This paper presents a novel multiaxial, cyclic viscoplasticity material model for high temperature low cycle fatigue of P91 power plant steel. The model incorporates mechanisms-based variable strain-rate sensitivity and the key high temperature cyclic deformation phenomena of cyclic softening and non-linear kinematic hardening. The model has been calibrated to accurately represent the cyclic high temperature constitutive behaviour of ‘as received’ P91 steel. Details on the material Jacobian, with the consistent tangent stiffness for finite element implementation, are presented. The multiaxial implementation is applied to a notched specimen under strain-controlled loading at 600°C and a thin walled pipe under representative pressurised thermomechanical fatigue loading conditions. It is shown that the model for variable strain-rate sensitivity of the present paper predicts significantly different Coffin–Manson notch fatigue life compared to the Chaboche power law model. Ratchetting is shown to be a key candidate failure mechanism for next generation thermomechanical power plant loading conditions, for thin walled pressurised pipes.
BarrettR.A., O'DonoghueP.E. and LeenS.B.: ‘An improved unified viscoplastic constitutive model for strain-rate sensitivity in high temperature fatigue’, Int. J. Fatigue, 2013, 48, 192–204.
2.
BarrettR.A., O'DonoghueP.E. and LeenS.B.: ‘Finite element modelling of the thermo-mechanical behaviour of a 9Cr martensitic steel’, in ‘Advanced materials modelling for structures’ (ed. AltenbachH. and KruchS.), 31–41; 2013, Berlin Heidelberg, Springer.
3.
SwindemanR.W., SantellaM.L., MaziaszP.J., RobertsB.W. and ColemanK.: ‘Issues in replacing Cr–Mo steels and stainless steels with 9Cr–1Mo–V steel’, Int. J. Press. Vessels Pip., 2004, 81, 507–512.
4.
ChabocheJ.L. and RousselierG.: ‘On the plastic and viscoplastic constitutive equations – Part I: rules developed with internal variable concept’, J. Press. Vessel Technol., 1983, 105, 153–158.
5.
ChabocheJ.L. and RousselierG.: ‘On the plastic and viscoplastic constitutive equations – Part II: application of internal variable concepts to the 316 stainless steel’, J. Press. Vessel Technol., 1983, 105, 159–164.
6.
KooG.H. and KwonJ.H.: ‘Identification of inelastic material parameters for modified 9Cr–1Mo steel applicable to the plastic and viscoplastic constitutive equations’, Int. J. Press. Vessels Pip., 2011, 88, 26–33.
7.
SaadA.A., HydeC.J., SunW. and HydeT.H.: ‘Thermal-mechanical fatigue simulation of a P91 steel in a temperature range of 400–600°C’, Mater. High Temp., 2011, 28, 212–218.
8.
FarragherT.P., ScullyS., O'DowdN.P. and LeenS.B.: ‘Development of life assessment procedures for power plant headers operated under flexible loading scenarios’, Int. J. Fatigue, 2013, 49, 50–61.
9.
FarragherT.P., ScullyS., O'DowdN.P. and LeenS.B.: ‘Thermomechanical analysis of a pressurized pipe under plant conditions’, J. Press. Vessel Technol., 2013, 135, 011204–011209.
10.
Vakili-TahamiF., HayhurstD.R. and WongM.T.: High-temperature creep rupture of low alloy ferritic steel butt-welded pipes subjected to combined internal pressure and end loadings, philosophical transactions: mathematical’,Phys. Eng. Sci., 2005, 363, 2629–2661.
11.
EspositoL. and BonoraN.: ‘A primary creep model for Class M materials’, Mater. Sci. Eng. A, 2011, A528, 5496–5501.
12.
ZhangT., McHughP.E. and LeenS.B.: ‘Finite element implementation of multiaxial continuum damage mechanics for plain and fretting fatigue’, Int. J. Fatigue, 2012, 44, 260–272.
13.
KupkovitsR.A. and NeuR.W.: ‘Thermomechanical fatigue of a directionally-solidified Ni-base superalloy: smooth and cylindrically-notched specimens’, Int. J. Fatigue, 2010, 32, 1330–1342.
14.
FlavenotJ.F. and SkalliN.: ‘A critical depth criterion for the evaluation of long life fatigue strength under multiaxial loading and a stress gradient’, in ‘Biaxial and multiaxial fatigue’ (ed. BrownM. W. and MillerK. J.); 1989, London, Mechanical Engineering Publications.
15.
StephensR.I., FatemiA., StephensR.R. and FuchsH.O.: ‘Metal fatigue in engineering’; 2001, New York, Wiley.
16.
ChabocheJ.L., KanoutéP. and AzzouzF.: ‘Cyclic inelastic constitutive equations and their impact on the fatigue life predictions’, Int. J. Plast., 2012, 35, 44–66.
17.
ZhangZ., DelagnesD. and BernhartG.: ‘Anisothermal cyclic plasticity modelling of martensitic steels’, Int. J. Fatigue, 2002, 24, 635–648.
18.
ChabocheJ.L.: ‘A review of some plasticity and viscoplasticity constitutive theories’, Int. J. Plast., 2008, 24, 1642–1693.
19.
BarrettR.A., O'DonoghueP.E. and LeenS.B.: ‘A unified viscoplastic model for high temperature low cycle fatigue of service-aged P91 steel’, Trans. ASME J. Press. Vessel Technol., 2013, to be published.
20.
KlocL., SklenickaV., DlouhyA. and KucharovaK.: in ‘Microstructural stability of creep resistant alloys for high temperature plant applications’ (ed. StrangA., CawleyJ. and GreenwoodG. W.), 445–455; 1998, London, The Institute of Materials.
21.
SkleničkaV., KuchařováK., SvobodaM., KlocL., BuršíkJ. and KroupaA.: ‘Long-term creep behavior of 9–12Cr power plant steels’, Mater. Charact., 2003, 51, 35–48.
22.
NabarroF.: ‘Creep at very low rates’, Metall. Mater. Trans. A, 2002, A33, 213–218.
23.
ZhaoL., JingH., XuL., AnJ. and XiaoG.: ‘Numerical investigation of factors affecting creep damage accumulation in ASME P92 steel welded joint’, Mater. Des., 2012, 34, 566–575.
24.
FournierB., SauzayM., BarceloF., RauchE., RenaultA., CozzikaT., DupuyL. and PineauA.: ‘Creep-fatigue interactions in a 9 Pct Cr–1 Pct Mo martensitic steel – Part II: microstructural evolutions’, Metall. Mater. Trans. A, 2009, A40, 330–341.
25.
SaadA.A., SunW., HydeT.H. and TannerD.W.J.: ‘Cyclic softening behaviour of a P91 steel under low cycle fatigue at high temperature’, Procedia Eng., 2011, 10, 1103–1108.
26.
SaadA.A.: ‘Cyclic plasticity and creep of power plant materials’, PhD thesis, University of Nottingham, UK, 2012.
27.
ZhangT., McHughP.E. and LeenS.B.: ‘Computational study on the effect of contact geometry on fretting behaviour’, Wear, 2011, 271, 1462–1480.
28.
Mohd TobiA.L., DingJ., BandakG., LeenS.B. and ShipwayP.H.: ‘A study on the interaction between fretting wear and cyclic plasticity for Ti–6Al–4V’, Wear, 2009, 267, 270–282.
29.
KluehR.L. and VitekJ.M.: ‘Fluence and helium effects on the tensile properties of ferritic steels at low temperatures’, J. Nucl. Mater., 1989, 161, 13–23.
30.
YaguchiM. and TakahashiY.: ‘Ratchetting of viscoplastic material with cyclic softening – Part 2: application of constitutive models’, Int. J. Plast., 2005, 21, 835–860.
31.
YaguchiM. and TakahashiY.: ‘Ratchetting of viscoplastic material with cyclic softening, part 1: experiments on modified 9Cr–1Mo steel’, Int. J. Plast., 2005, 21, 43–65.
32.
DunneF.P.E. and PetrinicN.: ‘Introduction to computational plasticity’; 2007, Oxford, Oxford University Press.
33.
‘Boiler and pressure vessel code’, Section II, Part D, ASME, NY, USA, 1998.
