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The fracture mechanics of aluminium-alloy gas cylinders
EngineeringFractureMechanics VoL 15, No. 1-2, pp. 1-20, 1981 Printed in Great Britain.
0013-7944/81/06001-20502.00/0 © 1981 Pergamon Press Ltd,
THE FRACTURE MECHANICS OF ALUMINUMALLOY GAS CYLINDERS K. R. BROWN~ Kaiser Aluminum & Chemical Corporation, Center for Technology, P.O. Box 877, Pleasanton, CA 94566, U.S.A. and B. ZYBENKO Australian Atomic Energy Commission, Lucas Heights, Private Mail Bag, Sutherland, NSW 2232, Australia Abstract--The failure pressures of sixteen 2219 aluminum alloy gas cylinders containing intentional defects were determined experimentally and compared with fracture mechanics predictions. The failure pressures predicted by two linear elastic fracture mechanics models for axially flawed cylinders were 10-70% low when the flaw was considered to bulge and ranged from 15% high to 40% low for restrained flaws. The ASME Boiler and Pressure Vessel Code gave approx. 15-45% conservative estimates for axial flaws in all cylinders except one containing a shallow flaw. A 20% overestimate was made for this cylinder. All predictions of a model developed for the American Gas Association for steel pipelines were very conservative, particularly for long axial defects where the failure pressures were underestimated by more than 300%. A similar conservative result was obtained for circumferentially flawed cylinders. This model was modified empirically to allow closer prediction of the failure pressure of axially flawed cylinders. Further models were developed to predict the failure of two cylinders each containing a dent superimposed on an axial flaw. Acoustic emission monitoring and source location during pressurization did not identify the known defects in most tests. It permitted uncertain nondestructive defect identification on only two cylinders. The inconsistent and uncertain result would not warrant the adoption of AE as an NDT tool on these cylinders.
As PARTof the Australian Atomic Energy Commission's program in fracture mechanics, sixteen cylindrical seamless aluminum alloy gas cylinders were pressurized to destruction. The cylinders were of AU6MGT alloy, a 6% copper alloy. The closest U.S. equivalent of this European designation is 2219; the mechanical properties of the cylinders were consistent with T6 temper. The vessels were of three sizes and wall thicknesses, Table 1. The three smaller vessels were from a different manufacturer, but were of similar hardness and spectrographic analysis. The cylinders were used for carbon dioxide storage and transport. Thirteen were removed from service because it was feared that they had received a faulty heat treatment during manufacture. It was considered that they could be susceptible to stress corrosion cracking, and could be dangerous. The remainder had reached their normal working life. As the gas bottles represented a valuable set of experimental samples, it was decided to test them to destruction and gather data for future safety assessment on similar components. Twelve cylinders were tested after artificial axial flaws were machined to various depths. Two cylinders contained circumferential flaws, and one cylinder was tested with no introduced defects. Two of the axially-flawed vessels were dented after machining and one (unflawed) cylinder was dented. The inclusion of dents was considered important as the fracture mechanics of crack-like flaws superimposed on dents is extremely relevant to pressurized components, but has been largely ignored. A combined flaw can result from accident or sabotage. Missiles from nearby explosions, falling objects or carelessly driven vehicles can also produce such a defect. The dent itself might be unintentionally designed or fabricated into a structure. "Flats" due to poor alignment during welding approximate a dent. The failure can be dynamic and accompany the rebound of the missile, or failure could occur later during an increase in service stress. A dent alone could be expected to develop cracks by stress corrosion or fatigue, as the dent can produce local residual stresses. At a later tPreviously Senior Research Scientist, Australian Atomic Energy Commission. 1
K. R. BROWNand B. ZYBENKO Table 1. Experimentaldetailsof gas cylinders oH
Equivalent Defect
Cylinder
Length
N9.
{mm)
Burst Pressure Wall Thickness ~ mm (MPa) Ultrasonic* Average Depth nom.{actual) Gauae Transducer Measured DepthGau4e Flaw Type Radius
Failure Hoop
Stress Relative (MPa)
Depth %
l
58
4.5
(4.6)
31
32.1
--
II.38
Axial
I00.75
274
40
2
I08
4.5
(4.7)
26
27.5
--
I0.64
Axial
I00.75
246
44
53
53.4
--
I0.06
No flaw
I00.75
3
531
(Yield 425)
4
408
4.5
(4.1)
26
27.6
--
ll.15
Axial
I00.75
235
37
5
33
4.5
(4.4)
34
33.6
--
ll.O0
Axial
I00.75
311
40
6
I04
0.9
(0.85)
44.5
45.6
7
107
2.2
(2.4)
38
38.6
8
Ill
6.7
(6,9)
16
9
ll2
8.1
(7.5)
lO
4.0
(4.3)
22
10
58
II
9.95-li.65
lO.41
Axial
I00.75
431
8
--
I0.72
Axial
I00.75
357
22
16.6
--
I0.77
Axial
I00,75
150
64
I0.8
--
I0.59
Axial
I00.75
95
71
22.7
--
8.10
Axial
85.4
232
53
46
46.4
--
8.05
Dent only
85.4
488
8.08
Axial + dent
85.4
21
74
ll.lO
Axial + dent
73
54 47
12
111
6
(6.0)
2
2.5
8.03-8.14
13
107
2.2
(6.0)
8
8.1
I0.61-II.05
14
58
2.7
(2.9)
22
23.1
--
6.15
Axial
70,2
215
15
150
II
If.3
--
6.27
Circumfer. + weld
70,2
123
16
158
37
37.2
6.12
Circumfer.
70,2
°A=212 %=424
2.7
(2.2)
6.20
100,75
36
*measured at crack tip
date the stress amplification caused by the dent could allow failure of the crack at an unexpectedly low stress. EXPERIMENTAL DETAILS 1. Flaws To check fracture mechanics models for the failure of pressurized cylinders, axial defect sizes were selected from a range of 0--400 mm in length and from 10-90% of the wall thickness in depth. Due to machining difficulties and wall thickness variations, these intended sizes were not always achieved, and the actual values are summarized in Table I. All machined flaws were made on the exterior of the cylinders with a milling cutter used for Charpy test specimens, i.e. 75 mm diameter, 450 included angle attd 0.25 mm tip radius. The profile of the resultant groove had circular ends and thus the cut was longer at the cylinder surface. An equivalent length was calculated such that the equivalent square-ended flaw of the same depth had the same profile area as the machined flaws. Actual flaw depths were measured after machining and the wall thicknesses adjacent to the flaw were checked with a calibrated ultrasonic thickness gauge. Dents were made in three bottles by pressing a solid steel cylinder 215 mm diameter by 75 mm approximately 10 mm into the empty gas bottle, with the axes of the steel cylinder and gas bottle perpendicular. This operation required loads of 9000-14000 kg. Some growth of the machined axial flaws was noted during unloading, so the crack was stained with machinist's dye for later measurement.
2. Strain gauging The behavior of the flaw was monitored in the early pressurizations by a clip gauge, as used for fracture toughness measurement [1]. This was placed across the center of the machined defect. However, the gauges were usually damaged by the vessel failure, so in later tests one or more strain gauges were placed on the vessel instead. The strain gauge outputs were fed via an amplifier to an X - Y recorder, and plotted against the internal pressure. Gauges were attached to the dented vessels in the positions described in Table 2. With the exception of those gauges in circumferentially flawed vessels, all gauges were oriented to detect hoop strain. Their locations and outputs are summarized in Table 2. 3. Acoustic emission Acoustic emission monitoring was conducted during pressurization using a FLIC-3 (Southwest Research Institute) flaw location computer. Three Dunegan transducers were attached by
The fracturemechanicsof aluminumalloy gas cylinders Table 2. Straindata Cylinder No.
F i r s t Detected Deviation from Linearlt X
Gau~e Type and Location
Flaw T ~
& Comment
LocaT Y i e l d Relative to General Yield
I
Cllp gauge across flaw
17.6 gauge ) 18.7 transducer) MPa pressure
Axial flaw
2
Clip gauged f a i l e d , no data
--
Axial flaw
3
Circumferential, gO0 from fracture i n i t i a t i o n
42.7 MPa pressure 428 MPa oH
Unflawed vessel, strain tensile
1.0
4
Clip gauge across flaw
I5.g MPa Pressure (transducer)
Axial flaw
0.37
5
Strain gauge Circumferential - S mm ahead of crack t i p
>28 MPa
Axial flaw
>0.65
6
Strain gauge Circumferentlal - 5 mm ahead of crack t i p
32.3 MPa pressure
Axial flaw
0.76
7
Strain gauge Circumferential - 5 mm ahead of crack t i p
27.5 M~a pressure
Axial flaw
0.65
8
Clip gauge across flaw
ND before f a i l u r e
Axial flaw
9
Clip gauge failed - no data
--
Axial flaw
I0
Circumferential strain gauge 5 mm ahead of flaw
I g . l MPa pressure
Axial flaw - very small plasticity
0.56
11
I. Circ. strain gauge 12 cm from center of dent on shoulder
0 MPa
Dent only. Strain gauge movement compressive from 0-35 MPa, thereafter tensile.
1.0
2. Circ. strain gauge at center of dent
<5 MPa (pressure)
Dent only. Strain gauge movement tenslle.
0.15
I . Adjacent to center of flaw and ci rcumferenti a l l y oriented
0.6 MPa pressure
0 * 0.6 MPa tensile strains; 0.65 MPa to 2.5 MPa ( f a i l u r e ) compressive, very small strain
2. 5 mm ahead of crack t i p , oriented ci rcomferenti a l l y
0
Strain tensile - plastic strains from s t a r t of test
0
13
Strain gauge 5 mm ahead of crack t i p - circumferential
5 MPa (gauge) 5.g MPa (transducer)
Fracture did not propagate past machined flaw - end of flaw outside dent
0.12
14
Circumferential SG at crack t i p + 5 mm
20 MPa pressure
Very small tensile strain
0.65
16
Axial SG at t i p of weld
8 MPa pressure
Burst 11.3 MPa Smell tensile strain
O, 26
16
I. Circumferential SG 6 mm from crack t i p
30.7 MPa pressure
Departure tensile to burst at 37 MPa
1.0
2. Axial SG. of crack
26.1 MPa pressure
Strain tensile
0.42*
12
5 mm ahead
0.41
*based on axial stress
silicon rubber cement in a triangle around the flaw, Fig. 1. The same location points were used for all cylinders. The FLIC-3 computer has a gating capacity to spatially filter AE sources, and this was set to detect only sources originating with 50 mm of the flaw ends or sides. In this way interference from extraneous sources could be minimized. During the testing of the unflawed vessel, the gate was set as wide as possible and all three input channels connected to the one transducer, to capture all activity from the vessel. The gate output was fed to one channel of an X - Y recorder and plotted against pressure registered by a transducer in the pumping circuit. Photographs were taken periodically of a storage CRO displaying the locations of the AE sources detected. Before pressurization was commenced on each bottle, an artificial piezoelectric AE source was placed at either end of the flaw to verify equipment function and identify the flaw position on the CRO.
4. Pressurization The cylinders with strain gauges attached were placed in a pit, filled with water and lashed down. The strain gauges were then connected, the acoustic emission transducers attached and their function checked with the artificial source. The vessels were then pressurized with a positive displacement air-hydro pump at a rate of roughly 10 MPa/min. Pressure was monitored by a calibrated gauge near the pump and separated from the cylinders by 7 meters of 6ram steel pressure pipe and a pressure transducer in the pressurization line 50 cm from the cylinders.
4
K.R. BROWNand B. ZYBENKO
5. Mechanical properties The mechanical properties were measured on tensile and fracture toUghness specimens cut from sections of one bottle, No. 13, that failed below the yield stress of the alloy. Both types of specimen were cut axially from the vessel wall in the vicinity of the artificial defect, but away from possible zones of localized plasticity. Fracture toughness specimens 55 mm long × 10 × 10 mm were notched across one face with the Charpy notch milling cutter, such that the crack plane corresponded to a circumferential flaw growing through the vessel wall. This crack orientation is likely to yield a higher measured fracture toughness than an axial crack; however, it was not possible to test an axially cracked specimen. The significance of this likely difference will be discussed when dealing with axial flaws. Three specimens were fatigue cracked from a shallow notch to the mid-section, and three were notched directly to the mid-section to estimate effect of crack sharpness on the measured fracture toughness. These results are shown in Tables 3 and 4. In other respects the procedure used in the standard fracture toughness test, ASTM E-399, were followed[l]. For the accuracy required in this study, the measured values of stress intensity were considered to be Ktc, particularly as the test results are applied in similar sections to those of the test samples. Within experimental error, no significant effect of notch acuity on the measured critical stress intensity could be detected; however, the maximum load recorded during the test increased relative to the load at crack initiation, i.e. Pmax/Po in Table 4, and exceeded the requirements of a valid test [I]. RESULTS AND DISCUSSION All vessels were successfully pressurized to failure at pressures up to 53 MPa (7700 psi). The failures were generally more spectacular the higher the failure pressure, Fig. 2. No vessel fragmented, but this would have been likely were the bottles gas filled. Visual and dye penetrant inspection of the interiors of three of the failed bottles revealed no stress corrosion cracking. The failure pressures are summarized in Table 1 tcgether with the cylinder and flaw dimensions. The results of strain gauging and acoustic emission monitoring during pressurization are presented in the following sections, which are in turn followed by comparisons of the actual failure conditions and the predictions of a number of relevant models. Many models other than those examined are available in the literature, but those selected are relatively common and tried. They are those likely to be applied in a safety evaluation by an engineer who is not a fracture mechanics specialist. The approaches are limited to those based on linear elastic fracture mechanics which, with appropriate valid or empirical corrections for plasticity, should be relevant to this aluminum alloy in these sections. Time precluded trials of the equally relevant crack opening displacement approach [27]. Table 3. Materialproperties E u r o p e a n d e s i g n a t i o n A U 6 M G T (update of d e s i g n a t i o n A U 6 M T U. S. d e s i g n a t i o n 2219-T6
Yield Stress
UT$
Elongation
Fracture Toughnes~
MPa(ksi)
MPa(ksi)
%
Klc MPa m,
12.5
--
Sample
1
317(45.9)
437(63.3)
2
311(45.1)
410(59.5)
Avg
314(45.5)
424(61.4)
12.5
Typical published p r o p e r t i e s for 2219-T6
290(42.0)
414(60.0)
i0
Hardness,
measured typical
Young's Modulus
1974)
(published)
.
.
.
. --
:~30
135 VPN ll0 BHN E = 73.1 x 103 MPa
(10.6 x i0 h psi)
The fracture mechanics of aluminum alloy gas cylinders
Fig. 1. Acoustic emission test mock-up.
Fig. 2. Aluminum alloy cylinders after testing to destruction.
5
6
K.R. BROWN and B. ZYBENKO
Fig. 3. Distribution of acoustic emission sources during the pressurization to failure of cylinder 6. The axial flaw runs between the two points indicated; there is a possible grouping at the right end of the flaw.
Fig. 4. Distribution of acoustic emission sources in cylinder 16. A possible (vertically aligned) grouping along the circumferential flaw is indicated. The straight line groupings running vertically and horizontally are artifacts resulting from sources outside the monitored area.
The fracture mechanics of aluminum alloy gas cylinders
Fig. 10. Fracture surfaces of the dented cylinders 12 (bottom) and 13 (top). The three features visible on each fracture face are (a) the machined groove, (b) ink-stained area that fractured during denting, (c) final fracture.
7
The fracturemechanicsof aluminumalloygas cylinders Table 4. Resultsof criticalstress intensitytests for the cylinderalloy .,Sample No.
Crack Type
Depth(mm)
K MPa m ½
Pmax/P~
i
Fatigue
5.6
33
i.ii
2
Fatigue
4.4
36
1.07
3
"V" notch
2.0
33
1.35
4
"V" notch
4.4
31.5
1.32
5
"V" notch
5.6
28.5
1.38
1. Strain gauging The results of strain monitoring are summarized in Table 2. The unflawed vessel, No. 3, showed a clear yield point and extensive plasticity before failing at a stress level above the uniaxial tensile strength of the material. All axially flawed vessels failed at general stresses below yield, but in all successful tests local plasticity was detected before failure, either by a strain gauge close to the flaw tip or a clip gauge across the flaw center. In the circumferentially flawed and welded cylinder (No. 15) only a small amount of plasticity was detected before failure, presumably because of the very low failure pressure, Table I. However, in cylinder 16 there was considerable circumferential and local axial plastic strain. Local plasticity occurred axially at the crack tip before general plasticity was detected circumferentially, despite the general axial stresses being only half the circumferential stresses. All three dented vessels showed plastic behavior right from the start of pressurization. The unflawed, but dented, vessel, No. 11, showed extensive yielding in the center of the dent, but nevertheless, the final failure pressure was close to that of the undamaged cylinder, No. 3. The behavior of a circumferentially oriented strain gauge on the shoulder of the dent in cylinder 11 reflected an interaction between compressive stresses developed by a wedging action as the dent was pushed out by the pressure, the tensile hoop stresses normally developed in pressurized cylinders and residual stresses associated with the dent. The gauge initially detected compressive strains which increased linearly with pressure from approximately 8-30 MPa; however, from 30-36 MPa these strains reached a maximum and decreased until failure at 46 MPa. The dent had been largely removed prior to failure; however, failure initiated in the dent, presumably at an area where ductility had been exhausted. When a flaw was also present, the failure pressures were reduced alarmingly. The combined effect of a flaw and a dent reduced the failure pressures to 15-30% of those expected for an equivalent flawed but undented vessel. 2. Acoustic emission monitoring The results of monitoring the cylinders during pressurization are summarized in Table 5. No data were obtained on two cylinders due to moisture in the transducer connections; the connections were sprayed by fine water jets from leaks that developed in the pressurization circuit after testing was under way. No data were obtained in two further cylinders because of masking by "white" noise generated at leaks. In all other tests, totalling twelve bottles, the equipment appeared to work satisfactorily; however, inexplicably no acoustic emission was detected from cylinder 10. Emission occurred in all other cylinders, but rarely were there sufficient counts to permit statistically significant localization. Some indication of grouping of activity along the flaw was obtained in cylinders 6 and 16; however, if the locations of flaws were unknown, it is doubtful if an observer would have attached any significance to the groupings, Figs. 3 and 4. It is possible that in a few tests the machined flaw may itself have interfered with location by shadowing one or two of the 3 transducers. This is more likely with deeper flaws, e.g. as in cylinder 8 in which localized activity was not perceived despite a relatively large number of counts. The source location computer was able to locate an artificial source at the flaw; however, more scatter was noted around deeper flaws. It has been claimed[3] that "natural" defects can yield more acoustic emission than "artificial" defects, presumably due to the
K. R. BROWNand B. ZYBENKO
10
Table 5. Acousticemissionmonitoringresults Cylinder No.
Total AE Counts During Entire Pressurization
Comments
17
No localization, no correlation with pressure.
24
16 of these counts occurred in final 5% of pressurization, but were scattered wide of flaw.
146
Gate set to include artefact a c t i v i t y , counts increased at accelerating rate as failure approached.
4
12
No localization, no correlation with pressure.
5
20
Final 15 counts in last 15% of pressurization no significant localization.
6
14
All counts in final 25% of pressurization, none in last I0%. Possible location at flaw ends of two clusters each of 3-4 counts, see Fig.
7
NO data
8
87
3
Leaking noises only masking a c t i v i t y - leak in pressure connector. Counts increased at an increasing rate as f a i l u r e approached, no s i g n i f i c a n t l o c a l i z a t i o n .
9
No data
One channel lost due to moisture.
IO
No data
No a c t i v i t y detected, equipment apparently OK.
II
4
12
12
13
No data
14
13
15
No data
16
208
All four counts detected in f i n a l 8% of pressurization. No l o c a l i z a t i o n ,
no c o r r e l a t i o n with pressure.
Leak noises masked a c t i v i t y . All 13 in f i n a l 12% of pressurization - no significant localization. Wet transducer connections due to ear l y leak. The gate included a r t e f a c t a c t i v i t y - 90% of t o t a l counts due to artefacts. Possible flaw location by a line of 6 points, see Fig.
presence of oxides, dirt and other phases. It is conceivable that more success may have been achieved with natural defects; however, it would be foolhardy to rely on this vague possibility during the NDTsafety assurance of these vessels, particularly as they are well maintained and are free of dirt or corrosion products. Further, in dirty or corroded structures extraneous emission from corrosion products and scale remote from defects may obscure emission generated in defects. It is unlikely that the use of more sophisticated monitoring equipment would have improved the present result, as the sensitivity and noise discrimination of the present transducers and preamplifiers compares favorably with more expensive equipment. Present inadequacies lie in the lack of sources in the cylinders rather than in the ability of the equipment to detect and handle the signals. The present results are disappointing, as most tests were conducted carefully under fairly ideal laboratory conditions, and with prior knowledge of the defect location. They suggest that extreme caution is necessary when interpreting the results of AE monitoring in the field, where conditions are often far from ideal, materials are frequently uncharacterized and defects are rare.
3. Burst pressures (a) Axially fla wed cylinders Preliminary plots of relevant data for axially flawed cylinders showed a clear relationship between flaw length and flaw depth, Figs. 5 and 6. The data were compared with the predictions of three models for the failure of axially flawed pressure vessels. The comparisons are summarized in Table 6. LEFM models. The results of the tests on simple axially flawed gas bottles were compared first with the predictions of two linear elastic fracture mechanics (LEFM) models[4, 5]. Both considered the vessel walls to be the equivalent of flat plates of width equal to the vessel wall thickness, and containing a single edge notch of length "a". The axial length of the flaw was
11
The fracture mechanicsof aluminumalloygas cylinders i
i
5 0 ~ 3(0)
4O )
3O
Experimentally determined curve for approx. / ' 4 0 % deep flaws
0.44)
O
4(0.37 o.
zo
\ o I.L
% AGA prediction I
5o
I I00
I 150
I 200
Flow length,
I 250
i 300
I 350
I 400
mm
Fig. 5. Plot of failure pressures for axially flawed cylinders against crack length, 2c. The cylinder numbers
and the relative flaw depths (in parentheses) are indicated. The broken curve represents the predictions of the AGA model[8].
~
t 3(0) 5O - N %
40 o
n
o
• 5(33) ,, ,, "
30
" ~
Experimental curve f;r 104-112turn long flaws
t, i.
I (58)
0 "~2(108) 4(408) ~ ( 5 8 }
e~
14(581
20
~
_ ~8(I
II)
o i,
9(112]
0
I 0 I
I 02
I 03
I 04
I 05
I 06
I 0.7
I o.e
Relative flaw depth
Fig. 6. Plot of failure pressures for selected axial flaws against the flaw depth relative to the wall thickness. The lengths of these selected flaws are in the range 104-112 ram--see Table 1.
ignored, and failure was considered to occur by propagation through the wall. In both models the crack tip stress intensity is given by:
K = crYx/(a + r) where o- is the applied tensile stress normal to the flaw (hoop stress), r is a crack tip plastic zone correction given by
r=(Ky/nv~(2)'cr \O'ys/ I
in which trrs is the material yield stress.
[61
K. R. BROWN and B. ZYBENKO
12
Table 6. Failurehoopstress predictionsfor axiallyflawedcylinders C[linder
No.
-LEFM
Model
1
LEFM
Model
1
115
185
2
105
175
4
135
195
5
120
185
Failure
Hoop
Stress,
2
Code
A.G.A.
AS~
175
MPa Model
Modified A.G.A. Model
Actual Result
87
275
274
150
q5
230
246
140
25
205
235
210
127
305
311 431
6
390
395
515
75
315
7
225
265
275
65
285
357
8
45
125
85
40
165
150
9
30
ii0
80
30
135
95
i0
80
170
150
75
235
232
14
115
210
180
75
230
215
The calibration factor, Y, in Model 1[4] = 1.99-0.41 ( t ) + 18.7(t)"-38.48 (t)3 + 53.85(t) 4 for
,6, and = 1/2(t ) 1/2(1-(t))-~/2(1 + 3 ( t ) ) for 0.3-< ( t ) - < 1,0
[61
In Model 215], "Y" is given by
5",/(7r) - [20- 1 3 ( t ) - 7 ( t ) 2 ] '/> Model 1 is derived for the case when the ends of the flat plate are free to rotate; Model 2 is derived for rigidly supported ends. The predictions of these models are given in Table 6 and Fig. 7. Model 2 gave better prediction than did Model 1; Model 1 underestimated the failure stress by 10%-70%; the results of Model 2 ranged from a 15% overestimate to 40% conservative. As most predictions were low, a lower toughness for axial flaws would further impair the agreement. The ASME boiler and pressure vessel code. The ASME Boiler and Pressure Vessel Code [7] is not designed to predict failure, but to provide an estimate of the safety of a cracked component. Thus a conservative result is to be expected when the model is used for prediction. The code is also based on linear elastic fracture mechanics and considers a component unsafe when the stress intensity at the tip of a crack approaches the critical stress intensity, Ktc, of the material. The stress intensity is evaluated from: Kt = ~r,~Mm~/(Tr)~/(a/Q) + ~bMb~/(~r)~/(a/Q)
where om, o% is the membrane and bending stresses; a is the minor half-diameter of embedded flaw; flaw depth for surface flaw; Q is a flaw shape parameter to be determined using tr,~ and
The fracturemechanicsof aluminumalloygas cylinders
13
500
LEFM analysis
Model
2
Model
I
400 •
500
7
14~ "0
07
0'05
200
Q_
04
140 • 0, 0 5 ioo
2 IO
90 0
I00
8 200
300
400
500
Actual failure stress a- h MPa
Fig. 7. Plot of actual failurehoop stresses versus those predictedby the LEFMmodelsdescribedin the test. the flaw geometry; Mm is the correction factor for membrane stresses; Mb is the correction factor for bending stresses. The shape f~tors and correction factors are determined graphically, and in the case of simple axial flaws, bending stresses were insignificant. The hoop stress at failure calculated from the ASME model is plotted against actual failure stress in Fig. 8. With the exception of the result for cylinder 6, all results are conservative by 15--45%. Both the actual and predicted failure stress of cylinder 6 were above the biaxial yield stress of the material, 425 MPa, so the unconservative result does not reflect on the suitability of the ASME model for safety evaluation. A.G.A. model. Another model for failure prediction is that developed by Kiefner, Eiber et al.[8] for the American Gas Association. The model is intended for flaws in steel line pipe materials. These have high toughness relative to high strength aluminum alloys, but the model was considered of potential suitability for the present study. It should also be noted that, unlike the ASME Code, the Kiefner et al., model is intended to predict failure and does not incorporate a safety margin. The model predicts failure when Kc2~"= In sec 2-~M(~) 8c6 z where ~ is the hoop stress level at failure (i.e. PR/t); P is the internal pressure level at failure; is the flow stress of the material; M is the Folias bulging factor; R is the radius of the pipe; t is the wall thickness; 2c is the length of the through-wall flaw; and Kc is material toughness. Although based on fracture mechanics, the model contains a degree of empirical adjustment based on experience. For example, the material's flow stress is taken as the yield stress, plus 10,000 psi, an assumption unlikely to be suitable for aluminum alloys. In the present work, the relevant flow stress was taken as the average of the yield (278 MPa) and ultimate tensile strength (532 MPa).
14
K.R. BROWNand B. ZYBENKO
E)
500
ASME analysis 400
300
7
14
20C
O
Q-
O
5
O,
IO @ 2 ioo 8
0
I00
200
300
400
500
Actual f a i l u r e stress o" h M P a
Fig. 8. Plot of the actual hoop stresses of axially flawed cylindersat failure against predictionsof the ASMEanalysis[7]. Various expressions are available for the Folias correction factor, M. The expression used in the present work was
I,- l M = Mp =
"
Mrt
for partial thickness axial flaws of depth "d".
L,- J where MT, for through-wall flaws, is Mr=
4( t)
1+1.61 c" .
Whereas Kiefner et al., used empirical correlations to obtain fracture toughness data from Charpy test results, we were able to measure directly the Kc of the aluminum alloy, Table 4. The predictions of this model are compared with experiment in Fig. 9. It can be seen that the predictions are a factor of about 3 too low and are excessively conservative. If a lower Kc for an axial flaw was used, the prediction would be worse. A plot of predicted failure stress against flaw length, Fig. 5, showed that for the present cylinders the model placed excessive weight on flaw length. The relatively poor agreement between these results for axial flaws and the predictions of models that allow for bending or bulging suggests that bending or bulging corrections may not be appropriate for shallow axially flawed cylinders of relatively low toughness materials, Table 6. These models include the AGA model which uses the bulging factor "M", and also the flate plate models that allow for rotation of the plate ends. The bulging factor in the AGA model is also used in other models[9] and is strongly dependent on the axial length of the flaw. For the cylinders studied, this is clearly inappropriate; the failure predictions were worse for longer flaws, Table 6.
The fracturemechanicsof aluminumalloygas cylinders
15
5000
•
AGA analysis
4000
Modified AGA
6
5 3000
J
7
.u_ 2000
Q_
~000
,• 90
0
Jooo
05 , 4 • • I0 0 ' •
8
6
7
02
•4 2oo0
3oo0
4000
5000
A c t u a l f a i l u r e stress o" h M P o
Fig. 9. Plot of the actual hoop stresses of axiallyflawedcylindersat failureagainstthe predictionof the AGAanalysis[8] and the empiricallymodifiedanalysisdescribedin the text. Although stress amplification due to bulging is evident in ductile materials where significant plastic flow permits bulging or buckling[8], an axial flaw in a cylinder of low toughness material would not be expected to bulge under elastic hoop loading any more than would a centercracked flat plate.
Modified A.G.A. model. To permit future evaluation of the safety of similar vessels, Kiefner's model was altered empirically to lessen its dependence on flaw length, and to fit the present data. The result: Kc2" 12Ir [¢rMptr] in SI units, O + c - ~ =lnsec L 46 J allows predictions which agree reasonably well with experiment, Fig. 9. One result, for cylinder 9, is non-conservative by approximately 40%, suggesting caution when using the model for extremely deep flaws. The model is approximately 30% conservative for the shallow flaws tested. (b) Circumferentially flawed cylinders This study of circumferential flaws is limited, as only two tests were conducted. However, the results were examined for agreement with those current models of the failure of circumferentially flawed cylinders that were considered appropriate to these vessels.
Cylinder 15. This cylinder contained a through-wall flaw spanning 35% of the cylinder circumference. The flaw was a hacksaw cut that had been made in the vessel to emphasize its rejection upon completion of its service life. To salvage the vessel for this test program the cut was made pressure tight by welding. A shallow single-pass MIG weld achieved a penetration of less than 2 mm, i.e. less than 35% of the wall thickness. It was desired only to stop leaks in the
16
K.R. BROWNand B. ZYBENKO
flaw, not to provide a structurally sound weld that would interfere with the use of an analysis for through-wall flaws. An appropriate analysis of failure is that due to Folias[10] for circumferential through-wall flaws. In this analysis, the failure stress (axial) is given by:
0- = c°s ' [exp 75GJ where o-* is the material flow stress, a weighted average of the yield stress, 0-~.,and tensile strength, 0-,. 0-* =~ o'y +
= (341.5 MPa) (for cylinder 15)
c is the half crack length (0.075 m); K is the material fracture toughness (32 MPa mm); I = 1+(~',~2/64) (= 1.0273). where ;12=(c2/Rt)~/(12(l - v)2) (41.87) in which R is the cylinder radius ( = 0.0702 m); t is the wall thickness ( -- 0.00627 m); and v is the material Poisson's ratio (O.33). In this analysis no allowance has been made for any strength contribution from the weld metal. When this analysis is applied to cylinder 15, an axial failure stress of 63 MPa is predicted. which agrees surprisingly well with the actual value of 61.5 MPa (half of oH in Table 1). This agreement may be fortuitous as failure in the test occurred by the cracking of the weld and its opening by about 0.5 mm. The flaw did not propagate circumferentially beyond the hacksaw cut and the Folias analysis is designed to predict this failure mode. It is possible that this mode may have occurred if the cylinders had contained gas instead of water. An alternative analysis based on the American Gas Association model for axial flaws and summarized by Wilkowski and Eiber[ll]t assumes that failure of a circumferential flawed cylinder will occur when K2~" lnsec [rcMrc0.] 8c0.*:1_ 20-* J where Mrc is a bulging factor for a through (T) circumferential (c) flaw and accounts for the stress amplification due to the curvature of the cylinder. This factor is given by several relationships including:
Mrc = 0.738 + 0,126/~
[121
Mrc = 1 + 0.00635A 2+ 0.00055A4
ll3i
Using these relationships, axial stresses, 0., of 42.4 MPa and 29.3 MPa are predicted. These clearly yield less satisfactory predictions than the Folias analysis.
Cylinder 16. This cylinder contained a machined "V" shaped groove aligned circumferentially around the mid-section and penetrating to 36% of the wall thickness. Failure was catastrophic, and although no fragmentation occurred, the two halves of the vessel separated at the flaw and hinged on the remaining ligament to open about 90°. Although failure occurred at the flaw, the failure hoop stress equalled the uniaxial tensile strength and it would appear that quite large circumferential surface flaws could be tolerated in these vessels when only pressure loading is involved. The LEFM models[4,5] used previously for axial flaws gave reasonable agreement with experiment for the surface flaw in this cylinder. Model 1 estimated an axial failure stress of 175 MPa (17% low) and Model 2 an estimate of 252 MPa (19% high). The failure of this cylinder was also analyzed using a modified relationship of that given previously for cylinder 15 in which Mrc is replaced by Mpc for partial thickness circumtlt shouldbe notedthat the relationshipfor Ais givenincorrectlyin this reference.
The fracture mechanicsof aluminumalloygas cylinders
17
ferential flaws, where d tMrc t
1-- ff and where d is the flaw depth and t the wall thickness. When using the two versions of M r c of Kihara[12] and of Adams[13] given previously, values of M p c of 1.21 and 1.34, respectively, were obtained. These allowed failure stresses predictions of 53.03 MPa and 47.6 MPa, respectively; both results agree poorly with the actual value of 212 MPa. (c) D e n t e d cylinders Although the cylinder containing a simple dent (No. I 1) failed at a pressure close to that of the undamaged cylinder, the two vessels containing a combined flaw and dent failed at pressures less than a third of those expected for an equivalent flawed but undented vessel. The magnitude of this synergistic effect could be underestimated in design, so attempts were made to develop a satisfactory model that would allow failure prediction or safety assessment. (1) Stress a n a l y s i s The dented area in all bottles was approximated by a flat circular section 80 mm in diameter. A flat section develops the highest pressure-induced tensile stresses on the exterior surface, but it should be noted that the stresses are markedly sensitive to dent profile. They change sign as the profile changes from convex to concave. The surface stresses caused by a pressure P acting on such a section of radius "q" and thickness "t" are given by: ab =
- 3Pq2(m + 8mr 2
1)
- 3Pq2(3m + 8mt 2
1)
and trb =
Equation 1 applies when the periphery of the circular section is rigidly fixed and eqn (2) when the periphery is supported flexibly and unrestrained [14]. The parameter "m" is the reciprocal of the Poisson's ratio for the material. In this case m was taken as 3. Although there is slight flexibility of the restraint on the dented area, as evidenced by the growth of the machined flaws during the removal of the denting load, the restraint in these thick-walled cylinders may be considered rigid. For completeness, the ranges of stress and stress intensities predicted by the rigid a0d flexible solutions are given in Tables 7 and 8. In addition to the bending induced surface stress, trb, a general hoop stress trh also acts normal to the machined flaw. This is given by Barlow's formula: Oh=
PR t
m
Table 7. ASME predictions of Stressin~nsitiesin dented cylinders(figuresin parenthesis are fora flexibly supported dent) Shape Membrane Bending Correction Factor S t r e s s S t r e s s Factors Q %,MPa Ob,MPa Mm Mb Cylinder 12
1.04
21
31 (77) ~3
Cylinder 13
l.O
73
53(131)
tNote that this equation is incorrectly inverted in Ref. [11]. EFM Vol. 15, No. I-2--B
2.2
2'2 l.l
Material Critical Stress Intensity K MPa m~2 Kc, MPa m~2 17(29) )
)
30(42) )
K. R. BROWNand B. ZYBENKO
18
Table 8. Predicted stress intensities in dented cyliaders by alternative LEFM analysis. (Figures in parenthesesare for a flexiblysupporteddent) Stress Intensity, K flPa m~2 ~h,MPa Kb(bending ) Kh(membrane) K(total
Cylinder
or,MPa
12
31 (77)
2~
12(31)
25
37(56)
13
53(131)
73
12(31)
35
47(66)
Material Critical Stress Intensity Kc, MPa m~2
32
where "R" is the vessel radius and "t" the wall thickness. The total surface stress can be taken as ~r = o'b + trh.
The axial stresses due to longitudinal bending in the dent and due directly to pressure have been neglected, as these act parallel to the machined flaw. Residual stresses. During the denting of the bottles with machined flaws, extensive crack growth commenced from the root of the machined flaw. As the root of the flaw is in compression during denting, crack growth must have occurred during unloading, under the influence of the residual stresses caused by the dent. The residual stresses were reduced by crack growth; however, the growth of the crack ceased before penetrating the wall, presumably when the crack tip stress intensity dropped to a finite value corresponding to arrest, KA. If the value of KA were known, an estimate could be made of the corresponding residual stress. The residual stress may also be estimated (a) from the pressure at which plastic deformation was first detected by a strain gauge on the outer surface of the central region of the dent. In the case of the unflawed dent, cylinder I !, plastic deformation was detected as soon as pressurization was commenced, suggesting that the surface residual stress was equal to the flow stress ( ~ 405 MPa); (b) from the critical stress intensity which must have been reached at the machined notch root during the unloading of the flawed bottles. This would give a minimum value; for the present bottles the minimum estimates of the surface residual stresses were 335 MPa and 365 MPa for bottles 12 and 13, respectively; (c) from the geometry of the deformation caused by the denting. The hoop strain induced in the circumference of the bottle approximated 1.5%, which exceeds the strain at yield, and from the uniaxial tensile test data approximates a flow stress of 380 MPa. It was not possible to verify the model presented above (in the dented and unflawed bottle, No. 11) because of the residual stress, nor was it possible to confirm the appropriate weighted average to account for the compliance of the periphery of the dent. It is clear that the residual stresses are high and must be considered in any treatment of similar dented components. The present work suggests that the residual stresses are equal to the flow stress in a simple dent. It should be noted that the sum of the hoop, bending, and residual stresses will reach the yield stress in compression on the inside surface of the dent, before tensile stresses reach the yield stress on the exterior. (2) Analysis o/ dented vessels using A S M E code An attempt was made to assess the applicability of the ASME Code[7] to the two dented and axially flawed vessels. Unlike in the cylinders containing simple axial flaws, the bending stresses, trb, are significant in the dented cylinders and were obtained from the above stress analysis. Because of the growth of the flaws during denting, the determination of most of the bending and membrane correction factors (Mb and Mm) required extrapolation of interpolated graphical data given in the code and hence these factors are subject to large errors. No attempt was made to obtain more accurate estimates from first principles. The results calculated without allowance for residual stress are shown in Table 7 as estimated stress intensities, K, at the crack tips; these should be compared with the measured fracture toughness of the material, K,.
The fracture mechanicsof aluminumalloygas cylinders
19
The use, or more strictly, misuse, of the code, yielded low estimates of the induced stress intensity at failure. There was no degree of conservatism that would allow a confident safety assessment. A conservative result can be obtained when allowance is made for residual stresses. It could be assumed that residual stresses are at yield, or that the crack tip stress intensity due to residual stress is equal to the critical stress intensity Kc. In the latter case, the assessment would be approximately 50 and 100% conservative, a result which is comparable to those obtained for the undented vessels. (3) Alternative [ailure analysis of dented vessels As in the ASME analysis, the stress intensity at the root of the flaw may be taken as the sum of the stress intensities due to the bending and the hoop or membrane stresses, i.e.
K = K~ + K~. When the flaw is long relative to the dent size;
2 K = 3' ~b" t m" fl(a]t) + trhX/(a + r). [2(a]t) where [l(a/t) = 2.9(a/t) 1/2- 4.6(a/t) 31~+ 21.8(a/t) 512
- 37.6(a/t) 7/2+ 38.7(a/t) 9/2 f2(a]t)= 27(a[t~ ( 1 - t )-3/2 " ( l + ~ -)
[6]
and r, a plastic zone correction K
2
= (~-~y~)/4~(2)7r
[2(a/t) is equivalent to "Y" in Model 1 used earlier for axial flaws. The expression for Kb uses the compliance expression from the ASTM Standard E-399 [1] equation for three-point-bend fracture toughness test specimens, and is written in terms of the surface stresses normal to the flaw axis. That for Kh is for a single-edge-notched tensile specimen [6]. The predicted stress intensities at failure are conservative and are 15 and 50% above the actual failure criterion, Kc. Subject to further experimental verification, it would appear that the proposed model would be suitable for assessing the safety of similarly damaged pressurized components when residual stresses might be overlooked. If due allowance is made for residual stresses, as was done in the ASME evaluation, the model is over 100% conservative. In all of the above treatments of dented cylinders, no allowance has been made for the potential reduction in fracture toughness associated with deformation at the crack tip during denting, nor for changes in flaw sharpness during crack growth. The flaws in the two vessels were machined prior to denting and both grew during denting. Because of the insensitivity of the measured fracture toughness to crack sharpness (Table 3), no significant effect would be expected due to sharpening of the machined notch by crack growth. Some effect of prestrain of the material ahead of the crack tip might be expected; however, the crack in cylinder 13 grew during unloading, through the plastically compressed zone, to approximately the neutral plane of the nett section ahead of the machined notch. Only small prestrain would have occurred in this region. Some compression of the notch root would have occurred in cylinder 12, which may explain the lower stress intensities at failure predicted by both the ASME and alternate analysis. Further studies of the effect of prestrain are warranted.
20
K.R. BROWN and B. ZYBENKO
CONCLUSIONS 1. Models have been selected that will allow the safety assessment of 2219-T6 aluminum alloy gas cylinders containing axial or circumferential defects. However, the models were selected only after experimental verification of their applicability and accuracy. For cylinders of a different alloy or different geometry, it would be necessary to be extremely conservative, perhaps excessively so, in order to assure safety. The economic penalties associated with excessive conservatism may warrant a full-scale testing program to confirm more accurate models for the new material or geometry. It is clear that the fracture mechanics of pressurized components have not been sufficiently developed to allow confident and economic assessment of even simple defect geometries in a sufficiently wide range of materials. 2. A dent superimposed on an external crack-like surface defect can exaggerate the effect of the defect by a factor of 3-6 for the dent and cylinder geometries and the alloy studied. The residual stress caused by the dent appears to be the most deleterious factor. Further studies of combined flaws are warranted and have been commenced. 3. Acoustic emission defect location could not be used with sufficient confidence as a non-destructive test in these cylinders. Little emission was detected and only vague indications were made of known defects in two of the twelve flawed cylinders monitored during pressurization. These indications may have been overlooked without foreknowledge of the defect location. As AE monitoring was relatively unsuccessful in tests under good conditions, the technique cannot be recommended as an NDT test of these vessels.
Acknowledgements--The authors are grateful to the staff of the Australian Atomic Energy Commission Testing and Inspection Departmentfor their assistance with setting up the tests. In particular we wish to thank Mr. Reg Gibbs whose experience made the testing program run smoothlyand safely. The advice and suggestionsof the AustralianWeldingResearch Associationwere most helpful in the planningof these tests. Thanks are also due Dr. Colin Chipperfieldfor his help with the draft of this paper.
REFERENCES [ll ASTM Standards E399-74, Plane strain fracture toughness testing of metallicmaterials. 1974Annual Book of ASTM Standards.
[2] M. G. Dawes and M. S. Kamath, The COD design curve approach to crack tolerance, Conf. on Tolerance of Flaws in Pressurized Components, 1978 Inst. Mech. Engng. London (1978). [3] H. Dunegan, Private Communication,Sydney, Australia(1978). [4] W. F. Brown and J. E. Strawley, ASTM STP 410 ASTM (1966). [5] D. O. Harris, J. Bus. Engng 89, 49 (1967) In Compendium of Stress Intensity Factors (Edited by D. P. Rooke and D. J. Cartwright). Ministryof Defence, UK, HMSO London (1976). [6] T. W. Orange, Some effects of experimentalerror in fracture testing. In Fracture Analysis, ASTM STP 560, p. 122 (1973). [7] ASME Boiler and Pressure Vessel Code, Section I l, In service inspectionof nuclear power plant components. 1974 Article A. 3000, p. 117. [8] J. W. Kiefner, W. A. Maxey,R. J. Eiber and A. R. Duffy, Failure stress levels of flaws in pressurizedcylinders.ASTM STP 536, p. 461 (1973). [9] G. T. Hahn, M. Sarrate and A. R. Rosenfield,Criteria for crack extension in cylindrical pressure vessels. Int. J. Fracture Mech. $(3), 187 (1969). [10] E. S. Folias, An axial crack in a pressurizedcylindricalshell. Int. J. Fract. Mech. 1, 104-113 (1965). [11] G. M. Wilkowskiand R. J. Eiber, Review of fracture mechanics approaches to definingcritical sizes of girth weld discontinuities. Welding Res. Council Bull. 239. New York (July 1978). [12] H. Kihara, T. Kanazawa, S. Machida and M. Hassain, Brittle fracture initiation in steel pipes. Mech. Behavior Materials. Japan Society of Material Science. [13] N. J. I. Adams,The influenceof curvature on stress intensityat the top of a circumferencecrack in a cylindricalshell. "Damage Tolerance in Aircraft Structures" ASTM STP 486, 39--49(1971). [14] R. J. Roark, Formulas [or Stress and Strain, 4th Edn. McGraw-Hill,Kogakusha,Tokyo. (Received 26 November 1980; received [or publication 18 February 1981)
0013-7944/81/06001-20502.00/0 © 1981 Pergamon Press Ltd,
THE FRACTURE MECHANICS OF ALUMINUMALLOY GAS CYLINDERS K. R. BROWN~ Kaiser Aluminum & Chemical Corporation, Center for Technology, P.O. Box 877, Pleasanton, CA 94566, U.S.A. and B. ZYBENKO Australian Atomic Energy Commission, Lucas Heights, Private Mail Bag, Sutherland, NSW 2232, Australia Abstract--The failure pressures of sixteen 2219 aluminum alloy gas cylinders containing intentional defects were determined experimentally and compared with fracture mechanics predictions. The failure pressures predicted by two linear elastic fracture mechanics models for axially flawed cylinders were 10-70% low when the flaw was considered to bulge and ranged from 15% high to 40% low for restrained flaws. The ASME Boiler and Pressure Vessel Code gave approx. 15-45% conservative estimates for axial flaws in all cylinders except one containing a shallow flaw. A 20% overestimate was made for this cylinder. All predictions of a model developed for the American Gas Association for steel pipelines were very conservative, particularly for long axial defects where the failure pressures were underestimated by more than 300%. A similar conservative result was obtained for circumferentially flawed cylinders. This model was modified empirically to allow closer prediction of the failure pressure of axially flawed cylinders. Further models were developed to predict the failure of two cylinders each containing a dent superimposed on an axial flaw. Acoustic emission monitoring and source location during pressurization did not identify the known defects in most tests. It permitted uncertain nondestructive defect identification on only two cylinders. The inconsistent and uncertain result would not warrant the adoption of AE as an NDT tool on these cylinders.
As PARTof the Australian Atomic Energy Commission's program in fracture mechanics, sixteen cylindrical seamless aluminum alloy gas cylinders were pressurized to destruction. The cylinders were of AU6MGT alloy, a 6% copper alloy. The closest U.S. equivalent of this European designation is 2219; the mechanical properties of the cylinders were consistent with T6 temper. The vessels were of three sizes and wall thicknesses, Table 1. The three smaller vessels were from a different manufacturer, but were of similar hardness and spectrographic analysis. The cylinders were used for carbon dioxide storage and transport. Thirteen were removed from service because it was feared that they had received a faulty heat treatment during manufacture. It was considered that they could be susceptible to stress corrosion cracking, and could be dangerous. The remainder had reached their normal working life. As the gas bottles represented a valuable set of experimental samples, it was decided to test them to destruction and gather data for future safety assessment on similar components. Twelve cylinders were tested after artificial axial flaws were machined to various depths. Two cylinders contained circumferential flaws, and one cylinder was tested with no introduced defects. Two of the axially-flawed vessels were dented after machining and one (unflawed) cylinder was dented. The inclusion of dents was considered important as the fracture mechanics of crack-like flaws superimposed on dents is extremely relevant to pressurized components, but has been largely ignored. A combined flaw can result from accident or sabotage. Missiles from nearby explosions, falling objects or carelessly driven vehicles can also produce such a defect. The dent itself might be unintentionally designed or fabricated into a structure. "Flats" due to poor alignment during welding approximate a dent. The failure can be dynamic and accompany the rebound of the missile, or failure could occur later during an increase in service stress. A dent alone could be expected to develop cracks by stress corrosion or fatigue, as the dent can produce local residual stresses. At a later tPreviously Senior Research Scientist, Australian Atomic Energy Commission. 1
K. R. BROWNand B. ZYBENKO Table 1. Experimentaldetailsof gas cylinders oH
Equivalent Defect
Cylinder
Length
N9.
{mm)
Burst Pressure Wall Thickness ~ mm (MPa) Ultrasonic* Average Depth nom.{actual) Gauae Transducer Measured DepthGau4e Flaw Type Radius
Failure Hoop
Stress Relative (MPa)
Depth %
l
58
4.5
(4.6)
31
32.1
--
II.38
Axial
I00.75
274
40
2
I08
4.5
(4.7)
26
27.5
--
I0.64
Axial
I00.75
246
44
53
53.4
--
I0.06
No flaw
I00.75
3
531
(Yield 425)
4
408
4.5
(4.1)
26
27.6
--
ll.15
Axial
I00.75
235
37
5
33
4.5
(4.4)
34
33.6
--
ll.O0
Axial
I00.75
311
40
6
I04
0.9
(0.85)
44.5
45.6
7
107
2.2
(2.4)
38
38.6
8
Ill
6.7
(6,9)
16
9
ll2
8.1
(7.5)
lO
4.0
(4.3)
22
10
58
II
9.95-li.65
lO.41
Axial
I00.75
431
8
--
I0.72
Axial
I00.75
357
22
16.6
--
I0.77
Axial
I00,75
150
64
I0.8
--
I0.59
Axial
I00.75
95
71
22.7
--
8.10
Axial
85.4
232
53
46
46.4
--
8.05
Dent only
85.4
488
8.08
Axial + dent
85.4
21
74
ll.lO
Axial + dent
73
54 47
12
111
6
(6.0)
2
2.5
8.03-8.14
13
107
2.2
(6.0)
8
8.1
I0.61-II.05
14
58
2.7
(2.9)
22
23.1
--
6.15
Axial
70,2
215
15
150
II
If.3
--
6.27
Circumfer. + weld
70,2
123
16
158
37
37.2
6.12
Circumfer.
70,2
°A=212 %=424
2.7
(2.2)
6.20
100,75
36
*measured at crack tip
date the stress amplification caused by the dent could allow failure of the crack at an unexpectedly low stress. EXPERIMENTAL DETAILS 1. Flaws To check fracture mechanics models for the failure of pressurized cylinders, axial defect sizes were selected from a range of 0--400 mm in length and from 10-90% of the wall thickness in depth. Due to machining difficulties and wall thickness variations, these intended sizes were not always achieved, and the actual values are summarized in Table I. All machined flaws were made on the exterior of the cylinders with a milling cutter used for Charpy test specimens, i.e. 75 mm diameter, 450 included angle attd 0.25 mm tip radius. The profile of the resultant groove had circular ends and thus the cut was longer at the cylinder surface. An equivalent length was calculated such that the equivalent square-ended flaw of the same depth had the same profile area as the machined flaws. Actual flaw depths were measured after machining and the wall thicknesses adjacent to the flaw were checked with a calibrated ultrasonic thickness gauge. Dents were made in three bottles by pressing a solid steel cylinder 215 mm diameter by 75 mm approximately 10 mm into the empty gas bottle, with the axes of the steel cylinder and gas bottle perpendicular. This operation required loads of 9000-14000 kg. Some growth of the machined axial flaws was noted during unloading, so the crack was stained with machinist's dye for later measurement.
2. Strain gauging The behavior of the flaw was monitored in the early pressurizations by a clip gauge, as used for fracture toughness measurement [1]. This was placed across the center of the machined defect. However, the gauges were usually damaged by the vessel failure, so in later tests one or more strain gauges were placed on the vessel instead. The strain gauge outputs were fed via an amplifier to an X - Y recorder, and plotted against the internal pressure. Gauges were attached to the dented vessels in the positions described in Table 2. With the exception of those gauges in circumferentially flawed vessels, all gauges were oriented to detect hoop strain. Their locations and outputs are summarized in Table 2. 3. Acoustic emission Acoustic emission monitoring was conducted during pressurization using a FLIC-3 (Southwest Research Institute) flaw location computer. Three Dunegan transducers were attached by
The fracturemechanicsof aluminumalloy gas cylinders Table 2. Straindata Cylinder No.
F i r s t Detected Deviation from Linearlt X
Gau~e Type and Location
Flaw T ~
& Comment
LocaT Y i e l d Relative to General Yield
I
Cllp gauge across flaw
17.6 gauge ) 18.7 transducer) MPa pressure
Axial flaw
2
Clip gauged f a i l e d , no data
--
Axial flaw
3
Circumferential, gO0 from fracture i n i t i a t i o n
42.7 MPa pressure 428 MPa oH
Unflawed vessel, strain tensile
1.0
4
Clip gauge across flaw
I5.g MPa Pressure (transducer)
Axial flaw
0.37
5
Strain gauge Circumferential - S mm ahead of crack t i p
>28 MPa
Axial flaw
>0.65
6
Strain gauge Circumferentlal - 5 mm ahead of crack t i p
32.3 MPa pressure
Axial flaw
0.76
7
Strain gauge Circumferential - 5 mm ahead of crack t i p
27.5 M~a pressure
Axial flaw
0.65
8
Clip gauge across flaw
ND before f a i l u r e
Axial flaw
9
Clip gauge failed - no data
--
Axial flaw
I0
Circumferential strain gauge 5 mm ahead of flaw
I g . l MPa pressure
Axial flaw - very small plasticity
0.56
11
I. Circ. strain gauge 12 cm from center of dent on shoulder
0 MPa
Dent only. Strain gauge movement compressive from 0-35 MPa, thereafter tensile.
1.0
2. Circ. strain gauge at center of dent
<5 MPa (pressure)
Dent only. Strain gauge movement tenslle.
0.15
I . Adjacent to center of flaw and ci rcumferenti a l l y oriented
0.6 MPa pressure
0 * 0.6 MPa tensile strains; 0.65 MPa to 2.5 MPa ( f a i l u r e ) compressive, very small strain
2. 5 mm ahead of crack t i p , oriented ci rcomferenti a l l y
0
Strain tensile - plastic strains from s t a r t of test
0
13
Strain gauge 5 mm ahead of crack t i p - circumferential
5 MPa (gauge) 5.g MPa (transducer)
Fracture did not propagate past machined flaw - end of flaw outside dent
0.12
14
Circumferential SG at crack t i p + 5 mm
20 MPa pressure
Very small tensile strain
0.65
16
Axial SG at t i p of weld
8 MPa pressure
Burst 11.3 MPa Smell tensile strain
O, 26
16
I. Circumferential SG 6 mm from crack t i p
30.7 MPa pressure
Departure tensile to burst at 37 MPa
1.0
2. Axial SG. of crack
26.1 MPa pressure
Strain tensile
0.42*
12
5 mm ahead
0.41
*based on axial stress
silicon rubber cement in a triangle around the flaw, Fig. 1. The same location points were used for all cylinders. The FLIC-3 computer has a gating capacity to spatially filter AE sources, and this was set to detect only sources originating with 50 mm of the flaw ends or sides. In this way interference from extraneous sources could be minimized. During the testing of the unflawed vessel, the gate was set as wide as possible and all three input channels connected to the one transducer, to capture all activity from the vessel. The gate output was fed to one channel of an X - Y recorder and plotted against pressure registered by a transducer in the pumping circuit. Photographs were taken periodically of a storage CRO displaying the locations of the AE sources detected. Before pressurization was commenced on each bottle, an artificial piezoelectric AE source was placed at either end of the flaw to verify equipment function and identify the flaw position on the CRO.
4. Pressurization The cylinders with strain gauges attached were placed in a pit, filled with water and lashed down. The strain gauges were then connected, the acoustic emission transducers attached and their function checked with the artificial source. The vessels were then pressurized with a positive displacement air-hydro pump at a rate of roughly 10 MPa/min. Pressure was monitored by a calibrated gauge near the pump and separated from the cylinders by 7 meters of 6ram steel pressure pipe and a pressure transducer in the pressurization line 50 cm from the cylinders.
4
K.R. BROWNand B. ZYBENKO
5. Mechanical properties The mechanical properties were measured on tensile and fracture toUghness specimens cut from sections of one bottle, No. 13, that failed below the yield stress of the alloy. Both types of specimen were cut axially from the vessel wall in the vicinity of the artificial defect, but away from possible zones of localized plasticity. Fracture toughness specimens 55 mm long × 10 × 10 mm were notched across one face with the Charpy notch milling cutter, such that the crack plane corresponded to a circumferential flaw growing through the vessel wall. This crack orientation is likely to yield a higher measured fracture toughness than an axial crack; however, it was not possible to test an axially cracked specimen. The significance of this likely difference will be discussed when dealing with axial flaws. Three specimens were fatigue cracked from a shallow notch to the mid-section, and three were notched directly to the mid-section to estimate effect of crack sharpness on the measured fracture toughness. These results are shown in Tables 3 and 4. In other respects the procedure used in the standard fracture toughness test, ASTM E-399, were followed[l]. For the accuracy required in this study, the measured values of stress intensity were considered to be Ktc, particularly as the test results are applied in similar sections to those of the test samples. Within experimental error, no significant effect of notch acuity on the measured critical stress intensity could be detected; however, the maximum load recorded during the test increased relative to the load at crack initiation, i.e. Pmax/Po in Table 4, and exceeded the requirements of a valid test [I]. RESULTS AND DISCUSSION All vessels were successfully pressurized to failure at pressures up to 53 MPa (7700 psi). The failures were generally more spectacular the higher the failure pressure, Fig. 2. No vessel fragmented, but this would have been likely were the bottles gas filled. Visual and dye penetrant inspection of the interiors of three of the failed bottles revealed no stress corrosion cracking. The failure pressures are summarized in Table 1 tcgether with the cylinder and flaw dimensions. The results of strain gauging and acoustic emission monitoring during pressurization are presented in the following sections, which are in turn followed by comparisons of the actual failure conditions and the predictions of a number of relevant models. Many models other than those examined are available in the literature, but those selected are relatively common and tried. They are those likely to be applied in a safety evaluation by an engineer who is not a fracture mechanics specialist. The approaches are limited to those based on linear elastic fracture mechanics which, with appropriate valid or empirical corrections for plasticity, should be relevant to this aluminum alloy in these sections. Time precluded trials of the equally relevant crack opening displacement approach [27]. Table 3. Materialproperties E u r o p e a n d e s i g n a t i o n A U 6 M G T (update of d e s i g n a t i o n A U 6 M T U. S. d e s i g n a t i o n 2219-T6
Yield Stress
UT$
Elongation
Fracture Toughnes~
MPa(ksi)
MPa(ksi)
%
Klc MPa m,
12.5
--
Sample
1
317(45.9)
437(63.3)
2
311(45.1)
410(59.5)
Avg
314(45.5)
424(61.4)
12.5
Typical published p r o p e r t i e s for 2219-T6
290(42.0)
414(60.0)
i0
Hardness,
measured typical
Young's Modulus
1974)
(published)
.
.
.
. --
:~30
135 VPN ll0 BHN E = 73.1 x 103 MPa
(10.6 x i0 h psi)
The fracture mechanics of aluminum alloy gas cylinders
Fig. 1. Acoustic emission test mock-up.
Fig. 2. Aluminum alloy cylinders after testing to destruction.
5
6
K.R. BROWN and B. ZYBENKO
Fig. 3. Distribution of acoustic emission sources during the pressurization to failure of cylinder 6. The axial flaw runs between the two points indicated; there is a possible grouping at the right end of the flaw.
Fig. 4. Distribution of acoustic emission sources in cylinder 16. A possible (vertically aligned) grouping along the circumferential flaw is indicated. The straight line groupings running vertically and horizontally are artifacts resulting from sources outside the monitored area.
The fracture mechanics of aluminum alloy gas cylinders
Fig. 10. Fracture surfaces of the dented cylinders 12 (bottom) and 13 (top). The three features visible on each fracture face are (a) the machined groove, (b) ink-stained area that fractured during denting, (c) final fracture.
7
The fracturemechanicsof aluminumalloygas cylinders Table 4. Resultsof criticalstress intensitytests for the cylinderalloy .,Sample No.
Crack Type
Depth(mm)
K MPa m ½
Pmax/P~
i
Fatigue
5.6
33
i.ii
2
Fatigue
4.4
36
1.07
3
"V" notch
2.0
33
1.35
4
"V" notch
4.4
31.5
1.32
5
"V" notch
5.6
28.5
1.38
1. Strain gauging The results of strain monitoring are summarized in Table 2. The unflawed vessel, No. 3, showed a clear yield point and extensive plasticity before failing at a stress level above the uniaxial tensile strength of the material. All axially flawed vessels failed at general stresses below yield, but in all successful tests local plasticity was detected before failure, either by a strain gauge close to the flaw tip or a clip gauge across the flaw center. In the circumferentially flawed and welded cylinder (No. 15) only a small amount of plasticity was detected before failure, presumably because of the very low failure pressure, Table I. However, in cylinder 16 there was considerable circumferential and local axial plastic strain. Local plasticity occurred axially at the crack tip before general plasticity was detected circumferentially, despite the general axial stresses being only half the circumferential stresses. All three dented vessels showed plastic behavior right from the start of pressurization. The unflawed, but dented, vessel, No. 11, showed extensive yielding in the center of the dent, but nevertheless, the final failure pressure was close to that of the undamaged cylinder, No. 3. The behavior of a circumferentially oriented strain gauge on the shoulder of the dent in cylinder 11 reflected an interaction between compressive stresses developed by a wedging action as the dent was pushed out by the pressure, the tensile hoop stresses normally developed in pressurized cylinders and residual stresses associated with the dent. The gauge initially detected compressive strains which increased linearly with pressure from approximately 8-30 MPa; however, from 30-36 MPa these strains reached a maximum and decreased until failure at 46 MPa. The dent had been largely removed prior to failure; however, failure initiated in the dent, presumably at an area where ductility had been exhausted. When a flaw was also present, the failure pressures were reduced alarmingly. The combined effect of a flaw and a dent reduced the failure pressures to 15-30% of those expected for an equivalent flawed but undented vessel. 2. Acoustic emission monitoring The results of monitoring the cylinders during pressurization are summarized in Table 5. No data were obtained on two cylinders due to moisture in the transducer connections; the connections were sprayed by fine water jets from leaks that developed in the pressurization circuit after testing was under way. No data were obtained in two further cylinders because of masking by "white" noise generated at leaks. In all other tests, totalling twelve bottles, the equipment appeared to work satisfactorily; however, inexplicably no acoustic emission was detected from cylinder 10. Emission occurred in all other cylinders, but rarely were there sufficient counts to permit statistically significant localization. Some indication of grouping of activity along the flaw was obtained in cylinders 6 and 16; however, if the locations of flaws were unknown, it is doubtful if an observer would have attached any significance to the groupings, Figs. 3 and 4. It is possible that in a few tests the machined flaw may itself have interfered with location by shadowing one or two of the 3 transducers. This is more likely with deeper flaws, e.g. as in cylinder 8 in which localized activity was not perceived despite a relatively large number of counts. The source location computer was able to locate an artificial source at the flaw; however, more scatter was noted around deeper flaws. It has been claimed[3] that "natural" defects can yield more acoustic emission than "artificial" defects, presumably due to the
K. R. BROWNand B. ZYBENKO
10
Table 5. Acousticemissionmonitoringresults Cylinder No.
Total AE Counts During Entire Pressurization
Comments
17
No localization, no correlation with pressure.
24
16 of these counts occurred in final 5% of pressurization, but were scattered wide of flaw.
146
Gate set to include artefact a c t i v i t y , counts increased at accelerating rate as failure approached.
4
12
No localization, no correlation with pressure.
5
20
Final 15 counts in last 15% of pressurization no significant localization.
6
14
All counts in final 25% of pressurization, none in last I0%. Possible location at flaw ends of two clusters each of 3-4 counts, see Fig.
7
NO data
8
87
3
Leaking noises only masking a c t i v i t y - leak in pressure connector. Counts increased at an increasing rate as f a i l u r e approached, no s i g n i f i c a n t l o c a l i z a t i o n .
9
No data
One channel lost due to moisture.
IO
No data
No a c t i v i t y detected, equipment apparently OK.
II
4
12
12
13
No data
14
13
15
No data
16
208
All four counts detected in f i n a l 8% of pressurization. No l o c a l i z a t i o n ,
no c o r r e l a t i o n with pressure.
Leak noises masked a c t i v i t y . All 13 in f i n a l 12% of pressurization - no significant localization. Wet transducer connections due to ear l y leak. The gate included a r t e f a c t a c t i v i t y - 90% of t o t a l counts due to artefacts. Possible flaw location by a line of 6 points, see Fig.
presence of oxides, dirt and other phases. It is conceivable that more success may have been achieved with natural defects; however, it would be foolhardy to rely on this vague possibility during the NDTsafety assurance of these vessels, particularly as they are well maintained and are free of dirt or corrosion products. Further, in dirty or corroded structures extraneous emission from corrosion products and scale remote from defects may obscure emission generated in defects. It is unlikely that the use of more sophisticated monitoring equipment would have improved the present result, as the sensitivity and noise discrimination of the present transducers and preamplifiers compares favorably with more expensive equipment. Present inadequacies lie in the lack of sources in the cylinders rather than in the ability of the equipment to detect and handle the signals. The present results are disappointing, as most tests were conducted carefully under fairly ideal laboratory conditions, and with prior knowledge of the defect location. They suggest that extreme caution is necessary when interpreting the results of AE monitoring in the field, where conditions are often far from ideal, materials are frequently uncharacterized and defects are rare.
3. Burst pressures (a) Axially fla wed cylinders Preliminary plots of relevant data for axially flawed cylinders showed a clear relationship between flaw length and flaw depth, Figs. 5 and 6. The data were compared with the predictions of three models for the failure of axially flawed pressure vessels. The comparisons are summarized in Table 6. LEFM models. The results of the tests on simple axially flawed gas bottles were compared first with the predictions of two linear elastic fracture mechanics (LEFM) models[4, 5]. Both considered the vessel walls to be the equivalent of flat plates of width equal to the vessel wall thickness, and containing a single edge notch of length "a". The axial length of the flaw was
11
The fracture mechanicsof aluminumalloygas cylinders i
i
5 0 ~ 3(0)
4O )
3O
Experimentally determined curve for approx. / ' 4 0 % deep flaws
0.44)
O
4(0.37 o.
zo
\ o I.L
% AGA prediction I
5o
I I00
I 150
I 200
Flow length,
I 250
i 300
I 350
I 400
mm
Fig. 5. Plot of failure pressures for axially flawed cylinders against crack length, 2c. The cylinder numbers
and the relative flaw depths (in parentheses) are indicated. The broken curve represents the predictions of the AGA model[8].
~
t 3(0) 5O - N %
40 o
n
o
• 5(33) ,, ,, "
30
" ~
Experimental curve f;r 104-112turn long flaws
t, i.
I (58)
0 "~2(108) 4(408) ~ ( 5 8 }
e~
14(581
20
~
_ ~8(I
II)
o i,
9(112]
0
I 0 I
I 02
I 03
I 04
I 05
I 06
I 0.7
I o.e
Relative flaw depth
Fig. 6. Plot of failure pressures for selected axial flaws against the flaw depth relative to the wall thickness. The lengths of these selected flaws are in the range 104-112 ram--see Table 1.
ignored, and failure was considered to occur by propagation through the wall. In both models the crack tip stress intensity is given by:
K = crYx/(a + r) where o- is the applied tensile stress normal to the flaw (hoop stress), r is a crack tip plastic zone correction given by
r=(Ky/nv~(2)'cr \O'ys/ I
in which trrs is the material yield stress.
[61
K. R. BROWN and B. ZYBENKO
12
Table 6. Failurehoopstress predictionsfor axiallyflawedcylinders C[linder
No.
-LEFM
Model
1
LEFM
Model
1
115
185
2
105
175
4
135
195
5
120
185
Failure
Hoop
Stress,
2
Code
A.G.A.
AS~
175
MPa Model
Modified A.G.A. Model
Actual Result
87
275
274
150
q5
230
246
140
25
205
235
210
127
305
311 431
6
390
395
515
75
315
7
225
265
275
65
285
357
8
45
125
85
40
165
150
9
30
ii0
80
30
135
95
i0
80
170
150
75
235
232
14
115
210
180
75
230
215
The calibration factor, Y, in Model 1[4] = 1.99-0.41 ( t ) + 18.7(t)"-38.48 (t)3 + 53.85(t) 4 for
,6, and = 1/2(t ) 1/2(1-(t))-~/2(1 + 3 ( t ) ) for 0.3-< ( t ) - < 1,0
[61
In Model 215], "Y" is given by
5",/(7r) - [20- 1 3 ( t ) - 7 ( t ) 2 ] '/> Model 1 is derived for the case when the ends of the flat plate are free to rotate; Model 2 is derived for rigidly supported ends. The predictions of these models are given in Table 6 and Fig. 7. Model 2 gave better prediction than did Model 1; Model 1 underestimated the failure stress by 10%-70%; the results of Model 2 ranged from a 15% overestimate to 40% conservative. As most predictions were low, a lower toughness for axial flaws would further impair the agreement. The ASME boiler and pressure vessel code. The ASME Boiler and Pressure Vessel Code [7] is not designed to predict failure, but to provide an estimate of the safety of a cracked component. Thus a conservative result is to be expected when the model is used for prediction. The code is also based on linear elastic fracture mechanics and considers a component unsafe when the stress intensity at the tip of a crack approaches the critical stress intensity, Ktc, of the material. The stress intensity is evaluated from: Kt = ~r,~Mm~/(Tr)~/(a/Q) + ~bMb~/(~r)~/(a/Q)
where om, o% is the membrane and bending stresses; a is the minor half-diameter of embedded flaw; flaw depth for surface flaw; Q is a flaw shape parameter to be determined using tr,~ and
The fracturemechanicsof aluminumalloygas cylinders
13
500
LEFM analysis
Model
2
Model
I
400 •
500
7
14~ "0
07
0'05
200
Q_
04
140 • 0, 0 5 ioo
2 IO
90 0
I00
8 200
300
400
500
Actual failure stress a- h MPa
Fig. 7. Plot of actual failurehoop stresses versus those predictedby the LEFMmodelsdescribedin the test. the flaw geometry; Mm is the correction factor for membrane stresses; Mb is the correction factor for bending stresses. The shape f~tors and correction factors are determined graphically, and in the case of simple axial flaws, bending stresses were insignificant. The hoop stress at failure calculated from the ASME model is plotted against actual failure stress in Fig. 8. With the exception of the result for cylinder 6, all results are conservative by 15--45%. Both the actual and predicted failure stress of cylinder 6 were above the biaxial yield stress of the material, 425 MPa, so the unconservative result does not reflect on the suitability of the ASME model for safety evaluation. A.G.A. model. Another model for failure prediction is that developed by Kiefner, Eiber et al.[8] for the American Gas Association. The model is intended for flaws in steel line pipe materials. These have high toughness relative to high strength aluminum alloys, but the model was considered of potential suitability for the present study. It should also be noted that, unlike the ASME Code, the Kiefner et al., model is intended to predict failure and does not incorporate a safety margin. The model predicts failure when Kc2~"= In sec 2-~M(~) 8c6 z where ~ is the hoop stress level at failure (i.e. PR/t); P is the internal pressure level at failure; is the flow stress of the material; M is the Folias bulging factor; R is the radius of the pipe; t is the wall thickness; 2c is the length of the through-wall flaw; and Kc is material toughness. Although based on fracture mechanics, the model contains a degree of empirical adjustment based on experience. For example, the material's flow stress is taken as the yield stress, plus 10,000 psi, an assumption unlikely to be suitable for aluminum alloys. In the present work, the relevant flow stress was taken as the average of the yield (278 MPa) and ultimate tensile strength (532 MPa).
14
K.R. BROWNand B. ZYBENKO
E)
500
ASME analysis 400
300
7
14
20C
O
Q-
O
5
O,
IO @ 2 ioo 8
0
I00
200
300
400
500
Actual f a i l u r e stress o" h M P a
Fig. 8. Plot of the actual hoop stresses of axially flawed cylindersat failure against predictionsof the ASMEanalysis[7]. Various expressions are available for the Folias correction factor, M. The expression used in the present work was
I,- l M = Mp =
"
Mrt
for partial thickness axial flaws of depth "d".
L,- J where MT, for through-wall flaws, is Mr=
4( t)
1+1.61 c" .
Whereas Kiefner et al., used empirical correlations to obtain fracture toughness data from Charpy test results, we were able to measure directly the Kc of the aluminum alloy, Table 4. The predictions of this model are compared with experiment in Fig. 9. It can be seen that the predictions are a factor of about 3 too low and are excessively conservative. If a lower Kc for an axial flaw was used, the prediction would be worse. A plot of predicted failure stress against flaw length, Fig. 5, showed that for the present cylinders the model placed excessive weight on flaw length. The relatively poor agreement between these results for axial flaws and the predictions of models that allow for bending or bulging suggests that bending or bulging corrections may not be appropriate for shallow axially flawed cylinders of relatively low toughness materials, Table 6. These models include the AGA model which uses the bulging factor "M", and also the flate plate models that allow for rotation of the plate ends. The bulging factor in the AGA model is also used in other models[9] and is strongly dependent on the axial length of the flaw. For the cylinders studied, this is clearly inappropriate; the failure predictions were worse for longer flaws, Table 6.
The fracturemechanicsof aluminumalloygas cylinders
15
5000
•
AGA analysis
4000
Modified AGA
6
5 3000
J
7
.u_ 2000
Q_
~000
,• 90
0
Jooo
05 , 4 • • I0 0 ' •
8
6
7
02
•4 2oo0
3oo0
4000
5000
A c t u a l f a i l u r e stress o" h M P o
Fig. 9. Plot of the actual hoop stresses of axiallyflawedcylindersat failureagainstthe predictionof the AGAanalysis[8] and the empiricallymodifiedanalysisdescribedin the text. Although stress amplification due to bulging is evident in ductile materials where significant plastic flow permits bulging or buckling[8], an axial flaw in a cylinder of low toughness material would not be expected to bulge under elastic hoop loading any more than would a centercracked flat plate.
Modified A.G.A. model. To permit future evaluation of the safety of similar vessels, Kiefner's model was altered empirically to lessen its dependence on flaw length, and to fit the present data. The result: Kc2" 12Ir [¢rMptr] in SI units, O + c - ~ =lnsec L 46 J allows predictions which agree reasonably well with experiment, Fig. 9. One result, for cylinder 9, is non-conservative by approximately 40%, suggesting caution when using the model for extremely deep flaws. The model is approximately 30% conservative for the shallow flaws tested. (b) Circumferentially flawed cylinders This study of circumferential flaws is limited, as only two tests were conducted. However, the results were examined for agreement with those current models of the failure of circumferentially flawed cylinders that were considered appropriate to these vessels.
Cylinder 15. This cylinder contained a through-wall flaw spanning 35% of the cylinder circumference. The flaw was a hacksaw cut that had been made in the vessel to emphasize its rejection upon completion of its service life. To salvage the vessel for this test program the cut was made pressure tight by welding. A shallow single-pass MIG weld achieved a penetration of less than 2 mm, i.e. less than 35% of the wall thickness. It was desired only to stop leaks in the
16
K.R. BROWNand B. ZYBENKO
flaw, not to provide a structurally sound weld that would interfere with the use of an analysis for through-wall flaws. An appropriate analysis of failure is that due to Folias[10] for circumferential through-wall flaws. In this analysis, the failure stress (axial) is given by:
0- = c°s ' [exp 75GJ where o-* is the material flow stress, a weighted average of the yield stress, 0-~.,and tensile strength, 0-,. 0-* =~ o'y +
= (341.5 MPa) (for cylinder 15)
c is the half crack length (0.075 m); K is the material fracture toughness (32 MPa mm); I = 1+(~',~2/64) (= 1.0273). where ;12=(c2/Rt)~/(12(l - v)2) (41.87) in which R is the cylinder radius ( = 0.0702 m); t is the wall thickness ( -- 0.00627 m); and v is the material Poisson's ratio (O.33). In this analysis no allowance has been made for any strength contribution from the weld metal. When this analysis is applied to cylinder 15, an axial failure stress of 63 MPa is predicted. which agrees surprisingly well with the actual value of 61.5 MPa (half of oH in Table 1). This agreement may be fortuitous as failure in the test occurred by the cracking of the weld and its opening by about 0.5 mm. The flaw did not propagate circumferentially beyond the hacksaw cut and the Folias analysis is designed to predict this failure mode. It is possible that this mode may have occurred if the cylinders had contained gas instead of water. An alternative analysis based on the American Gas Association model for axial flaws and summarized by Wilkowski and Eiber[ll]t assumes that failure of a circumferential flawed cylinder will occur when K2~" lnsec [rcMrc0.] 8c0.*:1_ 20-* J where Mrc is a bulging factor for a through (T) circumferential (c) flaw and accounts for the stress amplification due to the curvature of the cylinder. This factor is given by several relationships including:
Mrc = 0.738 + 0,126/~
[121
Mrc = 1 + 0.00635A 2+ 0.00055A4
ll3i
Using these relationships, axial stresses, 0., of 42.4 MPa and 29.3 MPa are predicted. These clearly yield less satisfactory predictions than the Folias analysis.
Cylinder 16. This cylinder contained a machined "V" shaped groove aligned circumferentially around the mid-section and penetrating to 36% of the wall thickness. Failure was catastrophic, and although no fragmentation occurred, the two halves of the vessel separated at the flaw and hinged on the remaining ligament to open about 90°. Although failure occurred at the flaw, the failure hoop stress equalled the uniaxial tensile strength and it would appear that quite large circumferential surface flaws could be tolerated in these vessels when only pressure loading is involved. The LEFM models[4,5] used previously for axial flaws gave reasonable agreement with experiment for the surface flaw in this cylinder. Model 1 estimated an axial failure stress of 175 MPa (17% low) and Model 2 an estimate of 252 MPa (19% high). The failure of this cylinder was also analyzed using a modified relationship of that given previously for cylinder 15 in which Mrc is replaced by Mpc for partial thickness circumtlt shouldbe notedthat the relationshipfor Ais givenincorrectlyin this reference.
The fracture mechanicsof aluminumalloygas cylinders
17
ferential flaws, where d tMrc t
1-- ff and where d is the flaw depth and t the wall thickness. When using the two versions of M r c of Kihara[12] and of Adams[13] given previously, values of M p c of 1.21 and 1.34, respectively, were obtained. These allowed failure stresses predictions of 53.03 MPa and 47.6 MPa, respectively; both results agree poorly with the actual value of 212 MPa. (c) D e n t e d cylinders Although the cylinder containing a simple dent (No. I 1) failed at a pressure close to that of the undamaged cylinder, the two vessels containing a combined flaw and dent failed at pressures less than a third of those expected for an equivalent flawed but undented vessel. The magnitude of this synergistic effect could be underestimated in design, so attempts were made to develop a satisfactory model that would allow failure prediction or safety assessment. (1) Stress a n a l y s i s The dented area in all bottles was approximated by a flat circular section 80 mm in diameter. A flat section develops the highest pressure-induced tensile stresses on the exterior surface, but it should be noted that the stresses are markedly sensitive to dent profile. They change sign as the profile changes from convex to concave. The surface stresses caused by a pressure P acting on such a section of radius "q" and thickness "t" are given by: ab =
- 3Pq2(m + 8mr 2
1)
- 3Pq2(3m + 8mt 2
1)
and trb =
Equation 1 applies when the periphery of the circular section is rigidly fixed and eqn (2) when the periphery is supported flexibly and unrestrained [14]. The parameter "m" is the reciprocal of the Poisson's ratio for the material. In this case m was taken as 3. Although there is slight flexibility of the restraint on the dented area, as evidenced by the growth of the machined flaws during the removal of the denting load, the restraint in these thick-walled cylinders may be considered rigid. For completeness, the ranges of stress and stress intensities predicted by the rigid a0d flexible solutions are given in Tables 7 and 8. In addition to the bending induced surface stress, trb, a general hoop stress trh also acts normal to the machined flaw. This is given by Barlow's formula: Oh=
PR t
m
Table 7. ASME predictions of Stressin~nsitiesin dented cylinders(figuresin parenthesis are fora flexibly supported dent) Shape Membrane Bending Correction Factor S t r e s s S t r e s s Factors Q %,MPa Ob,MPa Mm Mb Cylinder 12
1.04
21
31 (77) ~3
Cylinder 13
l.O
73
53(131)
tNote that this equation is incorrectly inverted in Ref. [11]. EFM Vol. 15, No. I-2--B
2.2
2'2 l.l
Material Critical Stress Intensity K MPa m~2 Kc, MPa m~2 17(29) )
)
30(42) )
K. R. BROWNand B. ZYBENKO
18
Table 8. Predicted stress intensities in dented cyliaders by alternative LEFM analysis. (Figures in parenthesesare for a flexiblysupporteddent) Stress Intensity, K flPa m~2 ~h,MPa Kb(bending ) Kh(membrane) K(total
Cylinder
or,MPa
12
31 (77)
2~
12(31)
25
37(56)
13
53(131)
73
12(31)
35
47(66)
Material Critical Stress Intensity Kc, MPa m~2
32
where "R" is the vessel radius and "t" the wall thickness. The total surface stress can be taken as ~r = o'b + trh.
The axial stresses due to longitudinal bending in the dent and due directly to pressure have been neglected, as these act parallel to the machined flaw. Residual stresses. During the denting of the bottles with machined flaws, extensive crack growth commenced from the root of the machined flaw. As the root of the flaw is in compression during denting, crack growth must have occurred during unloading, under the influence of the residual stresses caused by the dent. The residual stresses were reduced by crack growth; however, the growth of the crack ceased before penetrating the wall, presumably when the crack tip stress intensity dropped to a finite value corresponding to arrest, KA. If the value of KA were known, an estimate could be made of the corresponding residual stress. The residual stress may also be estimated (a) from the pressure at which plastic deformation was first detected by a strain gauge on the outer surface of the central region of the dent. In the case of the unflawed dent, cylinder I !, plastic deformation was detected as soon as pressurization was commenced, suggesting that the surface residual stress was equal to the flow stress ( ~ 405 MPa); (b) from the critical stress intensity which must have been reached at the machined notch root during the unloading of the flawed bottles. This would give a minimum value; for the present bottles the minimum estimates of the surface residual stresses were 335 MPa and 365 MPa for bottles 12 and 13, respectively; (c) from the geometry of the deformation caused by the denting. The hoop strain induced in the circumference of the bottle approximated 1.5%, which exceeds the strain at yield, and from the uniaxial tensile test data approximates a flow stress of 380 MPa. It was not possible to verify the model presented above (in the dented and unflawed bottle, No. 11) because of the residual stress, nor was it possible to confirm the appropriate weighted average to account for the compliance of the periphery of the dent. It is clear that the residual stresses are high and must be considered in any treatment of similar dented components. The present work suggests that the residual stresses are equal to the flow stress in a simple dent. It should be noted that the sum of the hoop, bending, and residual stresses will reach the yield stress in compression on the inside surface of the dent, before tensile stresses reach the yield stress on the exterior. (2) Analysis o/ dented vessels using A S M E code An attempt was made to assess the applicability of the ASME Code[7] to the two dented and axially flawed vessels. Unlike in the cylinders containing simple axial flaws, the bending stresses, trb, are significant in the dented cylinders and were obtained from the above stress analysis. Because of the growth of the flaws during denting, the determination of most of the bending and membrane correction factors (Mb and Mm) required extrapolation of interpolated graphical data given in the code and hence these factors are subject to large errors. No attempt was made to obtain more accurate estimates from first principles. The results calculated without allowance for residual stress are shown in Table 7 as estimated stress intensities, K, at the crack tips; these should be compared with the measured fracture toughness of the material, K,.
The fracture mechanicsof aluminumalloygas cylinders
19
The use, or more strictly, misuse, of the code, yielded low estimates of the induced stress intensity at failure. There was no degree of conservatism that would allow a confident safety assessment. A conservative result can be obtained when allowance is made for residual stresses. It could be assumed that residual stresses are at yield, or that the crack tip stress intensity due to residual stress is equal to the critical stress intensity Kc. In the latter case, the assessment would be approximately 50 and 100% conservative, a result which is comparable to those obtained for the undented vessels. (3) Alternative [ailure analysis of dented vessels As in the ASME analysis, the stress intensity at the root of the flaw may be taken as the sum of the stress intensities due to the bending and the hoop or membrane stresses, i.e.
K = K~ + K~. When the flaw is long relative to the dent size;
2 K = 3' ~b" t m" fl(a]t) + trhX/(a + r). [2(a]t) where [l(a/t) = 2.9(a/t) 1/2- 4.6(a/t) 31~+ 21.8(a/t) 512
- 37.6(a/t) 7/2+ 38.7(a/t) 9/2 f2(a]t)= 27(a[t~ ( 1 - t )-3/2 " ( l + ~ -)
[6]
and r, a plastic zone correction K
2
= (~-~y~)/4~(2)7r
[2(a/t) is equivalent to "Y" in Model 1 used earlier for axial flaws. The expression for Kb uses the compliance expression from the ASTM Standard E-399 [1] equation for three-point-bend fracture toughness test specimens, and is written in terms of the surface stresses normal to the flaw axis. That for Kh is for a single-edge-notched tensile specimen [6]. The predicted stress intensities at failure are conservative and are 15 and 50% above the actual failure criterion, Kc. Subject to further experimental verification, it would appear that the proposed model would be suitable for assessing the safety of similarly damaged pressurized components when residual stresses might be overlooked. If due allowance is made for residual stresses, as was done in the ASME evaluation, the model is over 100% conservative. In all of the above treatments of dented cylinders, no allowance has been made for the potential reduction in fracture toughness associated with deformation at the crack tip during denting, nor for changes in flaw sharpness during crack growth. The flaws in the two vessels were machined prior to denting and both grew during denting. Because of the insensitivity of the measured fracture toughness to crack sharpness (Table 3), no significant effect would be expected due to sharpening of the machined notch by crack growth. Some effect of prestrain of the material ahead of the crack tip might be expected; however, the crack in cylinder 13 grew during unloading, through the plastically compressed zone, to approximately the neutral plane of the nett section ahead of the machined notch. Only small prestrain would have occurred in this region. Some compression of the notch root would have occurred in cylinder 12, which may explain the lower stress intensities at failure predicted by both the ASME and alternate analysis. Further studies of the effect of prestrain are warranted.
20
K.R. BROWN and B. ZYBENKO
CONCLUSIONS 1. Models have been selected that will allow the safety assessment of 2219-T6 aluminum alloy gas cylinders containing axial or circumferential defects. However, the models were selected only after experimental verification of their applicability and accuracy. For cylinders of a different alloy or different geometry, it would be necessary to be extremely conservative, perhaps excessively so, in order to assure safety. The economic penalties associated with excessive conservatism may warrant a full-scale testing program to confirm more accurate models for the new material or geometry. It is clear that the fracture mechanics of pressurized components have not been sufficiently developed to allow confident and economic assessment of even simple defect geometries in a sufficiently wide range of materials. 2. A dent superimposed on an external crack-like surface defect can exaggerate the effect of the defect by a factor of 3-6 for the dent and cylinder geometries and the alloy studied. The residual stress caused by the dent appears to be the most deleterious factor. Further studies of combined flaws are warranted and have been commenced. 3. Acoustic emission defect location could not be used with sufficient confidence as a non-destructive test in these cylinders. Little emission was detected and only vague indications were made of known defects in two of the twelve flawed cylinders monitored during pressurization. These indications may have been overlooked without foreknowledge of the defect location. As AE monitoring was relatively unsuccessful in tests under good conditions, the technique cannot be recommended as an NDT test of these vessels.
Acknowledgements--The authors are grateful to the staff of the Australian Atomic Energy Commission Testing and Inspection Departmentfor their assistance with setting up the tests. In particular we wish to thank Mr. Reg Gibbs whose experience made the testing program run smoothlyand safely. The advice and suggestionsof the AustralianWeldingResearch Associationwere most helpful in the planningof these tests. Thanks are also due Dr. Colin Chipperfieldfor his help with the draft of this paper.
REFERENCES [ll ASTM Standards E399-74, Plane strain fracture toughness testing of metallicmaterials. 1974Annual Book of ASTM Standards.
[2] M. G. Dawes and M. S. Kamath, The COD design curve approach to crack tolerance, Conf. on Tolerance of Flaws in Pressurized Components, 1978 Inst. Mech. Engng. London (1978). [3] H. Dunegan, Private Communication,Sydney, Australia(1978). [4] W. F. Brown and J. E. Strawley, ASTM STP 410 ASTM (1966). [5] D. O. Harris, J. Bus. Engng 89, 49 (1967) In Compendium of Stress Intensity Factors (Edited by D. P. Rooke and D. J. Cartwright). Ministryof Defence, UK, HMSO London (1976). [6] T. W. Orange, Some effects of experimentalerror in fracture testing. In Fracture Analysis, ASTM STP 560, p. 122 (1973). [7] ASME Boiler and Pressure Vessel Code, Section I l, In service inspectionof nuclear power plant components. 1974 Article A. 3000, p. 117. [8] J. W. Kiefner, W. A. Maxey,R. J. Eiber and A. R. Duffy, Failure stress levels of flaws in pressurizedcylinders.ASTM STP 536, p. 461 (1973). [9] G. T. Hahn, M. Sarrate and A. R. Rosenfield,Criteria for crack extension in cylindrical pressure vessels. Int. J. Fracture Mech. $(3), 187 (1969). [10] E. S. Folias, An axial crack in a pressurizedcylindricalshell. Int. J. Fract. Mech. 1, 104-113 (1965). [11] G. M. Wilkowskiand R. J. Eiber, Review of fracture mechanics approaches to definingcritical sizes of girth weld discontinuities. Welding Res. Council Bull. 239. New York (July 1978). [12] H. Kihara, T. Kanazawa, S. Machida and M. Hassain, Brittle fracture initiation in steel pipes. Mech. Behavior Materials. Japan Society of Material Science. [13] N. J. I. Adams,The influenceof curvature on stress intensityat the top of a circumferencecrack in a cylindricalshell. "Damage Tolerance in Aircraft Structures" ASTM STP 486, 39--49(1971). [14] R. J. Roark, Formulas [or Stress and Strain, 4th Edn. McGraw-Hill,Kogakusha,Tokyo. (Received 26 November 1980; received [or publication 18 February 1981)