Prof. Luca Esposito Studio Scano Associato Safety & Integrity Piazzale Chiavris, Udine, ITALY (EU)

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1 EFFECTS OF SECONDARY CREEP FORMULATION ON API RESIDUAL LIFE EVALUATION Lorenzo Scano, Ph.D. Prof. Luca Esposito Udine, ITALY (EU) «Federico II» Department of Industrial Engineering Naples, ITALY (EU) 1

2 SUMMARY Due to its subtle and diverse nature, creep is a major culprit for the failure of pressure equipment operated at high temperatures Creep accumulated damage is typically evaluated through analytical procedures incorporated into the main Fitness-For-Service standards like the API Steady-state or secondary creep is typically the only stage assessed in most engineering applications Because of the widespread use of the Finite Elements method, a sound secondary creep formulation is crucial to predict the phenomenon onset From a microstructural standpoint, creep involves two distinct processes: diffusion and dislocation glide, both interconnecting and fostering timedependent plastic strain accumulation 2

3 SUMMARY Only dislocational, high-stress creep is usually taken into account by the widespread used Norton s power-law equation Nevertheless, neglecting the diffusive processes can be non-conservative in the low-stress regime or at points of stress relaxation In this work, the impact of the diffusional creep range on API creep residual life has been investigated for two HRSG assembly ASTM A335 P22 components The creep damage was evaluated via FEA and the API Larson- Miller procedure for three secondary creep formulations: a classical Norton s power-law, a double power-law including the diffusional range, and a hyperbolic-sine Garofolo s equation The creep damage was then correlated to the inelastic strain accumulation using a Monkman-Grant s relation and a ductility exhaustion approach 3

4 THE CREEP PHENOMENON Creep is a thermally-activated process inducing a time-dependent, progressive plastic strain accumulation at constant applied load and T > T homologous Three creep stages can be defined: Secondary creep is typically dominant for long-term exposures of pressure equipment operated at high temperatures! PRIMARY: decrease of the strain rate due to strain-hardening SECONDARY: constant strain rate, the softening processes balance the dislocation pile-up TERTIARY: increase of the strain rate, the actual damage sets on and leads to component crack and failure 4

5 THE CREEP PHENOMENON Creep is a complex and heterogeneous phenomenon and involves two distinct but interconnected processes: DIFFUSION: Thermally-activated formation and migration of vacancies within the material lattice Low-stress range at low (Coble creep) and high (Nabarro-Herring creep) temperatures Secondary creep formulation is linear: de/dt = A s DISLOCATION GLIDE+CLIMB: Major contribute to plastic strain. Dislocations move through slipping planes and can pass through obstacles, i.e., particles or other dislocations (CLIMBING), with the aid of diffusion High-stress range below the athermal yield stress Secondary creep formulation is a power law (PL): de/dt = A s n 5

6 SECONDARY CREEP FORMULATIONS For applications in the PVP field (long exposures), typically: Only the steady-state stage of creep is considered Only the dislocational mechanism is accounted for (Norton s law) 6

7 SECONDARY CREEP FORMULATIONS Extrapolating the application of the Norton s law (n > 3) into the diffusive regime (n = 1) can lead to unconservative predictions of the strain rate! 7

8 SECONDARY CREEP FORMULATIONS Extrapolating the application of the Norton s law (n > 3) into the diffusive regime (n = 1) can lead to unconservative predictions of the strain rate! At the same stress, the strain rate predicted with the extrapolation of the Norton s law is lower! 8

9 CASE STUDY Two components of an ASTM A335 P22 HRSG header were investigated Operating conditions: 10.4 MPa ( psi) 528 C (982 F) D h = mm (10 ) D t = 50.8 mm (2 ) 9

10 CASE STUDY C1 shell to head C2 tube to shell The components were chosen in order to investigate a diverse stress field: Low primary +secondary stresses at the shell to head junction (C1) High notch stresses at the unreinforced tube to shell interface (C2) High relaxation at stress concentrations, potentially driving the stress field into the dislocative regime of creep Creep damage evaluated for steady low stresses (C1) and for a time-dependent stress field under relaxation (C2) 10

11 MATERIAL DATA AND SECONDARY CREEP FORMULATION ASTM A335 P22 (annealed) NIMS database data Temperature range: C Data interpolated using a PL equation: de/dt = A e -Q/RT s n Diffusional and dislocational regimes evident at low and high stresses: Diffusional creep Dislocational creep A = Q = 249 kj/mol 535 kj/mol n =

12 MATERIAL DATA AND SECONDARY CREEP FORMULATION Experimental data extrapolated at the operating T = 528 C 3 secondary creep formulations: Standard Norton s PL: de/dt = A s n (n = 10.7) Double PL (DPL) including the diffusive, low n, range: de/dt = A s n (n = 10.7) de/dt = A s n (n = 2.14) Sinh Garofolo s equation: de/dt = B (sinh(c s)) n 12

13 FINITE ELEMENTS INELASTIC ANALYSIS C1 shell to head C2 tube to shell FE solid hexahedral elements Full weld details but NO weld creep data (not available) WSRF = 0.8 adopted Inelastic analysis with creep and plasticity from 0 to h 3 secondary creep constitutive equation: PL, DPL, SINH Evaluation points at locations critical for damage accumulation: Notch effects and triaxiality Inelastic stress redistribution 13

14 FINITE ELEMENTS INELASTIC ANALYSIS Diffusional effects included (DPL/SINH) Higher stress relaxation due to creep strain in the diffusive regime! 50x creep strain SINH vs h! C1: low stress range < 50 MPa (diffusional range) C1: DPL/SINH lead to markedly higher relaxation and creep strain accumulation 14

15 FINITE ELEMENTS INELASTIC ANALYSIS Diffusional effects included (DPL/SINH) Even at higher stresses relaxation drives the system into the diffusive regime. Here, more inelastic strain is accumulated and relaxation increases, fostering other creep strain accumulation 4x creep strain SINH vs h! C2: low and high stress range, time-dependent (relaxation) C2: DPL/SINH lead to higher relaxation and creep strain accumulation at low stresses 15

16 CREEP DAMAGE EVALUATION The creep damage in C1 and C2 was evaluated using three different methodologies: API time-fraction approach (Sec. 10 Level 3): Larson-Miller theory with minimum time-to-rupture data (P22) Residual life directly dependent on the Von Mises stress A triaxiality factor is included to account for strain concentration triaxiality stress factor Monkman-Grant correlation for time-to-rupture (P22 alloy): creep damage and time-to-rupture directly correlated to the strain rate 16

17 CREEP DAMAGE EVALUATION A ductility exhaustion method: Strain-based time-fraction approach Uniaxial ductility from experiments (NIMS data) Multiaxial ductility via a triaxiality factor (Rice and Tracey s theory) creep strain from FEA uniaxial ductility from tests triaxiality factor 17

18 COMPARISON OF THE RESULTS Damage using Norton s PL vs DPL and SINH C1: low stresses, diffusive range API relies on VM stress! DPL and SINH foster greater relaxation rates, hence the VM stress decreases along with API calculated damage Norton s PL conservative at points of stress concentration (C1-1, C2-X) because relaxation is dominant Norton s PL unconservative at points of stress redistribution (pipe outer surface) when in the diffusive regime (C1-2 and C1-3) 18

19 COMPARISON OF THE RESULTS Damage using Norton s PL vs DPL and SINH Monkman-Grant formulation: the strain rate is directly taken into account for the damage formulation Norton s PL unconservative at low stresses, with or without relaxation SINH tends to underestimate the damage in the dislocation-controlled region PL and DPL calculated damage converges at high stresses 19

20 COMPARISON OF THE RESULTS Damage using Norton s PL vs DPL and SINH Ductility exhaustion method: the strain rate is directly taken into account for the damage formulation Norton s PL unconservative at low stresses, with or without relaxation At stress concentrations (weld roots C1-1 and C2-2) triaxiality increases with time, hence the ductility exhaustion approach leads to higher creep damage 20

21 CONCLUSIONS Assessing the creep damage is crucial for the Fitness-For-Service analysis of pressure equipment operated at high temperatures for prolonged time intervals Creep is a complex phenomenon, involving, at the microstructural level, diffusive and dislocational processes; the former taking place in the lowstress range, the latter at higher stresses Creep typically evolves across three stages: primary, secondary and tertiary. In most applications in the PVP field, the secondary stage is dominant and it is defined by a constant strain rate (steady state) During most FFS evaluations, only the secondary creep is usually modeled via a Norton s power law formulation. This constitutive equation only assesses the accumulated strain due to the dislocational aspects of creep and neglects the diffusive regime 21

22 CONCLUSIONS If a component is operated in the low-stress range, or if the stresses relax over time at concentration points, the system can be driven into the creep diffusional range and the application of the Norton s law can be nonconservative In this work, the impact of diffusion in terms of creep damage has been assessed for the API Larson-Miller methodology and compared with two strain-based methods (Monkman-Grant and ductility exhaustion) Two ASTM A335 P22 components of a HRSG header were evaluated via FEA assessing points at different stress levels and degrees of relaxation The secondary creep was modeled with three formulations: a standard power-law (only dislocational creep), a double power-law and a Garofolo s hyperbolic sine equation (both diffusional and dislocational) 22

23 CONCLUSIONS When the creep damage was calculated according to API (VM stress dependent), the Norton s law proved conservative at points of concentrations because the stresses relax less when diffusion is not taken into account. On the other hand, it showed non-conservative results in the low-stress range where creep fosters a stress redistribution, e.g., at pipe outer surface When the creep damage was calculated with the two strain-based methods, the Norton s law lead to utterly non-conservative results because the damage is directly correlated to the accumulated strain that is inherently higher if the diffusive regime is also considered API Larson-Miller approach can be deemed conservative if the assessment is governed by the stress levels at concentrations. Yet, a thorough check on the overall creep strain is crucial to correctly estimate the component residual life 23

24 CONCLUSIONS THANK YOU! 24