Special Issue on Superfunctional Nanomaterials by Severe Plastic Deformation
Creep in Nanostructured Materials
2023 Volume 64 Issue 7 Pages 1566-1574
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2023 Volume 64 Issue 7 Pages 1566-1574
The creep behaviour and properties of nanostructured materials are attributed to their operating deformation mechanisms, which could be different from those in their coarse-grained counterparts. Accordingly, in this review, recent progress on the creep behaviour of nanostructured materials will be described. The results of large sets of tensile creep tests on selected more complex metallic materials are analysed for evaluating the effect of different SPD processing methods on creep resistance at high temperatures. The resultant creep characteristics are compared with those attained in unprocessed conditions of the same materials. By contrast to the creep behaviour of UFG pure metals SPD processing of more complex materials mostly exhibit no essentially improved creep resistance. Evaluated stress dependences of the creep rate and the creep life suggest that creep deformation mechanisms in UFG materials are similar to those operating in coarse-grained materials. However, creep mechanisms in SPD processed materials are not clearly resolved and this is due to complexity of phenomenon and very small number of studies that have been carried out before now.
Creep is defined as the time-dependent plastic strain under constant applied stress and/or load at a given temperature. Creep becomes especially important at elevated and high temperatures, typically above ∼0.4 Tm where Tm is absolute melting temperature. A thorough understanding of the creep behaviour of creep-resistant materials is essential for the sound design of high temperature components. At present there is a good understanding of the creep behaviour materials with conventional coarse-grained materials.1–8) Nevertheless, processing through the application of nondeformable procedures and severe plastic deformation (SPD) is now an accepted technology for producing nanostructured and bulk ultrafine-grained materials having grain sizes in the nanometer range.9–24) Nanostructured materials are commonly characterized by a grain size in the nanometer range (1–100 nm), while ultrafine-grained materials usually exhibit grain sizes in the submicrometer range. However, in the last decades ultrafine-grained materials have frequently been considered in many reports as nanostructured materials. During the last three decades, great progress has been made in developing several SPD processing techniques which are currently available.9,10,15,20) This has raised numerous speculations concerning the deformation and microstructural processes occurring in nanostructured and ultrafine-grained (UFG) materials under creep conditions. A question naturally arises about the possibility of new and unidentified creep mechanisms appearing in these materials where the grain size is exceptionally small. In nanostructured materials these mechanisms may be due to microstructure instability, the presence of non-equilibrium grain boundaries or very high intragranular dislocation densities. Recent studies have begun to examine the creep mechanisms occurring in UFG metallic materials processed by SPD techniques.25–31) However, the creep mechanisms in bulk UFG materials remain poorly understood and this is due to the relatively small number of studies that have been carried out in creep regime. Furthermore, since different SPD processing techniques and parameters may lead to essential differences in the initial microstructures of nanostructured materials, caution should be given when analysing the properties of UFG materials processed by various SPD method. This effect, which arises from the non-equilibrium nature of UFG materials is especially important in case of mechanical behaviour investigations. Special emphasis in creep behaviour studies should be given to the homologous temperature of nanostructured material which is important in SPD processing as well.20,23,24) Very recently, an extensive analysis of the experimental data from 31 different pure metals processed by SPD reported by Figueiredo et al.31) demonstrates that a modified model for grain boundary sliding at low temperature provides the capability of correctly predicting the flow stresses for metals having both high and low melting temperatures. A modified model provides an explanation for the softening behaviour observed in pure metals with low melting points.23,24) It is still not clear, however, whether a modified model for grain boundary sliding may be applied in case of structural materials with extensive intergranular precipitation.
Present paper has arisen in connection with long-term research activity of the Advanced High Temperature Materials Group at the Institute of Physics of Materials, Czech Academy of Sciences in Brno, Czech Republic. While our previous report30) has primarily been focused on the creep behaviour of UFG pure metals and binary alloys processed by equal-channel angular pressing (ECAP) only, the focus of this report has shifted to the creep behaviour of more complex mostly solution and precipitation strengthened metallic materials processed by various SPD procedures.
As it was noted earlier, creep deformation and fracture processes in coarse-grained metals and alloys are now well established.6–8) Our recent reports30) has begun to examine the creep processes and mechanisms occurring in ultrafine-grained pure model metals and their binary alloys processed by SPD procedure known as equal-channel angular pressing (ECAP).9,20) In this review we would like to focus on creep behaviour of nanostructured and UFG materials processed mainly by SPD methods, but also for general commentary of subject by the “bottom-up” nondeformable techniques. The results will primarily be demonstrated by experiments on structural materials and/or their bases.
2.1 Creep in nanostructured materials prepared by nondeformable proceduresBefore discussing the creep data of SPD processed materials it could be proper place for make a short mention of experimental creep studies carried out on nanostructured materials prepared by processing routes different from SPD.32) Together with the creep data some general relationships describing creep behaviour will be introduced.
Nieman et al.,33,34) Sanders et al.,35) Hahn and Averback,36) and Cui and Hahn37) performed their creep experiments on nanostructured Cu, Pd, Al–Zr and TiO2 which were processed by inert gas condensation, Wang et al.,38) Deng et al.,39) and Xiao and Kong40) on Ni–P and Fe–B–Si processed by amorphous crystallization. The creep behaviour of nanostructured Ni and its alloys prepared by electrodeposition was intensively investigated and reported by Wang et al.,41) McFadden et al.,42) Kottada and Chokshi,43) Sklenicka et al.,44–47) and others.48–52) According to the author’s knowledge from other nondeformable processing methods53) the creep behaviour was investigated by Taketani et al.54) on an aluminium alloy prepared by high pressure gas atomization. Several further results of the investigations of creep behaviour of nanostructured materials mostly on nano-Cu and nano-Al were reported in another papers.55–60) Furthermore, there have been several reviews devoted to a description of creep in nanostructured materials, notably, by Blum et al.,27) Mohamed and Li,61) and Yin.62)
In polycrystalline materials, there is the now classical and established phenomenological relationship between the steady state and/or minimum creep rate, $\dot{\varepsilon }$, and the applied stress, σ, of generalized form:6–8,63–65)
| \begin{equation} \dot{\varepsilon} = (AD_{0}Gb(b/d)^{p}(\sigma/G)^{n}\,\mathit{exp}(-Q_{C}/RT))/kT, \end{equation} | (1) |
A particular mechanism of creep in nanostructured materials can be identify through knowledge of two creep parameters, namely, by means of the stress exponent n of creep rate $\dot{\varepsilon }$ and the activation energy of creep QC. The stress exponent n can be evaluated through the following equation6)
| \begin{equation} n = (\partial\,\mathit{ln}\,\dot{\varepsilon}/\partial\,\mathit{ln}\,\sigma)_{T}. \end{equation} | (2) |
The activation energy of creep QC can be defined as6,8)
| \begin{equation} Q_{C} = [\partial\,\mathit{ln}\,\dot{\varepsilon}/\partial(-1/kT)]_{\sigma}. \end{equation} | (3) |
| \begin{equation} \dot{\varepsilon}\sim (\text{b/d})^{\text{p}}. \end{equation} | (4) |
Let us illustrate the creep behaviour of nanostructured materials processed by nondeformable procedures using the experimental creep results of electrodeposited monolithic UFG nickel (d ∼ 200 nm) and its nanostructured particle-reinforced Ni–SiO2 composite (d ∼ 60 nm).44–47) A summary of creep data is shown in Figs. 1(a) and 1(b) which were obtained at testing temperatures 293–573 K over a broad range of applied constant tensile stress σ. Figure 1(a) shows in double logarithmic plot the stress dependences of the minimum creep rate $\dot{\varepsilon }_{\text{m}}$ and the evaluated values of the stress exponents n. However, it is appropriate to identify individual creep regions6–8) and respective acting creep mechanisms using the temperature compensated minimum creep rate $\dot{\varepsilon }_{m}kT/DGb$ vs. normalized stress σ/G - Fig. 1(b). Analysis of the creep data leads to the suggestion that the creep behaviour in ultrafined-grained nickel and nanostructured Ni–SiO2 agrees with the five-power-law creep region8) with dislocation creep involving intragranular creep by glide and climb of dislocations and grain boundary-related processes.47) However, at normalized stresses σ/G higher than 6 × 10−3 power-law breaks down, and the stress exponent n increases exponentially with applied stress (Fig. 1(b)). It should be noted that the mechanisms responsible for the power-law breakdown6,8) observed at higher stresses are still not well established.72–74) Mohamed and Chauhan49) interpreted the creep behaviour of electrodeposited nanostructured Ni (d = 20 nm) in terms of the model based on dislocation-accommodated grain boundary sliding.
Stress dependence of the minimum creep rate $\dot{\varepsilon }_{\text{m}}$ of ultrafine-grained Ni and nanostructured Ni–SiO2 composite processed by electrodeposition: (a) the experimentally determined minimum creep rate $\dot{\varepsilon }_{\text{m}}$ vs. σ, and (b) the temperature compensated $\dot{\varepsilon }_{\text{m}}$ with normalized σ/G.47)
It should be mentioned that there are some factors which interfere a better understanding of creep behaviour of nanostructured materials prepared by nondeformable synthesis procedures. In principle, these procedures can hardly supply bulk materials and hence the miniature length of the gauge length of creep specimens may cause some uncertainty in the reliability of the reported creep experimental data. Creep behaviour of nanostructured materials is very sensitive to their initial microstructure. Differences in the initial microstructure of the tested materials due to different processing methods could influence mutual comparison of the experimental data. By contrast with experiments on SPD processed materials there is impossibility to compare creep behaviour of the same material in conventional coarse-grained and nanostructured states. Further, the reported creep experiments followed by detailed microstructural analyses are practically missing. Generally, only the grain size measurements are commonly available.
2.2 Creep in UFG materials processed by SPDThe UFG materials processes by SPD make it possible to perform studies that were not realizable in earlier creep experiments on coarse-grained materials. Some of the first creep experiments on SPD processes UFG materials were carried out on pure materials or model binary alloys.25–27,75,76) Due to progress in SPD procedures20,21,77) recent reports have begun to examine the creep behaviour on multi phases model materials and/or conventional structural creep-resistant materials. There have been reviews of creep on SPD materials published by Edalati et al.,20) Blum et al.,27) Yin,62) Sklenicka et al.,29) Kral et al.,30) Kawasaki et al.,78) and Pelleg.79) It should be noted that most experiments on creep behaviour of UFG materials have been limited to a small range of testing temperatures because of the instability of non-equilibrium grain boundaries. Further, the experimental results and their interpretation reported by different authors are not consistent with each other due to differences in the same processing procedure (e.g. a number of ECAP passes), creep testing techniques, inhomogeneity of microstructure, different porosity and impurity level, etc.
The grain and subgrain growth during creep of UFG materials processed by SPD at elevated and/or high temperatures makes creep experiments more difficult. Additionally, the stable grain and subgrain sizes in the UFG materials depend on the level of the applied stress. Therefore, due to considerable instability of grain structure experimental results on the creep behaviour have often been limited to a narrow limit of testing temperatures. From these reasons the present review will focus primarily on the creep behaviour of selected precipitation strengthened materials.
2.2.1 Zr–2.5%Nb alloyThe Zr–2.5%Nb precipitate-strengthened alloy is widely used as cladding material of nuclear fuel in light water reactors where high creep resistance is very important.80,81) Further, the zirconium alloys have high biocompatibility with human body tissues and can be used for different medical implants. The necessary strengthening of zirconium alloy can be potentially achieved by the methods of SPD.82,83) As a matter of fact, Terentyev et al.84) studied the static strength of the Zr–2.5%Nb alloy at room temperature after equal-channel angular pressing (ECAP).9,20,85) They reported that the formation of UFG structure substantially increases the ultimate tensile strength and yield strength by a factor 1.4 and 1.6, respectively, to those of coarse-grained state of alloy. By contrast, the ductility decreases more than by a factor of 2.
In the successive work Sklenicka et al.86) performed creep experiments on the identical Zr–2.5%Nb alloy processed by ECAP as reported by Terentyev et al.84) Creep tests were carried out at 623 K (∼ 0.29 Tm and operating temperature in light water reactor) using a tensile stress within the range from 120 to 300 MPa. All creep tests were run up to specimen failure. Billets of the unprocessed alloy were processed by ECAP at temperature 693 K by the route BC.87) The pressing was repeated up to a total of 6 ECAP passes. Creep curves in Fig. 2 show (a) the time dependence of the strain, ε, and (b) the variation of the time of creep exposure, t. Following findings can be reach from inspection of these data. First, the unprocessed alloy exhibits considerably longer creep life than the ECAP processed alloy (Fig. 2(a)). However, there is no difference in the fracture strain level εf ≈ 0.25 between the unpressed and ECAP processed alloy. Second, there is only a quasi-secondary stage of creep, however, when the steady state of creep disappears, it is still possible to define the minimum creep rate $\dot{\varepsilon }_{\text{m}}$ (Fig. 2(b)). The difference in the minimum creep rate between the ECAP processed and the unprocessed alloy consistently increases with increasing number of ECAP passes. Thus, these results imply that the unpressed alloy exhibits better creep resistance by comparison with the processed alloy. The stress dependences of the minimum creep rates $\dot{\varepsilon }_{\text{m}}$ of the unpressed alloy and the pressed alloy after different number of ECAP passes are shown in Fig. 3. The results demonstrate that both states of the alloy exhibit similar trends, which is clearly demonstrated by the characteristic curvature on double bi-logarithmic plots: the values of the stress exponent of the creep rate n (eq. (2)) gradually increase with increasing stress σ (3 ≤ n ≤ 22). Further, at the same value of stress σ the minimum creep rate $\dot{\varepsilon }_{\text{m}}$ increases with increasing number of ECAP passes (Fig. 3). Based on the above results Sklenicka et al.86) suggested that it is not necessary to invoke any new and different creep mechanism(s) in the processed Zr–2.5%Nb alloy. The faster creep rates in the processed alloys than in those of the unpressed ones have been explained in term of enhanced diffusivity in non-equilibrium grain boundaries, by the faster recovery of grain boundaries, by the increase in the rate of dislocation storage at grain boundaries and by the direct contribution of grain boundary sliding to creep rate. Creep mechanisms in coarse-grained zirconium and its alloys were analysed and discussed in earlier and recent works.81,88–94) However, operating creep mechanisms in zirconium alloys are not clearly established at present.
Creep curves of a Zr–2.5Nb alloy for the unpressed state and for the processed state by different number of ECAP passes: (a) standard creep curves of strain ε vs. time t, and (b) modified creep curves of strain rate $\dot{\varepsilon }$ vs. time t.86)
Stress dependence of (a) the minimum creep rate $\dot{\varepsilon }_{\text{m}}$, and (b) the time to fracture tf of a Zr–2.5Nb alloy of the unpressed state and the state after ECAP processing (6 passes).
In this section, the analysis will be undertaken to examine the flow characteristics of ECAP processed Al–0.2%Sc and Cu–0.2%Zr alloys where scandium and zirconium additions make UFG microstructure during high temperature creep more stable. Therefore, the study of creep behaviour of ultrafine-grained Al–0.2Sc and Cu–0.2Zr alloys continues by an effort to obtain a more complex description and understanding of flow in high-temperature creep of SPD processed precipitation or dispersion strengthened materials.
Initiative creep experiments on pure Al27,29,95–97) and Cu98–102) processed by ECAP were reported and discussed in more detail by Blum et al.,27) Sklenicka et al.,29) and Kral et al.30) In later works the creep behaviour of ultrafine-grained Al–0.2Sc alloy28,29,78,103–108) and Cu–0.2Zr109,110) processed by ECAP route BC87,111) were studied. The same processing ECAP route in our previous creep experiments on pure aluminium and copper provides an opportunity to compare their creep behaviour with their precipitation or dispersion strengthened alloys. However, it should be emphasized that the ultrafine grain sizes of pure Al and Cu produced by ECAP were not stable when testing in high temperature creep.112) By contrast, a scandium addition of ∼0.2 mass%Sc to pure aluminium and a zirconium addition of ∼0.2 mass%Zr to pure copper were sufficient to adequately retain UFG sizes of the alloys at selected creep testing temperatures.106,113)
Creep tests of Al–0.2Sc alloy were carried out at 473 K (a homologous temperature of 0.80), whereas Cu–0.2Zr alloy was tested at 673 K (a homologous temperature of 0.50). The stress dependences of the minimum creep rate $\dot{\varepsilon }_{\text{m}}$ and the time to fracture tf for alloys under investigations are depicted in Fig. 4. The results are shown both for the unprocessed and ECAP processed states of the alloys. For each alloy state the samples with different number of ECAP passes were crept under constant tensile load and the creep tests were run up to final fracture of the specimen. The difference in creep behaviour of both states of the alloys are easily demonstrated by logarithmically plotting the minimum creep rate $\dot{\varepsilon }_{\text{m}}$ and the time to fracture tf against the stress σ. Several important conclusions may be obtained from Fig. 4. The unpressed Al–0.2Sc and Cu–0.2Zr alloys consistently exhibit markedly higher values of the minimum creep rate $\dot{\varepsilon }_{\text{m}}$ (Fig. 4(a) and shorter values of the time to fracture tf (Fig. 4(b)). An exception to the rule presents behaviour of Cu–0.2Zr after 12 ECAP passes.
Stress dependences of (a) the minimum creep rate $\dot{\varepsilon }_{\text{m}}$, and (b) the time to fracture tf of Al–0.2Sc and Cu–0.2%Zr alloys.
The creep tests of coarse-grained (CG) state and alloy processed by 1–2 ECAP passes show that the increase of the strain rate with the stress is significantly faster in comparison with stationary line.110) It can be suggested that it is caused by damage occurring before stationary stage is reached. Actually, the fractographic investigation supports this suggestion.103) Therefore, the minimum strain rate determined in tension are influenced by fracture processes and should not be interpreted as stationary values resulting from uniform deformation. Similar creep behaviour was observed also in pure CG Cu.98–102) Creep results showed that UFG Cu tested in tension exhibited longer creep live than CG Cu. But opposite results were found when pure Cu was tested under compression.102)
In a similar way as in eq. (1), the constitutive equation for the time to fracture, tf, in its functional form gives:114)
| \begin{equation} t_{f} = B(\sigma)^{-m}\,\mathit{exp} (Q_{f}/RT), \end{equation} | (5) |
In this section we would like to demonstrate the effect of grain refinement on creep behaviour of a real structural material - an advanced tungsten and boron modified martensitic-ferritic 9% Cr creep resistant steel P92.115,116) At the same time the attention will be given to the effect of different method of severe plastic deformation on the creep behaviour, namely, high-pressure torsion (HPT),9,20,117) high-pressure sliding (HPS),118,119) and rotary swaging (RS).120–124) All mentioned SPD methods were applied at room temperature on coarse-grained (CG) creep-resistant P92 steel. However, various other factors can affect a mutual comparison of the creep results obtained by different SPD methods, for example, the values of the imposed equivalent strain εeq119) during SPD processing, microstructure homogeneity and stability, the presence of non-equilibrium grain boundaries or very high dislocation densities, creep conditions and testing mode.
A summary of results from extensive experiment on the creep behaviour of P92 steel at 873 K (a homologous temperature of 0.49) and under the stress interval from 50 to 300 MPa is presented in Fig. 5. The values of the imposed equivalent stress εeq were ∼20–30, ∼8 and ∼1.4 for the HPT, HPS and RS methods, respectively.119) Each SPD operation resulted in ultrafine grain size of the pressed specimens. It should be noted that the microstructure of martensitic-ferritric 9% Cr steels is not stable at high temperatures114–116) due to coarsening and dissolution of precipitates of secondary phases. Therefore, the service degradation of microstructure in selected HPT and HPS specimens of the steel was simulated using short-term stress-free isothermal ageing, which was carried out at 923 K for 500 h before creep exposure.119,125) Figure 5 shows that under the same loading conditions (the same applied stress σ) at 873 K, the ultrafine-grained microstructure states after SPD processing exhibit higher minimum creep rate $\dot{\varepsilon }_{\text{m}}$ (Fig. 5(a)) and significantly shorter time to fracture tf (Fig. 5(b)) in comparison with the coarse-grained (as-received) state of steel. However, somewhat different creep behaviour was observed at 773 K.121) The evaluated values of the stress exponent n correspond to dislocation (power-law) creep but at very high stresses the power-law breakdown8) can be expected. Similarity between values of n and m once more implies that operating deformation processes control fracture processes.
Stress dependences of (a) the minimum creep rate $\dot{\varepsilon }_{\text{m}}$, and (b) the time to fracture tf of martensitic-ferritic 9% chromium creep-resistant steel P92 in unpressed (CG) state and after following SPD processing: rotary swaging (RS), high-pressure sliding (HPS) and high-pressure torsion (HTP). For comparison, literature creep data on commercial coarse-grained P92 steel were adapted from Hasegawa.127)
These obvious differences in the creep behaviour between coarse-grained (CG) and UFG states have been explained by somewhat different operating deformation mechanisms. It can be suggested that the creep behaviour in a coarse-grained state is controlled by the intragranular climb of mobile dislocations, while creep in UFG states can be interpreted as a synergistic action of the dynamic recovery of free dislocations at high-angle grain boundaries and grain boundary-mediated deformation processes.
To the author’s knowledge, the study by Kostka et al.126) was the first work to use ECAP to gain a better understanding of the creep behaviour of a less advanced tempered martensitic-ferritic 9%Cr steel P91. The effect of long-term ageing and ECAP pressing of P91 was investigated at 923 K and 120 MPa. It was found that ECAP pressing of an overaged state of the steel results in much higher creep rates. Kostka et al.126) supposed that the creep rate of this steel increases after ECAP due to a high density of mobile dislocations.
The microstructure investigations showed that static annealing and creep testing caused significant grain coarsening.116,127) The comparison of grain size in the microstructure with various local strain revealed that creep strain has a significant influence on grain coarsening in UFG P92 steel. The results showed that fine grains in UFG P92 steel coarsen during creep testing up to the size near estimated stationary subgrain size128,129) and thus mainly high-angle grain boundaries are situated in the UFG microstructure during creep testing. The microstructure in CG P92 steel and steel processed by rotary swaging is different. The subgrain size is more or less similar to the estimated stationary subgrain size.
The investigation of precipitates in UFG P92 steel revealed that creep exposure at 873 K with time to fracture of about 3 h is sufficient for the formation of Laves phase115) which is significantly shorter time in comparison with its appearance in coarse-grained state. Hence, the detrimental Laves phase is formed much faster in UFG structure than in CG state. It was also observed that Laves phase is formed in the UFG microstructure during creep already at 773 K.
The results of a large set of tensile creep tests on more complex metallic materials were analysed for evaluating the effect of different SPD processing methods on creep resistance at high temperatures. The resultant creep characteristics were compared with those attained in unpressed conditions of materials. The main conclusions that are obtained in the present overview can be listed as follows:
Financial support for this work was provided by the Technology Agency of the Czech Republic (TACR) under Grant No. TN02000018 is gratefully acknowledged.
