- Email: [email protected]
Deformation and damage processes during creep of Incoloy MA957
Materials Science and Engineering A 386 (2004) 81–90
Deformation and damage processes during creep of Incoloy MA957 B. Wilshire∗ , T.D. Lieu Materials Research Centre, School of Engineering, University of Wales, Swansea SA28PP, UK Received 30 January 2004; received in revised form 1 July 2004
Abstract Tensile creep and creep facture properties at 873–973 K are reported for the oxide-dispersion-strengthened (ODS) ferritic steel, Incoloy MA957. The results are interpreted on the basis of information derived from microstructural studies, yield stress data, creep curve shape analyses and comparisons of tensile and compressive creep characteristics. Using this combination of approaches, the observed behaviour patterns can be rationalized in a manner consistent with the processes shown to govern strain accumulation and damage development during creep of ODS alloys produced with high grain aspect ratios. © 2004 Elsevier B.V. All rights reserved. Keywords: Creep fracture; Creep processes; Incoloy MA957; ODS alloys
1. Introduction MA957 was developed by INCO [1] for high-damagelevel nuclear applications. The alloy formulation was based on the fact that, while 10–13% Cr ferritic–martensitic steels display a high resistance to irradiation-induced void swelling [2–4], a serious loss of creep strength occurs above about 820 K. Hence, to extend the maximum temperature capability, attention was focused on oxide-dispersion-strengthened (ODS) ferritic steels containing yttria dispersions in a chromium-rich ferrite matrix, with MA957 having a nominal composition of Fe–14Cr–1Ti–0.3Mo–0.3Y2 O3 (wt.%). In general, the creep properties of ODS alloys are not only superior but also very different to those of the equivalent dispersion-free materials [5–8]. For example, the thermomechanical processing operations used to produce ODS alloys usually result in large grain aspect ratios (i.e. grain length divided by grain width), with the creep resistance increasing with increasing GAR [9]. The creep characteristics of high-GAR polycrystals are also anisotropic, with greater creep strengths recorded with tensile stresses applied parallel ∗
Corresponding author. Tel.: +44 1792 295243; fax: +44 1792 295244. E-mail address: [email protected] (B. Wilshire).
0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2004.07.047
rather than normal to the elongated grain axes [10]. Another distinctive feature of high-GAR polycrystals then emerges when the dependences of the minimum or secondary creep rate (˙εm ) on stress (σ) and temperature (T) are described using power law relationships of the form
Qc ε˙ m = Aσ exp − RT n
(1)
where the values of A, the stress exponent (n) and the activation energy for creep (Qc ) are commonly considered to vary when different mechanisms are dominant in different stress/temperature regimes. However, even when dislocation processes are known to be dominant, the n and Qc values usually differ markedly for pure metals and ODS alloys. With pure metals, n ∼ = 4–6, with Qc less than or equal to the activation energy for lattice diffusion (QL ), whereas n 4 and Qc QL when tensile stresses are applied parallel to the elongated grain axes of high-GAR polycrystals [5–8]. An early attempt to explain the large n and Qc values reported for particle-hardened alloys [11] suggested that creep occurs not under the full applied stress (σ) but under a reduced stress (σ − σ 0 ). In this way,
Q∗ ε˙ m = A (σ − σ0 ) exp − c RT ∗
m
(2)
82
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
where A∗ = A and m ∼ = 4, with Q∗c representing the temperature dependence of ε˙ m at constant (σ − σ 0 ), rather than at constant σ as in the determination of Qc (Eq. (1)). With the σ 0 approach, n ∼ = m and Qc ∼ = Q∗c when σ 0 ∼ = 0 or when σ 0 ∝ σ, whereas n > m and Qc > Q∗c when σ 0 is large and decreases with increasing temperature [12]. This basic idea has since been modified and extended considerably, with σ 0 now almost universally referred to as a ‘threshold’ stress, but σ 0 cannot be measured or predicted reliably. Consequently, increasing emphasis has been directed towards dislocation theories of dispersion strengthening although, as yet, no model provides a complete description of the complex behaviour of ODS alloys. Compared with the many experimental and theoretical studies concerned with the creep characteristics of ODS alloys, considerably less attention has been directed to the failure modes. For this reason, both the creep and creep fracture properties at 873–973 K are now reported for Incoloy MA957. Moreover, to clarify the processes controlling strain accumulation and damage development during tensile creep of high-GAR polycrystals, the present results are discussed in relation to information derived from a series of parallel investigations. These include: (a) microstructural studies, using optical as well as scanning and transmission electron microscopy; (b) comparisons of the creep rates recorded in tension and compression, with the stresses applied parallel to the elongated grain axes; (c) determinations of the temperature dependence of the yield strength; and (d) analyses of the variations in creep curve shape with changing stress and temperature.
sured to 10−5 . The transducer output was monitored automatically, so that over 500 strain/time readings were recorded throughout each test.
3. Results and discussion Under all test conditions investigated, normal creep curves were recorded, but the shapes of the curves varied with stress and temperature. These changes in curve shape are illustrated by the plots in Fig. 1, which show the creep strain (ε) and strain rate (˙ε) as functions of normalized time (t/tf ), where tf is the time to fracture. Yet, while the primary and tertiary strains vary (Fig. 1a), in all cases, a minimum rate (˙εm ) rather than a ‘secondary’ or ‘steady state’ value is reached when the decaying primary rate is offset by the tertiary acceleration (Fig. 1b). Although the primary and tertiary stages are usually the dominant features of a creep ‘curve’, it has become common practice to describe each curve by monitoring only ε˙ m , tf and the total creep strain to failure (εf ). However, with MA957, the ε˙ m , tf and εf measurements show high degrees of scatter. In fact, a set of six tests at 315 MPa and 923 K established that ε˙ m and tf could vary by a factor of ±2, while εf varied from 0.045 to 0.065. This scatter confirms that mechanical alloying
2. Experimental procedures MA957 bar was produced by mechanical alloying [13], i.e. co-milling of yttria and alloy steel powders, followed by compaction and extrusion. The subsequent heat-treatment schedule involved air-cooling after solution treatment for 1 h under vacuum at 1323 K before ageing for 25 h at 1073 K. The resulting microstructures were then studied using optical metallography, plus scanning and transmission electron microscopy techniques, which have been described elsewhere [14]. Cylindrical specimens of MA957, having diameters of 4 mm (with 9.5 mm threaded ends), were machined with 25.4 mm gauge lengths parallel to the extrusion axis. Tensile creep tests were then completed for stresses from 250 to 420 MPa at 873–973 K, using constant-stress machines [15]. In all cases, the specimens were heated to the creep temperature in 3 h and stabilized at temperature for 1 h before applying the load by means of a slow-release jack. High precision extensometers, incorporating a pair of differentialcapacitance transducers, allowed the creep strains to be mea-
Fig. 1. The variations in (a) creep strain, ε, and (b) creep strain rate, ε˙ , with normalized time, t/tf , for constant-stress tests carried out for MA957 under tensile stresses of 390 MPa at 898 K (tf ∼ = 92 ks), 340 MPa at 923 K (tf ∼ = 220 ks) and 290 MPa at 948 K (tf ∼ = 4353 ks), where tf is the time to fracture.
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
83
Fig. 4. Transmission electron micrograph showing the yttria particle dispersion present after solution treatment of MA957. Fig. 2. The stress dependences of the minimum creep rates recorded at 873–973 K for MA957.
is a difficult process, so the resulting alloys are somewhat inhomogeneous [16]. To minimize the extent to which this scatter limits identification of data trends, stress ranges were selected to give test durations varying from 1 to 5000 h. In this way, the results in Fig. 2 show that the stress and temperature dependences of ε˙ m for MA957 can be described using Eq. (1). Treating the log ε˙ m /log σ relationships at the various creep temperatures as a set of parallel straight lines, n ∼ = = 35 and Qc ∼ −1 815 kJ mol , consistent with the large n and Qc values typically recorded when dislocation processes control the creep properties of high-GAR polycrystals. 3.1. Microstructure dependence of creep properties The thermo-mechanical processing operations used to produce MA957 led to a fine elongated grain structure, with a grain aspect ratio of around seven (Fig. 3). Only yttria particles were discernible in the ferrite grains after solution treatment (Fig. 4), with stable -phase precipitates (Fe36 Cr22 Ti7 Mo3 ) forming mainly at grain boundaries during ageing (Fig. 5).
Fig. 3. Optical micrograph illustrating the elongated grain structure developed during manufacture of MA957.
The microstructures of MA957 are similar to those observed [14] for another nuclear-grade ODS ferritic steel, referred to as DT2203YO5, which has a nominal composition of Fe–13Cr–2.2Ti–1.5Mo–0.5Y2 O3 (wt.%). For both materials, the solution treatment and ageing conditions were identical, so the higher Ti and Mo levels resulted in the volume fractions of -phase precipitates being greater in DT2203YO5 than in MA957. Even so, comparable creep curves were recorded at 923 K for solution treated DT2203YO5 samples tested in the aged and non-aged conditions, indicating that the creep properties are not significantly affected by -phase precipitation [17]. As with the -phase content, the volume fraction of Y2 O3 particles in MA957 is low, so the extent to which the Y2 O3 dispersion impedes dislocation movement during creep must be limited. Thus, with the ODS alloy, MA956 (containing 0.5 wt.% Y2 O3 ), very different creep properties have been reported for samples produced with equiaxed and with elongated grain structures. The high-GAR MA956 displays impressive creep strengths and large n valves [18], whereas the equiaxed product shows poor creep strengths and the low n values normally found with dispersion-free materials [19]. Clearly, with the fully-recrystallised equiaxed MA956,
Fig. 5. Transmission electron micrograph showing the phase precipitates (central dark areas) present after solution treatment and ageing of MA957.
84
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
Fig. 6. Transmission electron micrograph showing the dislocation substructure retained after solution treatment and ageing of extruded MA957.
the small volume fraction of dispersoids has little effect on creep behaviour. It also appears that the poor creep strengths of equiaxed samples compared with high-GAR products are not attributable to differences in grain size and shape per se but to some microstructural feature related to the grain aspect ratio. Specifically, the ε˙ m values are identical for a nickel-based superalloy having equiaxed and elongated grain structures produced by conventional casting (CC) and directional solidification (DS), respectively [15]. Although differences in the failure mode result in the DS material exhibiting much longer creep lives, the creep rates do not depend on the grain aspect ratio. These observations support the view [20] that the dispersoid-stabilized dislocation substructures retained after thermo-mechanical processing, rather than the dispersoids themselves, determine the creep properties of high-GAR polycrystals. The reported GAR/creep strength correlation [9] can then be explained by the grain aspect ratio providing an indication of the retained dislocation density [20]. This proposal is fully consistent with the conclusions of a comprehensive study by Chou and Bhadeshia [16] of the effects of various heat-treatment schedules on the microstructures of extruded MA957. These authors emphasized that, although extrusion is carried out at relatively high temperatures, this operation cannot be classified as ‘hot working’, because the final microstructure represents a cold-deformed condition with elongated ferrite grains having high dislocation densities. Even annealing for over 160 h at 1428 K merely reduced rather than eliminated the high dislocation density introduced by extrusion [16]. Hence, solution treatment for 1 h at 1323 K and subsequent ageing for 25 h at 1073 K results in the present MA957 samples having an inhomogeneous retained dislocation substructure (Fig. 6). 3.2. Effects of pre-existing dislocation substructures The ways in which retained substructures determine the creep characteristics of high-GAR polycrystals can be understood by considering the effects of prestrain-imposed dislo-
Fig. 7. The stress dependences of the minimum creep rates recorded in tension at 773 K for a nickel–0.1 at.% gold alloy [18] prestrained by 0–0.2 in tension at room temperature (closed symbols) and for 99.993% nickel [19] prestrained by 0–0.11 in compression at the creep temperature of 773 K (open symbols).
cation substructures on the creep behaviour of single-phase materials. Thus, Fig. 7 shows the log ε˙ m /log σ relationships at 773 K for Ni–0.1 at.% Au specimens prestrained by 0–0.2 in tension at room temperature [21], with similar data sets reported recently for copper [22] and 316 stainless steels [23]. After prestraining, the testpieces were heated rapidly to the creep temperature, allowing recovery and rearrangement to occur without recrystallization. The dislocation density then increased with increasing prestrain, but creep properties different to those of the non-prestrained material were observed only with tensile prestrain levels which eliminated the plastic component of the initial strain on loading at the creep temperature [21]. For the Ni–0.1 at.% Au alloy, this criterion was satisfied for prestrains of 0.1 and 0.15 at low creep stresses and for a prestrain of 0.2 over the stress range covered (Fig. 7). When prestraining eliminates the plastic component of the initial loading strain, the dislocation density immediately after loading must be higher for the prestrained samples than for the non-prestrained specimens under the same stress/temperature conditions. Although recovery during the heating period creates some dislocation segments in the substructure which are able to move on loading, the high dislocation densities introduce stronger barriers to movement. This results in improved creep resistance and larger n values (Fig. 7), i.e., creep characteristics matching those observed for high-GAR polycrystals (Fig. 2). With single-phase materials, pre-existing dislocation substructures can be eliminated by recrystallization during prolonged creep exposure, even at relatively low temperatures. In contrast, the presence of small volume fractions of dispersoids (<0.5%) can stabilize the dislocation substructures [24], so that impressive creep strengths and large n values are displayed over extended stress/temperature ranges with high-GAR polycrystals (Fig. 2).
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
85
3.3. Creep in tension and compression Extrusion of ODS billets produces a grain structure elongated in the extrusion direction, just as equiaxed grains become elongated during tensile deformation. The retained substructures in high-GAR polycrystals are therefore equivalent to ‘tensile prestrains’ in the elongated grain directions. Yet, while large tensile prestrains decreased the tensile creep rates measured for the Ni–0.1 at.% Au alloy [21], compressive prestrains actually increased the subsequent tensile creep rates for pure nickel [25], as shown in Fig. 7. On this basis, if the dispersoid-stabilized ‘tensile’ substructures govern creep resistance, the creep strengths of high-GAR polycrystals should be significantly greater in tension than in compression. Conversely, if the dispersoids provide the key obstacles to dislocation movement, similar properties would be expected in tests carried out with the stress applied parallel to the elongated grain axes, irrespective of whether the stress is tensile or compressive. To evaluate these options for MA957, 4 mm diameter cylindrical testpieces were produced with 6 mm gauge lengths parallel to the elongated grain axis. Four specimens were tested in compression at stresses from 250 to 350 MPa at 948 K, using a servo-hydraulic machine under load control conditions. During the compression tests, barrelling of the specimens became discernible after low creep strains, such that the creep rate continued to decay slowly even after very long exposure times. Moreover, in an earlier investigation of the anisotropy of high-GAR polycrystals, the creep strength of MA6000 was found to be significantly lower with tensile stresses applied normal rather than parallel to the elongated grain axis, a result attributed to differences in grain boundary cavity development [10]. Hence, to avoid problems of data interpretation caused by cavity formation or by barrelling of the compression specimens with increasing strain, the present property comparisons are based on measurements of the initial creep rates (˙εi ). As evident from Fig. 8, the gradient of the tensile log ε˙ i /log σ plot is similar to that for the log ε˙ m /log σ data in Fig. 2, but substantially higher than the gradient of the compressive log ε˙ i /log σ plot, in line with the difference in n values found for the single-phase samples given large prestrains in tension and compression (Fig. 7). In addition, the initial rates in tension are substantially lower than the initial compressive rates (Fig. 8), consistent with the view that the dispersoid-stabilized substructures determine the creep properties of ODS alloys produced with grains elongated in the extrusion direction [20]. On this basis, it appears that creep of high-GAR polycrystals takes place by diffusion-controlled movement of dislocation segments in the retained substructures present within the elongated grains. However, the activation energy for creep of MA957 would then be expected to be comparable with that for lattice diffusion in ferrite (with Qc ∼ = 300 kJ mol−1 ). In−1 ∼ stead, Qc = 815 kJ mol when the temperature dependence of the creep rate (Fig. 2) is described using Eq. (1).
Fig. 8. The stress dependences of the initial creep rates recorded for MA957 at 948 K when tensile and compressive stresses were applied parallel to the elongated grain axes.
3.4. Variations in high-temperature yield stress Although large activation energies are normally found when Eq. (1) is used to define the behaviour of ODS alloys, lower Qc values are obtained with a relationship [26] which describes the creep rates of materials having equiaxed grain structures as p ADGb σ n b ε˙ m = (3) kT d G where D is the appropriate diffusivity, b the Burgers vector, k the Boltzmann’s constant, d the grain diameter, p the grain size exponent and G the shear modulus at the creep temperature. Yet, even allowing for the decrease in modulus with increasing temperature (Eq. (3)), plotting log ε˙ m against log(σ/G) does not give Qc ∼ = 300 kJ mol−1 for MA957. Unlike the elastic modulus which is temperature sensitive but does not vary significantly with changes in microstructure, creep properties are both temperature and microstructure dependent, as is the value of the yield stress (σ Y ) determined in high-strain-rate tests. For this reason, consideration is now given to an alternative approach to creep data representation [15,27], which analyses the various creep strain and creep rate parameters as functions of σ/σ Y rather than σ/G. Over a wide range of temperatures, the values of σ Y and the ultimate tensile stress (σ TS ) for MA957 in the as-extruded state have been determined at UKAEA, Harwell, and reported by Hamilton [28]. Within the batch-to-batch variability of high-GAR polycrystals produced by mechanical alloying [16], these results are in good agreement with the values obtained in the present study for MA957 samples which were solution treated and aged after extrusion (Fig. 9). 3.5. Analysis of creep curve shapes The idea that creep properties can be rationalized using σ Y values originated with an approach to creep curves shape analysis, termed the θ projection concept [15,27]. Although
86
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
Fig. 9. The temperature dependences of the high-strain-rate yield stress, σ Y , and the ultimate tensile stress, σ TS , for MA957 in the as-extruded state (open symbols) and after solution treatment and ageing (closed symbols).
Fig. 10. The relationship between the minimum creep rate, ε˙ m , and the tertiary product, θ 3 θ 4 , at 873–973 K for MA957.
introduced to obtain long-term design data by extrapolation of short-term test results, the predictive accuracy of the θ methodology could not be verified in the present study, because long-term property values are not available for MA957. Even so, the relevance of σ Y determinations is now illustrated by showing that the θ relationships are fully consistent with traditional methods of creep data representation. In line with the ε˙ /(t/tf ) plots presented in Fig. 1b, the θ concept envisages most normal curves in terms of decaying primary and accelerating tertiary stages. Modelling of the dislocation processes controlling strain accumulation and the damage processes causing the tertiary acceleration then describes the creep strain/time trajectory [15,27] as ε = θ1 (1 − exp(−θ2 t)) + θ3 (exp(θ4 t) − 1)
(4)
where θ 1 and θ 3 scale the primary and tertiary strains, while θ 2 and θ 4 are rate parameters governing the curvatures of the primary and tertiary components, respectively. Non-linear least-squares curve-fitting routines are available [15] to evaluate θ i (where i = 1, 2, 3, 4), with the θ values derived for MA957 describing each curve accurately over most of the creep life. As reported for numerous metals and alloys [14,27,29], the systematic variations in curve shape can then be quantified through plots of log θ i against (σ/σ Y ), with σ TS defining the maximum stress which can be applied at the creep temperature. However, properties such as ε˙ m are easily calculated from the θ values. With MA957, ε˙ m ∼ = θ3 θ4 (Fig. 10), so the procedures which quantify the stress and temperature dependences of the θ values [27] must also rationalize the log ε˙ m /log σ data in Fig. 2. Thus, the near-parallel log ε˙ m /(σ/σY ) plots at the various creep temperatures are superimposed, within scatter limits, by temperature compensation of ε˙ m through an Arrhenius term with an activation energy of ∼300 kJ mol−1 (Fig. 11), as expected for dislocation creep processes controlled by lattice diffusion in ferrite. The θ values relate not only to ε˙ m (Fig. 10) but also to standard strain parameters, as illustrated schematically in Fig. 12.
Fig. 11. The variations of ε˙ m exp(300,000/RT) with (σ/σ Y ) at 873–973 K for MA957.
Fig. 12. Schematic representation of the primary creep strain, εp , the tertiary creep strain, εt , the total creep strain to failure, εf , and the product of the minimum creep rate and rupture life, ε˙ m tf , in relation to the various θ parameters.
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
87
Fig. 13. The dependence of the creep rupture life, tf , on the tertiary rate parameter, θ 4 , at 873–973 K for MA957.
From Eq. (4), the total primary strain is θ 1 , with θ 1 ∼ = εp , where εp is the primary strain estimated for each curve by back-extrapolation of the minimum creep rate line to obtain the strain intercept at t = 0 (Fig. 12). Similarly, the tertiary strain (εt ) can be calculated from εf (Fig. 12), as εt = εf − εp
(5)
with Eq. (4) also allowing εt to be determined from the θ values as εt = θ3 (exp(θ4 tf ) − 1)
(6)
so that εt ∼ = 1.5θ 3 , because θ 4 tf ∼ = 1 (Fig. 13). Measurements taken directly from the creep curves then show that εf (and also εp and εt ) decrease with decreasing stress and temperature, although the data scatter complicates trend identification (Fig. 14). Despite this property variability, as with the θ values [27], εp , εt and εf vary sensibly with σ/σ Y (Fig. 15), i.e. the creep strains decrease as dislocation movement becomes progressively more difficult with decreasing stress, with very low strain values recorded when σ < σ Y . These results then provide a basis for analysis of the stress rupture behaviour of MA957.
Fig. 14. The stress dependences of the total creep strain to failure, εf , at 873–973 K for MA957.
Fig. 15. The dependences of (a) the primary creep strain, εp , (b) the tertiary creep strain, εt , and (c) the total creep strain to failure, εf , on σ/σ Y at 873–973 K for MA957.
3.6. Interrelation of creep and creep fracture properties The log ε˙ m /log σ plots in Fig. 2 almost mirror the log tf /log σ data in Fig. 16, suggesting [30] that ε˙ m tf = constant
(7)
so the rupture lives are determined by the rates of strain accumulation, i.e., creep fracture is strain controlled. However,
Fig. 16. The stress dependences of the creep rupture lives recorded at 873–973 K for MA957.
88
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
Fig. 17. The relationship between the minimum creep rate, ε˙ m , and the time to fracture, tf , at 873–973 K for MA957.
ε˙ m tf is not constant for MA957. Instead, the log ε˙ m /log tf relationships in Fig. 17 reveal that ε˙ m tf decreases as the applied stress is reduced, particularly at the higher test temperatures. Thus, ε˙ m tf varies in a manner similar to that for εf in Fig. 14, so that ε˙ m tf ∼ = χεf
(8)
where χ is a constant, i.e., Eq. (8) reduces to Eq. (7) when εf does not vary significantly with changing stress and temperature. This ε˙ m tf /εf relationship (Eq. (8)) also links to the creep damage tolerance parameter (λ) defined [31] as εf − εp εt λ= = ε˙ m tf ε˙ m tf
(9)
i.e., εt approximates to εf when εp is low, giving χ ∼ = 1/λ in Eq. (8). Using εt and ε˙ m tf measurements made directly from each creep curve, λ ∼ = 1.5 for MA957 (Fig. 18). This value is again consistent with the derived θ data because, over
Fig. 19. Optical micrographs showing the fracture appearance of longitudinal sections of MA957 testpieces which failed (a) under a stress of 315 MPa at 923 K and (b) under a stress of 400 MPa at 898 K. The tensile stress direction is horizontal.
the stress ranges covered at 873–973 K, ε˙ m ∼ = θ3 θ4 (Fig. 10). Hence, from Eq. (6) exp(θ4 tf ) − 1 (10) θ4 t f with θ 4 tf ∼ = 1 (Fig. 13), so that λ ∼ = 1.5. As evident from ∼ Fig. 12, λ = 1 when εt is low, with λ increasing as the tertiary stage becomes more pronounced. The magnitude of λ may therefore provide an indication of the processes influencing tertiary creep and fracture behaviour [32]. λ=
3.7. Tertiary creep and fracture processes
Fig. 18. The relationship between the tertiary creep strain, εt , and the product of the minimum creep rate and rupture life, ε˙ m tf , showing that the creep damage tolerance parameter, λ, is around 1.5 for MA957 tested over a range of stresses at 873–973 K.
Modelling of various damage processes has predicted [32] that λ ∼ = 1–2.5 when intergranular cavitation causes tertiary creep and fracture, with higher values expected when the tertiary stage begins as a consequence of necking (λ > 2.5) or precipitate coarsening (λ > 5). With MA957, λ ∼ = 1.5 (Fig. 18), but metallographic examination of fractured specimens shows that failure occurs in a transgranular not an intergranular manner. Moreover, a gradual transition in the detailed fracture mode becomes apparent (Fig. 19) as the creep deformation characteristics change on reducing the applied stress from above to below σ Y (Fig. 15). When the retained dislocation substructure (Fig. 6) severely limits strain accumulation at stresses less than σ Y (Fig. 15), microcracks nucleate on the short transverse bound-
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
aries and grow in a transgranular manner normal to the tensile stress axis. In long-term tests, the lengths of these transgranular cracks could be significantly greater than the widths of the elongated grains (Fig. 19a). Low ductility failure then occurs with negligible necking when the numbers and sizes of the developing cracks allow link up along paths almost parallel to the tensile stress direction, giving a ‘castellated’ fracture appearance (Fig. 19a). Microcracks also nucleate on the transverse boundaries when σ > σ Y , but regions ahead of the cracks can deform sufficiently to limit transgranular crack growth. Creep therefore continues until the attained strain levels are large enough to initiate necking. As the neck develops, shear link up of microcracks takes place on planes at ∼45◦ to the tensile axis, giving a ‘saw-tooth’ fracture appearance (Fig. 19b). In the present programme and in a previous study completed for two commercial aluminium alloys [29], tests were carried out using constant-stress equipment, so the tertiary acceleration cannot be due to stress intensification when the specimen cross-section decreases uniformly with increasing creep strain. However, even under constant true-stress conditions, many different processes can start the tertiary acceleration and more than one process can influence the subsequent rate of strain accumulation, while the mechanisms initiating the tertiary stage and causing failure can also be different. With MA957, no evidence was found to indicate the occurrence of local grain boundary migration, recrystallization or coarsening of the -phase precipitates over the stress/temperature ranges studied. For the microstructurallystable MA957, ε˙ ∼ = θ3 θ4 (Fig. 10) and θ 4 tf ∼ = 1 (Fig. 13) so Eq. (10) gives λ ∼ = 1.5 (Fig. 18) when tertiary creep and fracture are consequences of necking for σ > σ Y and transgranular cracking for σ < σ Y . Adopting the same approaches with the precipitation-hardened aluminium alloys [29], λ ∼ = 1.5 when cavitation processes were dominant with stable microstructures, whereas ε˙ m > θ3 θ4 and θ 4 tf > 1 so λ > 1.5 when tertiary began because of precipitate coarsening. Under constant true-stress conditions, λ > 1.5 when the tertiary stage is due to microstructural instability, but λ ∼ = 1.5 when tertiary creep and/or fracture are attributable to intergranular or transgranular cracking and/or necking. Information from a range of experimental approaches, which supplements the λ determinations, is therefore needed to quantify and explain the tertiary creep and fracture behaviour of alloys strengthened by dispersions of fine precipitates or insoluble particles.
4. Conclusions (1) Using a power law equation to describe the tensile creep data obtained at 873–973 K for MA957, n ∼ = 35 and Qc ∼ = 815 kJ mol−1 , in line with the large n and Qc values widely reported for high-GAR polycrystals. (2) Faster creep rates are recorded with compressive rather than tensile stresses applied parallel to the long grain
89
axes. This observation supports the view that the creep behaviour of high-GAR polycrystals is determined by the dispersoid-stabilized dislocation substructures retained after thermo-mechanical processing. (3) The complex creep strain and creep rate characteristics can be rationalized through the high-strain-rate yield stress at the creep temperature (σ Y ). The activation energy for creep is then comparable with that for lattice diffusion in ferrite (∼300 kJ mol−1 ), indicating that creep takes place by diffusion-controlled movement of dislocations within the substructure retained in the elongated grains. (4) Microstructural studies, together with quantitative curve shape analyses, show that fracture of MA957 occurs in a transgranular manner, with a transition in the detailed failure mode found on reducing the applied stress from above to below σ Y . Acknowledgement The authors wish to thank the Engineering and Physical Sciences Research Council for a research studentship awarded to TDL.
References [1] G.A.J. Hack, Denki-Seiko 57 (1986) 341. [2] D.S. Gelles, L.E. Thomas, in: J. Davies, D.J. Michel (Eds.), Ferritic Alloys for Use in Nuclear Energy Technologies, AIME, Warrendale, PA, 1984, p. 559. [3] J.J. Huet, Powder Metall. Rep. 40 (1985) 155. [4] E.A. Little (Ed.), Materials for Nuclear Reactor Core Applications, British Nuclear Energy Society, London, 1987, p. 47. [5] J. Lin, O.D. Sherby, Res. Mech. 2 (1981) 151. [6] J. Cadek, B. Ilschner, Acta Technol. CSAV 3 (1984) 280. [7] E. Arzt, Res. Mech. 31 (1991) 399. [8] B. Reppich, Z. Metall. 93 (2002) 605. [9] B.A. Wilcox, A.H. Clauer, Trans. AIME 236 (1966) 570. [10] R. Timmins, E. Arzt, Scripta Metall. 22 (1988) 1353. [11] K.R. Williams, B. Wilshire, Met. Sci. J. 7 (1973) 176. [12] J.D. Parker, B. Wilshire, Met. Sci. J. 9 (1975) 248. [13] J.S. Benjamin, Metall. Trans. 1 (1970) 2943. [14] R.W. Evans, J.A. Preston, B. Wilshire, E.A. Little, Mater. Sci. Eng. A 167 (1993) 65. [15] R.W. Evans, B. Wilshire, Creep of Metals and Alloys, The Institute of Metals, London, 1985. [16] T.S. Chou, H.K.D.H. Bhadeshia, Mater. Sci. Technol. 9 (1993) 890. [17] R.W. Evans, J.A. Preston, B. Wilshire, E.A. Little, J. Nucl. Mater. 195 (1992) 24. [18] J.C. Healy, M. Rees, J.D. Parker, R.C. Hurst, in: J.C. Earthman, F.A. Mohamed (Eds.), Proceedings of the 5th International Conference on Creep and Fracture of Engineering Materials and Structures, Warrendale, PA, TMS, 1997, p. 719. [19] R. Petkovic-Luton, D.S. Stolovitz, M.J. Luton, in: J.S. Benjamin, R.C. Benn (Eds.), Frontiers of High Temperature Materials II, INCO Alloys International, 1983, p. 73. [20] B. Wilshire, in: J.C. Earthman, F.A. Mohamed (Eds.), Proceedings of the 5th International Conference on Creep and Fracture of Engineering Materials and Structures, Warrendale, PA, TMS, 1997, p. 19.
90
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
[21] P.W. Davies, J.D. Richards, B. Wilshire, J. Inst. Met. 90 (1961/62) 431. [22] B. Wilshire, C.J. Palmer, Mater. Sci. Eng. A, in press. [23] B. Wilshire, M.R. Willis, Metal. Mater. Trans. 35A (2004) 563. [24] D. McLean, Mechanical Properties of Metals, Wiley, New York, 1962. [25] P.W. Davies, T.C. Finniear, B. Wilshire, J. Inst. Met. 91 (1962/63) 289. [26] A.K. Mukherjee, J.E. Bird, J.E. Dorn, Trans. ASM 62 (1969) 155.
[27] R.W. Evans, B. Wilshire, Introduction to Creep, The Institute of Materials, London, 1993. [28] M.L. Hamilton, PNNL-13168, 2000. [29] H. Burt, B. Wilshire, Metal. Mater. Trans. 35A (2004) 1691. [30] F.C. Monkman, N.J. Grant, Proc. ASTM 56 (1956) 593. [31] F.A. Leckie, D.R. Hayhurst, Acta Metall. 25 (1977) 1059. [32] M.F. Ashby, B.F. Dyson, in: S.R. Valluri (Ed.), Advances in Fracture Research, Pergamon Press, Oxford, UK, 1984, p. 3.
Deformation and damage processes during creep of Incoloy MA957 B. Wilshire∗ , T.D. Lieu Materials Research Centre, School of Engineering, University of Wales, Swansea SA28PP, UK Received 30 January 2004; received in revised form 1 July 2004
Abstract Tensile creep and creep facture properties at 873–973 K are reported for the oxide-dispersion-strengthened (ODS) ferritic steel, Incoloy MA957. The results are interpreted on the basis of information derived from microstructural studies, yield stress data, creep curve shape analyses and comparisons of tensile and compressive creep characteristics. Using this combination of approaches, the observed behaviour patterns can be rationalized in a manner consistent with the processes shown to govern strain accumulation and damage development during creep of ODS alloys produced with high grain aspect ratios. © 2004 Elsevier B.V. All rights reserved. Keywords: Creep fracture; Creep processes; Incoloy MA957; ODS alloys
1. Introduction MA957 was developed by INCO [1] for high-damagelevel nuclear applications. The alloy formulation was based on the fact that, while 10–13% Cr ferritic–martensitic steels display a high resistance to irradiation-induced void swelling [2–4], a serious loss of creep strength occurs above about 820 K. Hence, to extend the maximum temperature capability, attention was focused on oxide-dispersion-strengthened (ODS) ferritic steels containing yttria dispersions in a chromium-rich ferrite matrix, with MA957 having a nominal composition of Fe–14Cr–1Ti–0.3Mo–0.3Y2 O3 (wt.%). In general, the creep properties of ODS alloys are not only superior but also very different to those of the equivalent dispersion-free materials [5–8]. For example, the thermomechanical processing operations used to produce ODS alloys usually result in large grain aspect ratios (i.e. grain length divided by grain width), with the creep resistance increasing with increasing GAR [9]. The creep characteristics of high-GAR polycrystals are also anisotropic, with greater creep strengths recorded with tensile stresses applied parallel ∗
Corresponding author. Tel.: +44 1792 295243; fax: +44 1792 295244. E-mail address: [email protected] (B. Wilshire).
0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2004.07.047
rather than normal to the elongated grain axes [10]. Another distinctive feature of high-GAR polycrystals then emerges when the dependences of the minimum or secondary creep rate (˙εm ) on stress (σ) and temperature (T) are described using power law relationships of the form
Qc ε˙ m = Aσ exp − RT n
(1)
where the values of A, the stress exponent (n) and the activation energy for creep (Qc ) are commonly considered to vary when different mechanisms are dominant in different stress/temperature regimes. However, even when dislocation processes are known to be dominant, the n and Qc values usually differ markedly for pure metals and ODS alloys. With pure metals, n ∼ = 4–6, with Qc less than or equal to the activation energy for lattice diffusion (QL ), whereas n 4 and Qc QL when tensile stresses are applied parallel to the elongated grain axes of high-GAR polycrystals [5–8]. An early attempt to explain the large n and Qc values reported for particle-hardened alloys [11] suggested that creep occurs not under the full applied stress (σ) but under a reduced stress (σ − σ 0 ). In this way,
Q∗ ε˙ m = A (σ − σ0 ) exp − c RT ∗
m
(2)
82
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
where A∗ = A and m ∼ = 4, with Q∗c representing the temperature dependence of ε˙ m at constant (σ − σ 0 ), rather than at constant σ as in the determination of Qc (Eq. (1)). With the σ 0 approach, n ∼ = m and Qc ∼ = Q∗c when σ 0 ∼ = 0 or when σ 0 ∝ σ, whereas n > m and Qc > Q∗c when σ 0 is large and decreases with increasing temperature [12]. This basic idea has since been modified and extended considerably, with σ 0 now almost universally referred to as a ‘threshold’ stress, but σ 0 cannot be measured or predicted reliably. Consequently, increasing emphasis has been directed towards dislocation theories of dispersion strengthening although, as yet, no model provides a complete description of the complex behaviour of ODS alloys. Compared with the many experimental and theoretical studies concerned with the creep characteristics of ODS alloys, considerably less attention has been directed to the failure modes. For this reason, both the creep and creep fracture properties at 873–973 K are now reported for Incoloy MA957. Moreover, to clarify the processes controlling strain accumulation and damage development during tensile creep of high-GAR polycrystals, the present results are discussed in relation to information derived from a series of parallel investigations. These include: (a) microstructural studies, using optical as well as scanning and transmission electron microscopy; (b) comparisons of the creep rates recorded in tension and compression, with the stresses applied parallel to the elongated grain axes; (c) determinations of the temperature dependence of the yield strength; and (d) analyses of the variations in creep curve shape with changing stress and temperature.
sured to 10−5 . The transducer output was monitored automatically, so that over 500 strain/time readings were recorded throughout each test.
3. Results and discussion Under all test conditions investigated, normal creep curves were recorded, but the shapes of the curves varied with stress and temperature. These changes in curve shape are illustrated by the plots in Fig. 1, which show the creep strain (ε) and strain rate (˙ε) as functions of normalized time (t/tf ), where tf is the time to fracture. Yet, while the primary and tertiary strains vary (Fig. 1a), in all cases, a minimum rate (˙εm ) rather than a ‘secondary’ or ‘steady state’ value is reached when the decaying primary rate is offset by the tertiary acceleration (Fig. 1b). Although the primary and tertiary stages are usually the dominant features of a creep ‘curve’, it has become common practice to describe each curve by monitoring only ε˙ m , tf and the total creep strain to failure (εf ). However, with MA957, the ε˙ m , tf and εf measurements show high degrees of scatter. In fact, a set of six tests at 315 MPa and 923 K established that ε˙ m and tf could vary by a factor of ±2, while εf varied from 0.045 to 0.065. This scatter confirms that mechanical alloying
2. Experimental procedures MA957 bar was produced by mechanical alloying [13], i.e. co-milling of yttria and alloy steel powders, followed by compaction and extrusion. The subsequent heat-treatment schedule involved air-cooling after solution treatment for 1 h under vacuum at 1323 K before ageing for 25 h at 1073 K. The resulting microstructures were then studied using optical metallography, plus scanning and transmission electron microscopy techniques, which have been described elsewhere [14]. Cylindrical specimens of MA957, having diameters of 4 mm (with 9.5 mm threaded ends), were machined with 25.4 mm gauge lengths parallel to the extrusion axis. Tensile creep tests were then completed for stresses from 250 to 420 MPa at 873–973 K, using constant-stress machines [15]. In all cases, the specimens were heated to the creep temperature in 3 h and stabilized at temperature for 1 h before applying the load by means of a slow-release jack. High precision extensometers, incorporating a pair of differentialcapacitance transducers, allowed the creep strains to be mea-
Fig. 1. The variations in (a) creep strain, ε, and (b) creep strain rate, ε˙ , with normalized time, t/tf , for constant-stress tests carried out for MA957 under tensile stresses of 390 MPa at 898 K (tf ∼ = 92 ks), 340 MPa at 923 K (tf ∼ = 220 ks) and 290 MPa at 948 K (tf ∼ = 4353 ks), where tf is the time to fracture.
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
83
Fig. 4. Transmission electron micrograph showing the yttria particle dispersion present after solution treatment of MA957. Fig. 2. The stress dependences of the minimum creep rates recorded at 873–973 K for MA957.
is a difficult process, so the resulting alloys are somewhat inhomogeneous [16]. To minimize the extent to which this scatter limits identification of data trends, stress ranges were selected to give test durations varying from 1 to 5000 h. In this way, the results in Fig. 2 show that the stress and temperature dependences of ε˙ m for MA957 can be described using Eq. (1). Treating the log ε˙ m /log σ relationships at the various creep temperatures as a set of parallel straight lines, n ∼ = = 35 and Qc ∼ −1 815 kJ mol , consistent with the large n and Qc values typically recorded when dislocation processes control the creep properties of high-GAR polycrystals. 3.1. Microstructure dependence of creep properties The thermo-mechanical processing operations used to produce MA957 led to a fine elongated grain structure, with a grain aspect ratio of around seven (Fig. 3). Only yttria particles were discernible in the ferrite grains after solution treatment (Fig. 4), with stable -phase precipitates (Fe36 Cr22 Ti7 Mo3 ) forming mainly at grain boundaries during ageing (Fig. 5).
Fig. 3. Optical micrograph illustrating the elongated grain structure developed during manufacture of MA957.
The microstructures of MA957 are similar to those observed [14] for another nuclear-grade ODS ferritic steel, referred to as DT2203YO5, which has a nominal composition of Fe–13Cr–2.2Ti–1.5Mo–0.5Y2 O3 (wt.%). For both materials, the solution treatment and ageing conditions were identical, so the higher Ti and Mo levels resulted in the volume fractions of -phase precipitates being greater in DT2203YO5 than in MA957. Even so, comparable creep curves were recorded at 923 K for solution treated DT2203YO5 samples tested in the aged and non-aged conditions, indicating that the creep properties are not significantly affected by -phase precipitation [17]. As with the -phase content, the volume fraction of Y2 O3 particles in MA957 is low, so the extent to which the Y2 O3 dispersion impedes dislocation movement during creep must be limited. Thus, with the ODS alloy, MA956 (containing 0.5 wt.% Y2 O3 ), very different creep properties have been reported for samples produced with equiaxed and with elongated grain structures. The high-GAR MA956 displays impressive creep strengths and large n valves [18], whereas the equiaxed product shows poor creep strengths and the low n values normally found with dispersion-free materials [19]. Clearly, with the fully-recrystallised equiaxed MA956,
Fig. 5. Transmission electron micrograph showing the phase precipitates (central dark areas) present after solution treatment and ageing of MA957.
84
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
Fig. 6. Transmission electron micrograph showing the dislocation substructure retained after solution treatment and ageing of extruded MA957.
the small volume fraction of dispersoids has little effect on creep behaviour. It also appears that the poor creep strengths of equiaxed samples compared with high-GAR products are not attributable to differences in grain size and shape per se but to some microstructural feature related to the grain aspect ratio. Specifically, the ε˙ m values are identical for a nickel-based superalloy having equiaxed and elongated grain structures produced by conventional casting (CC) and directional solidification (DS), respectively [15]. Although differences in the failure mode result in the DS material exhibiting much longer creep lives, the creep rates do not depend on the grain aspect ratio. These observations support the view [20] that the dispersoid-stabilized dislocation substructures retained after thermo-mechanical processing, rather than the dispersoids themselves, determine the creep properties of high-GAR polycrystals. The reported GAR/creep strength correlation [9] can then be explained by the grain aspect ratio providing an indication of the retained dislocation density [20]. This proposal is fully consistent with the conclusions of a comprehensive study by Chou and Bhadeshia [16] of the effects of various heat-treatment schedules on the microstructures of extruded MA957. These authors emphasized that, although extrusion is carried out at relatively high temperatures, this operation cannot be classified as ‘hot working’, because the final microstructure represents a cold-deformed condition with elongated ferrite grains having high dislocation densities. Even annealing for over 160 h at 1428 K merely reduced rather than eliminated the high dislocation density introduced by extrusion [16]. Hence, solution treatment for 1 h at 1323 K and subsequent ageing for 25 h at 1073 K results in the present MA957 samples having an inhomogeneous retained dislocation substructure (Fig. 6). 3.2. Effects of pre-existing dislocation substructures The ways in which retained substructures determine the creep characteristics of high-GAR polycrystals can be understood by considering the effects of prestrain-imposed dislo-
Fig. 7. The stress dependences of the minimum creep rates recorded in tension at 773 K for a nickel–0.1 at.% gold alloy [18] prestrained by 0–0.2 in tension at room temperature (closed symbols) and for 99.993% nickel [19] prestrained by 0–0.11 in compression at the creep temperature of 773 K (open symbols).
cation substructures on the creep behaviour of single-phase materials. Thus, Fig. 7 shows the log ε˙ m /log σ relationships at 773 K for Ni–0.1 at.% Au specimens prestrained by 0–0.2 in tension at room temperature [21], with similar data sets reported recently for copper [22] and 316 stainless steels [23]. After prestraining, the testpieces were heated rapidly to the creep temperature, allowing recovery and rearrangement to occur without recrystallization. The dislocation density then increased with increasing prestrain, but creep properties different to those of the non-prestrained material were observed only with tensile prestrain levels which eliminated the plastic component of the initial strain on loading at the creep temperature [21]. For the Ni–0.1 at.% Au alloy, this criterion was satisfied for prestrains of 0.1 and 0.15 at low creep stresses and for a prestrain of 0.2 over the stress range covered (Fig. 7). When prestraining eliminates the plastic component of the initial loading strain, the dislocation density immediately after loading must be higher for the prestrained samples than for the non-prestrained specimens under the same stress/temperature conditions. Although recovery during the heating period creates some dislocation segments in the substructure which are able to move on loading, the high dislocation densities introduce stronger barriers to movement. This results in improved creep resistance and larger n values (Fig. 7), i.e., creep characteristics matching those observed for high-GAR polycrystals (Fig. 2). With single-phase materials, pre-existing dislocation substructures can be eliminated by recrystallization during prolonged creep exposure, even at relatively low temperatures. In contrast, the presence of small volume fractions of dispersoids (<0.5%) can stabilize the dislocation substructures [24], so that impressive creep strengths and large n values are displayed over extended stress/temperature ranges with high-GAR polycrystals (Fig. 2).
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
85
3.3. Creep in tension and compression Extrusion of ODS billets produces a grain structure elongated in the extrusion direction, just as equiaxed grains become elongated during tensile deformation. The retained substructures in high-GAR polycrystals are therefore equivalent to ‘tensile prestrains’ in the elongated grain directions. Yet, while large tensile prestrains decreased the tensile creep rates measured for the Ni–0.1 at.% Au alloy [21], compressive prestrains actually increased the subsequent tensile creep rates for pure nickel [25], as shown in Fig. 7. On this basis, if the dispersoid-stabilized ‘tensile’ substructures govern creep resistance, the creep strengths of high-GAR polycrystals should be significantly greater in tension than in compression. Conversely, if the dispersoids provide the key obstacles to dislocation movement, similar properties would be expected in tests carried out with the stress applied parallel to the elongated grain axes, irrespective of whether the stress is tensile or compressive. To evaluate these options for MA957, 4 mm diameter cylindrical testpieces were produced with 6 mm gauge lengths parallel to the elongated grain axis. Four specimens were tested in compression at stresses from 250 to 350 MPa at 948 K, using a servo-hydraulic machine under load control conditions. During the compression tests, barrelling of the specimens became discernible after low creep strains, such that the creep rate continued to decay slowly even after very long exposure times. Moreover, in an earlier investigation of the anisotropy of high-GAR polycrystals, the creep strength of MA6000 was found to be significantly lower with tensile stresses applied normal rather than parallel to the elongated grain axis, a result attributed to differences in grain boundary cavity development [10]. Hence, to avoid problems of data interpretation caused by cavity formation or by barrelling of the compression specimens with increasing strain, the present property comparisons are based on measurements of the initial creep rates (˙εi ). As evident from Fig. 8, the gradient of the tensile log ε˙ i /log σ plot is similar to that for the log ε˙ m /log σ data in Fig. 2, but substantially higher than the gradient of the compressive log ε˙ i /log σ plot, in line with the difference in n values found for the single-phase samples given large prestrains in tension and compression (Fig. 7). In addition, the initial rates in tension are substantially lower than the initial compressive rates (Fig. 8), consistent with the view that the dispersoid-stabilized substructures determine the creep properties of ODS alloys produced with grains elongated in the extrusion direction [20]. On this basis, it appears that creep of high-GAR polycrystals takes place by diffusion-controlled movement of dislocation segments in the retained substructures present within the elongated grains. However, the activation energy for creep of MA957 would then be expected to be comparable with that for lattice diffusion in ferrite (with Qc ∼ = 300 kJ mol−1 ). In−1 ∼ stead, Qc = 815 kJ mol when the temperature dependence of the creep rate (Fig. 2) is described using Eq. (1).
Fig. 8. The stress dependences of the initial creep rates recorded for MA957 at 948 K when tensile and compressive stresses were applied parallel to the elongated grain axes.
3.4. Variations in high-temperature yield stress Although large activation energies are normally found when Eq. (1) is used to define the behaviour of ODS alloys, lower Qc values are obtained with a relationship [26] which describes the creep rates of materials having equiaxed grain structures as p ADGb σ n b ε˙ m = (3) kT d G where D is the appropriate diffusivity, b the Burgers vector, k the Boltzmann’s constant, d the grain diameter, p the grain size exponent and G the shear modulus at the creep temperature. Yet, even allowing for the decrease in modulus with increasing temperature (Eq. (3)), plotting log ε˙ m against log(σ/G) does not give Qc ∼ = 300 kJ mol−1 for MA957. Unlike the elastic modulus which is temperature sensitive but does not vary significantly with changes in microstructure, creep properties are both temperature and microstructure dependent, as is the value of the yield stress (σ Y ) determined in high-strain-rate tests. For this reason, consideration is now given to an alternative approach to creep data representation [15,27], which analyses the various creep strain and creep rate parameters as functions of σ/σ Y rather than σ/G. Over a wide range of temperatures, the values of σ Y and the ultimate tensile stress (σ TS ) for MA957 in the as-extruded state have been determined at UKAEA, Harwell, and reported by Hamilton [28]. Within the batch-to-batch variability of high-GAR polycrystals produced by mechanical alloying [16], these results are in good agreement with the values obtained in the present study for MA957 samples which were solution treated and aged after extrusion (Fig. 9). 3.5. Analysis of creep curve shapes The idea that creep properties can be rationalized using σ Y values originated with an approach to creep curves shape analysis, termed the θ projection concept [15,27]. Although
86
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
Fig. 9. The temperature dependences of the high-strain-rate yield stress, σ Y , and the ultimate tensile stress, σ TS , for MA957 in the as-extruded state (open symbols) and after solution treatment and ageing (closed symbols).
Fig. 10. The relationship between the minimum creep rate, ε˙ m , and the tertiary product, θ 3 θ 4 , at 873–973 K for MA957.
introduced to obtain long-term design data by extrapolation of short-term test results, the predictive accuracy of the θ methodology could not be verified in the present study, because long-term property values are not available for MA957. Even so, the relevance of σ Y determinations is now illustrated by showing that the θ relationships are fully consistent with traditional methods of creep data representation. In line with the ε˙ /(t/tf ) plots presented in Fig. 1b, the θ concept envisages most normal curves in terms of decaying primary and accelerating tertiary stages. Modelling of the dislocation processes controlling strain accumulation and the damage processes causing the tertiary acceleration then describes the creep strain/time trajectory [15,27] as ε = θ1 (1 − exp(−θ2 t)) + θ3 (exp(θ4 t) − 1)
(4)
where θ 1 and θ 3 scale the primary and tertiary strains, while θ 2 and θ 4 are rate parameters governing the curvatures of the primary and tertiary components, respectively. Non-linear least-squares curve-fitting routines are available [15] to evaluate θ i (where i = 1, 2, 3, 4), with the θ values derived for MA957 describing each curve accurately over most of the creep life. As reported for numerous metals and alloys [14,27,29], the systematic variations in curve shape can then be quantified through plots of log θ i against (σ/σ Y ), with σ TS defining the maximum stress which can be applied at the creep temperature. However, properties such as ε˙ m are easily calculated from the θ values. With MA957, ε˙ m ∼ = θ3 θ4 (Fig. 10), so the procedures which quantify the stress and temperature dependences of the θ values [27] must also rationalize the log ε˙ m /log σ data in Fig. 2. Thus, the near-parallel log ε˙ m /(σ/σY ) plots at the various creep temperatures are superimposed, within scatter limits, by temperature compensation of ε˙ m through an Arrhenius term with an activation energy of ∼300 kJ mol−1 (Fig. 11), as expected for dislocation creep processes controlled by lattice diffusion in ferrite. The θ values relate not only to ε˙ m (Fig. 10) but also to standard strain parameters, as illustrated schematically in Fig. 12.
Fig. 11. The variations of ε˙ m exp(300,000/RT) with (σ/σ Y ) at 873–973 K for MA957.
Fig. 12. Schematic representation of the primary creep strain, εp , the tertiary creep strain, εt , the total creep strain to failure, εf , and the product of the minimum creep rate and rupture life, ε˙ m tf , in relation to the various θ parameters.
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
87
Fig. 13. The dependence of the creep rupture life, tf , on the tertiary rate parameter, θ 4 , at 873–973 K for MA957.
From Eq. (4), the total primary strain is θ 1 , with θ 1 ∼ = εp , where εp is the primary strain estimated for each curve by back-extrapolation of the minimum creep rate line to obtain the strain intercept at t = 0 (Fig. 12). Similarly, the tertiary strain (εt ) can be calculated from εf (Fig. 12), as εt = εf − εp
(5)
with Eq. (4) also allowing εt to be determined from the θ values as εt = θ3 (exp(θ4 tf ) − 1)
(6)
so that εt ∼ = 1.5θ 3 , because θ 4 tf ∼ = 1 (Fig. 13). Measurements taken directly from the creep curves then show that εf (and also εp and εt ) decrease with decreasing stress and temperature, although the data scatter complicates trend identification (Fig. 14). Despite this property variability, as with the θ values [27], εp , εt and εf vary sensibly with σ/σ Y (Fig. 15), i.e. the creep strains decrease as dislocation movement becomes progressively more difficult with decreasing stress, with very low strain values recorded when σ < σ Y . These results then provide a basis for analysis of the stress rupture behaviour of MA957.
Fig. 14. The stress dependences of the total creep strain to failure, εf , at 873–973 K for MA957.
Fig. 15. The dependences of (a) the primary creep strain, εp , (b) the tertiary creep strain, εt , and (c) the total creep strain to failure, εf , on σ/σ Y at 873–973 K for MA957.
3.6. Interrelation of creep and creep fracture properties The log ε˙ m /log σ plots in Fig. 2 almost mirror the log tf /log σ data in Fig. 16, suggesting [30] that ε˙ m tf = constant
(7)
so the rupture lives are determined by the rates of strain accumulation, i.e., creep fracture is strain controlled. However,
Fig. 16. The stress dependences of the creep rupture lives recorded at 873–973 K for MA957.
88
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
Fig. 17. The relationship between the minimum creep rate, ε˙ m , and the time to fracture, tf , at 873–973 K for MA957.
ε˙ m tf is not constant for MA957. Instead, the log ε˙ m /log tf relationships in Fig. 17 reveal that ε˙ m tf decreases as the applied stress is reduced, particularly at the higher test temperatures. Thus, ε˙ m tf varies in a manner similar to that for εf in Fig. 14, so that ε˙ m tf ∼ = χεf
(8)
where χ is a constant, i.e., Eq. (8) reduces to Eq. (7) when εf does not vary significantly with changing stress and temperature. This ε˙ m tf /εf relationship (Eq. (8)) also links to the creep damage tolerance parameter (λ) defined [31] as εf − εp εt λ= = ε˙ m tf ε˙ m tf
(9)
i.e., εt approximates to εf when εp is low, giving χ ∼ = 1/λ in Eq. (8). Using εt and ε˙ m tf measurements made directly from each creep curve, λ ∼ = 1.5 for MA957 (Fig. 18). This value is again consistent with the derived θ data because, over
Fig. 19. Optical micrographs showing the fracture appearance of longitudinal sections of MA957 testpieces which failed (a) under a stress of 315 MPa at 923 K and (b) under a stress of 400 MPa at 898 K. The tensile stress direction is horizontal.
the stress ranges covered at 873–973 K, ε˙ m ∼ = θ3 θ4 (Fig. 10). Hence, from Eq. (6) exp(θ4 tf ) − 1 (10) θ4 t f with θ 4 tf ∼ = 1 (Fig. 13), so that λ ∼ = 1.5. As evident from ∼ Fig. 12, λ = 1 when εt is low, with λ increasing as the tertiary stage becomes more pronounced. The magnitude of λ may therefore provide an indication of the processes influencing tertiary creep and fracture behaviour [32]. λ=
3.7. Tertiary creep and fracture processes
Fig. 18. The relationship between the tertiary creep strain, εt , and the product of the minimum creep rate and rupture life, ε˙ m tf , showing that the creep damage tolerance parameter, λ, is around 1.5 for MA957 tested over a range of stresses at 873–973 K.
Modelling of various damage processes has predicted [32] that λ ∼ = 1–2.5 when intergranular cavitation causes tertiary creep and fracture, with higher values expected when the tertiary stage begins as a consequence of necking (λ > 2.5) or precipitate coarsening (λ > 5). With MA957, λ ∼ = 1.5 (Fig. 18), but metallographic examination of fractured specimens shows that failure occurs in a transgranular not an intergranular manner. Moreover, a gradual transition in the detailed fracture mode becomes apparent (Fig. 19) as the creep deformation characteristics change on reducing the applied stress from above to below σ Y (Fig. 15). When the retained dislocation substructure (Fig. 6) severely limits strain accumulation at stresses less than σ Y (Fig. 15), microcracks nucleate on the short transverse bound-
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
aries and grow in a transgranular manner normal to the tensile stress axis. In long-term tests, the lengths of these transgranular cracks could be significantly greater than the widths of the elongated grains (Fig. 19a). Low ductility failure then occurs with negligible necking when the numbers and sizes of the developing cracks allow link up along paths almost parallel to the tensile stress direction, giving a ‘castellated’ fracture appearance (Fig. 19a). Microcracks also nucleate on the transverse boundaries when σ > σ Y , but regions ahead of the cracks can deform sufficiently to limit transgranular crack growth. Creep therefore continues until the attained strain levels are large enough to initiate necking. As the neck develops, shear link up of microcracks takes place on planes at ∼45◦ to the tensile axis, giving a ‘saw-tooth’ fracture appearance (Fig. 19b). In the present programme and in a previous study completed for two commercial aluminium alloys [29], tests were carried out using constant-stress equipment, so the tertiary acceleration cannot be due to stress intensification when the specimen cross-section decreases uniformly with increasing creep strain. However, even under constant true-stress conditions, many different processes can start the tertiary acceleration and more than one process can influence the subsequent rate of strain accumulation, while the mechanisms initiating the tertiary stage and causing failure can also be different. With MA957, no evidence was found to indicate the occurrence of local grain boundary migration, recrystallization or coarsening of the -phase precipitates over the stress/temperature ranges studied. For the microstructurallystable MA957, ε˙ ∼ = θ3 θ4 (Fig. 10) and θ 4 tf ∼ = 1 (Fig. 13) so Eq. (10) gives λ ∼ = 1.5 (Fig. 18) when tertiary creep and fracture are consequences of necking for σ > σ Y and transgranular cracking for σ < σ Y . Adopting the same approaches with the precipitation-hardened aluminium alloys [29], λ ∼ = 1.5 when cavitation processes were dominant with stable microstructures, whereas ε˙ m > θ3 θ4 and θ 4 tf > 1 so λ > 1.5 when tertiary began because of precipitate coarsening. Under constant true-stress conditions, λ > 1.5 when the tertiary stage is due to microstructural instability, but λ ∼ = 1.5 when tertiary creep and/or fracture are attributable to intergranular or transgranular cracking and/or necking. Information from a range of experimental approaches, which supplements the λ determinations, is therefore needed to quantify and explain the tertiary creep and fracture behaviour of alloys strengthened by dispersions of fine precipitates or insoluble particles.
4. Conclusions (1) Using a power law equation to describe the tensile creep data obtained at 873–973 K for MA957, n ∼ = 35 and Qc ∼ = 815 kJ mol−1 , in line with the large n and Qc values widely reported for high-GAR polycrystals. (2) Faster creep rates are recorded with compressive rather than tensile stresses applied parallel to the long grain
89
axes. This observation supports the view that the creep behaviour of high-GAR polycrystals is determined by the dispersoid-stabilized dislocation substructures retained after thermo-mechanical processing. (3) The complex creep strain and creep rate characteristics can be rationalized through the high-strain-rate yield stress at the creep temperature (σ Y ). The activation energy for creep is then comparable with that for lattice diffusion in ferrite (∼300 kJ mol−1 ), indicating that creep takes place by diffusion-controlled movement of dislocations within the substructure retained in the elongated grains. (4) Microstructural studies, together with quantitative curve shape analyses, show that fracture of MA957 occurs in a transgranular manner, with a transition in the detailed failure mode found on reducing the applied stress from above to below σ Y . Acknowledgement The authors wish to thank the Engineering and Physical Sciences Research Council for a research studentship awarded to TDL.
References [1] G.A.J. Hack, Denki-Seiko 57 (1986) 341. [2] D.S. Gelles, L.E. Thomas, in: J. Davies, D.J. Michel (Eds.), Ferritic Alloys for Use in Nuclear Energy Technologies, AIME, Warrendale, PA, 1984, p. 559. [3] J.J. Huet, Powder Metall. Rep. 40 (1985) 155. [4] E.A. Little (Ed.), Materials for Nuclear Reactor Core Applications, British Nuclear Energy Society, London, 1987, p. 47. [5] J. Lin, O.D. Sherby, Res. Mech. 2 (1981) 151. [6] J. Cadek, B. Ilschner, Acta Technol. CSAV 3 (1984) 280. [7] E. Arzt, Res. Mech. 31 (1991) 399. [8] B. Reppich, Z. Metall. 93 (2002) 605. [9] B.A. Wilcox, A.H. Clauer, Trans. AIME 236 (1966) 570. [10] R. Timmins, E. Arzt, Scripta Metall. 22 (1988) 1353. [11] K.R. Williams, B. Wilshire, Met. Sci. J. 7 (1973) 176. [12] J.D. Parker, B. Wilshire, Met. Sci. J. 9 (1975) 248. [13] J.S. Benjamin, Metall. Trans. 1 (1970) 2943. [14] R.W. Evans, J.A. Preston, B. Wilshire, E.A. Little, Mater. Sci. Eng. A 167 (1993) 65. [15] R.W. Evans, B. Wilshire, Creep of Metals and Alloys, The Institute of Metals, London, 1985. [16] T.S. Chou, H.K.D.H. Bhadeshia, Mater. Sci. Technol. 9 (1993) 890. [17] R.W. Evans, J.A. Preston, B. Wilshire, E.A. Little, J. Nucl. Mater. 195 (1992) 24. [18] J.C. Healy, M. Rees, J.D. Parker, R.C. Hurst, in: J.C. Earthman, F.A. Mohamed (Eds.), Proceedings of the 5th International Conference on Creep and Fracture of Engineering Materials and Structures, Warrendale, PA, TMS, 1997, p. 719. [19] R. Petkovic-Luton, D.S. Stolovitz, M.J. Luton, in: J.S. Benjamin, R.C. Benn (Eds.), Frontiers of High Temperature Materials II, INCO Alloys International, 1983, p. 73. [20] B. Wilshire, in: J.C. Earthman, F.A. Mohamed (Eds.), Proceedings of the 5th International Conference on Creep and Fracture of Engineering Materials and Structures, Warrendale, PA, TMS, 1997, p. 19.
90
B. Wilshire, T.D. Lieu / Materials Science and Engineering A 386 (2004) 81–90
[21] P.W. Davies, J.D. Richards, B. Wilshire, J. Inst. Met. 90 (1961/62) 431. [22] B. Wilshire, C.J. Palmer, Mater. Sci. Eng. A, in press. [23] B. Wilshire, M.R. Willis, Metal. Mater. Trans. 35A (2004) 563. [24] D. McLean, Mechanical Properties of Metals, Wiley, New York, 1962. [25] P.W. Davies, T.C. Finniear, B. Wilshire, J. Inst. Met. 91 (1962/63) 289. [26] A.K. Mukherjee, J.E. Bird, J.E. Dorn, Trans. ASM 62 (1969) 155.
[27] R.W. Evans, B. Wilshire, Introduction to Creep, The Institute of Materials, London, 1993. [28] M.L. Hamilton, PNNL-13168, 2000. [29] H. Burt, B. Wilshire, Metal. Mater. Trans. 35A (2004) 1691. [30] F.C. Monkman, N.J. Grant, Proc. ASTM 56 (1956) 593. [31] F.A. Leckie, D.R. Hayhurst, Acta Metall. 25 (1977) 1059. [32] M.F. Ashby, B.F. Dyson, in: S.R. Valluri (Ed.), Advances in Fracture Research, Pergamon Press, Oxford, UK, 1984, p. 3.