A J estimation scheme for surface cracks in piping welds

Transcription

1 2th International Conference on Structural Mechanics in Reactor Technology (SMiRT 2) Esoo, Finland, August 9-14, 29 SMiRT 2-Division II, Paer 1672 A J estimation scheme for surface cracks in iing welds Stéhane Marie 1, Patrick Le Delliou 2, Yann Kayser 1, Bruno Barthelet 3, Philie Gilles 4, Hubert Deschanels 5 1 Commissariat à l Energie Atomique (CEA) CEA, DEN, DM2S, SEMT, LISN, F Gif sur Yvette, France. 2 EDF R&D, Déartement MMC, Les Renardières, Moret s/loing Cedex, France 3 EDF Industry, Nuclear Power Oerations, Site Ca Amère, St Denis Cedex, France 4 AREVA NP, Tour AREVA, 9284 Paris La Défense Cedex 16, France 5 AREVA NP, 1 rue Juliette Récamier, Lyon Cedex 6, France Keyword : J integral, weld, analytical method The RSE-M and RCC-MR Codes rovide resectively rules and requirements for in-service insection of French Pressurized Water Reactor ower lants and for the design of high temerature nuclear comonent. The Code give non mandatory guidance for analytical evaluation of flaws (Aendices 5.3 and 5.4 for RSE-M and Aendix A16 for RCC-MR). Flaw assessment rocedures rely on fracture mechanics analyses based on simlified methods (i.e. analytical). Analytical methods are available to calculate the J integral in various cracked iing comonents (straight ie, taered transition, elbow and ie-to-elbow junction), submitted to mechanical loading (axial, in/out of lane bending moment, torsion moment, ressure), thermal loading as well as for combined loading. However, for the analysis of cracks in welds, they use the tensile roerties of the weakest material between the base material and the weld material. This induces some conservatism on the estimated J values. A cooerative rogram between EDF, CEA and AREVA NP was launched in 24 to develo a J estimation scheme which takes into account the strength mismatch effects. The scheme relies on the definition of an equivalent stress-lastic strain curve, as roosed in the R6 rule. This curve is then used with the analytical methods for homogeneous cracked comonents. In a first ste, the method is develoed for circumferential surface cracks in straight butt-welded ies submitted to mechanical loading. It takes into account the geometry of the weld joint (V-shaed), as well as the location of the crack within the weld. This aer recalls the background of the method, rovides the detailed formulae needed to aly the J- estimation scheme and finally resents the validation work, based on a large finite element database. 1. Introduction The RSE-M Code rovides rules and requirements for in-service insection of French Pressurized Water Reactor ower lant comonents. The RCC-MR is the French standard for the design of high temerature nuclear comonents. It has also been extended to the vacuum vessel of the ITER roject. Aendices 5.3 and 5.4 of the RSE-M code and Aendix A16 of the RCC-MR give non mandatory guidance for analytical evaluation of flaws, i.e. fracture mechanics analyses based on simlified methods. Analytical methods are rovided to calculate the J integral in various cracked iing comonents (straight ie, taered transition, elbow and ie-to-elbow junction) submitted to mechanical loading (in-lane bending moment, ressure, torsion moment), thermal loading, and combined loading (Marie and al., 27). However, for the analysis of cracks in welds, they use the tensile roerties of the weakest material between the base material and the weld material. This induces some conservatism on the estimated J values under mechanical loadings. A cooerative rogram between EDF, CEA and AREVA NP was launched in 24 to develo a J estimation scheme which takes into account the strength mismatch effects. In a first ste, the method is develoed for circumferential surface cracks in straight butt-welded ies submitted to mechanical loading. It takes into account the geometry of the weld joint (V-shaed), as well as the location of the crack within the weld. This aer resents the current state of develoment of this J estimationscheme.

2 2. Hyotheses and background The weld model considered is an idealized bi-material structure without HAZ (heat affected zone) and residual stresses. The two materials (weld and base) have the same elastic modulus, E and Poisson s ratio ν. The term mismatch refers here to the two materials having different stress-strain relationshis. The method is first develoed for a circumferential surface crack (either axi-symmetrical or semi-ellitical) in a straight butt-welded ie (V-shaed joint). t Loc. 3 φ r i r m Loc. 4 2h Loc. 1 Loc. 2 Figure 1 Weld geometry and crack location. The geometry of the weld is defined by the width of the root 2h i and the sloe of the groove φ w. Four crack locations are investigated (see figure 1). Currently, most of the work has been devoted to location #1 (centered crack).the methodology used in this aer is based on the R6 equivalent stressstrain curve aroach. This stress-strain curve is the one which gives the same J values as the mismatch weld case. This aroach was first develoed by Lei and Ainsworth (1997) for a CCT secimen. It consists in calculating an equivalent stress-strain curve from the base material and the weld stress-strain curves, using the limit load of the all-base material structure F Lb and the limit load of the mismatched structure F Lmis. The calculation has to be made at different levels of lastic strain on the stress-lastic strain curve. For each value, a local mismatch ratio and equivalent stress are defined as follow (see Figure 2) : M " w ( ) ( ) = and ( ) " ( ) ( ) ( ) ( ) ( ) FLmis / FLb 1 # w " + M FLmis / FLb # b " e " = M 1 b # (1) F Lmis has to be evaluated for the articular local mismatch ratio M. This equivalent stress-strain curve is then used in an homogeneous R6 Otion 2 analysis. However, considering first that the determination of the mismatch limit load is a difficult task, and secondly that the limit load ratio F Lmis /F Lb is not necessarily the arameter giving the best J-estimate, a slightly different definition was used for the equivalent stress-lastic strain curve: ( ) ( $ ( M) 1) # w( " ) + ( M $ ( M )# b( " ) " = # e with α(m) to be determined (3) M 1 Stress " (MPa) " yw " ye " yb Weld material Base material Equivalent material " w(2%) " e(2%) " b(2%) " w(9%) " e(9%) " b(9%) 2 1,2,4,6,8,1,12.2% Plastic strain, Figure 2 Definition of the mismatch ratio and of the equivalent stress-lastic strain curve

3 3. Develoment of the J-estimation scheme The aim of the work is to exress α(m) as a function of the mismatch ratio M and the geometrical arameters relative to the ie, the crack and the weld joint. Obviously, α(m) deends also on the tye of loading and the location of the crack within the weld. F.E. Data base First, a very large finite element database was built by CEA and EDF, including semi-ellitical and axi-symmetrical defects. The following arameters were investigated: relative ie wall thickness (r m /t = 5 or 1), relative size of the weld root 2*h i /t = 1/6 and sloe of the weld groove : φ w = 6. relative crack deth (a/t = 1/16 ; 1/4) and asect ratio (a/c = 1 or 1/3) for semi-ellitical defects For axi-symmetrical cracks, the loading tyes were the axial tensile load N 1 and the ressure P whereas for semi-ellitical cracks in-lane bending moment M 2 was added. Some cases of combined loading (P lus N 1 and P lus M 2 ) were studied. Two tyes of stress-strain relationshis were used: the Ramberg-Osgood tye and the bilinear tye. A Ramberg-Osgood stress-strain curve is defined by the following equation: n ' ' & ' E E # = + ( $ % ' " ) (4) A bilinear stress-strain curve is defined by two equations: " = if " (5) # E 1 # = + ( " ) if " the roortionality limit, E T tangent modulus E E " T Table 1 gives the values of the arameters for the R.O. (AR tye) and bilinear (AL tye) descrition of base material curve and the weld material curves. Table 1 Values of the arameters for the R.O. and bilinear stress-strain curves Curve label Μ σ (MPa) α n AR AR AR Curve label Μ σ (MPa) E T (MPa) AL AL AL A total of 198 2D and 28 3D cases have been considered for the determination of α(m). To validate the F.E. calculations, a benchmark was erformed between the three artners AREVA, CEA and EDF on about ten reresentative cases. Each artner used its own F.E. software. This first ste in the F.E. data base develoment was essential to comfort the confidence we have in our F.E. results. Analysis of the F.E. results From the F.E. calculations available in the data base, following imortant results are observed: For ressure loading, no noticeable mismatch effect is obtained: a comarable J estimation is given by the homogeneous calculation, considering the characteristics of the base metal. This means that for ressure loading, α(m) = 1 for all defect tyes, sizes and locations. For other mechanical loadings, for a given defect tye and size, the calculated J for location #1 and location #2 (see figure 1) are similar. For location #3, only a small reduction of the J values is observed with the mismatched configurations, so an homogeneous analysis using the base material stress-strain curve is aroriate (α(m) = 1), For location #4, secific (and lower) α(m) functions have to be develoed, as the effect of the base material is more significant than for location #1.

4 α(m) has then been determined only for N 1 or M 2 loadings, for defects at the locations #1 and #4. α(m) of the reference weld geometry In a first ste, the method was established for a articular ( reference ) weld geometry: 2*h i /t = 1/6 and φ w = 6. For each defect geometry and loading condition, to estimate α(m), an additional set of FE calculations was built, using Ramberg-Osgood stress-strain curves with a weld material having the same value of the exonent n than the base material (n = 6) and several values of the mismatch ratio ( ). These curves have a constant local mismatch ratio M(ε ) = M, whatever the value of the lastic strain. For each case, the arameter α(m) is otimized to have a F.E. J variation versus the imosed load calculated with the equivalent material similar to the variation obtained with the bimaterial F.E. calculation. In other words, the value of α(m) is the value which minimizes the relative error between the value of J given by the FE calculation considering an homogenous comonent with the equivalent material and the value of J given by the FE calculation considering the real weld joint. For the whole set of calculations, the values of α(m) are lotted in a diagram as a function of M. Figure 3 shows an examle of such a diagram, for an axi-symmetrical crack in a ie with r m /t = 1 loaded in tension. Finally, these values are fitted by a quadratic function of M, whose coefficients deend on the geometry of the ie (r m /t ratio) and of the crack (a/t ratio) : ( ' % & t a $ # ( 1) 2 ( M ) = 1+ % a + a + a "( Min( M ; 2.5) 1) + % b + b + b " [ Min( M ; 2.5) ] " % " rm t rm t ' & Moreover, this function equals 1 for M = 1 and M is uer-bounded to 2.5. The values of the coefficients a 1 to b 3 are given in Table 2 for an axi-symmetrical crack loaded in tension. Table 2 α(m) for an axi-symmetrical crack in tension. Values of the coefficients of the function t a $ # Axi-symmetrical crack location #1 Tension loading a b a b a b For the semi-ellitical cracks, the function α(m) deends also on the a/c ratio. The values of the coefficients a 1 to b 4 are given in Table 3 and Table 4 for a semi-ellitical crack loaded in tension and in bending resectively. ' t a a $ ' t a a $ 2 ( M ) = 1+ % a1 + a2 + a3 + a4 "( Min( M ; 2.5) 1) + % b1 + b2 + b3 + b4 "([ Min( M ; 2.5) ] 1) & rm t c # & rm t c # Table 3 α(m) for a semi-ellitical crack in tension. Values of the coefficients of the function Semi-ellitical crack location #1 Tension loading a b a b a b a b Table 4 α(m) for a semi-ellitical crack in bending. Values of the coefficients of the function Semi-ellitical crack location #1 Bending load a b a b a b a b 4.417

5 It should be noted that for the semi-ellitical cracks, the function is valid only for the deeest oint of the crack, which corresond to the highest values of J along the crack front in the considered cases. Pie Rm/t = 1 - Axi-symmetrical crack - location #1 - Axial tensile load alha(m) versus M alha(m) 1,6 1,5 1,4 1,3 a/t = 1/4 n = 6 a/t = 1/4 n = 1 function for a/t = 1/4 a/t = 1/16 n = 6 a/t = 1/16 n = 1 function for a/t = 1/16 1,2 1, ,25 1,5 1,75 2 2,25 2,5 Mismatch ratio M Figure 3 α(m) as a function of M for an axi-symmetrical crack loaded in tension. Other weld geometries 6 Pie Rm/t = 5 - semi-ellitical crack a/t = 1/8 - a/c = 1 loc. #1 Materials b/w AR1/AR23 - Elastic-lastic calculation - Axial load J deeest oint (kj/m2) Phiw = 6-2hi/t = 1/15 Phiw = 6-2hi/t = 1/6 Phiw = 6-2hi/t = 1/3 Phiw = 75-2hi/t = 1/15 Phiw = 75-2hi/t = 1/6 Phiw = 75-2hi/t = 1/3 Phiw = 9-2hi/t = 1/15 Phiw = 9-2hi/t = 1/6 Phiw = 9-2hi/t = 1/3 homogenous - AR Axial load N1 (MN) Figure 4 J at the deeest oint as a function of N 1 for a semi-ellitical crack. As shown on Figure 4, the geometry of the weld has a strong effect on the J value. For a given alied load, the value of J increases when the weld joint becomes narrower or/and when the sloe of the groove φ w increases. To extend the solution to other weld geometries, 48 additional F.E. calculations of ie with an internal axi-symmetrical defect at location #1 under N 1 loading have been realized with new geometrical arameters (bold data corresond to new values): relative ie wall thickness r m /t = 5, relative crack deth (a/t = 1/16 ;1/8 ; 1/4), relative size of the weld root (2*h i /t = 1/15 ; 1/6 ; 1/3), sloe of the weld groove (φ w = 6 ; 75 ; 9 ). Only ower-law material roerties are considered here. These new geometrical arameters have been chosen to cover a large anel of realistic weld joint configurations. Two corrections of the roosed α(m) solution are considered: a root width correction and a weld groove sloe one. The weld root width correction comes from Kim solution [4] for a CCT secimen with a constant weld width (φ w = 9 ) for the over-matching case: $ M if & % & % F ( %) 1 Lmis M, = # ' % 24(M 1) 1 M + 24 with ( M 1) / 5 t a " F + if % & % 1 = e and " =, Lb 1 h(a) " 25 % 25

6 where h ( a) h + a Tan( " ) = i 9 w is the half-width of the weld joint as the ti of the crack. The weld groove sloe correction is directly deduced from FE results for axi-symmetrical cracks under axial load. The correction was otimized to rovide the best tensile curve which leads to a J(N 1 ) curve with a FE calculation considering a homogeneous comonent similar to the curve obtained from bimaterial FE calculation. Table 5 local most severe under-estimation of J for ies with a axi-symmetrical defect under N 1 loading, for ower-law materials and average mismatch ratios (from σ y ratio) of 1.5 and 2.3 φ w ( ) t/a 2hi (mm) M 1.5 (%) M 2.3 (%) The extended solution α(m) is deduced from the reference weld joint solution α ref (M): & ( M) = MAX$ 1; $ % reference F (M)/ F L L,ref ( a / t, h / t, - )/ i w, *, 5. max(; / * * w ) ), 5. max(; - ' +.8/ * ( + 4 w 2 ) ) )# ' ' ( ' ( " The identification of the groove sloe correction was erformed searching an average good estimation of the reference FE values (with a reasonable conservatism), with limited local under-estimation. Table 6 resents for each case the local most severe under-estimation of J with this correction. Figure 5 shows some reresentative results. This extended solution determined for an axi-symmetrical defect is directly alied for a semi-ellitical defect assuming that: - the defect tye and loading tye influences are mainly taken into account in the α(m) equation, - the welded CCT (Centre Crack Tension) secimen limit load Kim s solution is still valid to account for the weld joint geometry effect.

7 8 FE bi-material calculation FE calculation with equivalent material tensile curve 4 16 FE bi-material calculation FE calculation with equivalent material tensile curve 8 7 Error 3 14 Error 7 J (kj/m_) Error (%) J (kj/m_) rm/t = 5 t/a = 4 2hi = 1 mm = 75 R.O Error (%) rm/t = 5 t/a = 16 2hi = 4 mm = 9 R.O E+ 5.E+6 1.E+7 1.5E+7 2.E+7 2.5E+7 3.E+7 N1 (N).E+ 5.E+6 1.E+7 1.5E+7 2.E+7 2.5E+7 N1 (N) Figure 5 FE results: Comarison between bimaterial case and homogeneous case with the equivalent material tensile curve ie with an axi-symmetrical defect under N 1 loading. To check the relevance of this direct transosition, 216 additional cases of ie with semi-ellitical defect under N 1 ou M 2 loading were erformed. For each case, two 3D FE calculation are erformed: one for the bi-material model, and one for the homogeneous comonent with the equivalent material tensile curve deduced from the roosed correction. The geometric arameters considered here are: for the ie: relative ie wall thickness r m /t = 5,, relative size of the weld root (2*h i /t = 1/15 ; 1/6 ; 1/3), sloe of the weld groove (σ w = 6 ; 75 ; 9 ). for the defect: relative crack deth (a/t = 1/16 ;1/8 ; 1/4), and rack asect ratio (a/c = 1 or 1/3) for semi-ellitical defects For each case, a good agreement was found between the bi-material calculation and the equivalent material analysis considering the roosed generalization. The equivalent material analysis gives a comarable or conservative estimation of J. No imortant local under-estimation is found. It confirms the relevance of the roosed generalization. Figures 6 and 7 resent relevant curves for ies with a semi-ellitical defect under resectively N 1 and M 2 loading FE bi-material calculation FE calculation with equivalent material tensile curve 2 FE bi-material calculation FE calculation with equivalent material tensile curve 3 J (kj/m_) r m/t = 5 c/a = 1 t/a = 8 2h i = 4 mm = 75 R.O. 1.5 J (kj/m_) rm/t = 5 c/a = 1 t/a = 16 2hi = 1 mm = 75 R.O. 1.5.E+ 5.E+6 1.E+7 1.5E+7 2.E+7 2.5E+7 3.E+7 N1 (N).E+ 1.E+9 2.E+9 3.E+9 4.E+9 5.E+9 6.E+9 M2 (N.mm) Figure 6 FE results: Comarison between bimaterial case and homogeneous case with the equivalent material tensile curve ie with a semi-ellitical defect under N 1 loading.

8 3 FE bi-material calculation 25 FE calculation with equivalent material tensile curve J (kj/m_) rm/t = 5 c/a = 3 t/a = 8 2hi = 1 mm = 75 R.O. 2.3.E+ 1.E+9 2.E+9 3.E+9 4.E+9 5.E+9 M2 (N.mm) Figure 7 FE results: Comarison between bimaterial case and homogeneous case with the equivalent material tensile curve ie with a semi-ellitical defect under M 2 loading 4. Cases of combined loading Considering that α(m) exression deends on loading nature, it is not ossible to aly directly revious analytical roosal to combined load. To define a unique equivalent material in such analysis, it is roosed to follow the stes described below: Determination of the amlification coefficients α i at elastic limit (α i M(.2%)) for each art of the combined load (internal ressure P, axial load N 1, global bending M 2 ) Definition of an equivalent material based on the maximal value of α i reviously determined: = Max = ; { 1 ; N1 M 2 } Alication of CEP/CLC method using modified load P, N 1 and M 2 for σ ref determination (K I estimation with un-modified P, N 1, and M 2 values) given by: ' ' ' P =. P N1 =. N1 M 2 =. M with = Max { } ; ; = N for M(.2%) M N 1 M 2 The validation has been erformed thanks 2D finite element calculations on axi-symmetrical configurations, considering circumferential defect in the middle of the weld (i.e. location 1 in 3) submitted to internal ressure P and axial loading N 1. For each case, 4 calculations were required: one taking into account base and weld material, one using only base metal, one using N 1 equivalent material without correction on the ressure load, and the last one using axial load equivalent material with a correction on internal ressure. Figure 8 resents the imact of the correction on ressure load in the error generated by the alication of the method. On the whole cases considered the redictions with the correction give good results: in most configuration under-estimation has disaear (see blue and green curves) and over-estimation are relatively limited. Difference (%) Mean error - with correction on ressure load Mean error - without correction on ressure load (a-) - with correction on ressure load (a-) - without correction on ressure load Configuration number Figure 8 - Comarison of rediction given by homogeneous analysis, equivalent based on N 1, with or without roosal ressure load correction. a - is the local worst under-estimation

9 5. Bilinear material Previous study showed that the methodology resented in this aer may give bad results for bilinear metal behaviour at the beginning of lasticity. It has been roosed to modify the beginning of the equivalent stress/strain curve in order to have a smoother transition in this zone. 6 finite element comutations (axi-symmetrical configuration, location #1) have been erformed (t/a={4;8;16,}r m /t={5;1}, φ={6 ; 7 ; 9 } and M={1.5;2.3}) in order to choose between 3 modification schemes. At the end, the one which gives the best results consists in of ower law with exonent.25 u to.6% of deformation: ( & ' corr ) 1 [ ( M(.6) ) 1].6 # * ' = + * ) ( $ % " Figure 9 resents the mean errors (A + +A - ) generated by the alication of the three roosed modifications. The final one (blue curve) was selected because the global mean error is the weakest and the number of local under-estimation (a - ) is very limited (see the extreme cases on figure 9)..25 $ corr ( ) = 1+ Extreme cases : h=4mm, t/a = 16mm Phi = 9 & 75 M = 2.3 J~15 kj/m² [ $ ( M(.6) )# 1] ".6 A + + A - (%) a - (%) $ corr ( ) = 1+ [ $ ( M(.1) )# 1] " ( & ' 1 corr ) 1 [ ( M(.6) ) 1].6 # * ' = + * ) ( $ % " N du cas N du cas Figure 9 Effect of the modifications roosed to deal with bilinear stress/strain curves In order to kee a method without any deendency on the stress/strain curve form, it is roosed to aly this correction even if metal behaviour can be fitted by Ramberg-Osgood law. The effect of this extension of the bilinear correction to R.O. curves has been checked on the revious 6 finite element calculations considering R.O. materials. Figure 1 shows that the consequences are limited; mean errors increase of almost 8% and the few local under-estimation are reduced. The roosal aears satisfactory. 12 Difference value (%) Mean error - Modified stress/strain curve Mean error - Stress/strain curve without modification (a-) - with modification (a-) - without modification Configuration number

10 Figure 1 Effect of the extension of the stress/strain curve correction on R.O. behaviour 6. Conclusion Aendix 5.4 of the RSE-M Code and Aendix A16 of the RCC-MR give non mandatory guidance for analytical evaluation of flaws, i.e. fracture mechanics analyses based on simlified methods, including evaluation of elastic stresses, stress intensity factors and the J-integral. For the analysis of cracks in welds, the resent methods use the tensile roerties of the weakest material between the base material and the weld material. This induces some conservatism on the estimated J values. A J-estimation scheme for cracks in welds was develoed, to take benefit of the mismatch between the tensile roerties of the weld material and those of the base material. This estimation scheme uses an equivalent stress-strain curve interolated from the base material and the weld stress-strain curves. Exlicit exressions of the weighing function called α(m) where M is the local mismatch ratio are given for an axi-symmetrical or a semi-ellitical crack in a straight ie loaded in axial tension or in bending. These exressions take into account the geometry of the weld joint (width of the root and sloe of the groove). Presently, they are available only for centered cracks at the ie inner surface. The validation is based on a large finite element database, comrising Ramberg-Osgood and bilinear stress-strain curves. Thanks to this equivalent tensile curve, more accurate estimation of J for cracked welds is ossible using analytical solutions develoed for homogeneous comonents (Le Delliou and al., 24 ; Marie and al., 27). Most recent work ermitted to take into account combined loading and bilinear materials in order to rovide good estimation of J at the earliest stage of lasticity. REFERENCES RCC-MR Code, 27 Edition, Design and Construction Rules for Mechanical Comonents of FBR Nuclear Islands and high temerature alications Aendix A16, vol. Z, Paris, AFCEN, Paris. RSE-M Code, 1997 Edition, 2 and 25 Addenda, "Rules for In-service Insection of Nuclear Power Plant Comonents", AFCEN, Paris R6 Revision 4: "Assessment of the Integrity of Structures containing Defects", Section III.8 "Allowance for strength mis-match effects" Kim, Y.-J., Schwalbe K.-H., and Ainsworth, R.A., 21, "Simlified J-estimations based on the Engineering Treatment Model for homogeneous and mismatched structures", Engng. Fract. Mech., Vol. 68, Kim, Y.-J., and Schwalbe K.-H., 21, "Mismatch effect on lastic yield loads in idealized weldments I. weld centre cracks", Engng. Fract. Mech., Vol. 68, Le Delliou, P., and al., 24, "Overview of flaw assessment methods in the RSE-M Code", Proc. ASME PVP Conference, Vol. 481, Lei, Y., and Ainsworth, R.A., 1997, "A J integral estimation method for cracks in welds with mismatched mechanical roerties", Int. J. Pres. Ves. & Piing, Vol. 7, Marie, S. and al., 27, "French RSE-M and RCC-MR code aendices for flaw analysis: Presentation of the fracture arameters calculation Parts I to V", Int. J. Pres. Ves. & Piing, Vol. 84, Marie, S and al, 28, Analytical method for the calculation of J arameter for surface cracks in iing welds, ASME PVP conference, Chicago, aer PVP