# Fileset

[1-s2.0-S2214785320387976-main.pdf](https://mdr.nims.go.jp/filesets/369b115e-d764-449c-ae59-162214e7ac8c/download)

## Creator

[Mainak Saha](https://orcid.org/0000-0001-8979-457X)

## Rights

[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

## Other metadata

[A brief discussion on the tensile creep deformation behaviour of wrought single-phase c-TiAl](https://mdr.nims.go.jp/datasets/7e84a77b-a4c7-4470-b3c2-f4da6cf9d006)

## Fulltext

A brief discussion on the tensile creep deformation behaviour of wrought single-phase γ-TiAlMaterials Today: Proceedings 46 (2021) 3187–3192Contents lists available at ScienceDirectMaterials Today: Proceedingsjournal homepage: www.elsevier .com/locate /matprA brief discussion on the tensile creep deformation behaviourof wrought single-phase c-TiAlhttps://doi.org/10.1016/j.matpr.2020.11.1892214-7853/� 2020 Elsevier Ltd. All rights reserved.Selection and peer-review under responsibility of the scientific committee of the International Conference on Materials, Manufacturing and Mechanical EngineSustainable Developments-2020.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).E-mail address: mainaksaha1995@gmail.comMainak SahaDepartment of Metallurgical and Materials Engineering, National Institute of Technology (NIT), Durgapur, Indiaa r t i c l e i n f o a b s t r a c tArticle history:Received 20 June 2020Received in revised form 18 September2020Accepted 7 November 2020Available online 10 January 2021Keywords:Apparent creep Activation energyStress exponentMinimum strain rateZener-Hollomon parameterSherby-Dorn parameterCreep deformation behaviour in single phase c-TiAl alloy has been an extensively studied topic since thelate 1970 s. A lot of literatures have reported creep behaviour of c-TiAl alloys, manufactured using differ-ent processing techniques [1–7]. The present discussion revisits the original work on understanding thetensile creep deformation behaviour of wrought single-phase c-TiAl alloy by Hayes et al. [8] and is aimedto develop an understanding of steady state creep, through strain vs strain rate and strain vs ln(strainrate) plots. Besides, it also attempts to study the variation of stress exponent with temperature between760 and 900⁰C and also, to determine activation energies using the two most common approaches,namely: Zener-Hollomon (Z-H) [9] and Sherby-Dorn (S-D, temperature compensated time approach)[10] for stress levels of 69.4 and 103.4 MPa between 760 and 900⁰C.� 2020 Elsevier Ltd. All rights reserved.Selection and peer-review under responsibility of the scientific committee of the International Confer-ence on Materials, Manufacturing and Mechanical Engineering for Sustainable Developments-2020. Thisis an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).1. Introduction 1.1. MotivationA series of reports on room temperature tensile deformationbehaviour of c- TiAl alloys show that the near- c, two phase com-positions having Al contents around 48 at.% possess the higheststrengths and ductilities [1–3,11–18]. Extensive creep deformationstudies have been carried out on a number of two phase near- cTiAI alloys produced by various processing routes [8,19–29]. Inaddition, compression creep studies have been carried out on anumber of binary single phase c-TiAl alloys and a number of liter-atures have reported that minimum strain rates during creep test-ing at different regimes of temperature and stress, is hugelydependent on the grain size of materials [1,8,19,30,31]. Minimumstrain rate of such intermetallic alloys may be defined in termsof Mukherjee-Bird-Dorn equation [32–34]. From a fundamentalpoint of view, a study of the creep deformation behaviour of singlephase TiAl is highly essential to provide useful insight into thedeformation behaviour of the two phase TiAl alloys.The work of Hayes et al. [8] presents and discusses an analysisof the minimum strain rate deformation as well as an analysis ofthe tertiary creep behaviour of a wrought single phase c-TiAl alloywithin temperature range of 760-1000⁰C and stress range of 32–345 MPa. The analysis by Hayes et al. [8] was carried out throughdetermination of apparent creep activation energies, at differenttemperature regimes, for various stresses, followed by theoreticalcalculation of stress exponents at different stress regimes, for dif-ferent temperatures. This was followed by the prediction of themain mechanism for creep rupture at different temperatures, in agiven stress range, using Monkmann-Grant (M�G) plots [9] andextensive microstructural characterisation using Optical micro-scope and the Transmission Electron Microscope (TEM) [8].The present discussion revisits the original work by Hayes et al[8] and is aimed to develop an understanding of steady state creep,through strain rate vs strain and ln(strain rate) vs strain plots.Besides, it also attempts to (i) determine variation in stress expo-nent with temperature between 760 and 900⁰C and (ii) to deter-mine activation energies through Zener-Hollomon (Z-H) andSherby-Dorn (S-D, temperature compensated time approach) forstress levels of 69.4 and 103.4 MPa between 760 and 900⁰C. Someof the major claims of the work by Hayes et al. [8] are:ering forhttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/https://doi.org/10.1016/j.matpr.2020.11.189http://creativecommons.org/licenses/by-nc-nd/4.0/mailto:mainaksaha1995@gmail.comhttps://doi.org/10.1016/j.matpr.2020.11.189http://www.sciencedirect.com/science/journal/22147853http://www.elsevier.com/locate/matprM. Saha Materials Today: Proceedings 46 (2021) 3187–3192� Wrought single phase c-TiAl alloy does not exhibit tertiarycreep between 760 and 900 ⁰C, at stress levels of 69.4 MPaand 103.4 MPa.� There is no steady state creep observed at 832 ⁰C, at stress levelsof 69.4 MPa, for both interrupted and uninterrupted tests.� c-TiAl alloys do not exhibit dislocation creep at 760⁰C, 832⁰Cand 900⁰C between stress level: 32–345 MPa.2. DiscussionTable 1 shows the composition of single phase c-TiAl alloy,forged, heat treated and finally subjected to tensile creep testing,as discussed in the work of Hayes et al [8]. As discussed earlier, thatonly constructing strain vs time plot to determine ‘‘min. strainTable 1Composition of the alloy (used by Hayes et al. [8]).El. Ti Al Nb Feat. % 45.9 52.9 0.91 0.048Fig. 1. (a) Strain rate vs Strain and (b) ln(strain rate) vs strain plots at 832 ⁰C for samplewere used by Hayes et al. [8] viz. 0.18% and 0.5% strain to fracture.Fig. 2. ln (strain rate, in h) vs 1/T plot (marked as black) and Sherby -Dorn plot (marked a69.4 MPa and (b) 103.4 MPa. (For interpretation of the references to colour in this figur3188rate” and designating the same to be the ‘‘steady state strain rate”,may be highly misleading for a number of materials, which do notexhibit steady-state creep [18]. Ti-53Nb-1Al, for instance, whethertested to rupture or terminated at mid-strains of 0.18% and 0.5% at832⁰C, exhibited a very less amount of steady-state creep. In thecase of creep test till rupture, significant primary creep is exhibitedwhereas, in the case of creep test terminated at 0.18% strain, thereis no primary creep regime and for the creep test till 0.5% strain,the primary creep regime is in between the two aforementionedextremes. In all cases, there is a very early onset of tertiary creep,However, the rate of tertiary creep in all the three samples is sig-nificantly different, as indicated by slopes of plots in Fig. 3 (a)and (b). Besides, from Fig. 1(a) and (b), the strain rate as well asstrain for initiation of tertiary creep in three samples, also vary,H O N C0.0219 0.1523 0.0026 0.0555subjected to interrupted tensile creep testing. 2 interruption (terminating) stressess red) to determine creep activation energies at different temperature regimes at (a)e legend, the reader is referred to the web version of this article.)Fig. 3. ln(min strain rate) vs strain plots at 760, 832 and 900⁰C.Fig. 4. Larson-Miller (L-M) plots at applied stresses of 69.4, 100 and 103.4 MPa.Fig. 5. Variation of log(rupture time, h) with temperature (⁰C) between 760 and900⁰C, at applied creep stress levels of 69.4 (blue), 100 (red) and 103.4 MPa (black).(For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)M. Saha Materials Today: Proceedings 46 (2021) 3187–3192to a small extent, with the sample having terminating strain of0.5% showing tertiary creep initiated at the lowest strain rate andthe highest strain.Table 3Larson-Miller constants and parameters at 69.4, 100 and 103.4 MPa between 760 and900⁰C.Stress (MPa) L-M constant (K) L-M Parameter69.4 1.74 14.05100 3.96 30.64103.4 4.15 34.02Fig. 6. Modified Monkman-Grant (M�G) parameter at 760, 832 and 900⁰C.2.1. Determination of activation energies between 760 and 1000⁰C at69.4 and 103.4 MPa2.1.1. At 69.4 MPaFrom Fig. 2(a), the apparent creep activation energies (deter-mined from slope of black curve representing ln(strain rate, in h)vs 1/T at 69.4 MPa) vary from 423.92 kJ/mol in regime 1 to409.82 kJ/mol in regime 2. Regimes 1 and 2 although seem to beindependent [35], but the values of activation energies in tworegimes, are found to be within experimental error. Moreover,Table 2Grain boundary and lattice diffusion activation energies (Qgb and QL (in kJ/mol), respectively) at different test temperatures between 760 and 900⁰C and creep stresses of 69.4 and103.4 MPa following the work of Hayes et al [8]. Qgb and QL have been calculated using Ashby’s approach [9,37].Temperature (⁰C) Stress (MPa) Q (kJ/mol) Qgb (kJ/mol) QL(kJ/mol)760 69.4 192 72 120760 103.4 304 114 190832 69.4 560 210 350832 103.4 405 151.88 253.13900 69.4 624 234 390900 103.4 519 194.63 324.383189Table 4M�G plot vs modified M�G plot (considering linear fit throughout entire creep life) at 760, 832 and 900⁰C. where p, C and R2 abbreviate for M�G exponent; M�G intercept andGoodness of fit, respectively.T (⁰C) P (M�G) C (M�G) R2 (M�G) P (modified M�G) C (modified M�G) R2 (modified M�G)760 �1.4 1.43 0.96 �1.56 1.61 0.97832 �1.3 1.31 0.93 �1.33 1.40 0.98900 �0.4 0.52 0.99 �0.68 0.69 0.99M. Saha Materials Today: Proceedings 46 (2021) 3187–3192the ZH (Zener Hollomon) parameter is obtained (from y-interceptof Fig. 2(a)) as 1.23e(14). Besides, Fig. 2(a) also shows rupture timevs 1/T plot (marked red) where SD parameter (determined fromthe y-intercept) is found to be 4.93e-14 and apparent creep activa-tion energy is determined (from slope of Fig. 2) as 329.03 kJ/mol.The transition temperature from Regime 1 to 2 is � 838.11 �C.2.1.2. At 103.4 MPaFrom the ln(strain rate, in h) vs 1/T (per K) plot (marked as redin Fig. 2(b)), ZH parameter (determined from y-intercept) is 1.11e(14) and apparent creep activation energies (determined fromslope of ln(strain rate, in h) vs 1/T plot) vary from 364.77 kJ/molin regime 1 to 377.68 kJ/mol in regime 2. Regimes 1 and 2 aresequential [36].Besides, Fig. 2(b) also shows rupture time vs 1/T plot (marked asblack) where S-D parameter (Sherby- Dorn parameter, determinedfrom y-intercept) is found to be 1.99e(�15) and Apparent Creepactivation Energy (determined from slope) is found to be345.65 kJ/mol. The transition temperature is decreasedto � 825.90⁰C about 14⁰C less than that at 69.4 MPa.It is observed that at 832 and 900⁰C, with increase in stress levelfrom 69.4 to 103.4 MPa, there is a decrease in apparent creep acti-vation energy, but the reverse trend is observed at 760⁰C. This issubject to further investigations using microstructural investiga-tion at 760⁰C, but is beyond the scope of discussion of the presentwork.2.2. Plots for determining stress exponent at 760, 832 and 900⁰CThe plot (Fig. 3) for 760⁰C (black curve) shows that processes in2 regimes must be independent. At Tr1: 244.69 MPa, the plot sug-gests that there is transition from dislocation glide controlled creepto dislocation climb controlled creep [36,38–43], suggesting aminor microstructural change leading to a change in creep defor-mation behaviour.Based on the red coloured plot at 832 �C (Fig. 3): (i) regime 1(from beginning to point Tr2) Stress exponent (from slope): 3;(ii) regime 2 (from points Tr2 to Tr3), Stress exponent: 4; (iii)regime 3 (from point Tr3 to end), Stress exponent: 4. Moreover,the red plot (in Fig. 3) also suggests that the cree mechanismsoperating at three aforementioned regimes are independent. AtTr 2: 66.68 MPa there is transition from dislocation glide controlledcreep to dislocation climb controlled which again suggests thatthere is change in mechanism in Dislocation creep due to minormicrostructural changes.Based on the blue coloured plot at 900 �C (Fig. 3): (i) regime 1(from beginning to Tr4): stress exponent: 5 and (ii) regime 2 (fromTr4 to end): stress exponent: 4. This suggests that power law creep[44] is continued but with a different slope (stress exponent)which again suggests transition from dislocation climb to disloca-tion glide controlled creep and thus, no major microstructuralchange.31902.3. Prediction of creep life using Larson-Miller (L-M) [45] andManson-Haferd (M�H) [46] parametersFrom Fig. 4, it may be inferred that creep life of the alloydecreases, due to onset of creep rupture [45–47], with increasein stress between 69.4 and 103.4 MPa and temperatures between760 and 900⁰C. Table. 3 shows Larson-Miller (L-M) constants andparameters at 69.4, 100 and 103.4 MPa between 760 and 900⁰C.It may be observed from Table 2. that with increase in stress levelsfrom 69.4 to 103.4 MPa, both L-M constants and parametersincrease between 760 and 900⁰C.Based on linear interpolation from Fig. 5, the M�H parameter atStresses: 69.4 MPa, 100 MPa and 103.4 MPa may be calculated tobe equal to �0.033, �0.031 and �0.014, respectively.2.4. Prediction of creep life using modified Monkman-Grant (M�G)parameter [9,48–52]From Fig. 6 and Table. 4, it may be observed that predominantcreep rupture mechanism is power law breakdown [18] at 760and 832⁰C, due to p being greater than �1.4 but at 900⁰C, owingto p equal to �0.4, the predominant creep rupture mechanismrequires further microstructural investigation and detailed analy-sis which is beyond the scope of the present study [53–55].Besides, it may also be observed that using modified M�G plots,the goodness of fit is much improved than using the originalM�G plots, implying that use of modified M�G plots improvesdata reliability [56].3. ConclusionsContradicting the claims of Hayes et al. [8], the various plots(Figs. 1-6), in the present discussion suggest that:� Creep life between 760 and 900 ⁰C, 69.4 MPa and 103.4 MPa isdominated hugely by tertiary creep.� Hardly, any Steady state is observed at 832 ⁰C, 69.4 MPa, forinterrupted tensile creep tests.� Dislocation creep tends to be the main deformation mechanismfor these alloys at 760⁰C, 832⁰C and 900⁰C between 32 and345 MPa.� Creep life of the alloy decreases, due to onset of creep rupture,with increase in stress between 69.4 and 103.4 MPa and tem-peratures between 760 and 900⁰C.4. Future scope of the workA small attempt has been made to revisit the understanding interms of creep behaviour in Ti-53Nb-1Al through strain rate vsstrain plots, followed by determination of activation energies andstress exponents for different temperature and stress regimes,based on the work already performed by Hayes et al. [8]. However,extensive microstructural characterisation is required in order tostudy changes in microstructure, associated with variation inapparent creep activation energies in different temperatureM. Saha Materials Today: Proceedings 46 (2021) 3187–3192regimes and variation of stress exponent in different stressregimes. Besides, the effect of grain size on creep behavior of thealloy also needs to be studied in great details.CRediT authorship contribution statementMainak Saha: Conceptualization, Data curation, Formal analy-sis, Funding acquisition, Investigation, Methodology, Projectadministration, Resources, Software, Supervision, Validation, Visu-alization, Writing - original draft, Writing - review & editing.Declaration of Competing InterestThe authors declare that they have no known competing finan-cial interests or personal relationships that could have appearedto influence the work reported in this paper.AcknowledgementMS would like to thank the Department of Metallurgical andMaterials Engineering, NIT Durgapur, for detailed discussions dur-ing the scripting of the brief discussion.References[1] J. Bieske, M. Franke, M. Schloffer, C. Körner. Intermetallics, ‘‘Microstructure andproperties of TiAl processed via an electron beam powder bed fusion capsuletechnology,” Elsevier, Accessed: Sep. 16, 2020. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0966979520304702.[2] M. Ilyas, M. Rizviul Kabir. Materials Science and Engineering A, ‘‘Modellinghigh temperature deformation of lamellar TiAl crystal using strain-rateenhanced crystal plasticity,” Elsevier, Accessed: Sep. 16, 2020. [Online].Available: https://www.sciencedirect.com/science/article/pii/S0921509320305955.[3] F. Zhao, J. Zhang, C. He, Y. Zhang, X. Gao, and L. Xie, ‘‘Molecular DynamicsSimulation on Creep Behavior of Nanocrystalline TiAl Alloy,” mdpi.com, doi:10.3390/nano10091693.[4] N. Neelam, S. Banumathy, G. V. S Nageswara Rao, A. Bhattacharjee. MaterialsToday Proceedings, ‘‘Study of microstructure and mechanical properties of c-Ti-46.5 Al-2Cr-(3.5 & 5.0) Nb alloys,” Elsevier, Accessed: Sep. 16, 2020.[Online]. Available: https://www.sciencedirect.com/science/article/pii/S2214785320352226.[5] V. Singh, C. Mondal, R. Sarkar, P.P. Bhattacharjee, P. Ghoshal, Materials Scienceand Engineering A, ‘‘Compressive creep behavior of a c-TiAl based Ti–45Al–8Nb–2Cr-0.2 B alloy: The role of b (B2)-phase and concurrent phasetransformations,” Elsevier, Accessed: Sep. 16, 2020. [Online]. Available:https://www.sciencedirect.com/science/article/pii/S0921509319316715.[6] Z. Duan, Y. Han, X. Song, H. Chen. Materials Science and Technology, ‘‘Creepbehaviour of equiaxed fine-grain c-TiAl-based alloy prepared by powdermetallurgy,” Taylor & Francis, Accessed: Sep. 16, 2020. [Online]. Available:https://www.tandfonline.com/doi/abs/10.1080/02670836.2020.1790098.[7] X. Xinxin, D. Wenfeng, W. Zhixin, L. ANGGEI. Chinese Journal of Aeronautics,‘‘Performance evaluation of creep feed grinding of c-TiAl intermetallics withelectroplated diamond wheels,” Elsevier, Accessed: Sep. 16, 2020. [Online].Available: https://www.sciencedirect.com/science/article/pii/S1000936120302636.[8] R.W. Hayes, P.L. Martin, Tension creep of wrought single phase c TiAl, ActaMetall. Mater. 43 (7) (Jul. 1995) 2761–2772, https://doi.org/10.1016/0956-7151(94)00486-2.[9] C. Zener, J.H. Hollomon, Effect of strain rate upon plastic flow of steel, J. Appl.Phys. 15 (1) (1944) 22–32, https://doi.org/10.1063/1.1707363.[10] R. Orr, O. Sherby, and J. Dorn, ‘‘Correlations of rupture data for metals atelevated temperatures,” 1953, Accessed: Sep. 16, 2020. [Online]. Available:https://www.osti.gov/servlets/purl/4425999.[11] J. Zhang, X. Li, D. Xu, R. Yang. Progress in Natural Science: MaterialsInternational , ‘‘Recent progress in the simulation of microstructureevolution in titanium alloys,” [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1002007119303557.[12] S. Saeedipour, A. Kermanpur. Journal of Materials Engineering andPerformance, ‘‘On the Microstructure and Solidification Behavior of N-Bearing Ti-46Al-8Ta (at.%) Intermetallic Alloys,” Springer, Accessed: Sep. 16,2020. [Online]. Available: https://link.springer.com/article/10.1007/s11665-019-04372-w.[13] L. Chen, T. E. James Edwards, F. di Gioacchino, W. J. Clegg, F. P. E. Dunne, andM.-S. Pham, ‘‘Crystal plasticity analysis of deformation anisotropy of lamellarTiAl alloy: 3D microstructure-based modelling and in-situ micro-3191compression.” Accessed: Sep. 16, 2020. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0749641919300026.[14] P.M. Hazzledine, Coherency and loss of coherency in lamellar Ti-Al,Intermetallics 6 (7–8) (1998) 673–677, https://doi.org/10.1016/s0966-9795(98)00034-x.[15] Y. Estrin, H. Mecking, A unified phenomenological description of workhardening and creep based on one-parameter models, Acta Metall. 32 (1)(1984) 57–70, https://doi.org/10.1016/0001-6160(84)90202-5.[16] L.M. Hsiung, T.G. Nieh, Creep deformation of fully lamellar TiAl controlled bythe viscous glide of interfacial dislocations, Intermetallics 7 (7) (1999) 821–827, https://doi.org/10.1016/S0966-9795(98)00135-6.[17] J.N. Wang, T.G. Nieh, The role of ledges in creep of TiAl alloys with fine lamellarstructures, Acta Mater. 46 (6) (1998) 1887–1901, https://doi.org/10.1016/S1359-6454(97)00434-5.[18] M.E. Kassner, Fundamentals of Creep in Metals and Alloys, Third Edition.Elsevier Inc., 2015.[19] R.W. Hayes, B. London, On the creep deformation of a cast near gamma TiAlalloy Ti48Al1 Nb, Acta Metall. Mater. 40 (9) (1992) 2167–2175, https://doi.org/10.1016/0956-7151(92)90134-Z.[20] S. Karthikeyan, G.B. Viswanathan, P.I. Gouma, V.K. Vasudevan, Y.W. Kim, M.J.Mills, Mechanisms and effect of microstructure on creep of TiAl-based alloys,Mater. Sci. Eng., A 329–331 (2002) 621–630, https://doi.org/10.1016/S0921-5093(01)01659-8.[21] A. Chatterjee, H. Mecking, E. Arzt, H. Clemens, Creep behavior of c-TiAl sheetmaterial with differently spaced fully lamellar microstructure, Mater. Sci. Eng.,A 329–331 (2002) 840–846, https://doi.org/10.1016/S0921-5093(01)01639-2.[22] T.E.J. Edwards et al., Deformation of lamellar c-TiAl below the general yieldstress, Acta Mater. 163 (2019) 122–139, https://doi.org/10.1016/j.actamat.2018.09.061.[23] Y.W. Kim, Intermetallic alloys based on gamma titanium aluminide, JOM 41(7) (1989) 24–30, https://doi.org/10.1007/BF03220267.[24] Y. Mishin and C. Herzig, ‘‘Diffusion in the Ti-Al system,” Acta Materialia, vol.48, no. 3. Elsevier Ltd, pp. 589–623, Feb. 09, 2000, doi: 10.1016/S1359-6454(99)00400-0.[25] K. Maruyama, R. Yamamoto, H. Nakakuki, N. Fujitsuna, Effects of lamellarspacing, volume fraction and grain size on creep strength of fully lamellar TiAlalloys, Mater. Sci. Eng., A 239–240 (1–2) (1997) 419–428, https://doi.org/10.1016/s0921-5093(97)00612-6.[26] H.S. Park, S.W. Nam, N.J. Kim, S.K. Hwang, Refinement of the lamellar structurein TiAl-based intermetallic compound by addition of carbon, Scr. Mater. 41(11) (1999) 1197–1203, https://doi.org/10.1016/S1359-6462(99)00266-3.[27] J. Beddoes, W. Wallace, L. Zhao, Current understanding of creep behaviour ofnear c-titanium aluminides, Int. Mater. Rev. 40 (5) (Jan. 2012) 197–217,https://doi.org/10.1179/095066095790151151.[28] M. Castillo-Rodríguez, M. L. Nó, J. A. Jiménez, O. A. Ruano, and J. San Juan, ‘‘Hightemperature internal friction in a Ti-46Al-1Mo-0.2Si intermetallic, comparisonwith creep behaviour,” Acta Materialia, vol. 103, pp. 46–56, Jan. 2016, doi:10.1016/j.actamat.2015.09.052.[29] W. Schillinger, H. Clemens, G. Dehm, A. Bartels, Microstructural stability andcreep behavior of a lamellar c-TiAl based alloy with extremely fine lamellarspacing, Intermetallics 10 (5) (2002) 459–466, https://doi.org/10.1016/S0966-9795(02)00021-3.[30] D. Banerjee, J.C. Williams, Perspectives on titanium science and technology,Acta Mater. 61 (3) (Feb. 2013) 844–879, https://doi.org/10.1016/j.actamat.2012.10.043.[31] C.Y. Teng, A. Du, D.S. Xu, Y. Wang, R. Yang, Effect of external stress on cnucleation and evolution in TiAl alloys, Intermetallics 65 (May 2015) 1–9,https://doi.org/10.1016/j.intermet.2015.05.003.[32] J. Bird, A. Mukherjee, J. E Dorn, Israel Universities Press, Jerusalem, 1969,‘‘Quantitative relation between properties and microstructure,” Accessed: Sep.16, 2020. [Online].[33] A. Mukherjee, R. Mishra, T. R Bieler, ‘‘Some critical aspects of high strain ratesuperplasticity,” Trans Tech Publ, Accessed: Sep. 16, 2020. [Online]. Available:https://www.scientific.net/MSF.233-234.217.pdf.[34] R. Mishra, A. Mukherjee. Materials Science and Engineering A, ‘‘The ratecontrolling deformation mechanism in high strain rate superplasticity,”Elsevier, Accessed: Sep. 16, 2020. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0921509397003213.[35] W. Zhang, X. Wang, Y. Wang, X. Yu, Y. Gao, Z. Feng, Type IV failure in weldmentof creep resistant ferritic alloys: II. Creep fracture and lifetime prediction, J.Mech. Phys. Solids 134 (Jan. 2020), https://doi.org/10.1016/j.jmps.2019.103775 103775.[36] A.H. Chokshi, Grain Boundary Processes in Strengthening, Weakening, andSuperplasticity, Adv. Eng. Mater. 22 (1) (Jan. 2020) 1900748, https://doi.org/10.1002/adem.201900748.[37] J. Weertman, Zener-Stroh crack, Zener-Hollomon parameter, and other topics,J. Appl. Phys. 60 (6) (Sep. 1986) 1877–1887, https://doi.org/10.1063/1.337236.[38] R.R. Eleti, A.H. Chokshi, A. Shibata, N. Tsuji, Unique high-temperaturedeformation dominated by grain boundary sliding in heterogeneousnecklace structure formed by dynamic recrystallization in HfNbTaTiZr BCCrefractory high entropy alloy, Acta Mater. 183 (Jan. 2020) 64–77, https://doi.org/10.1016/j.actamat.2019.11.001.[39] M. Kini, A.H. Chokshi, The influence of titania on creep in superplastic zirconia,J. Am. Ceram. Soc. 93 (6) (Jun. 2010) 1725–1731, https://doi.org/10.1111/j.1551-2916.2010.03617.x.https://doi.org/10.1016/0956-7151(94)00486-2https://doi.org/10.1016/0956-7151(94)00486-2https://doi.org/10.1063/1.1707363https://doi.org/10.1016/s0966-9795(98)00034-xhttps://doi.org/10.1016/s0966-9795(98)00034-xhttps://doi.org/10.1016/0001-6160(84)90202-5https://doi.org/10.1016/S0966-9795(98)00135-6https://doi.org/10.1016/S1359-6454(97)00434-5https://doi.org/10.1016/S1359-6454(97)00434-5http://refhub.elsevier.com/S2214-7853(20)38797-6/h0090http://refhub.elsevier.com/S2214-7853(20)38797-6/h0090http://refhub.elsevier.com/S2214-7853(20)38797-6/h0090https://doi.org/10.1016/0956-7151(92)90134-Zhttps://doi.org/10.1016/0956-7151(92)90134-Zhttps://doi.org/10.1016/S0921-5093(01)01659-8https://doi.org/10.1016/S0921-5093(01)01659-8https://doi.org/10.1016/S0921-5093(01)01639-2https://doi.org/10.1016/j.actamat.2018.09.061https://doi.org/10.1016/j.actamat.2018.09.061https://doi.org/10.1007/BF03220267https://doi.org/10.1016/s0921-5093(97)00612-6https://doi.org/10.1016/s0921-5093(97)00612-6https://doi.org/10.1016/S1359-6462(99)00266-3https://doi.org/10.1179/095066095790151151https://doi.org/10.1016/S0966-9795(02)00021-3https://doi.org/10.1016/S0966-9795(02)00021-3https://doi.org/10.1016/j.actamat.2012.10.043https://doi.org/10.1016/j.actamat.2012.10.043https://doi.org/10.1016/j.intermet.2015.05.003https://doi.org/10.1016/j.jmps.2019.103775https://doi.org/10.1016/j.jmps.2019.103775https://doi.org/10.1002/adem.201900748https://doi.org/10.1002/adem.201900748https://doi.org/10.1063/1.337236https://doi.org/10.1016/j.actamat.2019.11.001https://doi.org/10.1016/j.actamat.2019.11.001https://doi.org/10.1111/j.1551-2916.2010.03617.xhttps://doi.org/10.1111/j.1551-2916.2010.03617.xM. Saha Materials Today: Proceedings 46 (2021) 3187–3192[40] E. Schwaighofer, B. Rashkova, H. Clemens, A. Stark, S. Mayer, Effect of carbonaddition on solidification behavior, phase evolution and creep properties of anintermetallic b-stabilized c-TiAl based alloy, Intermetallics 46 (Mar. 2014)173–184, https://doi.org/10.1016/j.intermet.2013.11.011.[41] Q. Wang, L. Zeng, H. Ding, R. Chen, J. Guo, H. Fu, Microstructures andmechanical properties of directionally solidified C-containing c-TiAl alloys viaelectromagnetic cold crucible, Intermetallics 113 (Oct. 2019), https://doi.org/10.1016/j.intermet.2019.106587.[42] H. Fang et al., Effects of niobium on phase composition and improvingmechanical properties in TiAl alloy reinforced by Ti2AlC, Intermetallics 115(Dec. 2019), https://doi.org/10.1016/j.intermet.2019.106630.[43] W. Sprengel, T. Yamada, H. Nakajima, Interdiffusion in binary b-titaniumalloys, Defect Diff. Forum 143–147 (1997) 431–436, https://doi.org/10.4028/www.scientific.net/ddf.143-147.431.[44] G.H. Edward, M.F. Ashby, Intergranular fracture during power-law creep, ActaMetall. 27 (9) (1979) 1505–1518, https://doi.org/10.1016/0001-6160(79)90173-1.[45] T. Pollock, ‘‘Nondestructive Evaluation (NDE) Technology Initiatives Program(NTIP). Delivery Order 0041: Advanced Processing of Novel Ni-Based SingleCrystal Alloys,” 2004, Accessed: Sep. 16, 2020. [Online]. Available: https://apps.dtic.mil/sti/citations/ADA427337.[46] E. Pink, Physical significance and reliability of Larson-Miller and Manson-Haferd parameters, Mater. Sci. Technol (United Kingdom) 10 (4) (1994) 340–346, https://doi.org/10.1179/mst.1994.10.4.340.[47] M. Beschliesser et al., Designed fully lamellar microstructures in a c-TiAl basedalloy: Adjustment and microstructural changes upon long-term isothermalexposure at 700 and 800 �C, Mater. Sci. Eng., A 329–331 (Jun. 2002) 124–129,https://doi.org/10.1016/S0921-5093(01)01545-3.[48] G. Sundararajan, ‘‘The Monkman-Grant relationship,” Materials Science andEngineering A, vol. 112, no. C, pp. 205–214, Jun. 1989, doi: 10.1016/0921-5093(89)90360-2.3192[49] F. Dobeš, K. M Milička. Materials Science and Engineering A, ‘‘On theMonkman–Grant relation for small punch test data,” Elsevier, Accessed: Sep.16, 2020. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S092150930101975X.[50] C. Phaniraj, B. Choudhary, K. Rao, B. Raj. Scripta Materialia, 2003, ‘‘Relationshipbetween time to reach Monkman–Grant ductility and rupture life,” Elsevier,Accessed: Sep. 16, 2020. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1359646203000216.[51] H. Ali, M. Tamin. J. of Nuclear Materials, 2013, ‘‘Modified Monkman–Grantrelationship for austenitic stainless steel foils,” Elsevier, Accessed: Sep. 16,2020. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0022311512004709.[52] MONKMAN F. C., ‘‘An Empirical Relationship between Rupture Life andMinimum Creep Rate in Creep Rupture Tests,” Proc. ASTM, vol. 56, pp. 91–103,1956, Accessed: Sep. 16, 2020. [Online]. Available: https://ci.nii.ac.jp/naid/10006401917.[53] J. Manuel, A. Calderon, and M. L. Bañuelos, ‘‘An extension of the Monkman-Grant model for the prediction of the creep rupture time using small punchtests,” Springer, doi: 10.1007/s11340-014-9927-6.[54] M. Menon, H. Fang, D. Wu, M. Jenkins, M. Ferber. J. American Ceramic Society,1994, ‘‘Creep and Stress Rupture Behavior of an Advanced Silicon Nitride: PartIII, Stress Rupture and the Monkman–Grant Relationship,” Wiley OnlineLibrary, Accessed: Sep. 16, 2020. [Online]. Available: https://ceramics.onlinelibrary.wiley.com/doi/abs/10.1111/j.1151-2916.1994.tb05397.x.[55] M. Evans, Further analysis of the Monkman-Grant relationship for 2–25Cr-1Mo steel using creep data from the National Research Institute for Metals,Mater. Sci. Technol. 15 (1) (1999) 91–100, https://doi.org/10.1179/026708399773003367.[56] W. Gon Kim, S. Ho Kim, W. Seog Ryu, Evaluation of Monkman-Grantparameters for type 316LN and modified 9Cr-Mo stainless steels, Article J.Mech. Sci. Technol. 16 (11) (2002) 1420–1427, https://doi.org/10.1007/BF02985134.https://doi.org/10.1016/j.intermet.2013.11.011https://doi.org/10.1016/j.intermet.2019.106587https://doi.org/10.1016/j.intermet.2019.106587https://doi.org/10.1016/j.intermet.2019.106630https://doi.org/10.4028/www.scientific.net/ddf.143-147.431https://doi.org/10.4028/www.scientific.net/ddf.143-147.431https://doi.org/10.1016/0001-6160(79)90173-1https://doi.org/10.1016/0001-6160(79)90173-1https://doi.org/10.1179/mst.1994.10.4.340https://doi.org/10.1016/S0921-5093(01)01545-3https://doi.org/10.1179/026708399773003367https://doi.org/10.1179/026708399773003367https://doi.org/10.1007/BF02985134https://doi.org/10.1007/BF02985134 A brief discussion on the tensile creep deformation behaviour �of wrought single-phase γ-TiAl 1 Introduction 1.1 Motivation 2 Discussion 2.1 Determination of activation energies between 760 and 1000⁰C at 69.4 and 103.4MPa 2.1.1 At 69.4MPa 2.1.2 At 103.4MPa 2.2 Plots for determining stress exponent at 760, 832 and 900⁰C 2.3 Prediction of creep life using Larson-Miller (L-M) [45] and Manson-Haferd (M−H) [46] parameters 2.4 Prediction of creep life using modified Monkman-Grant (M−G) parameter [9,48–52] 3 Conclusions 4 Future scope of the work CRediT authorship contribution statement Declaration of Competing Interest Acknowledgement References