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Procedía Engineering 130 (2015) 930 - 947
Procedía Engineering
www.elsevier.com/locate/procedia
14th International Conference on Pressure Vessel Technology
More on Mixed Mode Cracking and Integrity Assessment of a Dissimilar Metal Weld for Ageing Nuclear Power Piping
L.F. Zenga *, C.P. Luob, L.G. Janssona
aÄF-Industry AB, 401 51 Göteborg, Sweden bEDRMEDESO AB, 412 50 Göteborg, Sweden
Abstract
This paper addresses a mixed mode driven cracking and relevant integrity assessment for applications in aging nuclear power
facilities. Following our earlier discussion on the use of mode-I based criteria in the current practice using R6-method, linear and
non-linear finite element analyses of a full-scale laboratory test, a Benchmark four-point bending test of a straight pipe with an
obliquely inserted crack in a dissimilar metal weld of ferritic steel (A508), austenitic steel (316L), weld material (308L) and
buttering material (309L/308L), is conducted. The behavior of the crack front at the load level, at which the crack initiation is
observed in the test, are computed and examined. Computed results confirm our earlier observation: For cases when mixed mode
loading conditions are significant, it is not conservative to use a purely mode-I based criterion for the fracture failure assessment,
refined approaches using J-integral or others must be used in order to achieve a reliable assessment.
©2015 The Authors.PublishedbyElsevierLtd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.Org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of ICPVT-14
Keywords: Crack; mixed mode; integrity; dissimilar material; non-linear finite element.
1. INTRODUCTION
Defect tolerance analyses for the integrity assessment of structures containing cracks or crack-like defects are generally conducted under the assumption of mode I loading conditions. Among various applications, a recommendation issued by the Swedish Radiation Safety Authority and its corresponding software (ProSACC) for the safety assessment of nuclear power facilities [1], such piping, reactor vessel and its internal components, is a
* Corresponding author. Tel.: +46 10 505 3264. E-mail address: lingfu.zeng@afconsult.com
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.Org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of ICPVT-14
doi: 10.1016/j.proeng.2015.12.244
typical case which is entirely based on a mode I based criterion for fracture failure. In this recommendation, the so-called R6-method developed by the British Central Electricity Generating Board (CEGB) [2] is applied and the failure assessment is made through the use of a general Failure Assessment Diagram (Option 1) of the R6-method. The basic assumption behind this methodology is that material damage initiated by a crack or flaw can be entirely described by two variables: a fracture failure variable Kr which is a measure of proximity to the failure of Linear Elastic Fracture Mechanics (LEFM), and a plastic failure variable Lr which is a measure of proximity to the failure ofplasticity. The fracture failure variable Kr is purely defined in term ofthe mode I cracking:
K p + KI
K„„
where Kp and K is the stress intensity factor for the primary (dead weight, external mechanical loads e.g. earthquake) and the secondary (e.g. thermal) stresses, respectively, Kcr is a critical stress intensity factor which practically sets to the mode I fracture toughness Kic, and p is a parameter for accounting the plastic effects caused by the interaction of primary and secondary stresses. The plastic failure variable Lr is defined as the ratio between the applied (primary) load (FAppited) and the corresponding limit load for the cracked structure under consideration
('FLimit),
Applied
Given a loading state described by a point (Kr, Lr), the assessment is to check if this point is located in the non-critical region as illustrated in Fig. 1 and the fracture failure will occur if this point found outside the non-critical region.
This recommendation is practical and provides numerous conveniences for defect tolerance analyses for cases for which geometries are typically simple, loading conditions are dominated by the mode I and analytical solutions to the stress intensity factors Ki are available in literature.
T i i I I I T
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Lr
Fig. 1. The failure assessment Kr-Lr diagram recommended by the Swedish Radiation Safety Authority [1].
There are, however, uncertainties for complicated situations appeared in most practical applications [3,4,5]. One of the most uncertain issues is the use of the mode I cracking assumption in this procedure. It is employed simply due to the unavailability of a thorough understanding of a detailed knowledge of the mixed mode driven failure mechanism, as indicated in Ref. 2, when the R6-method was developed in 1988. It has been observed for decades [2,6-12] that for cases which the crack-tip behavior is typically driven by a mixed mode condition, it is not conservative if the fracture failure assessment is made through simply using mode I based criteria.
There are several reasons why the assumption of pure mode I cracking can be accepted in the assessment of fracture failure for applications in safety-related nuclear power facilities. In addition to those mentioned in the report,
1.e. the lack of in-depth understanding of the failure mechanisms and sufficient toughness test data under mixed mode loadings and so forth, the large safety margin existing in the relevant design codes, for example, the ASME Boiler and Pressure Vessel Code [13], is possible the most responsible one as a large conservatism does naturally "compensate" a large amount of uncertainties and inaccuracies appeared in the evaluation of the fracture variable. It is, however, of great importance to realize that a mixed mode cracking occurs in most practical situations when complex loading and dissimilar materials are under consideration, and it is not conservative to treat such problems as a pure mode I cracking and to purely use mode I based criteria for a fracture assessment. For such cases, enhancements or corrections are necessary to ensure a reliable assessment. For typical mixed mode driven cracks, a reliable assessment can only be achieved through an accurate evaluation of both the driving force and resistance parameters under the mixed loading condition.
Zeng et al [14] examined recently analytic solutions to the crack-tip behavior for cases when the crack propagates straight-ahead (Mode I cracking) and in a kinked direction (Mixed mode cracking) and showed that for cases involving complex loadings or dissimilar materials, the energy release rate for a straight-ahead growth can be much less than that for a kinked growth. In this work, the most-known example of mixed mode cracking, namely, a plate with an angled crack, is investigated, and two concluding remarks are made: (1) it is not conservative if the assessment is made through using purely mode I based criteria, and (2) J-integral or other empirically based approaches, e.g. the "effective stress intensity factor", must be used in order to achieve a reliable assessment. Following this work, aiming at understanding the behavior of cracked dissimilar metal welds in aging nuclear power piping facilities, Zeng et al [15] analysed a full-scale laboratory test conducted jointly by French EDF and FRAMATOME-ANP (now AREVA), Finnish VTT, British TWI and several others for European Atomic Energy Community (EU Fifth Framework Program, 1998-2002) [16]. The test is a Benchmark four-point bending test of a straight pipe with an obliquely inserted crack in a dissimilar metal weld of ferritic steel (A508), austenitic steel (316L), weld material (308L) and buttering material (309L/308L).
This paper continues the analysis of this test. Non-linear finite element analysis using a Ramberg-Osgood's plasticity model is conducted and the behavior of the crack front at the load level, at which the crack initiation is observed in the test, e.g. J-integrals and other relevant parameters along the crack front, are computed and analyzed. Our purpose is to use the finite element analysis to understand the behavior of the crack front at the on-set of the crack initiation and to gain an in-depth understanding of the fracture assessments.
2. THE CRACKED DISSIMILAR METAL WELD AND THE FULL-SCALE TEST
This paper continues the analysis of this test. Non-linear finite element analysis using a Ramberg-Osgood's plasticity model is conducted and the behavior of the crack front at the load level, at which the crack initiation is observed in the test, e.g. J-integrals and other relevant parameters along the crack front, are computed and analyzed. Our purpose is to use the finite element analysis to understand the behavior of the crack front at the on-set of the crack initiation and to gain an in-depth understanding of the fracture assessments.
The dissimilar metal weld (DMW) was specially designed and fabricated to fully represent a 16" diameter girth weld connecting the pressuriser to the surge pipe line of a French N4 nuclear plant in accordance with French basic nuclear specifications for all relevant technical requirements. All technical details for material, welding, defect insertion, test set-up and so forth are described in Ref. 16 and references therein. Below, an overview is given.
Fig. 2. The technical details of the dissimilar metal weld (geometry, dimension and materials etc) [16].
Crack-fro
■rteiSliw
(Crack-tip radius: 0.4 mm)
Fig. 3. The sketch of the insertion of the defect (The maximum depth: about one-third of the wall thickness) into the DMW (upper) and its shape (lower) [16]. (We note that the crack-tip radius seems to be smaller than 0.4 mm originally given in Ref.16).
The parent pipe materials are on one side a forged low alloy steel (SA508 C13) and on the other part a forged stainless steel (316L). The two-layer buttering is done with 308 L and 309 L filler metal and the weld with 308 L filler metal (more than 90 weld passes). The overall dimension for the DMW is: 1040 mm length, 51 mm wall thickness and 453 mm outer diameter. See Fig 2. The defect, for which the maximum depth is about one-third of the wall-thickness and the crack-tip radius is about 0.4 mm, is inserted through a specially designed manufacturing
procedure to the buttering material about 1.5 mm from the fusion line between the buttering material and the alloy steel SA508 C13, see Fig. 3. Two prolongation arms, which is about 3500 mm in length, are thereafter welded to the DMW on the left and the right side to form a pipe beam, which is used for the Benchmark four-point bending test, see Fig. 4.The bending test was conducted under displacement control through applying a vertical displacement at two rams mounted to the pipe beam. In Fig. 5, the test-set-up is shown. The DMW was heated up (nearly uniformly) to 300"C and isolated before the displacement applied. Thereafter, the displacement is applied in a constant speed (0.3 mm/min) until the crack front advances nearly through the wall thickness. The key results, which are of interest for our purpose, are summarized below:
(1) The Critical Displacement loading at which the crack initiation takes place is about 115 mm and the corresponding CMOD (maximum Crack-Mouth-Opening Displacement) is about 0.8 mm.
(2) The Destructive Displacement loading is about 160 mm and the corresponding CMOD is about 3.4 mm (Estimated from Fig. 59, Ref. 16). The fracture profile after the destructive loading is shown in Fig. 6.
(3) Corresponding to the critical displacement (115 mm), the reaction forces at the two rams are measured to be about FC1=790 kN for Ram 1 and FC2= 1120 kN for Ram 2 (Estimated from Fig. 54, Ref 16).
(4) Corresponding to the destructive displacement (160 mm), the reaction forces at the two rams are measured to be about FD1=800 kN for Ram 1 and FD2= 1250 kN for Ram 2 (Estimated from Fig. 54, Ref 16).
The reaction forces measured at the two rams indicates that the test set-up, which ideally should produce a pure bending in the DMW, was not perfectly done as the reactions forces at the rams differ considerably. This has been realized during the test and discussed in Ref. 16 and after various adjustments, the final test was done through making an off-set of 285 mm from the inserted defect to the mid-point of the whole beam, see Fig. 7. In other words, the DMW has been moved 285 mm to the right support in the test.
1 - Austenitic base metal, 2 - Ferritic base metal, 3 - Dissimilar metal weld, 4 - Prolor>gation arms, 5 - Weld connecting austenitic base metal to prolongation arm, 6 - Weld connecting ferntic base metal to prolongation arm
Fig. 4. The straight pipe beam constructed by welding two extension arms to the DMW for the Benchmark test [16].
The support The ram
Outer span: 7 m
1^nner Displacements 3 m applied to the two rams in
0.3 mm/min
Fig. 5. The test set-up (left) and the four-point bending test through applied vertical displacements to the two rams mounted to the inner part of the pipe beam (right) [16].
Fig. 6. The fracture profile observed after the test (From different specimens. Upper - the circumferential section; Lower-the longitudinal section) [16].
Symmetric line I
Offset = 285 mm
Fig. 7. The off-set of 285 mm of the DMW in the four-point bending test [16].
3. THE CRACKED DISSIMILAR METAL WELD AND THE FULL-SCALE TEST
The reaction forces measured at the two rams indicates that the test set-up, which ideally should produce a pure bending in the DMW, was not perfectly done as the reactions forces at the rams differ considerably. This has been realized during the test and discussed in Ref. 16 and after various adjustments, the final test was done through making an off-set of 285 mm from the inserted defect to the mid-point of the whole beam, see Fig. 7. In other words, the DMW has been moved 285 mm to the right support in the test.
A great effort was made in characterizing the material data around the affected area during the welding process according to Ref. 16. Below, material data relevant to our finite element analysis and fracture assessment are summarized in Tables 1 and 2.
The materials are assumed to obey a von-Mises plasticity model with a Ramberg-Osgood hardening rule which is:
s = —ha- — E E
f v^1 a
where <5 and 8 represents the von-Mises equivalent stress and strain, respectively, and material constants are the initial yield stress a0, the elastic modulus E, and two other constants (a and n). The last two constants are
determined by assuming that the initial yielding (G0 = Gy ) takes place at a strain of 0.02% and the ultimate tensile
strength (au )ata strain of 10% for our calibration given in Tab. 1.
Table 1. Elasticity moduli (E), initial yield stress ( O y ) and tensile strength ( Ou ) at temperature 300°C [16] and calibrated Ramberg-Osgood model.
Material E ° u Ramberg-Osgood hardening rule
(GPa) (MPa) (MPa) a n
316L 139 213 453 0.130516 8.192
A508 172 463 640 0.074298 19.079
308L 165 346 441 0.095358 25.504
Buttering (308L+309L) 171 349 462 0.097994 22.058
Note: The Poisson's ratios are not given in Ref. 16 and for all materials we assume v=0.3.
Table 2. Toughness data characterized at temperature 300°C for the buttering material at regions near the defect[16].
Minimum value
Specimens/ tests Jic or J0>2 (kJ/m2)
CTJE25 single specimen *, Tab. 5 [16] 156
CTJE25 multiple specimens, Tab. 5 [16] 178
SENB, Tab. 6 [16] 53-63
Notched specimens, Tab. 7 [16] 130 -266
Project BIMET [17] 120
Vi - V2
53 kJ/m2 (53 mJ/mm2)
171-10" ■ 53-103
1- 0.32
=99.8x10« (P^Vm)
=ioo MPaVm =3156 MP^mm
Note: * Tests CTJE25 were made by the former French FRAMATOME-ANP (now AREVA) [18], with the measured locations about 1.5 from the lusion line in the buttering materials.
In Tab. 2, several representative test results are listed in the Tab. 2. The reported toughness data present a large scattering in various test results at temperature 300°C. As our prime interests are the crack initiation, the toughness data closest to the crack front in the buttering material are listed in the table. There are a number of explanations for the scattering of the test results, for which we refer to Ref. 16.
4. RESIDUAL STRESSES
There was a comprehensive study on the residual stresses inside the DWM region through non-destructive measurements by means of neutron diffraction [16]. In the area near the crack front (about 17 mm from the outer surface), the residual stress in the axial direction (along the pipe axis) is reported to be about 75 MPa (tension), which is considered to be low. In addition, it is commented that the measured residual strains and stresses in the axial and radial directions are of inferior quality due to material texture (Sec. 1.3, Ref. 16). Furthermore, it is suggested in Ref. 16 that the residual stresses are not likely to affect the crack initiation, which has also been observed in EUATOM's previous projects on DMW [17].
We note again that the main interest of the current report is the assessment of the crack initiation. In view of the poor quality of the measured residual stresses and the observations made from Refs. 16 and 17, the finite element computation and the subsequent fracture assessment conducted below in this report are made without accounting the effect of the residual stresses to avoid an unnecessary discussion of diffusive results. For the structural integrity assessment in general, it is aware that the residual stresses is not ignorable.
5. FINITE ELEMENT ANALYSES AND THE ASSESSMENT OF CRACK INITIATION
The DMW with the prolongation arms are modelled by using software ANSYS [19] with quadratic solid elements, SOLID186 (Brick) and SOLID187 (Tetra). While a relatively coarse mesh is used for the prolongation arms, a relatively fine mesh is used for the DMW region. In particular, a very fine mesh is used near the crack front in order to capture the behaviour in the vicinity of the crack front. See Fig. 8. Totally, there are 596,911 elements, 1,039,688 nodes and about 3.1 million unknown variables. Again, the present interest of the report is to numerically investigate the crack front behaviour when the arm displacement is 115 mm, at which the crack initiation is observed in the full scale test. The temperature in the whole DMW is nearly constant (300°C) and the test is a simply supported beam, which implies that the thermal effect is small and can be ignored. For other modelling details, we refer to Ref. 15, where the DMW materials are assumed to be fully linear elastic only.
(a) The DMW with its prolongation arms
Static Structural 2014-09*12 11:12 [S] Simply Support 1 [B] Simply Support 2 [CI Displacement uy= [D] Di splacement uy=
1000,00 2000,00 (mm)
(b) The DMW (Outside view)
2014-0!
(Fig. 8, Cont.)
(c) The buffering material and the inserted crack (Outside view)
(d) Mesh viewed from the right-cone surface of the inserted crack
Fig. 8 Finite element modeling of the four-point bending test (a) and the mesh near the crack front (c-d). 5.1. Linear finite element computation and assessment of crack initiation
For completeness, we show first in Tab. 3 some selected results from the linear finite element analysis. The "effective stress intensity", Kefrin. Tab. 3, is defined for accounting the mixed mode loading according to the R6-empircal approach (Appendix 7, Ref. 2). It is given by
(K,)2 + (Kn)2 + X(Km)2 (1 - v)
where A,=1.0.
The first three locations listed in Tab. 3, are selected by the maximum value of Ki, Kn or Km along the crack front. From Tab. 3, we can observe that |Ki/Kn|=7975/2021 « 4, |Ki/Km|=7975/129 « 62, which more clearly indicates an almost mode I condition at this locations. Hence, we can expect that this example deals with a mode I dominated crack. In addition, the maximum value of Ki does not take place at the mid-point of the crack front. At the mid-point, only Ki is relatively large and close to the maximum K-value, but not Kn and Km.
Table 3. The maximum values of the three stress intensity factors and its associated other two stress intensity factors (MP^mm and the J-integral (mJ/mm2)
Selection criterion Location / (mm) * Ki Kn Km Krff J-int
"Max Ki" 75.04 7975 -2021 129 9834 323
"Max Kn" 101.44 6822 2397 -175.4 8645 262
"Max Km" 7.34 3319 -354 2160 4752 57
"Mid-point" 86.09 6532 -1607 30 8040 250
Note: * The definition of the location "1" is given in Fig. 10.
Using the results given in Tab. 3, the crack initiation can be assessed using three alternatives: (1) Mixed mode cracking criterion; (2) Mode I cracking criterion; (3) R6-emripical "effective stress intensity factor" criterion for mixed mode cracking. The following three parameters ("fy, , T|eff), a measurement of "the degree of crack initiation", are defined
_ _ max(JINT)
" T (5a)
max(K.)
^C = „ 1 (5b)
„ _ max(Keff)
^K6ff -----(5c)
The crack initiation will occur if q > 1.0. In Tab. 4, an assessment is investigated for the four selected locations by assuming that the toughness value in the region of buttering material is: Jic= 53 mJ/mm2 or, correspondingly, Kic= 3156 MPaVmm , which is the minimum toughness value reported in Ref. 16. The degree of the crack initiation takes its maximum values at /=75.04 mm, which is highlighted in the table. An importance observation can be made from Tab. 4: It is not conservative to use a purely mode-I based criterion for the fracture failure assessment.
Table 4. The degrees of the crack initiation predictedby the three alternatives forthe locations l=75.04 mm, l=101.4 mm and l=7.34 mm.
Locati-on*Z (mm) Ki (MPaVmm ) Kefr (MP^mm ) J-int (mJ/mm2) % neff
75.04 7975 9834 323 6.1 2.5 4.5
101.04 6822 8645 262 4.9 2.1 2.7
7.34 3319 4752 57 1.1 1.0 1.5
86.09 6532 8040 250 4.7 2.1 2.5
Note: * The definition of the location "1" is given in Fig. 10.
J: linear
/-Integral (JINT) 5
Type: J-Integral (JINT) - Contour 5
Unit mJ/mm3
Time: 1 -__■
9/15/2014 9:19 AM
n 322.91 Max
.No crack initiation
Crack initiation
SeeFig. 10
(Crack initiation predicted by the mixed mode criterion)
SIFS (K1) 5
Type: SIFS-Contour 5 UniCMPa-mm A<0,5> Time: 1
9/15/2014 9:18 AM
D 7975.1 Max 5784 5793
-2413.6 Mln
No crack initiation
.Crack initiation
SeeFig. 10
(Crack initiation predicted by the mode I criterion)
Fig. 9 Crack initiation predicted by the mixed mode based criterion (Upper) and_hy_mode I based criterion (Lower). The crack front in red-color (Onset values: JIC= 178 mJ/mm2, KjC= 5784 MPaVmm).
Type: SIFS - Contour 5 Unit: MPa-mmA(Q,5) Time: 1
2014-09-18 16:11
0 7975,1 Max
5784 5783
-2418,6 Min
(Predicted by the mode I based Ki-criterion )
J: linear
J-lntegral (JINT) 5 Type: J-lntegral ()INT) - Contcuri Unit: mVmm3 Time: I
2014-09-18 16:12 n 322.91 Max
(Predicted by the mixed mode J-criterion )
Fig. 10 Crack initiation in predicted by the mode I and mixed mode based criteria for the region where the effect of the modes II and III is significant. The crack front in red-color (JiC= 178 mJ/mm2, KiC= 5784 MPa Vmm).
Fig. 11. Reaction forces at the two rams versus the applied displacement computed in the non-linear finite element analysis.
(Ram 1 - Displacement C; Ram 2 - Displacement D)
In Figs. 9 and 10, the crack initiation predicted by the mode I based criterion is compared to that by the mixed mode based criterion for a higher toughness value: Jic =178 mJ/mm2 (Kjc=5784 MPa Vmm ), which is considered to be more realistic [18].
The assessments above indicate the possibility for crack initiation by all three alternatives. This can be easily understood in view ofthe fact that the behaviour ofthe crack front, where the maximum J-integral value takes place, is dominated by the mode I loading for the location /=75.04 mm. A different conclusion can be observed if the behaviour of the crack front is dominated by mode II or mode III. This is the case for other two locations, in particular /=101.4 mm, Notice also that the degree of crack initiation indicated by using the mode I criterion is
smaller than those given by the other two alternatives (even if it is not a fully fair comparison by looking at the parameters "fy, and , as we have a relation of K2 ~J for isotropic elastic materials [20]).
The above assessments are made using results from linear finite element analysis as the prime interest of this report is the fracture assessment procedure recommended in Ref. 1 for which the Linear Fracture Mechanics is the basic assumption. Our results have shown that stresses in the whole DMW and a large part of the pipe material near the DMW are far beyond the yield stresses specified in Tab. 1. Hence, a large part of the materials in the DMW and in the prolongation arms close to the DMW must have undergone a severe plastic straining, which is indeed observed in the test [16]. The presence of a severe ductile failure can also be observed if the reaction forces, FC and FD, recorded in the test at the critical displacement (115 mm) and at the destructive displacement (160 mm), respectively, see Section 2, are used to estimate the plastic failure parameter:
T Ut \Ram 1 / T \Ram 2 1
Lr = max [(L,.) , \Lr) J
FC1 FC2
FD1 FD2
790 1120
800 1250
= 0.988
This observation of severe plasticity can be demonstrated in Fig. 12 below. 5.2. Non-linear finite element computation and assessment of crack initiation
Due to the large number of unknown variables (~3.1 million DOF), the computation is both time-consuming and numerically difficult. The computation is done by a placement-control on the two rams as in the test. Computed results are summarized as follows:
The maximum CMOD at the instant for which the crack initiation observed in the test is 0.7166 mm, which agrees reasonably well with the measured values (0.8 mm).
The reaction forces at the two rams versus the applied displacement are shown in Fig. 11. Compared to the measured reaction forces (At the critical displacement d=115 mm: 790 kN at Ram 1 and 1120 kN at Ram 2), the computed results are highly overestimated.
In Fig. 12, equivalent plastic strains along the crack front and on a through-pipe-axis-section at the mid-point of the crack front are shown. In the figure, the directions of the first principal plastic strain (Lower) in the vicinity of the mid-point of the crack front as viewed on a through-pipe-axis-section.
In Fig. 13, the computed J-integrals along the crack front are plotted. The crack initiation is assesses by assuming two different toughness: Jic=53 kJ/m2 and Jic=178 kJ/m2 for comparison with the linear analysis. Surprisingly, the J-integral results differ very little from those obtained in the linear elastic analysis (Fig. 9). Surprisingly, the results are quite similar to those obtained using a simple bilinear kinematic hardening rule [15].
It should be noted that there are several imperfections and uncertainties observed in the test, which presents great difficulties to entirely model and to simulate the test. Naming a few, it is commented in the Ref. 16 that the depth of the inserted defect varies between 16.2 mm and the designed depth (17 mm); the location of the inserted crack is about 0.9 to 1.7 mm, instead of 1.5 mm, from the fusion line; the crack-tip radius 0.4 mm; the applied displacement at which the crack initiation occurs varies from 78 mm to 135 mm (though being concluded to be 115 mm). Finally, we note that the computation of J-integral uses a "contour integration" which depends on the "contour-number" given by the user. The setting of this number is important and one needs to ensure the convergence of the elastic solution. Such uncertainties in the non-linear analysis have not been able to be verified due to the large finite element model and a long elapse computation time, for which we refer to Ref. 21.
Fig. 12 Plastic strains computed at the end of the loading history. Equivalent plastic strains along the crack front (Upper); Equivalent plastic strains (Middle) and the direction of the first principal plastic strain (Lower) in the vicinity of the mid-point of the crack front as viewed on a through-pipe-axis-section.
Fig. 13 Crack initiation predicted by the mixed mode criterion (J-integral) using the elastic-plastic material models. The predicted crack front in red-color. Two different toughness assumed: JIC= 53 kj/mm2 (Upper) and JIC=178 kj/m2 (Lower).
6. CONCLUDING REMARKS
The analyses have shown that the behaviour of the crack front in the DMW is largely on a mode I loading condition. However, the results can still demonstrate the following: Mode-1 based criteria are only adequate for the fracture failure assessment when mode-1 loading conditions are dominated. For cases when mixed mode conditions are significantly involved, it is not conservative to use a purely mode-I based criterion, refined approaches using J-integral or others must be used in order to achieve a reliable assessment.
The present paper addresses only the crack-front behaviour at the critical instant of crack initiation. A challenging task is to numerically trace the behaviour through the whole crack-growth process. The determination of the shape and size of the crack front as well as the growth direction at every time-instant is critical, for which a mode I based criterion will not work and a reliable growth criterion is crucial. This applies equally to the determination of the plastic failure parameter Lr. Apparently, much more work is needed for achieving a fully reliable structural integrity assessment.
Acknowledgements
The work presented in this report is partially funded by ÄFORSK, Agreement Ref. No. 12-315, which is gratefully acknowledged.
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