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Tensile creep of coarse-grained Ti3SiC2 in the 1000–1200 °C temperature range
Journal of Alloys and Compounds 361 (2003) 299–312
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Tensile creep of coarse-grained Ti 3 SiC 2 in the 1000–1200 8C temperature range a a, a b M. Radovic , M.W. Barsoum *, T. El-Raghy , S.M. Wiederhorn a
Department of Materials Engineering, Drexel University, Philadelphia, PA 19104, USA b National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
Received 12 March 2003; received in revised form 8 April 2003; accepted 8 April 2003
Abstract The tensile creep of coarse-grained, CG, Ti 3 SiC 2 samples, in the 1000–1200 8C temperature, T, and 10 MPa to 100 MPa stress, s, ranges, respectively, was studied. The creep behavior is characterized by three regimes: an initial, a secondary where the creep rate is at a minimum, ´~ min , and a tertiary regime. In the intermediate regime ´~ min is given by:
s ´~ min (s 21 ) 5 ´o exps1761d ] so
S D
2.060.1
S
2 458612 kJ / mol exp ]]]]] RT
D
where s0 51 MPa and ´0 51 s 21 . The times to failure are given by: t f (s)5exp(2260.3)´~ 21 min . The results presented herein confirm that: (a) dislocation creep is the dominant mechanism; (b) the high plastic anisotropy of Ti 3 SiC 2 results in large internal stresses during creep; (c) the response is dictated by a competition between the rates of generation and dissipation of these internal stresses; (d) at higher temperatures and / or lower strain rates the internal stresses can dissipate and the behavior is more ductile. Furthermore, in the tertiary creep regime, the creep appears to occur by a combination of dislocation creep and the formation of cavities and cracks. The coarse-grained samples have lower creep rates than their fine-grained (3–5 mm) counterparts, and their times to failure are longer. The latter is partially attributable to the ability of the larger grains, whose basal planes are normal to the applied load, to form tenacious crack bridges by delamination and kink band formation, in addition to the bridges that occur when the basal planes are parallel to the applied load. 2003 Elsevier B.V. All rights reserved. Keywords: Ceramics; Mechanical properties; High-temperature material; Microstructure
1. Introduction Based on our results to date the mechanical response of Ti 3 SiC 2 , and by extension the other M n11 AX n phases (where M is a transition metal, A is an A group element and X is carbon and / or nitrogen), is characterized by high fatigue resistance [1,2], damage tolerance [3–5] and a relatively high fracture toughness (8–12 MPa m 1 / 2 ) with R-curve behavior in which the fracture toughness can reach 16 MPa m 1 / 2 [1–3]. A brittle-to-ductile transition (BTD) occurs between 1100 and 1200 8C. When loaded slowly, the stress–strain curves in tension reach a broad maximum in stress. The plateau stress is a function of strain rate and is lower for lower strain rates [6,7]. *Corresponding author. E-mail address: [email protected] (M.W. Barsoum). 0925-8388 / 03 / $ – see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016 / S0925-8388(03)00435-3
Conversely, if loaded rapidly, the stress does not peak, but instead the material fails on the rising part of the stress– strain curves, i.e., the response is more brittle [6,7]. The strain rate sensitivity in tension, for both fine-grained and coarse-grained samples is high; viz. ¯0.55 (i.e., stress exponent ¯1.8) [6,7]. Recently it was shown that Ti 3 SiC 2 and hexagonal ice are quite comparable both at the atomic and macroscopic levels, when deformation is concerned [8]. Since both are plastically anisotropic, with only two independent basal slip systems, homogeneous plastic deformation is not possible; instead large internal stresses develop. If these stresses are not dissipated, the behavior is brittle. However, if they can be dissipated the response is much more ductile. This interpretation explains, in large part, the strong strain rate dependencies of the mechanical response. In contrast to ice that remains brittle even at ¯0.90 of its
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melting point, as noted above, Ti 3 SiC 2 goes through a BTD transition at temperatures between 1100 and 1200 8C. This transition is well documented in flexure [4,9] and tension [6,7]. In most metals, the BTD transition is associated with the thermal activation of additional slip systems, which in turn result in an increase in fracture toughness. In Ti 3 SiC 2 the fracture toughness drops from around 8–10 to about 4 MPa m 21 / 2 above the BTD transition temperature [2]. And while the exact nature of the BTD is not understood at this time, TEM and HRTEM studies [10–12] did not provide any evidence for the presence of non-basal dislocation, which leads us to eliminate the activation of other slip systems as a cause. Furthermore, it would be very difficult, if not impossible, to explain the drop in fracture toughness with increasing temperatures if other slip systems were initiated. For the same temperature and stress ranges reported here, the tensile creep of fine grained (¯5 mm) Ti 3 SiC 2 samples [13] occurs in three stages: a primary, where the strain rate decreases with time, a secondary or quasi-steady state where the strain rate reaches a minimum, and a tertiary stage. Creep occurs by a combination of plastic deformation and damage accumulation. Plastic deformation is the dominant mechanism during the primary and secondary creep regimes. The minimum creep rate is well represented by a power law expression (see Eq. (1)) with a stress exponent of 1.560.1 and an activation energy of 445610 kJ / mol. Creep results, and those obtained from tensile and stress relaxation tests, are in good agreement with each other suggesting that the same atomic mechanism is responsible for the plastic deformation [7,13]. Furthermore, the results of strain-transient dip and cyclic tests [7,13] provide strong evidence for the presence of large internal stresses during creep. These stresses are responsible for recoverable (anelastic) strains upon unloading, and are believed to be responsible for the initiation of intergranular microcracks and the acceleration of creep during the tertiary regime. Most recently we have shown that macroscopic polycrystalline Ti 3 SiC 2 cylinders can be compressed, at room temperature, to stresses of up to 1 GPa, and fully recover upon the removal of the load, while dissipating ¯25% of the mechanical energy [14]. The stress–strain curves at room temperature outline fully reversible, reproducible, rate-independent, closed hysteresis loops that are strongly influenced by grain size with the energy dissipated being significantly larger in the coarse-grained material. This phenomenon was attributed to the fully reversible formation and annihilation of incipient kink bands, IKBs, defined as near parallel dislocation walls of opposite polarity that remain attached, and are thus attracted to each other. Removal of the load allows the walls to collapse and the IKB to be totally eliminated. At temperatures higher than 1000 8C, the stress–strain loops are open and the response becomes strain rate dependent. Most germane to this work
is the fact that cyclic hardening was observed at 1200 8C, for the coarse-grained samples. This hardening was attributed to the dissociation of the IKBs and the coalescence of the latter to form regular kink bands (KBs) that in turn are no longer reversible and more important result in grain refinement. In other word, the response of the coarsegrained (see below) samples after modest stress cycling was comparable to the fine-grained samples. In this paper, we report on the tensile creep of coarsegrained, CG, Ti 3 SiC 2 samples, in the 1000–1200 8C temperature and 10–100 MPa stress ranges, respectively. Whenever possible the results are compared with previous work on the creep of fine-grained, FG, samples [13].
2. Experimental procedure The processing details are described elsewhere [6,3]. The CG samples, were prepared by reactive hot isostatic pressing (HIPing) of titanium (2325 mesh, 99.5%, Alfa Aesar, Ward Hill, MA), silicon carbide (2325 mesh, 99.5%, Atlantic Engineering Equipment, Bergenfield, NJ) and graphite (d m 51 mm, 99%, Aldrich, Milwaukee, WI) at 1600 8C under 40 MPa for 6 h. The resulting samples were fully dense, predominantly single-phase, with randomly aligned plate-like grains of the order of 30 mm and aspect ratio of 2.3 (Appendix A). The tensile creep measurement details can be found elsewhere [15]. Electro-discharge machined dog-bone specimens SR51 (prismatic gage section: 232.5312 mm 3 ) [16] were tested with no further surface preparation. The time dependence of the strain was monitored using a laser-extensometer [17]. All samples were heated to the testing temperature in ¯1.5 h, and held at that temperature for anywhere from 2 to 4 h before the load was applied. Most tests were performed under constant temperature and load up to fracture, or until the tests were aborted. In roughly a quarter of the samples, the load was increased after enough data were collected for the calculation of the minimum creep rate. However, to minimize the influence of damage accumulation, the stress was never increased more than once for any given sample. In addition to tensile creep, relaxation tests at 1200 8C, and strain transient dip, STD, tests at 1150 8C were carried out on an Instron 1 8500 testing machine, using procedures described in more detail in the literature [18–23]. In both,
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Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology and Drexel University, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.
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the strain was monitored as a function of time by a capacitive extensometer with a useful sensitivity of about 10 25 . In the relaxation tests, the samples were loaded at a constant strain rate up to the desired stress, at which time the cross-head motion was abruptly stopped, and the stresses and strains were monitored as a function of time [7]. For the STD tests, a sample was loaded and held at a stress, s, until the strain increased more or less linearly with time, at which point the load was immediately (,1 s) decreased by Ds. Three sets of STD tests were carried out on one sample. The first was at an initial stress of 40 MPa, followed by stress drops Ds of 4, 8, 12, 16, 20, 24 and 36 MPa; the second was at an initial stress s of 60 MPa, followed by Ds values of 4, 8, 16, 24, 26 and 56 MPa; the third was at an initial stress of 80 MPa, followed by Ds values of 4, 8, 16 and 76 MPa. When quasi steady state was established at the lower stresses (s 2Ds ), the stress was increased again to the initial s, and the test repeated. During this test the stress was never reduced below 4 MPa, which is the minimum stress required to keep the sample well aligned in the testing machine. Fracture surfaces of most samples were examined by scanning electron microscopy (SEM). In addition, select surfaces that were parallel to the applied load were ground and polished for optical microscopy (OM) and SEM analysis. Some of the polished samples were etched using
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HF:HNO 3 :H 2 O solution (1:1:1, v / v) in order to better expose the grains [4].
3. Results The effect of time, t, and stress, s on the tensile strain, ´, at 1100 8C is shown in Fig. 1a. The strain rate, ´~ , versus t curves for the same set of data are plotted in Fig. 1b. Three regimes are distinguishable: An initial transient regime, where ´~ decreases with t (inset in Fig. 1b). (ii) A secondary creep regime in which ´~ is more or less constant with time. This region is mostly absent in samples tested at stresses of 60 MPa or higher. In this regime, the creep rate reaches a minimum, ´~ min . (iii) A tertiary creep regime, in which ´~ increases until failure. (i)
A ln–ln plot of ´~ min versus s as a function of temperature, T, is shown in Fig. 2a; an Arrhenius plot of ´~ min is shown in Fig. 2b. Bilinear regression analysis (95% probability) of the results was carried out, assuming the power law relation between ´~ min , T and s to be [24,25]:
Fig. 1. Time and stress dependencies of (a) tensile strain and (b) strain rate of CG samples tested at 1100 8C. Plot (b) is obtained by differentiation of curves shown in (a). Insets are enlargements of the initial parts of the plots shown in (a) and (b).
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Fig. 2. (a) Ln–ln plot of ´~ min versus s as a function of temperature and testing technique. Solid black lines are results of a bilinear regression for CG microstructure. The results of tensile tests at 1200 8C (solid small circles), STD tests at 1150 8C (small solid triangles), and relaxation tests at 1200 8C (small open circles) are also shown. (b) Arrhenius plot of ´~ min at various stresses.
Q D S D expS 2 ] RT
s ´~ min 5 ´~ o A ] so
n
(1)
where A, n and Q are, respectively, a stress-independent
constant, stress exponent and activation energy for creep: ´~ 0 51 s 21 and so 51 MPa. A regression analysis, on the logarithmic form of Eq. (1) yields: A5exp (17.361) s 21 , n52.060.1 and Q5
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458612 kJ / mol. The small values of the standard error, and the high value for the coefficient of correlation (R 2 5 0.974), indicate that ´~ min can be well represented by Eq. (1), over the entire range of testing temperatures and stresses, viz.:
´~ min (s 21 ) 5 ´~ o exps1761d
S]ss D o
2.060.1
S
2 458612 kJ / mol exp ]]]]]] RT
D
(2)
The goodness of the fit, assuming n52, is shown in Fig. 3a, wherein the solid line is that of Eq. (2). Also plotted on the figure, as a dotted line, are the results for the FG microstructure [13]. A plot of (ln ´~ min ) /s n versus 1 /T (Fig. 3b) yields a straight line, with a slope that is almost identical to that of the FG microstructure (dashed line in Fig. 3b). These results clearly confirm that Q is not a
function of grain size, and that at all temperatures, ´~ min of the CG samples is lower than their FG counterparts. Coarse-grained specimens of the same shape and size as those used in this study were tested in tension at a constant cross-head displacement rate at 1200 8C [7]. Maximum (plateau) stresses reached during these tests as a function of strain rate are plotted in Fig. 2a as solid circles. These stresses represent a lower creep boundary, i.e., the lowest stress required to produce creep at the imposed rate. As in the case of the FG Ti 3 SiC 2 samples [13], the results of the tensile and creep tests are only comparable when a stress plateau is reached in the former. It is worth noting that only two of the CG samples tested in tension reached a plateau stress [7]. Data from relaxation tests at 1200 8C [7], plotted as small open circles in Fig. 2a, are also in good agreement with the data from creep tests at the same temperature. Select, but typical, curves obtained from STD tests at 1150 8C are plotted in Fig. 4. Small stress drops cause instantaneous contractions, followed by a period of zero creep rate (Fig. 4a,c), after which creep resumes and the creep rate increases to a new steady value. Large stress reductions (Fig. 4b,d) are followed by regions of negative creep, after the instantaneous contractions. The creep rate eventually goes to zero before it ultimately increases to a new steady state value. The negative creep regime is especially well pronounced for the last, and largest, load drop (Fig. 4b,d) that reduces s to 4 MPa. The minimum creep rates from the STD tests carried out at 1150 8C (solid small up triangles in Fig. 2a) are in good agreement with those from creep tests at the same temperature. The recovery rate, r, and the strain hardening coefficient, h, were calculated from the STD tests using the procedure described by Lloyd and McElroy [18]. The steady state creep rate was then calculated using the Bailey–Orowan equation as ´~ 5 r /h. The strain rates calculated using this approach are in good agreement with the ´~ min values measured during creep. For instance, the calculated steady state creep rates for the STD tests shown in Fig. 4a,c are: 8.6310 27 and 1.8310 26 s 21 , respectively; the ´~ min rates measured at 40 and 60 MPa are 8.13 10 27 and 1.8310 26 s 21 , respectively. Log–log plots of lifetime (or time to failure), t f , versus s (Fig. 5a) yield a series of parallel straight lines for each testing temperature. Also included in Fig. 5a are the lifetimes of the FG samples, shown as dotted lines, which, at any given temperature, are shorter than the CG samples. The results plotted in Fig. 5a suggest that the data can be fitted to a Monkman–Grant expression [26]:
S D
´~ min t f (s) 5 t o KMG ]] ´~ o Fig. 3. (a) Ln–ln plot of ´~ min ? exp Q /RT versus s for CG (solid lines) and FG (dashed lines) [13] microstructures. Inset shows a ln–ln plot of ´~ min versus s at 1100 8C and 1200 8C for both microstructures. (b) Ln–ln plot of ´~ min ? s 2n versus reciprocal temperature as a function of grain size.
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2m
(3)
where KMG , and m, are a dimensionless constant and the Monkman–Grant exponent, respectively; t 0 51 s. A leastsquares fit of the results (Fig. 5b), yields an m5160.06
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Fig. 4. Results of STD tests at 1150 8C. Black horizontal lines denote strain (left-hand side axes); gray lines are stress (right-hand side axes). In all tests initial stress s was reduced by Ds and then increased again up to s. (a) s 540 MPa, Ds 58 MPa; (b) s 540 MPa, Ds 520 MPa; (c) s 560 MPa, Ds 58 MPa; (d) s 560 MPa, Ds 524 MPa. At the end of each test the sample was unloaded down to 4 MPa. All results were obtained from one sample.
and KMG 5exp (2260.3). Also shown on the figure are the results for the FG samples [13]. The functional dependencies of the strains to failure on stresses and temperatures are shown in Fig. 5c. At high stresses, the strains to failure are ¯1 to 3% and comparable to the strains to failure in the FG samples (dashed line), which for reasons that are not clear, are a weak function of temperature [13]. Typical, low-magnification micrographs of the gage area in the vicinity of the fracture surface (Fig. 6) show that— as in the case in FG samples in creep [13] or tension [7]—deformation occurs without visible necking. Furthermore, specimens deformed in creep up to ¯3% are usually free of large cracks, or any other visible damage, within the gage area. If some microcracks are present they are few, and typically only in the near vicinity of the fracture surfaces (Fig. 7a,b). With increasing failure strains (.3%) more microcracks, that spread over the gage area, are observed (Fig. 7c,d). The network of cracks is obvious on the composite OM micrograph of a polished and etched gage area shown in Fig. 8. Cracks spread across almost the entire gage area in a direction more or less perpendicular to the applied load. Encircled detail is an example of a bridging grain. Clear evidence of slip can be seen in the OM micrographs of sample grain tested at 1000 8C and 40 MPa (Fig. 9). Steps at the grain boundary are presumably formed by slip along the basal planes, whose orientation is roughly determined from the grain shape (plate-like grains of Ti 3 SiC 2 are always elongated in direction of basal planes). Such features are not observed in undeformed samples. Delaminations along the basal planes (Fig. 10a) or grain boundary decohesion accompanied with delamination along basal planes (Fig. 10b) are frequently observed. Delaminations are usually accompanied by a deformation (bending, kinking) of lamina between two delamination
cracks. The bent grain shown in Fig. 10c is clear evidence of plastic deformation. Here again, such features are not observed in non-deformed samples. Delamination and kinking of the grains are shown in Fig. 10d. Select, but typical, SEM micrographs of fractured surfaces are presented in Fig. 11. A kinked lamina ‘sticking out’ of the fracture surface is shown in Fig. 11a. Such a grain must have served as a crack bridge before rupture. Another bridging grain sticking out from the fracture surface is shown in Fig. 11b. An example of a cavity remaining after failure and pullout of a large grain is shown in Fig. 11c. In order to monitor damage evolution more precisely, three tests were performed at 1050 8C and 60 MPa. The first two were interrupted after 21 and 49 h, the third was run to failure, viz. 94.5 h. The samples were then very carefully polished down to a 0.05-mm suspension of colloidal silica, using low loads in order to avoid pullouts. The central panel of Fig. 12, where the three creep curves are superimposed, demonstrates the good reproducibility between samples. SEM micrographs of gage and grip sections are compared in Fig. 12a–f. Some grain boundary decohesions are observed in the samples tested for 49 h at higher magnifications (inset in Fig. 12b). Microcracks and / or grain boundary decohesions (denoted by arrows) are obvious in the sample tested until fracture. In contrast, micrographs of the grip area (bottom row in Fig. 12) are free of damage, confirming that the damage observed in the gage area occurs during testing. In all samples tested an oxide layer formed, with a morphology—an inner oxide layer of SiO 2 and TiO 2 , and an outer layer of pure TiO 2 —identical to what was reported earlier [27]. It is worth noting, that the oxide layers that form in the beginning of the test do not influence the measured values of ´~ min for reasons discussed in Appendix B. A detailed study on the oxidation kinetics
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and the effect of stress on the latter are published elsewhere [28].
4. Discussion Based on our work to date [1–8,11–14] on the mechanical behavior of Ti 3 SiC 2 there is little doubt that: (a) dislocations play a dominant role in the deformation; (b) large internal stresses develop due to the paucity of operative slip systems; (c) the mechanical response of Ti 3 SiC 2 is essentially dictated by a competition between the rates of generation and dissipation of these internal stresses; and (d) at higher temperatures, and / or lower strain rates, these internal stresses can dissipate more readily. The results presented here are not only in complete agreement with these conclusions, but, more importantly, supply further strong evidence for their validity. Due to lack of space, we will focus mostly on the mechanism controlling the creep within the minimum creep rate regime. The characteristics of failure accumulation processes will be addressed only briefly here.
4.1. Phenomenological observations
Fig. 5. (a) Log–log plot of s versus time to failure, t f , for different temperatures; (b) log–log plot of ´~ min versus t f (Monkman–Grant plot); (c) Strain to failure versus s. In all cases, the solid and dashed lines were obtained by least squares fits of the results for CG and FG [13] microstructures, respectively.
Since ´~ min can be described by a single power law (Eq. (2); Figs. 2 and 3) it is fair to assume that the same thermally activated, rate-controlling mechanism(s), with an activation energy ¯460 kJ / mol, operates over the entire range of testing temperatures and stresses. Furthermore, the same thermally activated, rate-controlling mechanisms must be operative in the FG and CG samples (Fig. 3b). The results confirm that Q is not a function of grain size, and that at all temperatures, ´~ min of the CG samples were lower than their FG counterparts (inset in Fig. 3a). Since n is a function of grain size (Fig. 3a), it is not possible to calculate the grain size exponents, p, directly from the power law equations. Instead, an ‘effective’ grain size exponent was calculated assuming ´~ min ~d 2p , where d is average or equivalent grain size listed in Table 1. The problems associated with defining and measuring grain sizes in the microstructures tested here are discussed in Appendix A. Regardless of the technique used to quantify the grain sizes, the d CG /d FG ratio was found to be ¯6 (Table 2). Using this ratio, p was calculated (Table 1), and found to be a weak function of grain size ( p,1). Furthermore, with increasing T and s, the grain size difference becomes even less important; i.e., p decreases. This result is not too surprising and is consistent with our conclusion that the creep is dislocation based.
4.2. Evidence for internal stresses and stress relaxation Fig. 6. Photographs of, (a) initial samples, and samples tested at, (b) 1050 8C, 60 MPa, aborted after 50 h; (c) 1200 8C, 60 MPa, t f 53.86 h; (d) 1050 8C, 40 MPa, t f 5252 h; (e) 1000 8C, 60 MPa, t f 5230 h; (f) 1200 8C, 20 MPa, t f 532 h; (g) 1200 8C and 60 MPa, t f 53.86 h; (h) 1000 8C, 40 MPa, aborted after 830 h.
The negative creep observed upon high stress unloading (Fig. 4b,d) is evidence for the presence of internal stresses, whose values are higher than the stress to which the
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Fig. 7. OM micrographs of surfaces that were parallel to vertically applied load. Fracture surfaces at top of micrograph. Samples tested at: (a) 1000 8C, 80 MPa; t f 5114 h, ´f 52.3%; (b) 1100 8C, 40 MPa; t f 560 h, ´f 54.7%; (c) 1150 8C, 20 MPa; t f 561 h, ´f 54.8%; (d) 1200 8C, 20 MPa; t f 511.6 h, ´f 58.8%. Dark layers on both sides of specimens are oxide layers.
Fig. 8. Composite OM of polished and etched gage surface that was parallel to the vertically applied load. Branched microcracks spread from one side to the other. Encircled detail shows crack bridging. Test details: 1150 8C, 40 MPa, t f 561 h, ´f 58%.
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Fig. 9. OM of polished and etched gage surface that was parallel to the vertically applied load. Specimen with the duplex structure was tested at 1000 8C and 40 MPa. Decohesion of grain boundary is denoted by vertical arrow. Steps at grain boundary presumably formed by slip along basal planes whose direction is indicated on figure.
system are unloaded to [22,23]. Upon small s reductions, the period of zero creep is usually interpreted as direct evidence for recovery processes [22,23]. In addition the creep rates calculated from SDT tests using the Bailey– Orowan equation (derived assuming recovery-controlled creep) are in good agreement with those measured in the creep tests. This fact indicates that—like for FG Ti 3 SiC 2 [13], and hexagonal ice [29]—the recovery of internal stresses in CG Ti 3 SiC 2 play an important role during the creep. Comparing the shapes of the creep and tensile curves at different strain rates and / or stresses sheds more light on the problem. When the stresses used in creep, or the strain rates used in tension, are both low, good agreement is obtained between the two sets of data (Fig. 2a). Conversely, at stresses that are higher than 50 MPa, the quasi-steady state creep region, if present, is short (Fig. 1a) and, as important, the stress–strain curves in tension do not exhibit a maximum or plateau. The simplest explanation for both observations is that the response is determined by the relative rates at which the internal stresses accrue and dissipate. The excellent agreement between the results obtained from creep and stress relaxation tests (Fig. 2a) also imply that the same mechanisms operate in both. It is worth noting that the stress relaxation abilities of Ti 3 SiC 2 are limited; after several stress relaxation tests are repeated on
the same sample, the agreement is less good. This suggests that not all the internal stresses are relaxed during each cycle, which in turn would lead to damage accumulation.
4.3. Mechanisms controlling quasi-steady state creep For the reasons discussed in more detail in Appendix B, the values of ´~ min measured during the quasi-steady state creep are influenced minimally by oxidation. The effect of cavitation on ´~ min is not so clear. Results shown in Fig. 12 (sample tested at 1050 8C and 60 MPa) indicate that although the majority of cavities and microcracks develop during tertiary creep, some cavitation may occur even during the quasi-steady state regime where the minimum creep rate was measured. Determining the rate controlling atomic mechanism in creep, especially when the values of n and p do not agree with those predicted by classic creep models, is a nontrivial exercise. Even in a material as well studied as ice, the situation is still not entirely clear. These caveats notwithstanding, much can be learned about creep in Ti 3 SiC 2 from the results presented here and elsewhere [7,8,13,14]. The most compelling evidence that diffusion and / or grain boundary creep are not the dominant creep mechanisms can be found in the low values of p (Table 1). The classic models for diffusion and / or grain boundary
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Fig. 10. Micrographs of polished and etched gage surfaces that were parallel to vertically applied load showing: (a) OM of sample tested at 1000 8C and 80 MPa showing delamination denoted by arrows. Part of the grain between delamination cracks is slightly bent; (b) OM of sample tested at 1100 8C and 40 MPa. Bent lamella, denoted by arrow, serves as a crack bridge; (c) SEM of sample tested at 1150 8C and 20 MPa showing bent grain; (d) SEM of sample tested at 1050 8C and 40 MPa, showing simultaneous delamination and kinking of a grain.
controlled creep have p values of 2 to 3 [30–34]; the highest value of p calculated here is ¯0.9. On the other hand, the stress exponent measured in this work is lower that those predicted by dislocation based models [34]. It follows that the values for n and p reported in this study do not match values predicted by any known creep model in which one mechanism is dominant or rate controlling. Based on our work to date on the mechanical behavior of Ti 3 SiC 2 , and results of this work, there is little doubt that the following processes take place during creep: dislocation glide (Fig. 9), kinking (Fig. 10d) and cavitation (Fig. 12). Thus, we can speculate that the creep of Ti 3 SiC 2 is controlled by several mechanisms that operate nonsequentially or simultaneously as described recently by Goldsby and Kohlstedt [35] for hexagonal ice, and more generally by Langdon [36]. Glide of basal plane dislocations can take place only in favorably oriented grains, or soft grains, in which resolved shear stress exceeds a critical
value. During the short primary creep regime, basal plane dislocations in the soft grains glide and form pile-ups resulting in large internal stresses (manifested in STD tests). As the internal stresses increase, the creep rate decreases leading to a quasi-steady state regime. These internal stresses can be accommodated either by grain boundary cavitation and / or grain boundary sliding. It thus follows that creep in the secondary regime is probably controlled by the rate at which internal stresses are built up in dislocations pile-ups, kink-bands, walls, etc., and by the simultaneous rate at which these stresses are relaxed by grain boundary cavitations and / or grain boundary sliding. The discussion so far has been restricted to the secondary regime. However, when that regime ends and the tertiary regime begins is difficult to pinpoint for the simple reason that the two mechanisms are most probably occurring simultaneously, and thus there is no sharp delineation between them. At higher stresses and / or longer times, the
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Fig. 11. SEM of fracture surfaces showing: (a) delamination of a single grain with part of it sticking out of, and part in the fracture plane; (b) same sample, ruptured grain sticking out from the fracture plane; (c) cavity remaining in fracture plane due to the pullout of a grain that presumably served as a crack bridge.
formation of cavities and their linkage becomes more important leading to tertiary creep.
4.4. Tertiary creep and rupture Based on the shape of the creep curves (Fig. 1), the results shown in Fig. 12 and most of the micrographs
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shown in this paper, it is fair to assume that number of grain boundary and triple-point cavities increase with time and eventually coalesce into microcracks. Interestingly and philosophically it is not obvious from our results whether near failure we are dealing with creep or subcritical crack growth. This is especially true here since the tests were run in air and direct evidence for the penetration of oxygen along the cracks exists [28]. Another complicating factor is the reduction in cross-sectional area with time (Figs. 7 and 8). It is hereby acknowledged that much more work is needed to further understand what is occurring here. Not only are the ´~ min values for the CG samples lower than the FG ones (inset in Fig. 3a), but the t f values of the former are considerably longer; an enhancement that increases with decreasing testing stresses (Fig. 5a). Given that the oxidation kinetics are identical for both microstructures [28], the enhancements in t f must be due to the higher damage tolerance of the CG microstructure [1,2,5,8]. Said otherwise the coarser grains, as a direct result of their size, can sustain higher bridging stresses than the finer ones. In the remainder of this paper compelling microstructural evidence to support this notion is presented. The large concentration and size of the microcracks possible is clear in Figs. 7 and 8, especially at lower stresses. Comparing these micrographs with those of the FG samples [13], it is obvious that the size of the microcracks scale with grain size. The microstructural evidence also suggests the presence of two different crack bridging mechanisms. The first—in which grains whose basal planes are parallel to the direction of applied load serve as classic crack bridges— can be seen in the encircled area in Fig. 8 and in Fig. 11b,c. These grains can absorb energy either by plastic deformation or by frictional pull out. The second mechanism is more unusual. It begins with delaminations that are initiated on opposite sides of a single grain, but on different basal planes (Fig. 10a). These lamellae can also be formed from only one side of a grain if they are in the vicinity of a void at the grain boundary (denoted by arrows in Fig. 10b). With further deformation, the separated lamellae can deform significantly by bending before rupturing (Fig. 11a). This bending occurs by the formation of kink bands [10], the boundaries of which must clearly impede further delamination. For example, had the bending shown in Figs. 10b not occurred by dislocation motion, which result in kink boundaries, the delamination would have rapidly run across the entire grain. The fact that it does not is significant, and confirms that the kink-band based model for toughening in compression [10] is also applicable in tension. There is a distinction, however: in compression, the grains whose basal planes are parallel to the applied load are the ones that kink; in tension, the grains whose basal planes are normal to the applied load do. Samples deformed at high stresses, i.e., low strains to failure, fail with significantly less damage (Fig. 7a,b) and
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Fig. 12. Sequence of damage formation for specimens tested at 60 MPa and 1050 8C. Creep results are shown in middle panel. SEM micrographs of specimens’ gage are shown in the upper row; corresponding micrographs of grip area are shown in bottom row. (a,d) Test stopped after 21 h; (b,e) test stopped after ¯50 h; (c,f) specimen failed after ¯95 h.
Table 1 Grain size exponent, p, assuming ratio d CG /d FG 56 as a function of select temperatures and stresses; for measurement details see Appendix A Temp. (8C)
p
1000
0.80 0.60 0.40 0.33
1100
0.75 0.55 0.43 0.35
1200
0.91 0.71 0.50
the damage, if present, is in the near vicinity of the fracture surface. This observation is consistent with the fact that samples tested at higher stresses do not exhibit steady state creep but fail presumably before the balance between hardening and recovery processes takes place.
4.5. Technological importance Based on the results presented above it is fair to claim that—at a comparable stage of development i.e., ¯7 years from ‘discovery’—Ti 3 SiC 2 shows tremendous promise as a high temperature structural material. In this work, a polycrystalline sample sustained a tensile stress of 60 MPa for 800 h at 1000 8C in air before the run was aborted with the sample seemingly structurally intact. The record to date is a sample with a duplex microstructure (not discussed
M. Radovic et al. / Journal of Alloys and Compounds 361 (2003) 299–312 Table 2 Summary of grain size measurements for coarse-grained material used in this work and the fine-grained material used in Ref. [13] Grain length d l (mm)
Grain width d w (mm)
Aspect ratio d l /d w
Average lengths and widths of .1000 grains Fine-grained [13] 864 361.5 361.5 Coarse grained 42639 20616 261 [this work] d CG /d FG 5 7
Equivalent grain dia. (mm) ]] œ3 d 2l ? d w 663 33629
311
overall creep response thus depends on the rate of generation and dissipation of these internal stresses. The latter most probably occur by a combination of delaminations, grain boundary decohesions and triple point cavitations. The unusual and unique damage tolerance imparted to the CG samples even at 1200 8C is due to the formation of tenacious kink band-based bridges of grains whose basal planes are parallel to the applied load.
6
Acknowledgements Line (Heyn) intercept method ASTM E112—(.1000 intersections) Intercept Nominal Feret’s length grain size diameter (mm) (mm) (mm) Fine-grained [13] 4 4 5 Coarse grained 24 27 30 [this work] d CG /d FG 6 6 6
We thank Mark Shiber and David Von Rohr (Drexel University, PA) for helping us during the specimen preparation and optical microscopy. Help provided by William Luecke, Frantisek Lofaj, Ralph Krause Jr. (NIST, MD) is also greatly appreciated. This work was supported by the Army Research Office (DAAD19-00-1-0435).
Regardless of the method used to measure the grain size, the average size of the coarse grains in the CG samples was ¯6 times the size of the fine grains in the FG samples.
Appendix A here) that survived a stress of 20 MPa for 1500 h at 1000 8C before the test was aborted. These results are particularly noteworthy because they are those for a pure, single phase, polycrystalline material. Very few, if any, commercial high temperature structural materials are single phase and pure; rather they are multielemental solids that have been developed over half a century of intense research. As our understanding of the creep and oxidation of Ti 3 SiC 2 in particular, and the MAX phases, in general, deepens it is fair to assume that they will someday fulfill their potential. Another important observation that could prove vital to the successful use of Ti 3 SiC 2 as a structural component at high temperatures is both the extent and distribution of damage that can be sustained before failure (e.g., Figs. 7c and 8). This unique characteristic would render the non-destructive inspection of load bearing components straightforward and unambiguous, greatly decreasing the chances of catastrophic failure. Such components could even be fabricated and embedded with simple electrical circuits that could possibly monitor the resistance of a component continually during operation and thus provide an early warning to failure. Other advantages of Ti 3 SiC 2 are its machinability, low density and relatively low cost.
5. Conclusions The processes responsible for the tensile creep of CG Ti 3 SiC 2 are the same ones responsible for the creep of FG Ti 3 SiC 2 . In both cases the activation energy for creep is ¯460 KJ / mol. The stress exponents are also comparable, 2 for the CG and 1.5 for FG. The creep response is characterized by the presence of large internal stresses. The
Measurement of the grain size The microstructure of CG polycrystalline Ti 3 SiC 2 consists of mostly thin plate-like grains surrounded by areas in which the grains are much smaller [4]. Thus, the nontrivial question arises: What is the relevant grain size to be used to interpret the creep results? In order to estimate equivalent grain sizes in both, the CG samples tested in this study, and FG structure tested in our previous study [13], two different grain size measurement techniques were applied. In the first, the lengths, d l , and widths, d w , of more than 1000 individual grains were measured by optical microscopy. The equivalent grain ]] size was calculated by 3 2 means of geometric average ( œ d l ? d w ), assuming the grains are ellipsoidal in shape. In other words, we assume the equivalent grain size to be the diameter of an equiaxed grain having the same volume as the plate-like grains of Ti 3 SiC 2 . The second measurement technique was based on the line intercept method (ASTM E112) in which the intercept length is proportional to the volume fraction of grain boundaries. In this case, the nominal grain size calculated and Farat’s diameter represent the diameters of the equiaxial grains having the same volume fraction of grain boundaries as in the microstructures tested. Here again over 1000 individual intercepts were measured The results are summarized in Table 2, together with the ratios of grain diameters for the CG and FG microstructures, d CG and d FG , respectively, measured using the two methods outlined above. From the results it is obvious that d CG /d FG ¯6. It is worth noting the slight difference in the aspect ratios between CG and FG structure. Also, the grain size
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distribution is narrower in the FG samples than in the CG ones, but neither exhibit a bimodal distribution. Also, average intercept lengths calculated from measurements in two orthogonal directions do not vary significantly indicating no alignment of the microstructure.
Appendix B Here we show that the reduction in cross-sectional area due to oxidation has a negligible effect on the measured values of minimum creep rate. For example, consider the samples tested at 1000 8C. Taking into account the heating soaking times, the minimum creep rate was established, conservatively, after ¯20 h. The thickness of the oxide layer at 1000 8C and 20 h is ¯40 mm [28], which reduces the cross-sectional area by ¯7%. If we assume, again conservatively, that the oxide layers are non-load bearing, such a decrease in cross-sectional area translates to an ¯14% increase in the minimum creep rate. If we consider more severe testing conditions 21200 8C, the minimum creep rate is established after ,5 h, including heating and pre-soaking times. In this case the increase in the minimum creep rate is ¯36%; a value that is relatively small compared to the errors in measurement of the minimum creep rate. Note this conclusion does not apply to the tertiary creep regime where the effects of the penetration of oxygen into the cracks [28] is unknown. The repeat of this work in inert atmospheres is indicated to better understand the role of oxygen in the tertiary regime.
References [1] C.J. Gilbert, D.R. Bloyer, M.W. Barsoum, T. El-Raghy, A.P. Tomsia, R.O. Ritchie, Fatigue-crack growth and fracture properties of coarse and fine-grained Ti 3 SiC 2 , Scripta Mater. 42 (2000) 761–767. [2] D. Chen, K. Shirato, M.W. Barsoum, T. El-Raghy, R.O. Ritchie, Cyclic fatigue-crack growth and fracture properties in Ti 3 SiC 2 ceramics at elevated temperatures, J. Am. Ceram. Soc. 84 (2001) 2914. [3] T. El-Raghy, M.W. Barsoum, Processing and mechanical properties of Ti 3 SiC 2 . Part I: reaction path and microstructure evaluation, J. Am. Cream. Soc. 82 (1999) 2849–2854. [4] T. El-Raghy, M.W. Barsoum, A. Zavaliangos, S.R. Alidade, Processing and mechanical properties of Ti 3 SiC 2 . Part II: effect of grain size and deformation on temperature, J. Am. Ceram. Soc. 82 (1999) 2855–2859. [5] M.W. Barsoum, T. El-Raghy, Synthesis and characterization of a remarkable ceramic: Ti 3 SiC 2 , J. Am. Ceram. Soc. 79 (1996) 1953– 1956. [6] M. Radovic, M.W. Barsoum, T. El-Raghy, J. Seindersticker, S.M. Wiederhorn, Tensile properties of Ti 3 SiC 2 in the 25–1300 8C temperature range, Acta Mater. 48 (2000) 453–459. [7] M. Radovic, M.W. Barsoum, T. El-Raghy, S.M. Wiederhorn, W.E. Luecke, Effect of temperature, strain rate and grain size on mechanical response of Ti 3 SiC 2 in tension, Acta Mater. 50 (2002) 1297–1306. [8] M.W. Barsoum, M. Radovic, P. Finkel, T. El-Raghy, Ti 3 SiC 2 and ice, Appl. Phys. Lett. 79 (2001) 479–481.
[9] J.-F. Li, W. Pan, F. Sato, R. Watanabe, Mechanical properties of polycrystalline Ti 3 SiC 2 at ambient and elevated temperatures, Acta Mater. 49 (2001) 937. [10] M.W. Barsoum, L. Farber, T. El-Raghy, Dislocation, kink bands and room temperature plasticity of Ti 3 SiC 2 , Met. Mater. Trans. 30A (1999) 1727–1738. [11] L. Farber, M.W. Barsoum, A. Zavaliangos, T. El-Raghy, Dislocations and stacking faults in Ti 3 SiC 2 , J. Am. Ceram. Soc. 84 (1998) 1677–1681. [12] L. Farber, I. Levin, M.W. Barsoum, HRTEM study of low angle boundary in plastically deformed Ti 3 SiC 2 , Phil. Mag. Lett. 79 (1999) 4103–4112. [13] M. Radovic, M.W. Barsoum, T. El-Raghy, S.M. Wiederhorn, Tensile creep of fine grained (3–5 mm) Ti 3 SiC 2 in the 1000–1200 8C temperature range, Acta Mater. 49 (2001) 4103–4112. [14] M.W. Barsoum, T. Zhen, S. Kalidindi, M. Radovic, A. Murugaiah, Dislocation-based fully reversible compression of Ti 3 SiC 2 up to 1 GPa, Nature Mater. 2 (2003) 107–111. [15] D.F. Carroll, S.W. Wiederhorn, D.E. Roberts, Technique for tensile creep testing of ceramics, J. Am. Ceram. Soc. 72 (1989) 1610– 1624. [16] J.D. French, S.M. Wiederhorn, Tensile specimens for ceramic components, J. Am. Ceram. Soc. 79 (1996) 550–552. [17] W.E. Luecke, J.D. French, Sources of strain measurement error in flag-based extensometry, J. Am. Ceram. Soc. 79 (1996) 1617–1626. [18] G.J. Lloyd, R.J. McElroy, A model for quantitative interpretation of high-temperature stress relaxation phenomena: the effect of anelasticity, Phil. Mag. 32 (1975) 231–244. [19] C.N. Ahlquist, W.D. Nix, The measurement of internal stress during creep of Al and Al–Mg alloys, Acta Met. 19 (1971) 373–385. [20] G.J. Lloyd, R.J. McElroy, On anelastic contribution to creep, Acta Met. 22 (1974) 339–348. [21] J.D. Parker, B. Wilshire, Rate-controlling processes during creep of super-purity Al, Phil. Mag. A 41 (5) (1980) 665–680. [22] J.P. Poirier, Microscopic creep models and the interpretation of stress-drop tests during creep, Acta Met. 25 (1977) 913–917. [23] S. Takeuchi, A.S. Argon, Steady-state creep of single-phase crystalline matter at high temperature, J. Mater. Sci. 11 (1976) 1542– 1566. [24] H.J. Frost, M.F. Ashby, in: Deformation-Mechanism Maps, Pergamon, London, 1982. [25] J.P. Poirier, in: Creep of Crystals, Cambridge University Press, Cambridge, 1985. [26] F.C. Monkman, N.J. Grant, An empirical relationship between rupture life and minimum creep rate in creep-rupture tests, Proc. Am. Soc. Test. Mater. 56 (1956) 593–620. [27] M.W. Barsoum, T. El-Raghy, L. Ogbuji, Oxidation of Ti 3 SiC 2 in air, J. Electrochem. Soc. 144 (1997) 2508–2516. [28] M.W. Barsoum, L.H. Ho-Duc, M. Radovic, T. El-Raghy, Long time oxidation study of Ti 3 SiC 2 , Ti 3 SiC 2 / SiC and Ti 3 SiC 2 / TiC composites in air, J. Electrochem. Soc. 150 (2003) B166–175. [29] P. Duval, M.F. Ashby, I. Anderman, Rate controlling process in creep of polycrystalline ice, J. Phys. Chem. 8 (1983) 4066–4076. [30] F.R.N. Nabarro, Deformation of crystals by the motion of single ions, in: Report of a Conference on Strength of Solids (Bristol), The Physical Society, London, UK, 1948, pp. 75–90. [31] R.L. Coble, A model for boundary diffusion controlled creep in ceramic materials, J. Appl. Phys. 34 (1963) 1679–1682. [32] T.G. Langdon, A unified approach to grain boundary sliding in creep and superplasticity, Acta Metall. Mater. 42 (7) (1994) 2437–2443. [33] A.K. Mukherjee, Rate controlling mechanism in superplasticity, Mater. Sci. Eng. 8 (1971) 83–89. [34] W.R. Cannon, T.G. Langdon, Review creep of ceramics, J. Mater. Sci. 18 (1983) 1–50. [35] D.L. Goldsby, D.L. Kohlstedt, Superplastic deformation of ice: experimental observations, J. Geophys. Res. 106 (2001) 11017– 11030. [36] T.G. Langdon, Grain boundary sliding as deformation mechanism during creep, Phil. Mag. 22 (1970) 689–700.
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Tensile creep of coarse-grained Ti 3 SiC 2 in the 1000–1200 8C temperature range a a, a b M. Radovic , M.W. Barsoum *, T. El-Raghy , S.M. Wiederhorn a
Department of Materials Engineering, Drexel University, Philadelphia, PA 19104, USA b National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
Received 12 March 2003; received in revised form 8 April 2003; accepted 8 April 2003
Abstract The tensile creep of coarse-grained, CG, Ti 3 SiC 2 samples, in the 1000–1200 8C temperature, T, and 10 MPa to 100 MPa stress, s, ranges, respectively, was studied. The creep behavior is characterized by three regimes: an initial, a secondary where the creep rate is at a minimum, ´~ min , and a tertiary regime. In the intermediate regime ´~ min is given by:
s ´~ min (s 21 ) 5 ´o exps1761d ] so
S D
2.060.1
S
2 458612 kJ / mol exp ]]]]] RT
D
where s0 51 MPa and ´0 51 s 21 . The times to failure are given by: t f (s)5exp(2260.3)´~ 21 min . The results presented herein confirm that: (a) dislocation creep is the dominant mechanism; (b) the high plastic anisotropy of Ti 3 SiC 2 results in large internal stresses during creep; (c) the response is dictated by a competition between the rates of generation and dissipation of these internal stresses; (d) at higher temperatures and / or lower strain rates the internal stresses can dissipate and the behavior is more ductile. Furthermore, in the tertiary creep regime, the creep appears to occur by a combination of dislocation creep and the formation of cavities and cracks. The coarse-grained samples have lower creep rates than their fine-grained (3–5 mm) counterparts, and their times to failure are longer. The latter is partially attributable to the ability of the larger grains, whose basal planes are normal to the applied load, to form tenacious crack bridges by delamination and kink band formation, in addition to the bridges that occur when the basal planes are parallel to the applied load. 2003 Elsevier B.V. All rights reserved. Keywords: Ceramics; Mechanical properties; High-temperature material; Microstructure
1. Introduction Based on our results to date the mechanical response of Ti 3 SiC 2 , and by extension the other M n11 AX n phases (where M is a transition metal, A is an A group element and X is carbon and / or nitrogen), is characterized by high fatigue resistance [1,2], damage tolerance [3–5] and a relatively high fracture toughness (8–12 MPa m 1 / 2 ) with R-curve behavior in which the fracture toughness can reach 16 MPa m 1 / 2 [1–3]. A brittle-to-ductile transition (BTD) occurs between 1100 and 1200 8C. When loaded slowly, the stress–strain curves in tension reach a broad maximum in stress. The plateau stress is a function of strain rate and is lower for lower strain rates [6,7]. *Corresponding author. E-mail address: [email protected] (M.W. Barsoum). 0925-8388 / 03 / $ – see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016 / S0925-8388(03)00435-3
Conversely, if loaded rapidly, the stress does not peak, but instead the material fails on the rising part of the stress– strain curves, i.e., the response is more brittle [6,7]. The strain rate sensitivity in tension, for both fine-grained and coarse-grained samples is high; viz. ¯0.55 (i.e., stress exponent ¯1.8) [6,7]. Recently it was shown that Ti 3 SiC 2 and hexagonal ice are quite comparable both at the atomic and macroscopic levels, when deformation is concerned [8]. Since both are plastically anisotropic, with only two independent basal slip systems, homogeneous plastic deformation is not possible; instead large internal stresses develop. If these stresses are not dissipated, the behavior is brittle. However, if they can be dissipated the response is much more ductile. This interpretation explains, in large part, the strong strain rate dependencies of the mechanical response. In contrast to ice that remains brittle even at ¯0.90 of its
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melting point, as noted above, Ti 3 SiC 2 goes through a BTD transition at temperatures between 1100 and 1200 8C. This transition is well documented in flexure [4,9] and tension [6,7]. In most metals, the BTD transition is associated with the thermal activation of additional slip systems, which in turn result in an increase in fracture toughness. In Ti 3 SiC 2 the fracture toughness drops from around 8–10 to about 4 MPa m 21 / 2 above the BTD transition temperature [2]. And while the exact nature of the BTD is not understood at this time, TEM and HRTEM studies [10–12] did not provide any evidence for the presence of non-basal dislocation, which leads us to eliminate the activation of other slip systems as a cause. Furthermore, it would be very difficult, if not impossible, to explain the drop in fracture toughness with increasing temperatures if other slip systems were initiated. For the same temperature and stress ranges reported here, the tensile creep of fine grained (¯5 mm) Ti 3 SiC 2 samples [13] occurs in three stages: a primary, where the strain rate decreases with time, a secondary or quasi-steady state where the strain rate reaches a minimum, and a tertiary stage. Creep occurs by a combination of plastic deformation and damage accumulation. Plastic deformation is the dominant mechanism during the primary and secondary creep regimes. The minimum creep rate is well represented by a power law expression (see Eq. (1)) with a stress exponent of 1.560.1 and an activation energy of 445610 kJ / mol. Creep results, and those obtained from tensile and stress relaxation tests, are in good agreement with each other suggesting that the same atomic mechanism is responsible for the plastic deformation [7,13]. Furthermore, the results of strain-transient dip and cyclic tests [7,13] provide strong evidence for the presence of large internal stresses during creep. These stresses are responsible for recoverable (anelastic) strains upon unloading, and are believed to be responsible for the initiation of intergranular microcracks and the acceleration of creep during the tertiary regime. Most recently we have shown that macroscopic polycrystalline Ti 3 SiC 2 cylinders can be compressed, at room temperature, to stresses of up to 1 GPa, and fully recover upon the removal of the load, while dissipating ¯25% of the mechanical energy [14]. The stress–strain curves at room temperature outline fully reversible, reproducible, rate-independent, closed hysteresis loops that are strongly influenced by grain size with the energy dissipated being significantly larger in the coarse-grained material. This phenomenon was attributed to the fully reversible formation and annihilation of incipient kink bands, IKBs, defined as near parallel dislocation walls of opposite polarity that remain attached, and are thus attracted to each other. Removal of the load allows the walls to collapse and the IKB to be totally eliminated. At temperatures higher than 1000 8C, the stress–strain loops are open and the response becomes strain rate dependent. Most germane to this work
is the fact that cyclic hardening was observed at 1200 8C, for the coarse-grained samples. This hardening was attributed to the dissociation of the IKBs and the coalescence of the latter to form regular kink bands (KBs) that in turn are no longer reversible and more important result in grain refinement. In other word, the response of the coarsegrained (see below) samples after modest stress cycling was comparable to the fine-grained samples. In this paper, we report on the tensile creep of coarsegrained, CG, Ti 3 SiC 2 samples, in the 1000–1200 8C temperature and 10–100 MPa stress ranges, respectively. Whenever possible the results are compared with previous work on the creep of fine-grained, FG, samples [13].
2. Experimental procedure The processing details are described elsewhere [6,3]. The CG samples, were prepared by reactive hot isostatic pressing (HIPing) of titanium (2325 mesh, 99.5%, Alfa Aesar, Ward Hill, MA), silicon carbide (2325 mesh, 99.5%, Atlantic Engineering Equipment, Bergenfield, NJ) and graphite (d m 51 mm, 99%, Aldrich, Milwaukee, WI) at 1600 8C under 40 MPa for 6 h. The resulting samples were fully dense, predominantly single-phase, with randomly aligned plate-like grains of the order of 30 mm and aspect ratio of 2.3 (Appendix A). The tensile creep measurement details can be found elsewhere [15]. Electro-discharge machined dog-bone specimens SR51 (prismatic gage section: 232.5312 mm 3 ) [16] were tested with no further surface preparation. The time dependence of the strain was monitored using a laser-extensometer [17]. All samples were heated to the testing temperature in ¯1.5 h, and held at that temperature for anywhere from 2 to 4 h before the load was applied. Most tests were performed under constant temperature and load up to fracture, or until the tests were aborted. In roughly a quarter of the samples, the load was increased after enough data were collected for the calculation of the minimum creep rate. However, to minimize the influence of damage accumulation, the stress was never increased more than once for any given sample. In addition to tensile creep, relaxation tests at 1200 8C, and strain transient dip, STD, tests at 1150 8C were carried out on an Instron 1 8500 testing machine, using procedures described in more detail in the literature [18–23]. In both,
1
Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology and Drexel University, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.
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the strain was monitored as a function of time by a capacitive extensometer with a useful sensitivity of about 10 25 . In the relaxation tests, the samples were loaded at a constant strain rate up to the desired stress, at which time the cross-head motion was abruptly stopped, and the stresses and strains were monitored as a function of time [7]. For the STD tests, a sample was loaded and held at a stress, s, until the strain increased more or less linearly with time, at which point the load was immediately (,1 s) decreased by Ds. Three sets of STD tests were carried out on one sample. The first was at an initial stress of 40 MPa, followed by stress drops Ds of 4, 8, 12, 16, 20, 24 and 36 MPa; the second was at an initial stress s of 60 MPa, followed by Ds values of 4, 8, 16, 24, 26 and 56 MPa; the third was at an initial stress of 80 MPa, followed by Ds values of 4, 8, 16 and 76 MPa. When quasi steady state was established at the lower stresses (s 2Ds ), the stress was increased again to the initial s, and the test repeated. During this test the stress was never reduced below 4 MPa, which is the minimum stress required to keep the sample well aligned in the testing machine. Fracture surfaces of most samples were examined by scanning electron microscopy (SEM). In addition, select surfaces that were parallel to the applied load were ground and polished for optical microscopy (OM) and SEM analysis. Some of the polished samples were etched using
301
HF:HNO 3 :H 2 O solution (1:1:1, v / v) in order to better expose the grains [4].
3. Results The effect of time, t, and stress, s on the tensile strain, ´, at 1100 8C is shown in Fig. 1a. The strain rate, ´~ , versus t curves for the same set of data are plotted in Fig. 1b. Three regimes are distinguishable: An initial transient regime, where ´~ decreases with t (inset in Fig. 1b). (ii) A secondary creep regime in which ´~ is more or less constant with time. This region is mostly absent in samples tested at stresses of 60 MPa or higher. In this regime, the creep rate reaches a minimum, ´~ min . (iii) A tertiary creep regime, in which ´~ increases until failure. (i)
A ln–ln plot of ´~ min versus s as a function of temperature, T, is shown in Fig. 2a; an Arrhenius plot of ´~ min is shown in Fig. 2b. Bilinear regression analysis (95% probability) of the results was carried out, assuming the power law relation between ´~ min , T and s to be [24,25]:
Fig. 1. Time and stress dependencies of (a) tensile strain and (b) strain rate of CG samples tested at 1100 8C. Plot (b) is obtained by differentiation of curves shown in (a). Insets are enlargements of the initial parts of the plots shown in (a) and (b).
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302
Fig. 2. (a) Ln–ln plot of ´~ min versus s as a function of temperature and testing technique. Solid black lines are results of a bilinear regression for CG microstructure. The results of tensile tests at 1200 8C (solid small circles), STD tests at 1150 8C (small solid triangles), and relaxation tests at 1200 8C (small open circles) are also shown. (b) Arrhenius plot of ´~ min at various stresses.
Q D S D expS 2 ] RT
s ´~ min 5 ´~ o A ] so
n
(1)
where A, n and Q are, respectively, a stress-independent
constant, stress exponent and activation energy for creep: ´~ 0 51 s 21 and so 51 MPa. A regression analysis, on the logarithmic form of Eq. (1) yields: A5exp (17.361) s 21 , n52.060.1 and Q5
M. Radovic et al. / Journal of Alloys and Compounds 361 (2003) 299–312
458612 kJ / mol. The small values of the standard error, and the high value for the coefficient of correlation (R 2 5 0.974), indicate that ´~ min can be well represented by Eq. (1), over the entire range of testing temperatures and stresses, viz.:
´~ min (s 21 ) 5 ´~ o exps1761d
S]ss D o
2.060.1
S
2 458612 kJ / mol exp ]]]]]] RT
D
(2)
The goodness of the fit, assuming n52, is shown in Fig. 3a, wherein the solid line is that of Eq. (2). Also plotted on the figure, as a dotted line, are the results for the FG microstructure [13]. A plot of (ln ´~ min ) /s n versus 1 /T (Fig. 3b) yields a straight line, with a slope that is almost identical to that of the FG microstructure (dashed line in Fig. 3b). These results clearly confirm that Q is not a
function of grain size, and that at all temperatures, ´~ min of the CG samples is lower than their FG counterparts. Coarse-grained specimens of the same shape and size as those used in this study were tested in tension at a constant cross-head displacement rate at 1200 8C [7]. Maximum (plateau) stresses reached during these tests as a function of strain rate are plotted in Fig. 2a as solid circles. These stresses represent a lower creep boundary, i.e., the lowest stress required to produce creep at the imposed rate. As in the case of the FG Ti 3 SiC 2 samples [13], the results of the tensile and creep tests are only comparable when a stress plateau is reached in the former. It is worth noting that only two of the CG samples tested in tension reached a plateau stress [7]. Data from relaxation tests at 1200 8C [7], plotted as small open circles in Fig. 2a, are also in good agreement with the data from creep tests at the same temperature. Select, but typical, curves obtained from STD tests at 1150 8C are plotted in Fig. 4. Small stress drops cause instantaneous contractions, followed by a period of zero creep rate (Fig. 4a,c), after which creep resumes and the creep rate increases to a new steady value. Large stress reductions (Fig. 4b,d) are followed by regions of negative creep, after the instantaneous contractions. The creep rate eventually goes to zero before it ultimately increases to a new steady state value. The negative creep regime is especially well pronounced for the last, and largest, load drop (Fig. 4b,d) that reduces s to 4 MPa. The minimum creep rates from the STD tests carried out at 1150 8C (solid small up triangles in Fig. 2a) are in good agreement with those from creep tests at the same temperature. The recovery rate, r, and the strain hardening coefficient, h, were calculated from the STD tests using the procedure described by Lloyd and McElroy [18]. The steady state creep rate was then calculated using the Bailey–Orowan equation as ´~ 5 r /h. The strain rates calculated using this approach are in good agreement with the ´~ min values measured during creep. For instance, the calculated steady state creep rates for the STD tests shown in Fig. 4a,c are: 8.6310 27 and 1.8310 26 s 21 , respectively; the ´~ min rates measured at 40 and 60 MPa are 8.13 10 27 and 1.8310 26 s 21 , respectively. Log–log plots of lifetime (or time to failure), t f , versus s (Fig. 5a) yield a series of parallel straight lines for each testing temperature. Also included in Fig. 5a are the lifetimes of the FG samples, shown as dotted lines, which, at any given temperature, are shorter than the CG samples. The results plotted in Fig. 5a suggest that the data can be fitted to a Monkman–Grant expression [26]:
S D
´~ min t f (s) 5 t o KMG ]] ´~ o Fig. 3. (a) Ln–ln plot of ´~ min ? exp Q /RT versus s for CG (solid lines) and FG (dashed lines) [13] microstructures. Inset shows a ln–ln plot of ´~ min versus s at 1100 8C and 1200 8C for both microstructures. (b) Ln–ln plot of ´~ min ? s 2n versus reciprocal temperature as a function of grain size.
303
2m
(3)
where KMG , and m, are a dimensionless constant and the Monkman–Grant exponent, respectively; t 0 51 s. A leastsquares fit of the results (Fig. 5b), yields an m5160.06
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Fig. 4. Results of STD tests at 1150 8C. Black horizontal lines denote strain (left-hand side axes); gray lines are stress (right-hand side axes). In all tests initial stress s was reduced by Ds and then increased again up to s. (a) s 540 MPa, Ds 58 MPa; (b) s 540 MPa, Ds 520 MPa; (c) s 560 MPa, Ds 58 MPa; (d) s 560 MPa, Ds 524 MPa. At the end of each test the sample was unloaded down to 4 MPa. All results were obtained from one sample.
and KMG 5exp (2260.3). Also shown on the figure are the results for the FG samples [13]. The functional dependencies of the strains to failure on stresses and temperatures are shown in Fig. 5c. At high stresses, the strains to failure are ¯1 to 3% and comparable to the strains to failure in the FG samples (dashed line), which for reasons that are not clear, are a weak function of temperature [13]. Typical, low-magnification micrographs of the gage area in the vicinity of the fracture surface (Fig. 6) show that— as in the case in FG samples in creep [13] or tension [7]—deformation occurs without visible necking. Furthermore, specimens deformed in creep up to ¯3% are usually free of large cracks, or any other visible damage, within the gage area. If some microcracks are present they are few, and typically only in the near vicinity of the fracture surfaces (Fig. 7a,b). With increasing failure strains (.3%) more microcracks, that spread over the gage area, are observed (Fig. 7c,d). The network of cracks is obvious on the composite OM micrograph of a polished and etched gage area shown in Fig. 8. Cracks spread across almost the entire gage area in a direction more or less perpendicular to the applied load. Encircled detail is an example of a bridging grain. Clear evidence of slip can be seen in the OM micrographs of sample grain tested at 1000 8C and 40 MPa (Fig. 9). Steps at the grain boundary are presumably formed by slip along the basal planes, whose orientation is roughly determined from the grain shape (plate-like grains of Ti 3 SiC 2 are always elongated in direction of basal planes). Such features are not observed in undeformed samples. Delaminations along the basal planes (Fig. 10a) or grain boundary decohesion accompanied with delamination along basal planes (Fig. 10b) are frequently observed. Delaminations are usually accompanied by a deformation (bending, kinking) of lamina between two delamination
cracks. The bent grain shown in Fig. 10c is clear evidence of plastic deformation. Here again, such features are not observed in non-deformed samples. Delamination and kinking of the grains are shown in Fig. 10d. Select, but typical, SEM micrographs of fractured surfaces are presented in Fig. 11. A kinked lamina ‘sticking out’ of the fracture surface is shown in Fig. 11a. Such a grain must have served as a crack bridge before rupture. Another bridging grain sticking out from the fracture surface is shown in Fig. 11b. An example of a cavity remaining after failure and pullout of a large grain is shown in Fig. 11c. In order to monitor damage evolution more precisely, three tests were performed at 1050 8C and 60 MPa. The first two were interrupted after 21 and 49 h, the third was run to failure, viz. 94.5 h. The samples were then very carefully polished down to a 0.05-mm suspension of colloidal silica, using low loads in order to avoid pullouts. The central panel of Fig. 12, where the three creep curves are superimposed, demonstrates the good reproducibility between samples. SEM micrographs of gage and grip sections are compared in Fig. 12a–f. Some grain boundary decohesions are observed in the samples tested for 49 h at higher magnifications (inset in Fig. 12b). Microcracks and / or grain boundary decohesions (denoted by arrows) are obvious in the sample tested until fracture. In contrast, micrographs of the grip area (bottom row in Fig. 12) are free of damage, confirming that the damage observed in the gage area occurs during testing. In all samples tested an oxide layer formed, with a morphology—an inner oxide layer of SiO 2 and TiO 2 , and an outer layer of pure TiO 2 —identical to what was reported earlier [27]. It is worth noting, that the oxide layers that form in the beginning of the test do not influence the measured values of ´~ min for reasons discussed in Appendix B. A detailed study on the oxidation kinetics
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and the effect of stress on the latter are published elsewhere [28].
4. Discussion Based on our work to date [1–8,11–14] on the mechanical behavior of Ti 3 SiC 2 there is little doubt that: (a) dislocations play a dominant role in the deformation; (b) large internal stresses develop due to the paucity of operative slip systems; (c) the mechanical response of Ti 3 SiC 2 is essentially dictated by a competition between the rates of generation and dissipation of these internal stresses; and (d) at higher temperatures, and / or lower strain rates, these internal stresses can dissipate more readily. The results presented here are not only in complete agreement with these conclusions, but, more importantly, supply further strong evidence for their validity. Due to lack of space, we will focus mostly on the mechanism controlling the creep within the minimum creep rate regime. The characteristics of failure accumulation processes will be addressed only briefly here.
4.1. Phenomenological observations
Fig. 5. (a) Log–log plot of s versus time to failure, t f , for different temperatures; (b) log–log plot of ´~ min versus t f (Monkman–Grant plot); (c) Strain to failure versus s. In all cases, the solid and dashed lines were obtained by least squares fits of the results for CG and FG [13] microstructures, respectively.
Since ´~ min can be described by a single power law (Eq. (2); Figs. 2 and 3) it is fair to assume that the same thermally activated, rate-controlling mechanism(s), with an activation energy ¯460 kJ / mol, operates over the entire range of testing temperatures and stresses. Furthermore, the same thermally activated, rate-controlling mechanisms must be operative in the FG and CG samples (Fig. 3b). The results confirm that Q is not a function of grain size, and that at all temperatures, ´~ min of the CG samples were lower than their FG counterparts (inset in Fig. 3a). Since n is a function of grain size (Fig. 3a), it is not possible to calculate the grain size exponents, p, directly from the power law equations. Instead, an ‘effective’ grain size exponent was calculated assuming ´~ min ~d 2p , where d is average or equivalent grain size listed in Table 1. The problems associated with defining and measuring grain sizes in the microstructures tested here are discussed in Appendix A. Regardless of the technique used to quantify the grain sizes, the d CG /d FG ratio was found to be ¯6 (Table 2). Using this ratio, p was calculated (Table 1), and found to be a weak function of grain size ( p,1). Furthermore, with increasing T and s, the grain size difference becomes even less important; i.e., p decreases. This result is not too surprising and is consistent with our conclusion that the creep is dislocation based.
4.2. Evidence for internal stresses and stress relaxation Fig. 6. Photographs of, (a) initial samples, and samples tested at, (b) 1050 8C, 60 MPa, aborted after 50 h; (c) 1200 8C, 60 MPa, t f 53.86 h; (d) 1050 8C, 40 MPa, t f 5252 h; (e) 1000 8C, 60 MPa, t f 5230 h; (f) 1200 8C, 20 MPa, t f 532 h; (g) 1200 8C and 60 MPa, t f 53.86 h; (h) 1000 8C, 40 MPa, aborted after 830 h.
The negative creep observed upon high stress unloading (Fig. 4b,d) is evidence for the presence of internal stresses, whose values are higher than the stress to which the
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Fig. 7. OM micrographs of surfaces that were parallel to vertically applied load. Fracture surfaces at top of micrograph. Samples tested at: (a) 1000 8C, 80 MPa; t f 5114 h, ´f 52.3%; (b) 1100 8C, 40 MPa; t f 560 h, ´f 54.7%; (c) 1150 8C, 20 MPa; t f 561 h, ´f 54.8%; (d) 1200 8C, 20 MPa; t f 511.6 h, ´f 58.8%. Dark layers on both sides of specimens are oxide layers.
Fig. 8. Composite OM of polished and etched gage surface that was parallel to the vertically applied load. Branched microcracks spread from one side to the other. Encircled detail shows crack bridging. Test details: 1150 8C, 40 MPa, t f 561 h, ´f 58%.
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Fig. 9. OM of polished and etched gage surface that was parallel to the vertically applied load. Specimen with the duplex structure was tested at 1000 8C and 40 MPa. Decohesion of grain boundary is denoted by vertical arrow. Steps at grain boundary presumably formed by slip along basal planes whose direction is indicated on figure.
system are unloaded to [22,23]. Upon small s reductions, the period of zero creep is usually interpreted as direct evidence for recovery processes [22,23]. In addition the creep rates calculated from SDT tests using the Bailey– Orowan equation (derived assuming recovery-controlled creep) are in good agreement with those measured in the creep tests. This fact indicates that—like for FG Ti 3 SiC 2 [13], and hexagonal ice [29]—the recovery of internal stresses in CG Ti 3 SiC 2 play an important role during the creep. Comparing the shapes of the creep and tensile curves at different strain rates and / or stresses sheds more light on the problem. When the stresses used in creep, or the strain rates used in tension, are both low, good agreement is obtained between the two sets of data (Fig. 2a). Conversely, at stresses that are higher than 50 MPa, the quasi-steady state creep region, if present, is short (Fig. 1a) and, as important, the stress–strain curves in tension do not exhibit a maximum or plateau. The simplest explanation for both observations is that the response is determined by the relative rates at which the internal stresses accrue and dissipate. The excellent agreement between the results obtained from creep and stress relaxation tests (Fig. 2a) also imply that the same mechanisms operate in both. It is worth noting that the stress relaxation abilities of Ti 3 SiC 2 are limited; after several stress relaxation tests are repeated on
the same sample, the agreement is less good. This suggests that not all the internal stresses are relaxed during each cycle, which in turn would lead to damage accumulation.
4.3. Mechanisms controlling quasi-steady state creep For the reasons discussed in more detail in Appendix B, the values of ´~ min measured during the quasi-steady state creep are influenced minimally by oxidation. The effect of cavitation on ´~ min is not so clear. Results shown in Fig. 12 (sample tested at 1050 8C and 60 MPa) indicate that although the majority of cavities and microcracks develop during tertiary creep, some cavitation may occur even during the quasi-steady state regime where the minimum creep rate was measured. Determining the rate controlling atomic mechanism in creep, especially when the values of n and p do not agree with those predicted by classic creep models, is a nontrivial exercise. Even in a material as well studied as ice, the situation is still not entirely clear. These caveats notwithstanding, much can be learned about creep in Ti 3 SiC 2 from the results presented here and elsewhere [7,8,13,14]. The most compelling evidence that diffusion and / or grain boundary creep are not the dominant creep mechanisms can be found in the low values of p (Table 1). The classic models for diffusion and / or grain boundary
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Fig. 10. Micrographs of polished and etched gage surfaces that were parallel to vertically applied load showing: (a) OM of sample tested at 1000 8C and 80 MPa showing delamination denoted by arrows. Part of the grain between delamination cracks is slightly bent; (b) OM of sample tested at 1100 8C and 40 MPa. Bent lamella, denoted by arrow, serves as a crack bridge; (c) SEM of sample tested at 1150 8C and 20 MPa showing bent grain; (d) SEM of sample tested at 1050 8C and 40 MPa, showing simultaneous delamination and kinking of a grain.
controlled creep have p values of 2 to 3 [30–34]; the highest value of p calculated here is ¯0.9. On the other hand, the stress exponent measured in this work is lower that those predicted by dislocation based models [34]. It follows that the values for n and p reported in this study do not match values predicted by any known creep model in which one mechanism is dominant or rate controlling. Based on our work to date on the mechanical behavior of Ti 3 SiC 2 , and results of this work, there is little doubt that the following processes take place during creep: dislocation glide (Fig. 9), kinking (Fig. 10d) and cavitation (Fig. 12). Thus, we can speculate that the creep of Ti 3 SiC 2 is controlled by several mechanisms that operate nonsequentially or simultaneously as described recently by Goldsby and Kohlstedt [35] for hexagonal ice, and more generally by Langdon [36]. Glide of basal plane dislocations can take place only in favorably oriented grains, or soft grains, in which resolved shear stress exceeds a critical
value. During the short primary creep regime, basal plane dislocations in the soft grains glide and form pile-ups resulting in large internal stresses (manifested in STD tests). As the internal stresses increase, the creep rate decreases leading to a quasi-steady state regime. These internal stresses can be accommodated either by grain boundary cavitation and / or grain boundary sliding. It thus follows that creep in the secondary regime is probably controlled by the rate at which internal stresses are built up in dislocations pile-ups, kink-bands, walls, etc., and by the simultaneous rate at which these stresses are relaxed by grain boundary cavitations and / or grain boundary sliding. The discussion so far has been restricted to the secondary regime. However, when that regime ends and the tertiary regime begins is difficult to pinpoint for the simple reason that the two mechanisms are most probably occurring simultaneously, and thus there is no sharp delineation between them. At higher stresses and / or longer times, the
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Fig. 11. SEM of fracture surfaces showing: (a) delamination of a single grain with part of it sticking out of, and part in the fracture plane; (b) same sample, ruptured grain sticking out from the fracture plane; (c) cavity remaining in fracture plane due to the pullout of a grain that presumably served as a crack bridge.
formation of cavities and their linkage becomes more important leading to tertiary creep.
4.4. Tertiary creep and rupture Based on the shape of the creep curves (Fig. 1), the results shown in Fig. 12 and most of the micrographs
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shown in this paper, it is fair to assume that number of grain boundary and triple-point cavities increase with time and eventually coalesce into microcracks. Interestingly and philosophically it is not obvious from our results whether near failure we are dealing with creep or subcritical crack growth. This is especially true here since the tests were run in air and direct evidence for the penetration of oxygen along the cracks exists [28]. Another complicating factor is the reduction in cross-sectional area with time (Figs. 7 and 8). It is hereby acknowledged that much more work is needed to further understand what is occurring here. Not only are the ´~ min values for the CG samples lower than the FG ones (inset in Fig. 3a), but the t f values of the former are considerably longer; an enhancement that increases with decreasing testing stresses (Fig. 5a). Given that the oxidation kinetics are identical for both microstructures [28], the enhancements in t f must be due to the higher damage tolerance of the CG microstructure [1,2,5,8]. Said otherwise the coarser grains, as a direct result of their size, can sustain higher bridging stresses than the finer ones. In the remainder of this paper compelling microstructural evidence to support this notion is presented. The large concentration and size of the microcracks possible is clear in Figs. 7 and 8, especially at lower stresses. Comparing these micrographs with those of the FG samples [13], it is obvious that the size of the microcracks scale with grain size. The microstructural evidence also suggests the presence of two different crack bridging mechanisms. The first—in which grains whose basal planes are parallel to the direction of applied load serve as classic crack bridges— can be seen in the encircled area in Fig. 8 and in Fig. 11b,c. These grains can absorb energy either by plastic deformation or by frictional pull out. The second mechanism is more unusual. It begins with delaminations that are initiated on opposite sides of a single grain, but on different basal planes (Fig. 10a). These lamellae can also be formed from only one side of a grain if they are in the vicinity of a void at the grain boundary (denoted by arrows in Fig. 10b). With further deformation, the separated lamellae can deform significantly by bending before rupturing (Fig. 11a). This bending occurs by the formation of kink bands [10], the boundaries of which must clearly impede further delamination. For example, had the bending shown in Figs. 10b not occurred by dislocation motion, which result in kink boundaries, the delamination would have rapidly run across the entire grain. The fact that it does not is significant, and confirms that the kink-band based model for toughening in compression [10] is also applicable in tension. There is a distinction, however: in compression, the grains whose basal planes are parallel to the applied load are the ones that kink; in tension, the grains whose basal planes are normal to the applied load do. Samples deformed at high stresses, i.e., low strains to failure, fail with significantly less damage (Fig. 7a,b) and
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Fig. 12. Sequence of damage formation for specimens tested at 60 MPa and 1050 8C. Creep results are shown in middle panel. SEM micrographs of specimens’ gage are shown in the upper row; corresponding micrographs of grip area are shown in bottom row. (a,d) Test stopped after 21 h; (b,e) test stopped after ¯50 h; (c,f) specimen failed after ¯95 h.
Table 1 Grain size exponent, p, assuming ratio d CG /d FG 56 as a function of select temperatures and stresses; for measurement details see Appendix A Temp. (8C)
p
1000
0.80 0.60 0.40 0.33
1100
0.75 0.55 0.43 0.35
1200
0.91 0.71 0.50
the damage, if present, is in the near vicinity of the fracture surface. This observation is consistent with the fact that samples tested at higher stresses do not exhibit steady state creep but fail presumably before the balance between hardening and recovery processes takes place.
4.5. Technological importance Based on the results presented above it is fair to claim that—at a comparable stage of development i.e., ¯7 years from ‘discovery’—Ti 3 SiC 2 shows tremendous promise as a high temperature structural material. In this work, a polycrystalline sample sustained a tensile stress of 60 MPa for 800 h at 1000 8C in air before the run was aborted with the sample seemingly structurally intact. The record to date is a sample with a duplex microstructure (not discussed
M. Radovic et al. / Journal of Alloys and Compounds 361 (2003) 299–312 Table 2 Summary of grain size measurements for coarse-grained material used in this work and the fine-grained material used in Ref. [13] Grain length d l (mm)
Grain width d w (mm)
Aspect ratio d l /d w
Average lengths and widths of .1000 grains Fine-grained [13] 864 361.5 361.5 Coarse grained 42639 20616 261 [this work] d CG /d FG 5 7
Equivalent grain dia. (mm) ]] œ3 d 2l ? d w 663 33629
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overall creep response thus depends on the rate of generation and dissipation of these internal stresses. The latter most probably occur by a combination of delaminations, grain boundary decohesions and triple point cavitations. The unusual and unique damage tolerance imparted to the CG samples even at 1200 8C is due to the formation of tenacious kink band-based bridges of grains whose basal planes are parallel to the applied load.
6
Acknowledgements Line (Heyn) intercept method ASTM E112—(.1000 intersections) Intercept Nominal Feret’s length grain size diameter (mm) (mm) (mm) Fine-grained [13] 4 4 5 Coarse grained 24 27 30 [this work] d CG /d FG 6 6 6
We thank Mark Shiber and David Von Rohr (Drexel University, PA) for helping us during the specimen preparation and optical microscopy. Help provided by William Luecke, Frantisek Lofaj, Ralph Krause Jr. (NIST, MD) is also greatly appreciated. This work was supported by the Army Research Office (DAAD19-00-1-0435).
Regardless of the method used to measure the grain size, the average size of the coarse grains in the CG samples was ¯6 times the size of the fine grains in the FG samples.
Appendix A here) that survived a stress of 20 MPa for 1500 h at 1000 8C before the test was aborted. These results are particularly noteworthy because they are those for a pure, single phase, polycrystalline material. Very few, if any, commercial high temperature structural materials are single phase and pure; rather they are multielemental solids that have been developed over half a century of intense research. As our understanding of the creep and oxidation of Ti 3 SiC 2 in particular, and the MAX phases, in general, deepens it is fair to assume that they will someday fulfill their potential. Another important observation that could prove vital to the successful use of Ti 3 SiC 2 as a structural component at high temperatures is both the extent and distribution of damage that can be sustained before failure (e.g., Figs. 7c and 8). This unique characteristic would render the non-destructive inspection of load bearing components straightforward and unambiguous, greatly decreasing the chances of catastrophic failure. Such components could even be fabricated and embedded with simple electrical circuits that could possibly monitor the resistance of a component continually during operation and thus provide an early warning to failure. Other advantages of Ti 3 SiC 2 are its machinability, low density and relatively low cost.
5. Conclusions The processes responsible for the tensile creep of CG Ti 3 SiC 2 are the same ones responsible for the creep of FG Ti 3 SiC 2 . In both cases the activation energy for creep is ¯460 KJ / mol. The stress exponents are also comparable, 2 for the CG and 1.5 for FG. The creep response is characterized by the presence of large internal stresses. The
Measurement of the grain size The microstructure of CG polycrystalline Ti 3 SiC 2 consists of mostly thin plate-like grains surrounded by areas in which the grains are much smaller [4]. Thus, the nontrivial question arises: What is the relevant grain size to be used to interpret the creep results? In order to estimate equivalent grain sizes in both, the CG samples tested in this study, and FG structure tested in our previous study [13], two different grain size measurement techniques were applied. In the first, the lengths, d l , and widths, d w , of more than 1000 individual grains were measured by optical microscopy. The equivalent grain ]] size was calculated by 3 2 means of geometric average ( œ d l ? d w ), assuming the grains are ellipsoidal in shape. In other words, we assume the equivalent grain size to be the diameter of an equiaxed grain having the same volume as the plate-like grains of Ti 3 SiC 2 . The second measurement technique was based on the line intercept method (ASTM E112) in which the intercept length is proportional to the volume fraction of grain boundaries. In this case, the nominal grain size calculated and Farat’s diameter represent the diameters of the equiaxial grains having the same volume fraction of grain boundaries as in the microstructures tested. Here again over 1000 individual intercepts were measured The results are summarized in Table 2, together with the ratios of grain diameters for the CG and FG microstructures, d CG and d FG , respectively, measured using the two methods outlined above. From the results it is obvious that d CG /d FG ¯6. It is worth noting the slight difference in the aspect ratios between CG and FG structure. Also, the grain size
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distribution is narrower in the FG samples than in the CG ones, but neither exhibit a bimodal distribution. Also, average intercept lengths calculated from measurements in two orthogonal directions do not vary significantly indicating no alignment of the microstructure.
Appendix B Here we show that the reduction in cross-sectional area due to oxidation has a negligible effect on the measured values of minimum creep rate. For example, consider the samples tested at 1000 8C. Taking into account the heating soaking times, the minimum creep rate was established, conservatively, after ¯20 h. The thickness of the oxide layer at 1000 8C and 20 h is ¯40 mm [28], which reduces the cross-sectional area by ¯7%. If we assume, again conservatively, that the oxide layers are non-load bearing, such a decrease in cross-sectional area translates to an ¯14% increase in the minimum creep rate. If we consider more severe testing conditions 21200 8C, the minimum creep rate is established after ,5 h, including heating and pre-soaking times. In this case the increase in the minimum creep rate is ¯36%; a value that is relatively small compared to the errors in measurement of the minimum creep rate. Note this conclusion does not apply to the tertiary creep regime where the effects of the penetration of oxygen into the cracks [28] is unknown. The repeat of this work in inert atmospheres is indicated to better understand the role of oxygen in the tertiary regime.
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