--- 1 --- Application o the linear matching method to eep-atigue ailure analysis o uciorm weldment manuactured o the austenitic steel AISI type 316N(L) Yevgen Gorash and Haoeng Chen Department o Mechanical & Aerospace Engineering, University o Strathclyde, James Weir Building, 75 Montrose Street, Glasgow G1 1XJ, UK Keywords: eep, damage, inite element analysis, FSRF, low-cycle atigue, type 316 steel, weldment 1. Introduction This paper demonstrates the recent extension o the Linear Matching Method (LMM) to include cyclic eep assessment [1] in application to a eep-atigue analysis o a uciorm weldment made o the stainless steel AISI type 316N(L). The obtained results are compared with the results o experimental studies implemented by Bretherton et al. [2] with the overall objective to identiy atigue strength reduction actors (FSRF) o austenitic weldments or urther design application. These studies included a series o strain-controlled tests at 550 C with dierent combinations o reversed bending moment and dwell time Δt. Five levels o reversed bending moment histories corresponding to deined values o al strain range Δε in remote parent material (1%, 0.6%, 0.4%, 0.3%, 0.25%) were used in combination with three variants o eep-atigue conditions: pure atigue, 1 hour and 5 hours o dwell period Δt o hold in tension. An overview o previous works devoted to analysis and simulation o these experiments [2] and highlight o the LMM development progress could be ound in [3]. Recently [1] the LMM has been much improved both theoretically and numerically including more accurate predictions o the stabilised cyclic response o a structure under eep conditions, and more accurate assessments o the resulting cyclic and residual stresses, eep strain, plastic strain range, ratchet strain and the elastic ollow-up actor. Previously, Ponter and Chen [4] applied the earlier version o the LMM or the desiption o elastic, plastic and eep material behaviour to the numerical assessments o a uciorm weldment using the R5 standard eep-atigue model according to the methodology o the lie assessment Procedure R5 [5]. Those results [4] were acceptable, but not perect in sense o agreement with corresponding experiments [2]. In act, the analyses presented in this paper revisit previous LMM assessments [4] o the same experimental studies [2] using the improved method [1], more accurate modelling o the weld structure and the material behaviour o its regions including LCF endurance, eep and long-term strength properties. In contrast to [4], eep damage is assessed using time raction rule instead o ductility exhaustion recommended in R5 Procedure [5], which provides over-conservatism in combination with time-hardening eep law. The non-linear eep-atigue interaction diagram instead o linear is also ound to be more suitable or the assessment o itical eep-atigue damage. 2. Structural model The geometry o the weldment specimen, shown schematically in Fig.1a, is reconstructed rom [2] based on the given sketches o the uciorm weldment and the Manual Metal Arc (MMA) welding procedure. A continuous plate o width 200 mm and length o 1.8 m is divided, at its centre, into two parts, each o which is welded to the surace o a third plate o length 100 mm. The weld area is subdivided into 3 regions: the parent material, assumed to be uniorm away rom the weld; the weld metal, deposited material during multi-pass welding process; and the heat-aected zone (HAZ), a thin layer between the weld and parent material. These regions are expected to have dierent mechanical properties including elasticity, plasticity, atigue and eep, caused by miostructural transormations during the multi-pass welding process. The FE-mesh or a 2D symmetric model o the specimen assumes a plane strain conditions since the specimen width (200 mm) is almost by an order o magnitude greater than the specimen thickness (26 mm) according to Fig.1a. The FE-mesh includes 5 separate areas with dierent material properties denoted in Fig.1b. Introduction o 2 additional material types (material without eep and ally elastic material) with reduced sets o parent material properties in the location o bending moment application avoids excessive stress concentrations in ratcheting and eep analysis. The FE-model consists o 977 inite elements o type CPE8R: 8-node biquadratic plane strain quadrilaterals with reduced integration.
a --- 2 --- b Figure 1: Geometrical and analysis parameters o the uciorm weld specimens: a) dimensions and applied loading; b) FE-mesh with designation o dierent materials, boundary conditions and mechanical loading Figure 2: Assumed schematic loading history or the bending moment M in: a) ully-reversed pure atigue tests; b) ully-reversed eep-atigue tests with dwells Δt in tension; c) non-symmetric pure atigue tests For the purpose o shakedown and eep analysis using LMM, the conversion rom straincontrolled test conditions to orce-controlled loading in simulations has been carried out. Although the gradual inease o applied loading during the initial cycles [2] demonstrate signiicant cyclic hardening eects o the specimen material behaviour, which is typical or the steel AISI type 316N(L), such a simpliication is valid considering that saturated cyclic structural response is dominant during the whole duration o tests. Thereore, in numerical simulations the arms o the specimen are subjected to 3 variants o bending moment history illustrated schematically in Fig.2. Pure atigue analysis assumes a rapid reversal o bending moment o magnitude ΔM var as shown in Fig. 2a. Creep-atigue analysis assumes a rapid reversal o bending moment o magnitude ΔM var separated by dwell periods o duration Δt when the moment is maintained constant at M = ΔM var / 2 as shown in Fig.2b. Shakedown analysis assumes compound bending moment consisting o variable component o magnitude ΔM var and constant shit o value M const, hereby orming a load space as shown in Fig.2c. The bending moment M is applied through the linear distribution o normal pressure P over the section o plate as shown in Fig. 1b with the area moment o inertia I x in regard to horizontal axis X: 3 P y M y I X with I X a b 12, (1) where the width o plate a = 200 mm, the thickness o plate b = 26 mm, and y is a vertical coordinate o plate section assuming the coordinate origin in the mid-surace. 3. Material models and constants Mechanical properties o the materials composing uciorm weldment manuactured o the steel AISI type 316N(L) include the ollowing material behaviour models and constants at 550 C. The conventional Ramberg-Osgood equation or the cyclic stress-strain curve, showing a smooth elastic-plastic transition, implemented in LMM code or the eep-atigue analysis is ollowing 1/ E B E E 2 2 2 with 3 2(1 ), (2) where Δε is the al strain range; Δσ is the al stress range in MPa; B and β are plastic material constants; E is the eective elastic modulus in MPa deined using the Young s modulus E in MPa and the Poisson s ratio ν = 0.3, which are the elastic properties used in both R-O and EPP models. The dependence o al strain range Δε in % on the number o cycles to pure LCF ailure N* is usually deined by a quadratic polynomial unction [6] or S-N diagrams as ollows
--- 3 --- 2 2 m1 m1 4m2 m0 log log m0 m1 log N m2 log N log N, (3) 2m2 where the coeicients o polynomial (3) deined by itting the R66 endurance curves or parent and weld material o the steel AISI type 316N(L) at 550 C reported in [6] have the ollowing values: m 0p = 1.73339, m 1p = 0.72959, m 2p = 0.06170 and m 0w = 1.85169, m 1w = 0.76094, m 2w = 0.05951. The primary eep strain is desibed by the conventional time hardening orm o power-law model or the Norton-Bailey equation, which has the ollowing uniaxial orm: n m n m1 A t or [ A/( m 1)] t, (4) where is the eep strain, σ is the applied stress in MPa, t is the time in hours; A, n and m are the eep constants identiied by itting Eq.(4) to the primary stage o experimental eep curves [2]. The time to eep rupture t* dependent on stress σ is desibed by the reverse power-law: k t B, (5) where B and k are the eep constants identiied by itting Eq.(5) to the experimental eep rupture data [2, 7]. The whole set o material parameters or dierent weld zones is reported in Tab.1. It should be noted that the constants corresponding to elasticity and saturated cyclic plasticity were taken rom [2]. The constants corresponding to primary eep strain and eep rupture o parent and weld material were identiied employing the least squares method, while those constants or the HAZ were identiied by logarithmic (A, B) and simple (n, m, k) averaging o parent and weld properties. Table 1: Material parameters or the steel AISI type 316N(L) at 550 C itting the experimental data [2, 7] Zone Elastic Saturated cyclic plasticity Primary eep strain Creep rupture E (MPa) B (MPa) β σ y (MPa) n m1 A (MPa h ) n m k B (MPa h) k Parent 160000 1741.96 0.29960 270.662 6.604E-19 5.769-0.55 2.172E+26 8.927 Weld 122000 578.99 0.10162 307.894 6.597E-23 7.596-0.5 5.993E+29 10.61 HAZ 154000 1632.31 0.25304 338.731 6.600E-21 6.683-0.525 1.291E+28 9.768 4. Structural integrity assessments The design limits were evaluated with an elastic-perectly-plastic (EPP) model and a von Mises yield condition using material constants (E, σ y and ν) reported in Tab.1, the history o bending moment according to Fig.2c, and the LMM [8] capable o upper and lower ratchet limit identiication. The limit moment and shakedown limit have the ollowing values respectively: M lim = 10559430 (N mm) and ΔM sh = 13614160 (N mm). The normalised moment is deined as the relation o variable moment range to shakedown limit: M M var / Msh, where Mmax M lim / M sh 1.55124. Hereby, or the M 0.5 1.55124. speciic case o uciorm weldment specimen (see Fig. 1a) the design limits are The corresponding Bree interaction diagram and other details could be ound in [3]. The basic routine o the proposed evaluation procedure or eep-atigue damage assessment o uciorm weldments is the same as o the PNC time raction procedure [9] developed by the Power Reactor and Nuclear Fuel Development Corporation (Ibaraki, Japan). The key dierences between the PNC procedure and the proposed procedure are indicated in [3]. The general concept o the proposed eep-atigue evaluation procedure considering time raction rule or eep-damage assessment is illustrated on Fig.3 and consists o 5 steps. Step 1: Saturated hysteresis loop. This step involves inelastic FEA using LMM in CAE-system ABAQUS incorporating FORTRAN user material subroutine UMAT, which includes implementation o Ramberg-Osgood model (2) and primary eep model (4) with material constants rom Tab.1. The modiication o the original LMM code [1] implemented in this work comprises the conversion rom EPP model to R-O model, which provides more reasonable desiption o stress-strain response. The most important outputs or urther eep-atigue evaluation are Δε, stress σ 1 in the beginning o dwell period and elastic ollow-up actor Z E /. Step 2: Fatigue damage. This step is based upon the Δε identiied in Step 1 and polynomial unction (3) or S-N diagrams characterising LCF properties. The atigue damage accumulated per 1 cycle is calculated using the value o N* derived rom R66 atigue endurance curves [6].
--- 4 --- Step 3: Stress relaxation. This step is based upon the relaxation problem with elastic ollow-up, which has the analytical solution or stress unction in case o time-hardening eep model (4): 1/ 1n m1 d Z d 1n t E A 1 n Z 0 t Z 1 1 and 1 t Z 1,,,,, dt E dt Z m 1 (6) E where Z and σ 1 are taken rom Step 1; A, n and m are eep constants or Eq. (4) rom Tab.1. The average stress over the dwell period Δt is deined numerically as a mean value o the nonintegrable unction ( tz,, 1) on some closed interval t[0 t], as shown in Fig.3. Step 4: Creep damage. This step is based upon the identiied in Step 3 and eep rupture curves (5) characterising eep endurance properties. The eep damage accumulated per 1 cycle is calculated considering time raction rule and using the experimental eep rupture data [2, 7]. Step 5: Creep-atigue interaction. This step is based upon the values o Figure 3: The general concept o eep-atigue evaluation procedure considering time raction rule or eep-damage assessment based on the PNC procedure [9] al atigue eep and damage, where the values o 1c and 1c are taken rom Step 2 and Step 4 respectively. The output o evaluation procedure N (number o cycles to ailure under eep-atigue interaction conditions) is usually deined employing the damage interaction diagrams [10], as shown in Fig.3. The most commonly used types o damage diagrams are desibed in [3, 10]. In the ormulation o this procedure, a novel approach to construct the non-linear damage diagram proposed by Skelton and Gandy [10] assuming eep-atigue and atigue-eep damage interactions was ound the most suitable in combination with time raction rule: a N b N 1 0, a [ ] [ ] 1 1 N ( b b 4 ac) / (2 a), 2 2, 2 2 2 1c 1c 1c 1c 1 where 2 b 1c 1c where the key parameter N is derived by solving the quadratic equation. This diagram provides a reasonable approximation to the well-known ASME bi-linear diagram with intersection o (0.3, 0.3). 5. Validation and extrapolation o results The experimental studies o uciorm weldment [2] have been simulated employing the FEA with the LMM based upon FE-model and loading conditions desibed in Sect.2 and the material models desibed in Sect.3. The outputs o the LMM have been processed by the proposed eep-atigue evaluation procedure desibed in Sect.4. The 5 variants o normalised moment M used in the FEA and their correspondence to Δε in tests are deined numerically as 1.4705 1, 1.1538 0.6, 0.9255 0.4, 0.7774 0.3, 0.691 0.25. The ollowing unction similar to the R-O model (2) is ormulated: p M p M p M (8) 3 1 2, where p 1 = 0.2817, p 2 = 0.17649 and p 3 = 3.11051 are the itting parameters corresponding to the particular geometry o the parent material plate shown in Fig.1a. The complete summary o experimental and corresponding simulation conditions as well as outputs in the orm o number o cycles to ailure N and location o ailure is reported in [3]. The (7)
ratio between the atigue and eep --- 5 --- components o the al damage indicates that with Δt = 1 hour the atigue damage is dominant, whereas when Δt is ineased to 5 hours eep damage becomes dominant. Visual comparison o the observed and predicted N in Fig.4 or 3 variants o dwell period Δt shows that 9 o the 11 simulations accurately predict the experimental results. [6]: [2]: Figure 4: Results o eep-atigue assessment in application to uciorm weldment and comparison with experiments [2] Since the proposed approach is successully validated against experimental data (see Fig.4), it can be used or the ormulation o an analytic assessment model suitable or the ast estimation o N or a variety o loading conditions. The low computational eort required by the LMM compared to other computational techniques makes it possible and relatively easy to extrapolate numerical predictions or loading conditions not captured by the available experiments [2]. This extrapolation comprises the extension o the Δt duration up to 10000 hours and a number o additional FE-simulations with LMM. The whole array o obtained results reported in [3] or the same set o applied M is itted using the least squares method by the ollowing power-law unction or N dependent on arguments M and Δt: bt log N a t M with a t a log t 1 a and b t b log t 1 b, (9) 1 2 1 2 where the independent itting parameters: a 1 = 0.4921, a 2 = 3.708929, b 1 = 0.0255, b 2 = 0.754959. Having deined N by Eq.(9), the residual service lie in years is thereore dependent on the duration o 1 cycle, which consists o dwell period Δt and relatively short time o deormation: L N t / (365 24) 2 ( M ) / ( 365 24 60 60), (10) where the unction or ( M ) is taken in the orm (8). The engineering parameters N and L characterising eep-atigue durability have the key importance or design applications. For ease o use, both parameters determined by Eqs (9) and (10) respectively can be represented in the orm o a design contour plot, illustrated and discussed in [3]. According to the classiication in R5 Volume 2/3 [5, 6] and manuacturing procedure [2], the uciorm weldment belongs to the Type 2 (Dressed). Weldments are considered to be composed o parent material and the dierence in Δε o the weldment compared to the parent material is taken into account by using a Fatigue Strength Reduction Factor (FSRF). The variety o FSRFs or the uciorm weldment obtained in previous works is reported in [3]. However, all these values do not take into account the inluence o the dwell Δt duration and, thereore, eep on atigue endurance reduction. This limitation is eliminated by the application o the analytic model (9), which is transormed using Eq.(8) into the conventional orm or o S-N diagrams similar to Eq.(3): parent 1/ bt p3 / bt ( N ) p 1 a( t) log( N ) p 2 a( t) log( N ) FSRF x-weld ( N, t), (11) where the S-N diagram or parent material plate is deined by Eq.(3) with the ollowing polynomial coeicients reerring to [6]: m 0 = 2.2274, m 1 = 0.94691 and m 2 = 0.085943.
--- 6 --- Figure 5: Dependence o FSRF on duration o dwell Δt Figure 6: Comparison o the observed and predicted N The resultant dependence o FSRFs on duration o Δt is illustrated in Fig.5, which shows signiicant enhancement o FSRF or Δt > 1 hour caused by eep. For pure atigue FSRF min = 1.69, FSRF max = 2.06 and average FSRF = 1.77. Dependence o FSRF on Δt can be itted as ollows: 2 3 FSRF( t) 0 1 log( t 1) 2 log( t 1) 3 log( t 1), (12) where the itting parameters are 0 =1.7685, 1 = 0.53422, 2 = 0.00574 and 3 = 0.02509. 6. Conclusions Comparison o the observed and predicted N with the proposed LMM-based approach or 3 types o experiments shows that simulation o 9 o 11 ally available tests is very close to the line o optimal match, as shown in Fig.6. Simulation o the other 2 experiments produces non-conservative results with an inaccuracy actor equal to 1.6, which is avourable compared to the actor o 2 allowable or engineering analysis. The proposed unction or FSRF depending on dwell time Δt (12) or Type 2 (Dressed) weldments and shown in Fig.5 allows to improve design techniques e.g. in R5 Procedure [5] by considering the signiicant inluence o eep. Reerences [1] Chen, H.F., Chen, W., Ure, J. Linear matching method on the evaluation o cyclic behaviour with eep eect. // Proc. ASME Pressure Vessels & Piping Con. (PVP2012-78065). Toronto, Canada: ASME; 2012, July 15-19. [2] Bretherton, I., Knowles, G., Hayes, J.-P., Bate, S.K., Austin, C.J. PC/AGR/5087: Final report on the atigue and eep-atigue behaviour o welded uciorm joints. // Report or British Energy Generation Ltd no. RJCB/RD01186/R01; Serco Assurance; Warrington, UK; 2004. [3] Gorash, Y., Chen, H.F. Creep-atigue lie assessment o uciorm weldments using the linear matching method. // Int. J. Press. Vess. Piping, 2012; 14 p., under review. [4] Ponter, A.R.S., Chen, H.F. Modeling o the behavior o a welded joint subjected to reverse bending moment at high temperature. // J. Press. Vess. Technol., 2007; 129(2): 254-261. [5] Ainsworth, R.A., editor. R5: An Assessment Procedure or the High Temperature Response o Structures. Procedure R5: Issue 3. // British Energy Generation Ltd, Gloucester, UK; 2003. [6] Bate, S.K., Hayes, J.-P., Hooton, D.G., Smith, N.G. Further analyses to validate the R5 volume 2/3 procedure or the assessment o austenitic weldments. // Report or British Energy Generation Ltd no. SA/EIG/11890/R002; Serco Assurance; Warrington, UK; 2005. [7] NIMS Creep Data Sheet No. 45A; National Institute or Materials Science; Tsukuba, Japan; 2005. [8] Chen, H.F. Lower and upper bound shakedown analysis o structures with temperature-dependent yield stress. // J. Press. Vess. Technol., 2010; 132(1): 011202:1-8. [9] Wada, Y., Aoto, K., Ueno, F. Creep-atigue evaluation method or type 304 and 316FR SS. // Creep-atigue damage rules or advanced ast reactor design. Vienna: IAEA; 1997, p. 75-86. [10] Skelton, R.P., Gandy, D. Creep-atigue damage accumulation and interaction diagram based on metallographic interpretation o mechanisms. // Mater. High Temp., 2008; 25(1): 27 54.