Creep-fatigue life assessment of high-temperature weldments using the linear matching method Yevgen Gorash & Haofeng Chen Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow, UK [email protected] [email protected], http://www.thelmm.co.uk & 1. Theoretical Background and the Linear Matching Method max s min s e s max s min s e s max s min s e s max s min s e s max s min s e s purely elastic behavior elastic shakedown max s min s e s r & low-cycle fatigue everse plasticity ratchetting followed by incremental collapse instantaneous collapse 1 0 0 1 2 lim / P P tm y / s s ¾ ¾ ¾ ¾ variable von Mises thermo - mechanical stress yield stress taken as 0.2% plastic strain offset constant component of applied mechanical load limit load, the maximum load that a structure can s tm y lim P P s s afely carry without instantaneous collapse 1.1 Bree diagram with responses to cyclic loading 1 y s s e 1 i E + i E 2 i E + 3 i E + 3 i e + 2 i e + 1 i e + i e 1.2 Fundamentals of the Linear Matching Method 2 • belongs to the group of modified elastic modulus methods; • has the character of a non-linear programming method; • with each step involves the solution of a linear problem; • each solution satisfies the condition of force equilibrium; • non-linear constitutive assumptions are imposed sequentially; • strain rate histories give rise to equilibrium residual stress fields; • solution is the minimum of a functional of the strain rate history; • generates inelastic solutions for the stabilized cyclic state; • compatible with standard finite element codes, e.g. ABAQUS. • Life Assessment Methods and Design Codes – R5 Procedure, ASME N47 and RCC-MR (1980's – today) based on Neuber's Rule • Conventional incremental (transient) FEA • Direct Cyclic Analysis (DCA) incorporated into ABAQUS • Direct Methods using Static or Kinematic Bounding Theorem (Koiter, 1960) Alternatives to the LMM: • Modified Modulus Method (MMM) for limit load analysis (Ponter, early 1990’s) • MMM modified for elastic shakedown analysis (Ponter & Carter, 1997) • MEM implemented as ABAQUS UMATs (Ponter & Engelhardt, 2000) • Linear Matching Method (LMM) implemented in ABAQUS for reverse plasticity (global shakedown) & ratchet boundary evaluation (Ponter & Chen, 2001) • LMM further developed to evaluate R5 related parameters (Ponter & Chen, 2005) Development of the LMM framework: 2. Testing & modelling of cruciform weldment 2.1 Experimental facility and specimen with typical failures 3 620 800 1500 Load points Furnance Weld Servo motor Moving crosshead Furnance Deflection monitor Load cell Specimen Roller Box 550 C ° 1) fatigue failure at weld toe corresponding to 1.0% of total strain range 2) fatigue failure remote from weld corresponding to 0.4% of total strain range Typical failure locations: 1 2 2.2 Dimensions (mm) of the cruciform weldment specimen 3 2.3 Parameters of the FE-model 100 26 60° 72 200 3 3 3 26 3 59 2 R25 50 M M Temperature: 550 C ° P parent material heat-affected zone weld metal material without creep totally elastic material 1) 977 CPE8R finite elements: 8-node biquadratic plane strain quadrilaterals with reduced integration 2) 3 variants of dwell period - pure fatigue, 1 hour, 5 hours 3) 5 variants of reverse bending moment corresponding to equal to 1.0%, 0.6%, 0.4%, 0.3% and 0.25% of total strain M ε Δ () [ ] 3 200 26 Area Moment of Inertia: , 13...13 12 X X M y I Py y I ´ ´ = Þ = Î- X Y 4. Creep-Fatigue Evaluation Procedure 4.1 Creep-fatigue evaluation procedure with time fraction rule 4 s 1 2 3 tot De cr Ds s e cr e s total strain range number of cycles to failure tot De N * Saturated hysteresis loop S-N diagram for low-cycle fatigue f 1c 1 N * = w Fatigue damage accumulated per 1 cycle: stress time ( ) 1 0 1 , , t t Z dt t D = D ò s s s Stress relaxation behaviour t D 1 s Z 1 s 2 s 2 s stress time to rupture t * Creep rupture curve cr 1c t t * D = w Creep damage accumulated 1 cycle: per fatigue damage creep damage Creep-fatigue interaction diagram 1 f w cr w 1 f cr f f 1c cr cr 1c 1 N N N + £ ü ï = Þ ý ï = þ å å å w w w w w w 1 2 3 5 4 4.2 FEA/LMM results corresponding to Δ = 1% and Δ = 5h ε t tot 0 1.287e-03 2.617e-03 3.947e-03 5.277e-03 6.607e-03 7.937e-03 9.268e-03 1.060e-02 1.193e-02 1.326e-02 1.459e-02 1.592e-02 0 1.782e-04 3.576e-04 5.370e-04 7.164e-04 8.958e-04 1.075e-03 1.255e-03 1.434e-03 1.613e-03 1.793e-03 1.972e-03 2.152e-03 0 28.804 59.079 89.354 119.629 149.904 180.178 210.453 240.728 271.003 301.278 331.553 361.828 0 24.069 49.601 75.132 100.664 126.195 151.727 177.258 202.790 228.321 253.853 279.384 304.916 total strain range Δε tot equiv. creep strain ε cr equiv. vM stress (MPa) 5h t D= equiv. vM stress (MPa) eq vM s eq vM s 4.3 Creep-fatigue evaluation results of the cruciform weldment 0.2 1 total strain range (%) 200 1000 10000 100000 number of cycles to failure 0.5 Results of FEA with LMM: X-weld fatigue X-weld = 1h X-weld = 5h Δt t Δ Available LCF tests fittings : 5 parent R66 curve weld R66 curve X-weld LCF tests Results of X-weld testing : 3 X-weld fatigue X-weld = 1h X-weld = 5h Δt t Δ Δε tot , % Δt = 0 h Δ = 1 h t Δ = 5 h t FEA/LMM experiments 3 FEA/LMM experiments 3 FEA/LMM experiments 3 N* failure N* failure N* failure N* failure N* failure N* failure 1.0 857 T 918 T 430 T 562 U 278 T 275 P 0.6 4062 T 2499 U 1673 T 1048 U 967 T 943 W 0.4 17025 T 15747 P 6270 T 6512 U 3168 T — — 0.3 45374 W 38127 P 19776 T 21488 W 9679 T — — 0.25 90056 W 66847 P 52221 T — — 26901 T — — (U) Specimen failed at the undercut close to the weld toe in the parent plate (T) Specimen failed at the weld toe propagating through the HAZ (P) Specimen failed in parent plate remote from weld (W) Specimen failed in weld metal 5. Analysis of the Obtained Results 5.1 Analytical functions for cycles to failure and residual life Δt, dwell time (hours) 0 0.5 1 2 5 10 100 1000 10000 1.470528 857 500 430 362 278 223 95 33 8 1.153799 4062 2037 1673 1339 967 746 307 122 42 0.925507 17025 7963 6270 4756 3168 2294 799 308 121 0.777426 45374 24952 19776 14931 9679 6755 1963 635 230 0.691045 90056 63964 52221 40511 26901 18869 5116 1415 434 var sh M M M D = D % normalized moment a 1 a 2 b 1 b 2 −0.4921 3.708929 0.0255 0.754959 ( ) ( ) ( ) ( ) ( ) ( ) 3 1 2 tot tot 1 2 2 2 1 3 1 2 ( ) log( ) , 365·24 (365·24·60·60) 0.2817, 0.17649 log 1 l , 3.110 og 1 ( ) 51 b t p t a t a t a b t b M t N a tM L N M pM pM p p t b p e e e - D é ù D D = D = + ê ú ë û D = + = = Þ D D = D+ + D = D+ + = % % & % % % å å å where - dependent parameter with s: 5.2 Design contour plot for creep-fatigue durability 0.01 0.1 1 10 100 1000 10000 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 dwell time (hours) normalised moment 10 20 50 100 200 500 1000 2000 5000 10000 20000 50000 100000 200000 500000 1000000 2000000 No. of cycles life (years) tests 1000 300 100 30 10 3 1 0.3 0.1 0.03 0.01 0.003 fatigue dominant creep dominant 5.3 Comparison of the observed and predicted * N 100 1000 10000 100000 100 1000 10000 100000 optimal match factor of 2 factor of 1.6 LMM (fatigue) LMM (Δt = 1h) LMM (Δt = 5h) analitic (fatigue) analitic (Δt = 1h) analitic (Δt = 5h) Non-conservative Conservative experimental cycles to failure predicted cycles to failure 5.4 Dependence of FSRF on duration of dwell period 7 Δt 1 2 3 4 5 6 7 8 0.01 0.1 1 10 100 1000 10000 maximum average minimum FSRF dwell time (hours) FSRF 2 3 0 1 2 3 0 1 2 3 , FSRF( ) log( 1) log( 1) log( 1) 1.7685, 0.53422, 0.00574, 0.02509 t f f t f t f t f f f f D = + D+ + D+ + D+ = = = = where ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 3 2 tot 0 1 2 1 tot 1 p 2 0 1 arent x-weld 2 log log log , , log log 2.2274, 0.94691 and 0.085943 p b t b t m m N m N a t a t p p N N m m m D D D = + + æ ö æ ö D D ç ÷ ç ÷ D = + ç ÷ ç ÷ è ø è ø = =- = å å å å e e ( ) ( ) ( ) parent tot x-weld tot FSRF , , N N t N t D D = D D å å å e e 3. Properties of the steel AISI type 316N(L) at 550° -0.01 -0.005 0 0.005 0.01 -400 -300 -200 -100 0 100 200 300 400 -0.01 -0.005 0 0.005 0.01 -400 -300 -200 -100 0 100 200 300 400 total strain total strain stress stress saturated (R-O) 1st cycle (R-O) saturated (EPP) saturated (tests) 1st cycle (tests) parent material MMA weld metal 3.1 Rate-independent cyclic plasticity 3 1 tot 3 2( , 2 2 2 1 ) E B E E D D D æ ö = + ç ÷ è = + ø b s s n e Zone E (MPa) B (MPa) β σ y (MPa) Parent 160000 1741.96 0.29960 270.662 Weld 122000 578.99 0.10162 307.894 HAZ 154000 1632.31 0.25304 338.731 Deformation plasticity (Ramberg-Osgood model): 3.2 Creep strain and rupture 3,6 0 0.01 0.02 0.03 0.04 0.05 0 500 1000 1500 2000 2500 time creep strain 100 1000 100 1000 10000 100000 parent tests weld tests parent model weld model stress time to rupture parent material: 390, 349, 310 and 285 MPa MMA weld metal: 270, 250 and 215 MPa 3 6 parent test (285 MPa) weld test (270 MPa) parent model (285 MPa) weld model (270 MPa) 3 3 cr cr 1 1 n m n m A t A t m + = = + & e s e s () Time to creep rupture: k B t * = s s Time-hardening power-law: Zone Primary creep strain Time to creep rupture A (MPa /h ) -n m+1 n m B (MPa h) k k Parent 6.604E-19 5.769 -0.55 2.172E+26 8.927 Weld 6.597E-23 7.596 -0.5 5.993E+29 10.61 HAZ 6.600E-21 6.683 -0.525 1.291E+28 9.768 0.1 1 1000 10000 100000 parent material MMA weld metal R66 fatigue endurance curves 5 number of cycles total strain range (%) 3.3 Low-cycle fatigue endurance 5 tot 2 0 1 2 tot 2 3 0 1 2 3 log( ) log( ) log( ) log( ) log( ) log( ) log( ) m m N m N m m N m N m N * * * * * D = + + D = + + + and e e Zone Quadratic Cubic parent MMA weld parent MMA weld m 0 1.73339 1.85169 2.40906 1.93432 m 1 -0.72959 -0.76094 -1.25128 -0.82500 m 2 0.06170 0.05951 0.19399 0.07585 m 3 -0.01102 -0.00137 References [1] Bree J. Elastic-plastic behaviour of thin tubes subjected to internal pressure and intermittent high-heat fluxes with application to fast-nuclear-reactor fuel elements. , 1967; : 226-238 // In: [2] Chen H.F., Chen W. and Ure J. Linear matching method on the evaluation of cyclic behaviour with creep effect. // In: . Toronto, Canada: ASME; 2012, July 15-19 [3] Bretherton I. Reports by AEATechnology plc. and Serco Assurance (Warrington, UK) for British Energy Generation Ltd.: no. (1998), no. (1999), no. (2000), no. (2004) [4] Wada Y.,Aoto K. and Ueno F. Creep-fatigue evaluation method for type 304 and 316FR SS. // In: . Vienna, Austria: IAEA; 1997, p. 75–86 [5] Bate S.K. Further analyses to validate the R5 volume 2/3 procedure for the assessment of austenitic weldments. // Report for British Energy Generation Ltd. no. ; Serco Assurance (Warrington, UK); 2005 [6] Data sheets on the elevated-temperature properties for base metals, weld metals and welded joints of 18Cr-12Ni-Mo-middle N-low C hot rolled stainless steel plates (SUS 316- HP). ; National Institute for Materials Science; Tsukuba, Japan; 2005 [7] Ainsworth R.A., editor. R5: British Energy Generation Ltd (Gloucester, UK); 2003 Journal of Strain Analysis 2(3) Proc. ASME Pressure Vessels & Piping Conf. et al. R/NE/432 AEAT-3406 AEAT- 3406 RJCB/RD01186/R01 Creep-fatigue damage rules for advanced fast reactor design et al. SA/EIG/11890/R002 NIMS Creep Data Sheet No. 45A An Assessment Procedure for the High Temperature Response of Structures. Procedure R5: Issue 3. (PVP2012) Acknowledgements The authors deeply appreciate the EPSRC of the United Kingdom for the financial support in the frames of research grant no. EP/G038880/1, the University of Strathclyde for hosting during the course of this work, and EDF Energy for the experimental data. Engineering and Physical Sciences Research Council 6. Conclusions 1) 2) 3) ≤ 4) cases cases 5) 6) The series of have been implemented with LMM using: and corresponding constants to describe plastic strains under saturated cyclic conditions; and corresponding constants to describe creep strains during primary creep stage. The amount of damage per cycle caused by is estimated using: experimentally defined dependent on numerically defined total strain range for the fatigue damage ( ); experimentally defined dependent on the average stress during dwell period for the creep damage ; the during dwell period is defined as a mean value of analytical function for stress during relaxation dependent on elastic follow-up factor ( ), initial stress and time. A non-linear is used to define the caused by both creep and fatigue, which can’t exceed one ( + 1). Basing upon this interaction, the number of cycles to creep-fatigue failure ( ) is defined. Comparison of the observed and predicted cycles to failure with creep-fatigue FEA/LMM for 3 types of experiments shows, that simulation of 9 of total available 11 is very close to . Simulation of other 2 produces results with factor of difference equal to , which is even better than the factor acceptable for engineering analysis equal to . Sets of creep-fatigue FEA/LMM results analysis corresponding to 0, 0.5, 1, 2, 5 and 10 hours are fitted by and used for of cycles to failure ( *) depending on dwell period and normalized moment intended for design application. Further research will be devoted to parametric studies of the influence of variation of weldment geometrical parameters on the number of cycles to failure ( *) and formulation of a to describe the corresponding dependence. creep-fatigue analyses creep-fatigue interaction creep-fatigue diagram 1.6 2 • Ramberg-Osgood material model power-law model in “time hardening” form relation for number of cycles to fatigue failure ( *) relation for time to creep rupture ( *) average stress total damage optimal match non-conservative analytical function contour plot mathematical relation • • • • N t ω Z ω ω N N N f f cr ( ) ω cr