In this article, a semi-analytical method to estimate elastic follow-up factor as input to estimate the transient creep C(t) parameter under secondary loading is presented and validated against finite element results for a cracked two-bar structure under constant displacement loading. Predicted values of C(t) agree well with the finite element results for both elastic-creep cases and for elastic-plastic cases with the same creep and plastic hardening exponents. For elastic-plastic-creep cases with different creep and plastic hardening exponents, the proposed method gives good predictions at long time but can under- or over-predict C(t) at short time.
AinsworthRA.The assessment of defects in structures of strain hardening materials. Eng Fract Mech1984; 19: 633–642.
2.
AinsworthRA.The treatment of thermal and residual stresses in fracture assessments. Eng Fract Mech1986; 24: 65–76.
3.
RocheRL.Modes of failure – primary and secondary stresses. J Press Vess: T ASME1988; 110: 234–239.
4.
AinsworthRADeanDWBuddenPJ. Creep and creep-fatigue crack growth for combined loading: extension of the advice in R5 volume 4/5 appendix A3. British Energy Report, E/REP/BDBB/0059/GEN/04. London: British Energy; May2010.
LeiY. A validation of the newly extended method for the estimation of the creep crack tip characterising parameters using existing finite element results. British Energy Report, E/REP/BDBB/0083/GEN/05. London: British Energy; November2005.
7.
LeiYDeanDW. Finite element RCC-MR creep analysis of circumferentially cracked cylinders under combined residual stress and mechanical load. In: Proceedings of 17th European conference on fracture, Brno, Czech Republic, 2–5 September 2008, pp.2556–2563. European Structural Integrity Society.
8.
FujiokaT.Simplified estimate of elastic-plastic J-integral of cracked components subjected to secondary stresses by the enhanced reference stress method and elastic follow-up factors. Int J Pres Ves Pip2013; 108–109: 28–39.
9.
EDF Energy. R5 issue 3: assessment procedure for the high temperature response of structures. Gloucester: EDF Energy Generation; 2003.
10.
AinsworthRAHootonDG.R6 and R5 procedures: the way forward. Int J Pres Ves Pip2008; 85: 175–182.
11.
MiuraNTakahashiYNakayamaY. Development of simplified evaluation method for creep-fatigue crack propagation. Nucl Eng Des2008; 238: 435–442.
12.
SongTKKimYJNikbinK. Approximate J estimates for circumferential cracked pipes under primary and secondary stresses. Eng Fract Mech2009; 76: 2109–2125.
13.
SongTKKimYJNikbinK. Estimation of the transient creep parameter C(t) under combined mechanical and thermal stresses. Eng Fract Mech2010; 77: 685–704.
14.
RobinsonEL.Strain piping design to minimize creep concentration. Trans ASME1955; 77: 1147–1162.
15.
BoyleJTNakamuraK.The assessment of elastic follow-up in high temperature piping systems – overall survey and theoretical aspects. Int J Pres Ves Pip1987; 29: 167–194.
16.
KasaharaNNagataTIwataK. Advanced creep-fatigue evaluation rule for fast breeder reactor components: generalization of elastic follow-up model. Nucl Eng Des1995; 155: 499–518.
17.
SongTKOhCYKimYJ. Approximate J estimates for combined primary and secondary stresses with large elastic follow-up. Int J Pres Ves Pip2013; 111–112: 217–231.
18.
AinsworthRA.Consideration of elastic follow-up in the treatment of combined primary and secondary stresses in fracture assessments. Eng Fract Mech2012; 96: 558–569.
19.
HoffNJ.Approximate analysis of structures in the presence of moderately large creep deformations. Q Appl Math1954; 12: 49–55.
20.
EDF Energy. R6: assessment of the integrity of structures containing defects (revision 4). Gloucester: EDF Energy Generation; 2013.
