FE Analysis of Creep of Welds - Challenges and Difficulties

Transcription

1 FENET FENET Workshop --Finite Finite Element Element Analysis Analysis of of Creep Creep and and Viscoelasticity Majorca, Spain Majorca, Spain March March 2004 FE Analysis of Creep of Welds - Challenges and Difficulties Prof. A.A. Becker, Prof. T.H. Hyde and Dr. W. Sun University of Nottingham UK 1

2 Weld Metal (WM) Heat-affected Zones (HAZ) Parent Material (PM) A typical weld Weld Crack Cracks in Welds 2

3 z D/2 T PM σ a PM h 1 h (HAZs) centre-line of the pipe L centre-line of the weld p i HAZ (LT) HAZ (HT) θ w o /2 h WM h 1 WM Dimensions (mm) and loading of P91 pipe weldment A typical FE mesh 3

4 PM WM PM HAZ Finite Element Analysis of creep damage in welds 4

5 Practical Difficulties in modelling welds Material properties for the HAZ are very difficult to obtain (since it is not possible to use uniaxial specimens for laboratory tests). HAZ material properties are not constant across the HAZ region. Welds are often anisotropic Weld repair in aged pipes creates new HAZ regions whose material properties are difficult to obtain. To estimate failure (creep rupture) time, conventional creep laws may be inadequate. Continuum damage mechanics may have to be used. Residual stresses are difficult to determine. Weld repair creates new more complex residual stresses. Effect of heat treatment of welds needs to be assessed. 5

6 Difficulties in FE Modelling of welds The HAZ exists in a narrow band, which requires several layers of very small elements Modelling three-dimensional welds (e.g. around nozzles and pipe branches) requires very fine 3D meshes, which can be prohibitive. Residual stresses are difficult to implement in FE analysis. Continuum damage mechanics are not easily available in commercial FE codes (may require writing user-subroutines ). Very small time increments are needed as damage accumulates in elements. 6

7 Obtaining Creep Material Properties of Welds 7

8 High-temperature creep testing laboratory at University of Nottingham Mayes servo-electric creep-fatigue machine (250KN) at University of Nottingham 8

9 Creep Specimen with extensometer 9

10 Creep Tests required for welded structures Parent Metal (PM) properties Uniaxial round bar test Notched round bar tests Weld Metal (WM) properties Uniaxial round bar test Notched round bar tests Heat-Affected-Zone (HAZ) properties Cross-weld specimen containing PM, HAZ and WM Impression (indentation) creep test on the HAZ area 10

11 M Uniaxial ridged specimen (Single material) Semi-circular Bridgeman notch M Notched bar specimen (Single material) 11

12 WM HAZ 12.5 Semi-circular Bridgeman notch 7.5 PM M Notched bar specimen (multi-material) PM HAZ WM M Cross-weld waisted specimen (Multi-material) 12

13 PM WM PM Circumferential pipe weld HAZ HAZ PM WM PM PM WM Positions of multi-material specimens 2.5 mm 1 mm indenter Loading direction PM HA Z HAZ WM HAZ 10 mm Impression creep (HAZ) specimens 2.5 mm 13

14 Creep strain (σ 2 > σ 1 ) σ 2 σ 1 Creep strain rate primary tertiary tertiary secondary secondary primary Time (a) Primary, secondary and tertiary creep stages (b) Creep strain rate Time. log(ε) t 3 t 2 t 1 log(σ) ε 2 ε 3 ε 1 (ε 3 > ε 2 > ε 1 ) (t 3 > t 2 > t 1 ) log(σ) log(t) (c) Isochronous and isostrain creep curves Uniaxial Creep curves 14

15 Creep Material Laws Uniaxial Norton- Bailey Creep Law In general, the stress-strain relationship in a uniaxial creep test, under a constant load, can be represented by the following equation: where ε c is the creep strain σ is the nominal stress t is the time T is the temperature. c ε = f ( σ,t,t ) To represent primary and secondary creep in isothermal conditions, the Norton-Bailey material law is often used: c n ε = Aσ m t where A, n and m are material properties 15

16 Multi-axial Norton-Bailey creep law c = A ( ) t m ε eq σeq n where ε eq is the equivalent (Von Mises) strain σ eq is the equivalent (Von Mises) stress For Cartesian components of strain: where S ij is the deviatoric stress (n-1) ( σ ) S t c 3 = m A (m-1ij ε& ij eff 2 16

17 Continuum damage mechanics creep law n-1 c 3 σ eq Sij & ε = A m ij t 2 1-ω 1-ω where A, m and n are material constants, σ eq is the equivalent (von Mises) stress S ij is the deviatoric stress. Damage Parameter, ω The damage parameter, ω, is a scalar quantity varying from ω = 0 (no damage) to ω = 1 (total failure) 17

18 Rupture Stress The rate of change of ω can be expressed in terms of a "rupture stress", σ r, as follows: χ ω& = M m φ t ( σr ) ( 1- ω) where M, φ and χ are continuum damage material constants. The rupture stress is assumed to be a function of the maximum principal stress, σ 1, and the equivalent stress, σ eq, : σ r ( α ) eq = α σ1 + 1 σ where α is a tri-axial material constant which ranges from α = 1 (maximum principal stress dominant) to α = 0 (equivalent stress dominant). 18

19 Obtaining creep damage material parameters For PM and WM materials All damage parameters (except α) can be obtained from conventional uniaxial creep tests The tri-axial parameter α can be obtained by an iterative approach based on matching FE failure time to the experimental notched bar failure time For HAZ material Trial-and error procedure based on an educated estimation of initial values The iterative procedure is repeated until the FE failure time is consistent with the experimental failure time at all stress levels If possible, a parametric sensitivity study should be performed to determine the influence of each parameter on failure time 19

20 Summary of tests and FE analyses needed for obtaining creep damage material parameters Test specimen Material Test data required By creep testing Plain bar PM and WM Steady state A, n, χ, M, φ Creep strain rate, failure time Notched bar PM and WM Failure time α (single material) Indentation HAZ Steady state strain rate A, n By FE modelling Cross weld (Multi-material) Notched bar (multi-material) PM, WM and HAZ PM, WM and HAZ Failure time χ, M, φ Failure time χ, M, φ 20

21 Creep analysis of weld repairs Strain MPa 82 MPa 87 MPa 93 MPa 100 MPa fitting Time (hrs) Fitted and tested uniaxial creep strain curves of a P91 parent material at 650 o C 21

22 w damage Aged PM h Aged WM θ Aged PM T Service-aged weld with damage Aged HAZ HAZ generated in the aged PM by welding Aged PM New WM Aged PM Fully repaired weld HAZ generated by welding Aged PM New WM Aged PM Partial weld repair (a) HAZ generated by welding Aged PM New WM Aged WM Partial weld repair (b) Schematic Diagram of Weld Repair Strategies 22

23 Initial damage distribution in the fullrepaired weld. (Initial damage in the aged material was obtained at t repair = 15,000 h) Damage distribution in the full-repaired weld at failure (t f = 9,946 h) (Initial damage in the aged material was at t repair = 15,000 h) 23

24 y d b y z x t b y o Branc h Dip T p o bo x b y Main Pipe Axial centre line of the pipe x A pipe with an isolated T-branch. y y d b z T p x S y L y R Branc t b b y b x Main D p o Axial centre line of the i Fig. 4 A pipe with two identical T-branches at a separation of S. A pipe with two identical T-branches x 24

25 Creep analysis of welded Inco718 sheets φ Dimensions in mm B=3.2 (thickness) 38 R25 R Weld bead Uniaxial tensile and creep specimen for welded Inco718 sheet 25

26 Welded plate warp angle (~5 ) Welded INCO718 sheets Creep-fatigue welded specimen 26

27 Weld bead close-up FE Model of weld bead FE Analysis of distortion in welded Inco718 sheets 27

28 Creep Law 60 min = : & ε σ Typical FE creep analysis : Von Mises stress contours after creep time of hrs near the weld bead 28

29 F sec Loading history Typical FE creep/fatigue Analysis Axial stress contours near the weld bead 29

30 FE mesh of one portion of TBH using tetrahedral element (in ABQAUS CAE 6.3) Constructed TBH (in ABQAUS CAE 6.3) FE creep analysis of aero-engine component Tail Bearing Housing (TBH) 30

31 Von Mise stress contour of TBH after 2000 hrs 31

32 Typical Local stress contour of TBH fatigue analysis at peak load 32

33 FE benchmarks for creep damage FE Creep Damage Benchmarks * A uniaxial round bar A biaxial perforated plate A tri-axial notched bar A multi-material cross-weld specimen * A.A. Becker, T.H. Hyde, W. Sun, and P. Andersson Benchmarks for Finite Element Analysis of Creep Continuum Damage Mechanics J. Computational Materials Science, Vol. 25, (2002). 33

34 y σ Material: Geometry x 2D FE mesh 3D FE mesh Titanium Alloy at 650 o C Creep Strain MPa FE-DAMAGE 175 MPa FE-DAMAGE 200 MPa FE-DAMAGE 225 MPa FE-DAMAGE 250 MPa FE-DAMAGE ABAQUS UM A T Creep Damage M Pa FE-DAM AGE 175 M Pa FE-DAM AGE 200 M Pa FE-DAM AGE 225 M Pa FE-DAM AGE 250 M Pa FE-DAM AGE Time (hours) Time (hours) (a) strain (b) damage Benchmark 1 : Uniaxial round bar 34

35 y σ L/2 = 50 R = x Geometry (mm) FE mesh Material: Titanium Alloy at 650 o C (σ = 140 MPa) eq Position 1 FE-DAMAGE Position 2 FE-DAMAGE Position 1 ABAQUS UMAT Position 2 ABAQUS UMAT Time (hours) Creep Damage Position 1 FE-DAMAGE Position 2 FE-DAMAGE Position 1 ABAQUS UMAT Position 2 ABAQUS UMAT Time (hours) (a) Equivalent strain (b) Damage Benchmark 2 : Biaxial perforated plate 35

36 y σ? x x Material : 0.5Cr0.5Mo0.25V steel at 640 o C (σ nom = 70 MPa) R R = = Geometry (mm) FE mesh yy Position 1 FE-DAMAGE Position 2 FE-DAMAGE Position 1 ABAQUS UMAT Position 2 ABAQUS UMAT Time (hours) eq/p Position 1 FE-DAMAGE Position 2 FE-DAMAGE Position 1 ABAQUS UMAT Position 2 ABAQUS UMAT Time (hours) Creep Damage Position 1 FE-DAMAGE Position 2 FE-DAMAGE Position 1 ABAQUS UMAT Position 2 ABAQUS UMAT Time (hours) (a) y-direction strain (b) normalised equivalent stress (c) damage Benchmark 3: Notched bar 36

37 y WM HAZ 1 2 PM x Material : Service-aged steel weldment (½Cr½Mo¼V: 2¼Cr1Mo) at 640 o C Geometry (mm) FE mesh εyy Position 1 FE-DAMAGE Position 2 FE-DAMAGE Position 1 ABAQUS UMAT Position 2 ABAQUS UMAT σeq/p Position 1 FE-DAMAGE Position 2 FE-DAMAGE Position 1 ABAQUS UMAT Position 2 ABAQUS UMAT Creep Damage ω Position 1 FE-DAMAGE Position 2 FE-DAMAGE Position 1 ABAQUS UMAT Position 2 ABAQUS UMAT Time (hours) (a) y-direction strain Time (hours) (b) Normalised equivalent stress Time (hours) (c) damage Benchmark 4 : Multi-material cross-weld specimen 37

38 Concluding Remarks There are many difficulties/challenges in obtaining accurate creep material parameters for use in FE models of welds and weld repairs FE models of large 3D welded structures, such as branch pipes, requires very fine meshes. Sub-modelling may be required. Residual stresses are difficult to calculate and difficult to implement in FE analysis. Continuum damage mechanics are not easily available in commercial FE codes, and require a great deal of effort by the FE user. Weld repair complicates analysis by the introduction of new HAZ layer FE benchmarks for creep damage are useful in assessing the accuracy of FE codes 38

39 Recommendations for Future Work Better procedures for obtaining all creep material properties by experimental tests Incorporation of creep damage as a standard material law in commercial FE software Analysis of crack initiation and propagation in welded regions Incorporating microstructural changes in creep material laws Easier incorporation of weld residual stresses in FE analysis Better understanding of the effects of heat treatment during the weld process 39