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Procedía Engineering 130 (2015) 835 - 844
Procedía Engineering
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14th International Conference on Pressure Vessel Technology
Structural Integrity Analysis of Cracked Pressure Vessel Welds Using Conventional and Constraint-Modified Failure Assessment
Diagrams
W.Y. Penga, H.J. Jina, S.J. Wua*
aSchool of Materials Science and Engineering, Beihang University, Beijing 100191, China
Abstract
In this study, four assessment procedures were used for the integrity analysis of the cracked A1 alloy pressure vessel welds
(PVWs), and the four methods are (1) to use BS 7910 Option 1 that is a conventional procedure, (2) to involve a modification to
the FAD but retain the definition ofKr, (3) to retain the FAD but modifie the definition ofKr (4) to use constraint-based FAD and
true Kmat values for SENB specimens with different a/W values. The fracture toughness tests were performed for single-edge
notched bending (SENB) specimens with different a/W values to obtain the corresponding Kmat values and to determine the
relationship between crack tip constraint (via a/W) and fracture toughness. To determine the constraint-based FAD curves, finite
element analyses were performed to derive the functional relationships between normalized load and Q-constraint for SENB
specimens. The results showed that the predictions using the second and third procedures was in good agreement with the
experimental results of residual strength, and that BS 7910 Option 1 procedure was proved to be conservative for the shallow-
cracked vessel specimens, and that the fourth method overestimated the residual strength.
©2015 The Authors.Published byElsevierLtd. 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: Q-Constraint; FAD procedures; Cracked pressure vessel welds; Aluminum alloy; Structural integrity assessment.
* Corresponding author. Tel.: +86-010-82316326; fax: 86-010-82316326. E-mail address: wusj@buaa.edu.cn
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.2015.12.204
Nomenclature
a flaw height for surface flaw
c half flaw length for surface flaw
M Weibull model exponent
r, 0 the polar coordinates taken from the crack tip
B section thickness in plane of flaw
CTOD crack tip opening displacement
D outside diameter of pressure vessel
E elasticity modulus
J J-integral
Kr fracture ratio of applied elastic K value to Kmat
Kmat fracture toughness
Lr ratio of applied load to yield load
N strain hardening exponent
Q normalized hydrostatic stress used as a constraint parameter
QP, Qs values of Q for primary stress, secondary stress, respectively
S specimen span
T elastic T-stress
w specimen width
a, k parameter defining influence of constraint on fracture toughness
PQ normalized constraint parameter
Oy yield stress
oee stress field at a specific position ahead of the crack tip
SENB single edge notched bending specimen
SE(T) single edge notched tension specimen
SSY small scale yielding
LSY large scale yielding
FAD fatigue assessment diagram
BM specimen span
HAZ heat affected zone
WM weld metal
PVWs pressure vessel welds
1. Introduction
In certain engineering structures, the failure of a structural component due to the existence of flaws is quite catastrophic, which may result in serious economic and environmental consequences. However, to determine if a structure containing flaws requires a repair, an acceptance level is required to define the size of defects. Engineering structures containing defects might be responsible for structural failure during the fabrication stage or during the service life. The structural significance of such imperfections, particularly crack-like flaws need to be assessed to prevent failure of the component during service [1]. In particular, welded structures require special procedure for structural integrity assessment of the welding flaws. Fracture assessment procedures for welded components containing flaws play an important role in the design, manufacture and safe operation of pressure vessels, piping and storage tanks [2].
Several important standard procedures have been published for the defects assessment of welded structures in the past few years, such as the BS7910 [3] and R6 [4]. These standard procedures are based on the failure assessment diagrams (FADs), which was initially developed from the two-criterion assessment proposed by Dowling and Townley [5]. In the FAD procedures, the integrity of cracked components is assessed by calculating the two extremes of fracture behavior separately, linear elastic and plastic collapse behavior. In the last few years, defect
assessment procedures based on the FAD concept have been widely used to assess the integrity of engineering components containing defects [6-8].
However, a conservative implication in the conventional FAD methodologies is that the assessment uses fracture toughness values obtained from tests on deeply cracked specimens according to established experimental standards and validity criteria. Consequently, defect assessments in low constraint structural components using conventional FAD methodologies may be overly conservative and pessimistic. There has been considerable research [9-12] on these low constraint effects in order to quantify the geometry dependence of the fracture toughness using so-called constraint parameters. This has led to constraint-based FADs within the BS7910 [3] and R6 [4] procedures. However, there are few investigations that discuss in detail the integrity assessment of cracked PVWs based on different constraint-modification FAD procedures by comparing the outcomes with the conventional FAD procedures.
The purpose of this study is to assess the application capability of the four defect assessment procedures including (1) to use BS 7910 Option 1 that is a conventional procedure, (2) to involve a modification to the FAD but retain the definition of Kr, (3) to retain the FAD but modify the definition of Kr (4) to use constraint-based FAD and true Kmat values for SENB specimens with different a/W values. Further, the aim is to broaden current understanding on the effect of Q-constraint on defect assessment procedures for these components.
2. Constraint-based failure assessment diagrams
2.1. J-Q characterization of near tip fields
There are many studies indicating that the material resistance to fracture was increased when the crack length of specimens decreased [13-15]. In general, it was found that Q-constraint can provide a good characterization for crack front stress fields [16]. The Q-stress that is derived from the HRR stress field proposed by Hutchinson [17] as well as by Rice and Rosengren [18] was adopted to develop the degree of constraint for cracked specimens and structures. A second term was incorporated into elastic-plastic fracture mechanics and the HRR theory to accommodate the constraint effects in fracture mechanics [19]. The Q-stress is normalized by the yield stress and defined by the Eq. (1) as follows:
Gij =(°1j)hrr+Q^ , Ssj (1)
where (aij)mR is the HRR field, ay is the stress field ahead of the crack tip, and 5ij is the Kronecker delta. O'Dowd and Shih [20, 21] proposed that the first HRR term was replaced by a small-scale yielding solution obtained from modified boundary layer analyses with T = 0. Here, T is the elastic T-stress. Then the equation (1) is represented by
= (o^SSY^O+QCySij (2)
ij/SSY;t=0
for \0\<— and 1.5 <^< 5
Based on the Eqs. (2) and (3), Q may be evaluated as the difference between the actual stress field and the small-
scale yielding reference solution, as follows:
°y J/°y
where Cgg is the opening stress component, and the difference field is evaluated at the microscale distance r = 2J/o y , which is the location where the effective fracture mechanism is initiated. Further details on the J-Q methodology can be found in [9,22].
2.2. Modified FAD
Constraint effects can be introduced in the FAD procedures by modifying the failure assessment curves as a function of crack configurations, loading and stress-strain behavior. Following the work of Ainsworth and O'Dowd [23], these effects are incorporated into the FAD procedures by quantifying the constraint in terms of the load ratio, Lr. The load dependence of constraint is characterized by the hydrostatic parameter Q that is expressed as follows:
Q = PQLr (5)
where the parameter Pq is, in general, a function of crack geometry, material strain hardening properties and load.
In this study, the effect of residual stress as a secondary stress in an as-welded component is considered. It may be estimated for Qp > 0 from [24]
Q = QP+QS (6)
where Qs> 0
To evaluate constraint effects, it is necessary not only to have a measure of structural constraint, but also a measure of the dependence of material toughness on constraint. A constraint-dependent fracture toughness, K^at can be associated with structural constraint by
K^at=Kmat[l+a(-PQLr)i ] (7)
where a and k are material constants describing the influence of constraint on fracture toughness, and Pq is a normalized measure of the structural constraint. The failure assessment line is then written as
Kr=f(Lr)(KQat/Kmat) (8)
where K<Qna is defined by equation (7), this becomes
Kr=f(Lr)[l+a(-PQLr/] (9)
3. Fracture toughness tests
Aluminum alloy grade 2014 is used for the fabrication of pressure vessel and fuel case in aerospace industry, due to its light weight, high strength and superior ductility. All welded joints were made by automatic TIG welding. Fracture toughness tests were performed for base metals (BM), heat affected zone (HAZ) and weld material (WM). The specimens with different a/W values were tested to obtain the corresponding Kmat values. Three-points bending specimens and the loading geometry were shown in Fig. 1. The notch was made parallel to the welding direction at two locations (centre of weld and HAZ) in welded specimens and perpendicular to the rolling direction in BM. The notch position in the HAZ specimens was about 1 mm away from the weld-fusion line. In order to guarantee the reproducibility of the fracture toughness results, at least 7 specimens were tested for each type (BM, WM and HAZ)
and the average values were obtained as the corresponding CTOD. Fatigue pre-cracking and fracture toughness tests were carried out on a servo hydraulic controlled material testing machine at 15 Hz and stress ratio 0.1 in laboratory environment. The load versus crack opening displacement was recorded through the software program in the computer, and the CTOD values were calculated according to the British Standard (BS 7448).
4. Results and discussion
4.1. Fracture toughness
Average crack tip opening displacement (CTOD) values of BM, HAZ and WM were obtained as 67.36 prn, 42.5 prn, 50.28 prn, respectively. The minimum fracture toughness appears in the HAZ, indicating that the integrity of the PVWs is largely dependent on the HAZ. The BM has the highest fracture toughness values and the smallest data scatter compared with that of HAZ and WM. The fracture toughness values for SENB specimens with different crack length (a/W) are shown in Fig. 2. It can be seen that the fracture toughness was reduced with the increase of crack length and SENB specimen with a/W=0.1 had the highest fracture toughness duo to the loss of constraint at the crack-tip.
Fig. 1. Three-points bending specimen: all lengths in mm.
Fig. 2. The facture toughness values for SENB specimens with different crack length.
4.2. Q-parameter for SENB fracture specimens
The SENB specimens generally show the high local stress triaxiality under fully plastic conditions. Huang and Brocks [25] have shown that the stress triaxiality is affected by the load intensity and the crack length in plane-strain conditions before the plastic zone spreads over the uncracked ligament. Fig. 3 shows finite element analysis results for the variation of the Q-parameter with normalized load, Lr for the SENB specimens. Kim et al. [26] and Neimitz et al. [27] studied the variation of the Q-parameter with deformation level for various crack depths by finite element analyses, showing that at load levels smaller than the limit load, the Q-parameter gradually decreases as a/W decreases for shallow-cracked specimens, while Q-values are close to 0 for deeply cracked specimens with a/W > 0.5. The studies on variations of the Q-values with normalized load by Donoso et al [16] as well as by Cravero et al [9] also show the similar feature. As clearly revealed in Fig. 3, the evolution of Q-stress greatly depends on crack lengths, as characterized by the ratio of a/W for the SENB specimens. For shallow-cracked specimens, Q-values decrease with increasing load as the induced plastic deformation at the crack tip reduces the constraint, thus showing that the material resistance to fracture is raised. With the increase of applied loads, i.e. increasing the plastic zone size, the Q-stresses in front of crack tip decrease and the stress fields develop towards the plane stress state for shallow-cracked specimens [26]. For deeply cracked specimens with a/W = 0.5, 0.6 and 0.7, the values of crack-tip constraints remain almost constant for all ranges ofload levels.
o.o -0.2 -0.4
-0.6 -0.8 -1.0
Fig. 3. Q-parameter along with normalized load for the SENB specimens with various crack lengths [28].
4.3. The fracture assessment of SENB specimens
The functional relationship of Lr versus Q for SENB specimens with a/W = 0.1-0.5 was adopted to determine constraint-based FAD curves. In this study, the fracture toughness tests were performed for SENB specimens with different a/W values to obtain the corresponding Kmat values and to determine the relationship between crack tip constraint (via a/W) and fracture toughness. The parameters a and k used to describe the constraint modified fracture toughness were obtained by means of curve-fitting, and the values of a and k were 1.079 and 1.664, respectively [28].
The residual strengths of SENB specimens with a/W = 0.1-0.5 were predicted based upon four procedures. The first uses BS 7910 Option 1 that is a conventional procedure. The second involves a modification to the FAD but retains the definition of Kr. The third retains the FAD but modifies the definition of Kr. The fourth is to use constraint-based FAD and true Kmat values for SENB specimens with different a/W values. As shown in Fig.4. It can be seen that for shallow-cracked specimens, due to low-constraint Q values, there is a significant difference between BS 7910 Option 1 and constraint-based FAD curves. For deeply cracked specimens with a/W = 0.5, the effect of constraint-correction on the BS 7910 Option 1 is not pronounced. However, the constraint-based FAD curves lie outside the BS7910 Option 1 FAD curve for all cases. This implies that the BS7910 Option 1 is more conservative than constraint-based FADs.
The plastic zone size of shallow cracked specimens is larger and the plastic deformation is easy and homogeneous, thus the crack-tip stress can relax fully and stress triaxiality in front of crack tip decreases. Some
experimental studies have shown that the fracture toughness of shallow-cracked specimens is better than that of deeply cracked specimens [14, 16]. The primary source of enhancement arises from the effect of constraint on plastic deformations at the crack tip and subsequent effect on critical loads. For shallower cracks, the strain accumulation rate is much smaller than that for deeper cracks. Therefore, the improved toughness related to constraint loss implies that there is in fact an enhanced safety margin of FADs, and the loss of crack tip constraint leads to enhanced resistance to both cleavage and ductile tearing.
The verification tests of residual strength were carried out for SENB specimens with different crack depths. In Fig. 5, the residual strength predictions using the aforementioned procedures are compared with the experimental values for SENB specimens with a/W = 0.1~0.5. For shallow-cracked specimens, the predictions using the BS 7910 Option 1 are much more conservative whereas the predictions based on modification to the FAD and modification to Kr are in good agreement with the experimental values. However, assessment results using constraint-based FADs and true Kmat values for SENB specimens with different a/W values are overestimated. For deeply cracked specimens, the residual strength predictions using the four procedures are similar and consistent with the experimental values. Clearly, the shallow-cracked specimens have the lower constraint ahead of the crack tip and the deeply cracked specimens have Q-constraint values close to 0.
BS 7910 Option 1
Conatraint-b&sed FAD ftirve; &IW-0 1 Constraint-based FAO curve: aW=0 2 Constraint-based FAD curve: aW-0.3 Constraint-based FAD curve: a*W-0A Constraint-based FAO curve; a№=0 5
Fig. 4. The fracture assessment of SENB specimens for different crack lengths using four different procedures.
Fig. 5. Comparisons ofresidual strength predictions and experimental values for SENB specimens.
4.4. The integrity assessment of the PVWs with cracks
The constraint-based FADs obtained from the constraint-designed SENB specimens and BS 7910 Option 1 procedures are adopted to predict the residual strength of PVWs with varying semi-elliptical external surface crack
geometries. The pressure vessel used in this study is the large-scale shell structure with the thickness B=6mm and the outside diameter D=3350mm. The a/W-ratio for SENB specimens matches the a/B-ratio for the cracked PVWs. The residual stress as the secondary stress is measured by using the indentation-strain method [29]. According to the residual stress distributions in weldedjoint, the tensile residual stress is 21-38% of the yield stress.
To verify the predictive capability of BS 7910 Option 1 and constraint-based FADs, the internal pressurized burst tests were performed on the longitudinal seam welds with different external axial surface crack configurations for 2014 Al alloy pressure vessels. The external diameter of the specimens is 3350 mm, the wall thickness is 6mm, and the length is 6250 mm. Fracture assessments were carried out on the tested vessel specimens with different cracks sizes measured by crack depth and crack length, ax2c: (1) 1.2x4.8 mm, (2) 1.8x18 mm, (3) 2.4^16 mm, (4) 3x20 mm.
Figures 6 presents the FAD curves and analytical predictions based on the four procedures for each analyzed crack configuration. Fig. 7 compares the residual strength predictions using the four procedures with the experimental values. The residual strength predictions from BS 7910 Option 1 show conservatism for shallow cracked vessel specimens, especially for the vessel specimens with 1.2x4.8mm and 1.8x18mm. It is attributed to the lower Q-constraint ahead of the crack tip and enhanced toughness due to the loss of crack-tip constraint. The predicted results from the constraint-based FADs and modification to Kr for shallow-cracked specimens show much better agreement with the experimental results, thus indicating that the conservatism in the BS 7910 Option 1 is reasonably reduced by the Q-constraint modified FAD procedures. For the deeply cracked vessel specimen (3x20mm), the constraint-based corrections have little effect on the residual strength predictions, which is greatly related to Q-constraint ahead of the crack tip close to 0. However, residual strength using the fourth method that involves a modification to the FAD and Kr is overestimated.
Fig. 6. Residual strength predictions for the tested PVWs specimens with different crack configurations using four different procedures.
Fig. 7. Comparisons ofresidual strength predictions and experimental values for the cracked PVWs specimens using four procedures.
5. Conclusions
(1) There is a significant difference between BS 7910 Option 1 and constraint-based FAD curves for shallow-cracked specimens due to low constraint Q-values ahead of the crack tip. However, the effect of constraint-correction on the BS 7910 Option 1 is not pronounced for deeply cracked specimens due to high Q-constraint.
(2) The residual strength predictions based on the modification to the FAD and modification to Kr were in close agreement with the experimental results, and the BS 7910 Option 1 showed conservatism for shallow-cracked PVWs specimens. However, residual strength using the method that involves a modification to the FAD and Kr is overestimated for shallow-cracked specimens.
(3) The two procedures of modification to the FAD and modification to Kr provided more satisfactory results for the integrity assessments of the PVWs, compared to the experimental results.
Acknowledgments
The authors would like to acknowledge the financial support from the National Ministry of Industry and Information Technology Project (M J-F-2011-34). The authors would also like to thank Prof. Peter Flewitt of the University ofBristol for helpful discussions.
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