calculated length calculation. Data are from CG-C material at 1373K in curve assumes a uniform fiber stress of 800 MPa argon(Table 3 and Fig. 7b)
3736 HENAGER et al.: SUBCRITICAL CRACK GROWTH: PART I linear least squares fit (dashed curves). The fit parameters are in close agreement to the fits obtained from the displacement–time curves and the fiber creep data (Table 4). Of course, since the specimen strain is proportional to the specimen displacement, this connection is expected. However, it is not obvious that this would also hold for crack length. We further checked the hypothesis that fiber creep is controlling crack extension and permanent strain in these materials by comparing the permanent strain as a function of time (Table 2) with the calculated creep strain of Nicalon-CG and Hi-Nicalon fibers for the same time period using equation (2). The result is shown in Fig. 8 for Nicalon-CG. This comparison is approximate, but the observed reasonable agreement suggests our rough strain calculations are of the correct magnitude. The comparison assumes a uniform fiber stress of 800 MPa and indicates good agreement for the CG-C materials (Fig. 8). The agreement is less good for the single Hi-C data point (Table 2) but is within a factor of two (5.7×103 calculated and 1.2×102 for specimen Hi-C-2). Therefore, it seems reasonable to suggest that the strain in the damage zone can be accounted for by fiber creep. Finally, we qualitatively analyzed the hysteresis loops for changes in loop width. We observed no changes in loop widths as a function of time for any of the specimens for which hysteresis loops were obtained, although we note that these loops lack the fidelity of loops from tensile tests. Since the loop width is sensitive to the value of the sliding stress [39–41, 58], we conclude that there is no time-dependence for the sliding stress in this experiment, with the above caveat. A change in width would suggest that a time-dependent interphase damage mechanism was operative. Therefore, it is unlikely that any other time-dependent mechanism, such as interphase oxidation or viscous sliding between the fiber and matrix, is operable in argon [5]. This turns out not to be the case for those materials tested in argon–oxygen mixtures [4, 42, 59] (Fig. 5b) for which loop width changes in bending are readily observed. Fig. 8. Experimental strains (Table 2) compared to calculated creep strain for Nicalon-CG fibers at 1373 K. The calculated curve assumes a uniform fiber stress of 800 MPa. 4.4. Crack velocities The crack velocity as a function of time is shown in Fig. 9a for the CG-C materials, calculated from the crack length as a function of the time curve of Fig. 7b. Crack velocities are in the range of 109 m/s after long times, but are quite substantial (5×108 m/s) at short times. This is compared with a calculated crack velocity curve using an effective elastic crack methodology presented in previous studies [2–4, 13, 35, 60], based on the use of specimen compliance [61]. There is no calculable relation between compliance and crack length (damage zone extent) without a priori knowledge of the crack density and crack-face forces as a function of time, temperature, and applied load. In general, these are not known. Making the appropriate connection between crack length and compliance requires an explicit crack-bridging model and cannot be accomplished by a simple elastic crack argument. This is particularly true when multiple cracking occurs. The linear-elastic compliance-crack length relation [3] should underpredict actual crack lengths since the bridging forces stiffen a mode-I crack relative to an unbridged crack (Fig. 9b). Since this is not observed, we conclude that the multiple Fig. 9. (a) Experimental crack velocity, calculated from the derivative of the fitted crack length vs. time curve in Fig. 7b, compared to an effective elastic-crack calculation [3]. (b) Experimental crack length compared to effective elastic-cracklength calculation. Data are from CG-C material at 1373 K in argon (Table 3 and Fig. 7b)