Modern Creep Lifing Techniques for Gas Turbine Research

Transcription

1 Modern Creep Lifing Techniques for Gas Turbine Research W J Harrison, M T Whittaker Rolls-Royce/Swansea UTC in Materials Institute of Structural Materials

2 Contents Introduction Modern single point prediction methods for nickel based superalloys Recent advances in creep curve methods Hardening rules and their application to creep under non-constant load. Finite element modelling Cold creep modelling

3 Introduction Good quality creep data is essential for designing critical components in gas turbine aeroengines. Numerical methods are used to correlate observed creep behaviour to applied test conditions. These methods range from simple empirical equations which relate single properties to test data to methods which attempt to predict micromechanical phenomenon within the material. Computer based models, based on these methods are used to predict creep behaviour in complex components. Creep Strain MPa 275MPa MPa 325MPa 350MPa MPa Fit 275MPa Fit MPa Fit 325MPa Fit 350MPa Fit C 850 C C C t 4 t Time C fit (s) 850 C fit C fit t 1 e 3 e Stress (MPa) 950 C fit log10(rupture Time) (s)

4 Simple prediction methods log10(minimun Creep Rate) (s-1) The stress (σ) and temperature (T) dependence of t f and m can be calculated using the power law: C 850 C 900 C 950 C 960 C M t f A Q exp RT n c m log10(rupture Time) (s) log10(minimun Creep Rate) (s-1) C 850 C 900 C 950 C 800 C Fit 850 C Fit 900 C Fit 950 C Fit Stress (MPa) Although useful for simple predictions A and n may vary over a wide range of test conditions.

5 Hyperbolic Tangent Method Stress rupture data at each temperature can be represented using a hyperbolic tangent function. Stress TS TS 2 TS k 2 1 TS t 1tanh k.log 2 ti Inflection point Test data t i log(time) Functions are then used to interpolate k and t i with temperature.

6 Hyperbolic Tangent: Rupture Lives Hyperbolic tangent representation of stress rupture data. Stress (MPa) C 850 C 900 C 950 C 800 C HT 850 C HT 900 C HT 950 C HT log10(rupture Time) (s)

7 enter RR clearance number or meeting details Rolls-Royce University Technology Centre in Materials Zwick Creep Seminar 12 th September 2012 Wilshire Method More recently the Wilshire method has been shown to accurately relate creep properties to test conditions. * 1 f exp exp u c UTS Q k t RT * 3 exp exp w c UTS Q k t RT * 2 exp exp v c m UTS Q k RT This method has the advantage of extrapolating well with temperature and allowing for distinct changes in material behaviour.

8 Wilshire Method: Rupture Lives Representation of stress rupture lives using the Wilshire method. Stress (MPa) C 850 C 900 C 950 C 800 C Fit 850 C Fit 900 C Fit 950 C Fit C 100 ln(-ln(stress/uts)) C 900 C 950 C Fit log10(rupture Time) (s) ln(tf.exp(-q*/rt))

9 Wilshire Method: Rupture Lives Minimum creep rate predictions using the Wilshire method with a change in behaviour at σ Y. 1.00E-05 ln(-ln(ns)) C 600 C 650 C 675 C 700 C 725 C 750 C Fit Minimum Creep Rate (s-1) 1.00E E E E E E E Stress (MPa) 550 C C 650 C C 700 C C ln(mcr.exp(qc/rt)) 750 C 550 C Fit 600 C Fit 650 C Fit 675 C Fit 700 C Fit 725 C Fit 750 C Fit

10 Wilshire Method: Single Crystal Rupture Lives Predictions of rupture lives of a single crystal nickel base superalloy. Stress 750 C 800 C 850 C 900 C 950 C 1000 C 1050 C 1100 C 1150 C 750 C Fit 800 C Fit 850 C Fit 900 C Fit 950 C Fit 1000 C Fit 1050 C Fit 1100 C Fit 1150 C Fit Time to rupture

11 Creep Curve Predictions For aerospace applications, component life is often limited by creep strain exceeding a specified limit. The equations above represent current methods for extrapolating t f and m, however an understanding of these values alone is not sufficient for component design since they do not quantify the full shape of a creep curve. Strain Time

12 Creep Curve Predictions Extension of Wilshire method to predict times to strain. Stress (MPa) UTS exp k 3 t Q exp RT * c w ε 0.05% 0.1% 0.2% 0.5% 1.0% 2.0% 0.05% Fit 0.1% Fit 0.2% Fit 0.5% Fit 1.0% Fit 2.0% Fit Time (s)

13 Creep Curve Predictions Creep curve predictions using the Wilshire method. Creep Strain MPa 275MPa 300MPa 325MPa 350MPa 250MPa Fit 275MPa Fit 300MPa Fit 325MPa Fit 350MPa Fit Time (s)

14 Theta-Projection Method An alternative method to predict creep curves is to fit a function to the creep strain vs time data, an example of this is the theta (θ) projection method. 1 2 t 4 t 1 t 1 e 3 e

15 NRC Creep Method A deformation-mechanism-based creep model with similarities to θ. t 1 p 1exp exp Mkt ' 1 ttr M' ε p and t tr are dependent on the contribution of grain boundary sliding (GBS) to creep. M and k are dependent on the rates of GBS, dislocation glide and climb predicted using: p exp QA s A0 RT u g c n exp QB B0 RT u m exp QC C0 RT u

16 Hardening Models Time, strain and life-fraction based hardening methods are often used to quantify the effects of prior creep strain on creep rate.

17 Constitutive method based on Theta Another method is to base creep rate on internal state variables for dislocation hardening (H), dislocation recovery (R) and internal creep damage (W): where the rate of accumulation of H, R and W is given as: These values can then be related to test conditions using the θ coefficients:

18 Variable Stress/Temperature Creep Curves Faster than expected creep rates on stress/temperature change tests in Waspaloy.

19 Comparison of Hardening Models Stress/temperature change experiments.

20 Comparison of Hardening Models Stress/temperature change experiments.

21 Finite Element Modelling These creep curve/hardening methods can be incorporated into finite element models to predict creep behaviour in complex components.

22 Finite Element Modelling: Stress Relaxation Uniaxial stress relaxation predicted using the Wilshire method.

23 Finite Element Modelling: Notched Specimens Stress relaxation in notched specimen.

24 Finite Element Modelling: Continuum Damage Element failure predicted when failure is exceeded at each integration point in the element.

25 Finite Element Modelling: Small Punch Creep Creep models used to create a greater understanding of the small punch creep test.

26 Finite Element Modelling: High Temperature Fatigue Creep models used to predict stress relaxation and creep damage around a propagating fatigue crack

27 Finite Element Modelling: High Temperature Fatigue Creep damage ahead of a fatigue crack, calculated using the θ-projection method.

28 Finite Element Modelling: Cold Creep A cold creep model has been used to predict HCF lives of Ti-64 notched specimens with R=0.8 based on uniaxial creep data at 20 C. where: t 1loge 2t 1 3t i n A i i = 1,3 i

29 Summary Modern creep prediction methods such as the Wilshire equations are applicable to titanium alloys and nickel-based superalloys for aerospace applications. Numerical observations can be related to micromechanical phenomenon. A recent creep curve method based on the Wilshire equations can accurately extrapolate strain/time data Creep tests at non-constant stress and temperature have been used to validate hardening method. Finite-element models based on the θ-projection method and the Wilshire technique have been applied more complex systems A computationally based cold creep method has been introduced which can predict time-dependent effects in Ti-alloys.

30 Acknowledgements The financial support from EPSRC is greatly appreciated. The technical support and data from Rolls-Royce plc, has been fundamental to this work. Particular thanks to Steve Williams.

31 Any questions?