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Prediction of linepipe fracture behaviour from laboratory tests
Int. J. Pres. Ves. & Piping 12 (1983) 1-27
Prediction of Linepipe Fracture Behaviour from Laboratory Tests B. Holmes, A. H. Priest & E. F. Walker British Steel Corporation, SheffieldLaboratories, Swinden House, Moorgate, Rotherham, S. Yorks $60 3AR, Great Britain (Received: 22 January, 1982)
ABSTRACT Data obtained from full scale pipeline burst tests forming part of the American Iron and Steel Institute (AIS1) and the European Pipe Research Group (EPRG) programmes have been correlated with measurements of the shear fracture propagation energy and potential energy available. The former was obtained from the ~C, and Battelle energies using a previously derived two-parameter expression. For the combined A IS1 baseline and EPRG 'separated' and'non-separated" data, this expression explained considerably more of the variability than did the three generally used theories which only incorporate ~C,. values. There was also found to be no significant effect of pipe wall thickness when fracture occurred in the fully shear mode. Results from A ISl 'separated" materials did not generally fit the above two-parameter expression but they could be accommodated into a threeparameter expression which also incorporated values for yield stress and strain hardening exponent. The reason Jor this has been attributed to possible differences in the strain rate sensitivity of these materials and the presence of separations may not be significant.
INTRODUCTION Three well known relationships associated respectively with Battelle, 1'2 AISI 3 and British Gas 4 have been applied to the prediction of the outcome of full scale pipeline burst tests in terms of defining limiting 1
Int. J. Pres. Ves. & Piping0308-O161/83/O012-O001/$03.00 © Applied Science Publishers Ltd, England, 1983. Printed in Great Britain
2
B. Holmes, A. H. Priest, E. F. Walker
Charpy energy values to resist fracture propagation. Whilst these relationships were reasonably successful when applied to certain of the AISI test data, weaknesses were exposed in dealing with the results of the EPRG test programme. 5 Suggested reasons are as follows: (a)
The supposed effect of thickness is different in the three 'theories' and must be wrong in at least two of them. (b) Because of the small size of the Charpy test piece, no allowance is made for the plastic deformation accompanying fracture in a linepipe. (c) The existing relationships propose an agreement between terms which are expressed in unusual units which are not related to any known physical process and are difficult to relate to fracture energy. These difficulties have been known for some time and up to now considerable effort has been devoted to developing a better method of characterising the shear fracture resistance of linepipe steels. The twoparameter approach 6 appears to be a promising alternative since all of the above criticisms are resolved, and the total energy for fracture is governed by two constants, R c and So. An attempt has now been made to apply the approach, based on laboratory tests, to the practical results of full scale burst tests using the existing data. The main components of the proposed treatment are as follows: (a)
R~ and S~ values ideally determined from impact tests on at least two specimens with significantly different ligament length are used to define the fracture resistance from the original equation U B( W - a)
-2Rc+S~(W-a )
(1)
The term R~ is assumed to equate to the energy associated with the initiation and propagation of the shear fracture whilst Sc governs the energy absorbed as a consequence of associated plastic deformation. A value of 2R¢ is chosen to represent the condition during pipeline fracture as this is thought to be very similar to the situation which develops in a tension test. (b) In a pipeline, the extent of plastic deformation in eqn (1) is governed not by ( W - a) but by a simple function of the diameter of the pipe.
Prediction of linepipe fracture behaviour
3
(c) Fracture propagation energy is plotted against the total energy available for unit area of fracture which is virtually equal to the stored energy of the high pressure gas. This simple procedure ensures that the dimensions of both the energy available and the energy required for fracture are the same. (d) Linear boundaries are drawn through the lowest arrest data point and the highest propagate data point. These represent 100 per cent confidence limits in respect of the data available because it is felt that in the area of linepipe failure, a single unpredicted failure is unacceptable. The propagate boundary should therefore define minimum values of fracture propagation energy required to guarantee crack arrest.
FACTORS A F F E C T I N G E V A L U A T I O N OF Re A N D S c F R O M RESULTS OF T O U G H N E S S TESTS Before the concept expressed in eqn (1) could be used as a practical procedure, information was required on a number of factors which could have influenced the linearity of the relationship derived. For instance, as discussed below, data from small ligament lengths tend to fall below the linear relationship and it is, therefore, necessary to know the minimum ligament length required to avoid this. Other factors are thickness B, test piece geometry, notch acuity, strain rate and temperature. When the influence of the above factors is understood it should be possible to devise a standard testing procedure so that values of Re and S¢ can be determined unambiguously. Records of the ]Cv and Battelle fracture energies for burst test materials are documented and this should enable an estimate of the R¢ and S¢ values to be calculated and be used to quantify the resistance to fracture of pipelines more precisely than hitherto. The influence of the above variables on R¢ and S¢ has been assessed by performing appropriate tests on six samples of pipeline steel including normalised, controlled rolled, and quenched and tempered materials. An example of the data derived from slow rate tests on CT test pieces from several steels is shown in Fig. 1, where it can be seen there are linear relationships of the form shown in eqn (1). Data are also included which indicate that fracture energy increases with loading rate and that specimen geometry has little or no influence on the results. Controlled
4
B. Holmes, A. H. Priest, E. F. Walker
Energy per unit area, J/mm 2 L Controlled 2.0
/
/ / ' ~
rolled
!
,
~
e /
o
Controlled rolled
4.o
/ ~
a/. -'~a°/°a/"
°a/
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4.o
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..~/~0
~"
2.0
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&j
Normalised
6.0
4.o
~
0~
0 ~"
2.0
I
0
Fig. 1.
50 Ligament
I
i00 length,
150
mm
Energy per unit area as a function of ligament length. • Impact rate; × C, type (notched); + ~C V(notched); (3 Slow rate CT; A Slow rate S E N B
Prediction of linepipe fracture behaviour Energy
per
unit
area,
5
J/mm 2
4.o
3.o
2.O
1.O
"/"
o/ O
Fig. 2.
l 50 Ligament
l ioo
length,
I 150
mm
Influence of temperature and small ligament sizes (cerium treated steel). • 20 °C; × 0°C; + - 2 5 ° C ; C) - 5 0 ° C
rolled, normalised, and also quenched and tempered materials assumed the same general relationship. For the quenched and tempered material, however, the Re and Sc values were significantly lower than for the original normalised material, probably because of the higher tensile properties of this material. Similar data were obtained at various test temperatures in the range 0 to - 5 0 eC for cerium treated steels and an example is shown in Fig. 2 where it can be seen that there was very little effect of temperature on the energy per unit area values. The deviation from linearity for ligament lengths of less than 30 mm is of significance. The effects of thickness on fully shear fracture are shown as a function of the ligament length for two of the materials in Fig. 3. No significant difference was observed in the results for test pieces machined from the surface or centre region of the material but nevertheless the average values were used. It can be seen that there was generally very little effect of thickness on the energy per unit area values for ligament lengths in the approximate range 30-60 m m where the data are obtained from test pieces machined from a single thick plate. Conflicting reports have been made on the influence of thickness on the shear fracture resistance of linepipe materials. Indeed several authors make different specific allowances for this in calculations for predicting the performance of pipelines using a power term for B in the range ¼to 1.
6
B. Holmes, A. H. Priest, E. F. Walker
For example, Fearnehough 7 and Judy and Goode 8 use a factor of B 1/2. The explanation for these different opinions becomes apparent when a comparison is made of U/A values for test pieces of different thickness at different ligament length. When, for instance, ( W - a) values are greater than 30 m m as in Fig. 3 there is no influence of thickness on U/A values, but when the ligament size is reduced to below about 2 0 m m then a significant difference is observed. The difference is particularly marked in Energy
per unit
area,
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4.0
Standard
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/ /
++J
~
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Fig. 3. Influenceof thickness. • 3 m m ;
iOO length,
J
150
mm
× 6ram; + 12ram; O 25ram; • 35ram.
test pieces for the Charpy test which of course has been the standard test method for many years. The magnitude of the difference is clearly shown to be a function of the toughness of the material tested in Fig. 4 where a comparison is made between U/A values for full thickness (B = 12.7 or 16.0 mm) and ~Cv (B = 6.67 mm) nominal Charpy tests at different levels of toughness. F r o m Fig. 2 it is shown that below a ligament size of about 25 m m the data do not fit the linear relationship; a reduction in U/A occurs so that the values extrapolate to a value of zero at zero ligament length. The minimum ligament length necessary to avoid such deviations is related to the thickness and toughness of the steel so that this size probably varies with increasing thickness, yield stress and toughness. Consequently, Charpy type test pieces exhibit a greater influence of thickness for the tougher materials. Considerable detailed work would be required to prove this point; however, for thicknesses up to 16mm a
Prediction of linepipe fracture behaviour
7
minimum ligament size of about 30 mm would seem to be adequate in order for the data to fit the linear relationship. It has been shown that the difference between U/A values for machined notched and fatigue cracked test pieces is a function of Re. The values of U/A for the notched full thickness Charpy-type test pieces shown in Fig. 1 are, therefore, increased in proportion to their toughness so that they fit the linear relationship from pre-cracked large ligament impact test pieces A
UX , J/mm2 o.6-
o.4-
B = 16ram / , ¢ ' 0.2 0
I
2o Fig. 4.
I
40
I
Cv, J
60
I
80
i
100
Influence of thickness o n C h a r p y type values.
almost exactly (Fig. 1). This coincidence may be of use in avoiding the necessity for at least one large sized impact test. Whilst considerable effort has been put into elucidating the influence of crack velocity on the total energy available for fracture in pipelines, there is very little consistent information available on the influence of this factor on the actual fracture resistance of linepipe. The relationship illustrated in Fig. 5 shows that on increasing the displacement velocity from that of a conventional fracture toughness test (strain rate = 3 x 10 - 4 s - 1) to that of an impact test (strain rate = l 0 2 s - l ) , the total fracture energy is increased by approximately 40 per cent for a range of materials. Within the range of rates investigated, several interesting observations can be made. Comparison of the impact and slow rate data in Fig. 1 indicates that the greatest part of the increase in energy is due to the higher S c values at high rates. This increase in S c is accompanied by an increased level of strain in the plastic region indicated by the larger
8
B. Holmes, A. H. Priest, E. F. Walker Energy per unit ar~a (W-a) = 30mm, J/mm
4.0
for
--
! o
3.0
/
2.0 J
I
1.0 10 -4
i0
I
_9
~
1 Strain
Fig. 5.
I
rate,
s
-i
10 2
Influence of strain rate. Q , x , + Controlled rolled; O Normalised.
lateral contraction in impact tests. If small scale test results were used to assess the influence of rate then, because U/A values for these are closely related to R c, errors could be made in evaluating the rate sensitivity of low toughness materials. As strain rate behaviour is dominated by Sc the overall fracture resistance of larger structures will always increase with rate. It is desirable, if at all possible, to understand the relationship between the energy values obtained from fatigue and machined notch test pieces so that the latter can be used and a suitable allowance made to bring the values down to those obtained on fatigue cracked test pieces. The data shown in Fig. 6 indicate that the difference in energy per unit area A U/A
Prediction of linepipefracture behaviour U
9
J/mm 2 0.6
o.4
0.2
..~---~ 0
J
I
2O
I
I
/40
60
I
80
I
i00
~C v , J Fig. 6.
Influence of n o t c h acuity o n C h a r p y type values.
between machined and fatigue cracked Charpy test pieces increases with increasing ]Cv. From this work it has been established that within reasonable limits of accuracy, it is possible to calculate lower bound Re and S c values from relatively inexpensive tests on machined notched SENB test pieces, the relationship being: U B( W - a)
- 0-95R~ (machined notch) + S¢( W - a)
(2)
At the large ligament lengths likely to be related to the fracture of a pipeline the fracture propagation energy is dominated by plastic deformation governed by S c and any errors introduced by this approximation of Re will be small.
EVALUATION AND PREDICTION OF PIPELINE BURST TEST PERFORMANCE In order to compare the results of burst tests with laboratory fracture data it has been necessary to gather together data on pipeline burst tests and establish that sufficient information exists to permit an appropriate comparison to be made. Clearly any pipeline test for which insufficient data exists has had to be excluded from the selected results.
10
B. Holmes, A. H. Priest, E. F. Walker
Results were obtained from 66 AISI full scale burst tests, 3 including 30 tests which represented the baseline data, together with laboratory fracture and tensile properties. The pipe diameter varied from 406 to 1219mm and the wall thickness was in the range 7.92 to 18.29 mm. Tests were excluded from the baseline data for one of the following reasons: (a) No, or insufficient, backfill was used. (b) The pipe was used as a crack initiator and therefore was of insufficient length to allow for sufficient crack deceleration. (c) The pipe exhibited 'separated'* behaviour during fracture. (d) A reasonable judgement could not be made as to whether or not the crack arrested. Similarly, results were obtained from 25 E P R G full scale burst tests 5 together with laboratory fracture and tensile properties. The pipe diameter varied from 914 to 1219mm and the wall thickness was in the range 12-7 to 25-4mm. The tensile properties in most cases consisted of both yield stress and tensile strength and the values of work hardening exponent were derived from the following equation using an iterative procedure: =
F2"7183try] "
try trUE p/~
J
(3)
where O'y is the yield stress, a, the tensile strength, n the work hardening exponent and E Young's modulus. The yield stress values were mainly obtained from strip tensile specimens according to the API standard. It was found that the work hardening exponent was related to the tensile properties by the following equation: n=0.025+0"3L
~u
d
(4)
Where no tensile strength result was available, the value of n was estimated from the general inverse relationship between n and try, Fig. 7. Estimates for the parameters R c and Sc in eqn (1) were obtained from the * 'Separated' behaviour relates to the occurrenceof cleavagecracks normal to the fracture surface parallel to the rolling plane; they are caused by the triaxiality of stress when certain metallurgical features are present.
Prediction of linepipefracture behaviour
11
Work hardening exponent o.13
0.12
•
® ee
0.ii
O.iO
•
/xx X
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ee
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0.05
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1
7oo
Yield stress, N/mm Fig.
7.
Relationship between strain hardening exponent and yield stress. • AISI data; x EPRG data; © 'Separated'.
2C v and Battelle (DWTT) fracture energies using the procedure previously presented. The values of the total potential energy available per unit area, however, were obtained from the equation put forward by van Elst e t a l . 9 which was as follows: potential energy =
In P22 + 4
(5)
where D is the pipe diameter, P, the pressure in the pipe, P2 the ambient pressure, a the applied stress and E Young's modulus. Toughness requirements have been calculated using formulae from the
B. Holmes, A. H. Priest, E. F. Walker
12
three main 'theories' developed in recent years by Battelle, AIS1 and British Gas; these formulae are as follows: Battelle
Cv =2"38 x lO-5(~r~(Rt) 1/3)
J
(6)
where D = 2R is the pipe diameter (mm), t is the wall thickness (mm), a n is the hoop stress (N/mm 2) and C v is the required toughness (J) (2/3 Charpy V-notch specimen). AISI C v = 2"38 x 10-4(a~SD °5)
J
(7)
British Gas
( Cv=
R
1'713t~.5-0"2753
R 125) . ~ o"Hx 10 -3
J
(8)
The constants in the British Gas relationship are likely to change as more data are included in the analysis. It can be seen that the influence of wall thickness is particularly important in the interpretation of these relationships. The AISI relationship shows that there is no influence of wall thickness; Battelle requires higher toughness values at increasing wall thickness, whereas for the British Gas equation the required toughness decreases as the wall thickness increases. One of the problems in correlating shear fracture propagation energy, obtained from laboratory tests, with the data from full scale tests is in deciding what the ligament length ( W - a ) should correspond to in a pipeline. The size of the plastically deformed regions is governed by the diameter and not the ligament length as in a test piece. A further difference is that the hoop stress approximates to pure tension compared with the usual bending stress in laboratory tests. The value of R c is therefore increased by a factor of two due to the crack not having to pass through material previously deformed in compression as in the laboratory bend and compact tension tests. The shear fracture propagation energy per unit area (SFPE) can therefore be represented by an equation of the form: SFPE = 2Re + ZScD (9) where Z is a constant. In order to obtain the value for Z, an optimisation
Prediction of linepipefracture behaviour 2R
c
13
+ O.12SeD J/mm 2
12 x
8
AISI (Baseline)dala~
x
0
•
I
~
e °
I
I
12
EPRG ('Non-separated')d a t a
J
0 Fig. 8.
|
500 i000 Potentialenergyavailable~J/mm2
Propagation energy as a function of available potential energy. • × Arrest.
!
1500 Propagate;
technique was employed for the ratio (shear fracture propagation energy: potential energy available). This optimisation was carried out until the minimum ratio for an arrest point divided by the maximum ratio for a propagate point was at its maximum:. This is referred to as the gradient ratio. Z value > 1 would be ideal as this would indicate complete separation of the arrest and propagate data points whereas a value < 1 would indicate some region of overlap. As the existing AISI and Battelle relationships have been shown to predict the behaviour of the baseline AISI burst tests, these data were initially included in an optimisation analysis. The value obtained for Z in eqn (9) was 0.12 and the gradient ratio was 0.91. This measure of shear fracture propagation energy is plotted as a function of the available potential energy in Fig. 8 where it can be seen
B. Holmes, A. H. Priest, E. F. Walker
14
2R
c
+ 0.12S D c J/mm 2 12 A I SI
J 'Separated')
/ ~_ I / ~
data
/ /
-'t
8
4
-
5.-J
o/
I
I
I
12
EPRG
O Fig. 9.
('Separated')
data
x
500 I000 Potential energy available~ J/ram2
~
~
~'-
1500
Propagation energy as a function of available potentiaJ energy. • Propagate; x Arrest.
there was a small region of overlap for the arrest and propagate data points. It is now possible to compare the results from other test series with the expression in eqn (9) with Z = 0.12. The 'non-separated' EPRG data are presented in Fig. 8 with the overlap region for the AISI baseline data being represented by the broken lines. Only one arrest point was outside the region encompassing the baseline data and this was responsible for a reduction in the gradient ratio to 0.83. The material which exhibited 'separated' behaviour is similarly presented in Fig. 9 together with the overlap region for the AISI baseline data. For the AISI 'separated' material, there was considerable deviation of propagate data points from this overlap region, resulting in a gradient ratio of 0.64, whereas for the E PRG 'separated' material there were only minor deviations resulting in a gradient ratio of 0.86. The list of gradient ratios is presented in Table 1. A
15
Prediction of linepipe fracture behaviour
TABLE ! Gradient Ratios Data
AISI (baseline) AISI + EPRG ('non-separated') AISI + AISI Cseparated') AISI + EPRG ('separated') AISI + EPRG ('separated' and 'non-separated') AISI + AISI ('separated') + EPRG Cseparated' and 'non-separated')
P E - 2Rc + 0.12SoD
Battelle
A ISI
British Gas
0.91
0.95
0.94
0.78
0.83
0.74
0.59
0.64
0-64
0'64
0.58
0.45
0.86
0,77
0.66
0.55
0-81
0.62
0.53
0-48
0.58
0.52
0.44
0.39
further analysis of the AISI baseline data, together with all the EPRG data, resulted in a value for Z of 0-14 with a gradient ratio of 0.82. This small difference (0.12-0.14) supports the opinion that the basic expression could be used to predict fracture energy requirements to avoid propagation. However, if the AISI 'separated' data are also included in an optimisation a value of Z of 0-24 was obtained with a gradient ratio of only 0.59. Because data from both the 'separated' and 'non-separated' EPRG material showed only minor deviations from the overlap region for the AISI baseline data, it was decided to include them in an attempt to investigate if there was an effect which could be attributed to the thickness of the pipe. The shear fracture propagation energy as a function of the available potential energy is presented for the various thicknesses of pipe in Fig. 10; the lines shown indicate the boundary positions for both arrest and propagate data points. From the propagate data points it can be clearly seen that there is no real evidence of any effect due to pipe wall thickness. Figure 10 also illustrates quite clearly the linear relationship between both the propagate and arrest boundaries and the available potential energy. The analytical technique used in this investigation could have been rightly criticised if the optimisation analysis had been strongly
16
B. Holmes, A. H. Priest, E. F. Walker 2R
c
+ 0.12S
c
D
12 +
Arrest @
8
4
0
1
1
I
12 /
Propagate
8
0
1 500 Potential
I energy
i0oo available, J/mm 2
I 150o
Fig. 10. Propagation energy as a function of available potential energy for baseline AISI and combined EPRG data. Thickness: • 7-9-9-9mm; × 11.9-12.5mm; +14.215-9mm: ~ 18.3ram; [] 25-4mm.
influenced by individual data points which could have had a disproportionate effect on the gradient of the boundary. This is nullified by the data in Fig. 10 which show that numerous data points lie close to the boundary and are related to a wide range of potential energy values. The degree of overlap between these boundaries represented by their gradient ratio is probably largely accounted for by the inaccuracies in determining R c and Sc from the ~Cv value which is known to be in error. The AISI non-baseline data, excluding those where 'separations' occurred, are presented in a similar manner to the other data in Fig. 11. This consisted mainly of propagate data points, except where indicated, and it can be seen that they were generally in agreement with the AISI baseline data denoted by the broken lines, with a small number of exceptions; these include instances where propagation had occurred
Prediction of linepipefracture behaviour
17
2R c + 0 . 1 2 S c D J/mm 2 12
//
10
/
// /
,// 6
Arrest
4
lJ /
./D/ 2
/
x
+P ~
Arrest
,, o
o
// //
o
~ /
/ / /
/
o I 500 Potential
I i000 e n e r g y a v a i l a b l e , J/ram2
I 1500
Fig. 1 !. Propagation energy as a function of available potential energy for non-baseline AISI data. • Initiator pipe; + Crack arrested and reinitiated in special test section; x Normalised pipe; A Insufficient backfill on pipe; V Excursion in crack speed thought to be caused by instrumentation on pipe; [] No backfill on pipe.
because of insufficient or no backfill and also because it was an initiator pipe; the deviated arrest data point was associated with the material being in the normalised condition; however, when E P R G data are included the normalised material came within the general scatter of the combined data. Toughness requirements, in the form of 2C v values, calculated using formulae from the relationships proposed by Battelle, AISI and British Gas, are presented as a function of the actual ICy values in Figs 12 and 13; also included are the boundary positions for both arrest and propagate data points. For the AISI 'separated' material and the various E P R G materials, the boundary positions for the AISI baseline data are denoted by broken lines. Corresponding gradient ratios were obtained and are presented in Table 1 where it can be seen they were highest for Battelle and then generally followed by AISI and British Gas. For the AISI baseline
18
B. Holmes, A. H. Priest, E. F. Walker
~C v at J 80
O°C
/
AISI
(Baseline)
EPRG ( ' N o n - s e p a r a t e d ' )
data
Battelle
S)
. .d;~ /
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4o
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120 Calculated
Fig. 12.
I
Gas
.J 4o
I
0
I
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I
120
Cv , J
Relationship between observed and calculated ~C~ values. • x Arrest.
Propagate:
data, the Battelle and AISI theories are compatible and thus this data produced quite high values for the gradient ratios whereas the British Gas theory gave a somewhat lower value. The gradient ratio decreased upon the further addition of data and this appeared to be equally pronounced with either the AISI 'separated' data or the combined EPRG data. The main difference between these two sets of data, however, is that the inclusion of the combined EPRG data generally changed the boundary positions for both arrest and propagate data points equally, whereas the
Prediction of linepipefracture behaviour
AISI ]C v at J 120
('Separated')
EPRG
data
0°C
19
('Separated')
data
Battelle
.J
80
/ /,/,"".S" :
/>--
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/ /
I I/I
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I
1
40
80
I
120 Calculated
Fig. 13.
0
4o
I
I
80
120
~ Cv, J
Relationships between observed and calculated ~Cv values. • × Arrest.
Propagate;
20
B. Holmes, A. H. Priest, E, F. Walker
AISI 'separated' data only changed the boundary position for the propagate data points. This effect of the combined E P R G data on the gradient ratio was very much greater than that observed when a measure of the shear fracture propagation energy was used; the effects due to the AISI 'separated' data, however, were very similar.
DISCUSSION
Comparison with previous relationships The values of R c and Sc are plotted as a function of the 2C v energy in Fig. 14 and as a function of the D W T T energy, corrected to a constant thickness, in Fig. 15. It can be seen that the only reliable relationships were between R c and 2C v energy, and Sc and D W T T energy. This is due to the scatter between D W T T and ~C v results as shown in Fig. 16 even though the general relationship is quite good. The indications therefore are that at least two measurements of energy are required in order to obtain a reasonably accurate value for the shear fracture propagation energy. This would appear to be confirmed when the AISI baseline data are considered together with the combined E P R G data as the gradient ratio was considerably higher for the shear fracture propagation energy approach as compared to the three other relationships which only incorporated 2C v values. In order to derive more accurate values for the shear fracture propagation energy, the two measurements of energy should be obtained fron SENB test pieces with widely different ligament lengths of not less than 30 ram.
Influence of pipe wall thickness Before the D W T T results on the 25.4 m m thick pipeline material were available it was thought that there could have been an effect associated with pipe wall thickness. It was therefore decided to use a parameter which included both pipe diameter and wall thickness and this was based on the length of a tangent to the inner surface within the wall thickness; the calculated value for the parameter was 1.75x/(Dt - fl) which approximates to the length of a tangent from the inner diameter to the outer diameter surface. This parameter, instead of pipe diameter, was incorporated into the optimisation analysis for the AISI baseline data and a value for Z of
Prediction of linepipe fracture behaviour
21
Rc, J/ram 2
/
/ I~XI
1.0
•
I
S , J/ram 3 c 0.06
I
I
@ @
@ @
x x
0.05
x
x
0.04
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~x
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°~°° •
0.03
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@e ee~e °
0.O2
O. Ol
O
I 20
l 40
I I 60 80 3 C v at O°C, J
I i00
l 120
Fig. 14. Relationships between Re, S c and 2C v energy. • AISI data; x E P R G data.
B. Holmes, A. H. Priest, E. F. Walker
22
Rc, J/mm2
O O
,xx
1.0
I K X
I(
O0
A +"
•'..-'v "
~:-
o Sc , J/mm3 0.06
.
0.05
/ X
f e
x/
• •
o.o4 0.03
...~.. ~
x
0.02
0.01 o
Fig. 15.
O
I 2000
I i 4000 6000 DWTT (Corrected to thickness of 12.Smm), J
Relationships between Re, S c a n d D W T T energy. • AISI d a t a ; x E P R G data.
Prediction of linepipefracture behaviour DWTT (Corrected t o thickness of 12.5mm), J 50o0 /
[
23
®~@@ "
4000
/
®
®
."" x ~ "
3000
x
2000
I000
0
I
l
0
l
I
20
40
I
I
60 80 Cv at 0°C, J
I
i00
I
120
Fig. 16. Relationship between DWTT and ~CVenergies. • AISI data; x EPRG data; O 'Separated'.
0.28 with a gradient ratio of 0.99 was obtained as compared with a gradient ratio of 0.91 for pipe diameter alone. The EPRG data generally fitted this relationship, with the exception of the 25-4 mm thick material for which there was considerable over-estimation of the shear fracture propagation energy. It was therefore the results from these thicker materials which finally confirmed that there was no significant effect of wall thickness either on the basic parameters R c and S c or on the size of the plastic region emanating from the crack surface. Further assessment
Many of the results from AISI materials which exhibited 'separated' behaviour do not comply with either the AISI baseline data or with data from the EPRG materials, some of which were also 'separated', irrespective of whether the approach used a measurement of shear fracture propagation energy or the relationships incorporating 2C v values. Other factors which might have had an influence were therefore investigated. A plot of the strain hardening exponent as a function of the yield stress is
24
B. Holmes, A. H. Priest, E. F. Walker
presented in Fig. 7; the various AISI and E P R G materials are denoted and those which exhibited 'separated' behaviour are also identified. It can be clearly seen that within the range examined the AISI "separated" materials generally had a combination of low work hardening exponent together with a high yield stress value. This combination may in part be connected with the quite large amounts of warm working during controlled rolling which are associated with the 'separated' type of behaviour; however, this does not explain why the E P R G 'separated' material generally had somewhat higher work hardening exponents and lower yield stress values, unless there was a difference in the degree of 'separated' behaviour or microstructural differences contributed. The effects due to both yield stress and strain hardening exponent were incorporated into the two parameters R c and Sc in the previously derived equation, but very little improvement was obtained in the gradient ratio resulting from optimisation analyses. However, if an additional term incorporating yield stress (kN/mm 2) as a function of pipe diameter was introduced there was a significant improvement in the gradient ratio; this was further improved when the strain hardening exponent was also included. The shear fracture propagation energy (SFPE) obtained from an optimisation analysis of the AISI baseline, AISI 'separated' and combined E P R G data was: SFPE = 2R c + 0.12ScD + 0.08OynD
( l 0)
with a gradient ratio of 0.79. This was considerably higher than the value of 0"59 obtained using the two-parameter approach. If the same threeparameter approach was applied to the AISI baseline data, the equation obtained included only a small contribution from the additional term. SFPE = 2R~ + 0.10S~D + 0.008CrynD
(11)
The gradient ratio was 0.93 as compared to 0.91 for the two-parameter equation. From this analysis therefore it may be noted that for materials such as those represented by the AISI baseline or 'separated' and 'non-separated' E P R G data the use of a two-parameter approach would appear to be perfectly adequate in order to obtain a measurement of the shear fracture propagation energy. IfAISI 'separated' type material is also included then there would appear to be the need for a three-parameter approach in order to satisfactorily explain the variability. The reason for this difference between the AISI and E P R G 'separated' materials is not fully understood. It may be connected with factors which bear no relationship
Prediction of linepipe fracture behaviour
25
to the extent of separations. For instance higher strength steels may not demonstrate the same increase in fracture propagation energy with rate as do the lower strength steels (Fig. 1); consequently at the high rates associated with a running crack in a pipeline their fracture resistance may be over-estimated by laboratory impact tests in comparison with lower strength materials. The third term in eqn (10) may account for energy absorbed in a process not connected with crack propagation; for instance the energy absorbed in the buckling and ovalising deformation in front of the crack would be expected to be related to the tensile properties.
P R E D I C T I O N OF M I N I M U M F R A C T U R E ENERGY R E Q U I R E M E N T S F O R G U A R A N T E E OF ARREST As a result of these observations it should be possible to use this new approach to indicate the fracture requirements in order to prevent the occurrence of running shear fracture in pipelines. A measurement of the required shear fracture propagation energy can be derived from the relationship with the potential energy available and the R c and S¢ values can be obtained from their respective relationships with the 2C v or D W T T energy. This is illustrated by considering the fracture resistance required for a gas pipeline which will have a minimum diameter (D) of 914 m m at a thickness of 25 m m and support a gas pressure of 17.24 N / m m 2 (2500 psi). Measurements of shear fracture propagation energy (2R c + 0.12 ScD) derived for the AISI baseline and also the combined E P R G data are shown as a function of the potential energy available in Figs 8 and 9. The lines indicate the boundary positions for both arrest and propagate points and those for the AISI baseline data are compared with the E P R G data in the lower illustrations where the former boundaries are shown by broken lines. The upper line for the E P R G data therefore represents the boundary above which no propagation occurred. The available potential energy, which is in effect the stored energy in the gas, for the hypothetical pipeline is obtained from the equation put forward by van Elst et al. 9 This results in a value of 740 J/mm 2 and from Fig. 9 it is seen that the shear fracture propagation energy required to prevent propagation at this potential energy is 5.5J/mm 2. If a 2/3 Charpy specification value (joules) is now selected this can be compared with an equivalent R¢ value by use of Fig. 14. The Sc value may now be calculated from eqn (9), using the relationship between SFPE and
26
B. Holmes, d. H. Priest, E. F. Walker
PE at the upper limit boundary beyond which no propagation occurred. An equivalent DWTT energy (joules per mm 2) can then be obtained by reference to Fig. 15. The statistical expression which incorporates the above relationships is: PE = 1.86(3Cv) 2 1"16 + 0.179(DWTT)D (12) It should be recognised, however, that the accuracy of this equation is inferior to that of eqn (9) and is only marginally simpler to calculate. CONCLUSIONS It has been shown that laboratory fracture data, consisting of ~Cv and DWTT energies, may be used to provide a more useful prediction of shear fracture arrest in pipelines by using a two-parameter expression. It was found that the AISI baseline data together with the combined EPRG data could be better explained by the two-parameter approach than by previous relationships which only incorporated the 2Cv values. Examination of the data also confirmed that there was no significant effect of pipe wall thickness on shear fracture propagation behaviour. Results from AISI 'separated' materials generally do not comply with either the AISI baseline data or with data from the EPRG test programme some of which were also 'separated'. However, the addition of a further term incorporating yield stress and strain hardening exponent considerably improved the predictability; the addition of this further term had only a very small effect on the AISI baseline data alone. For materials such as those represented by the AISI baseline or EPRG 'separated' and 'non-separated' data, it is suggested that the use of a twoparameter approach would be perfectly adequate in order to obtain a measurement of the shear fracture propagation energy. It is concluded that the low work hardening exponent and high yield stress values of the AISI 'separated' materials may have affected their strain rate sensitivity and hence their shear fracture propagation resistance in full scale tests. ACKNOWLEDGEMENTS The authors wish to thank Dr K.J. Irvine, Manager, BSC Sheffield Laboratories for permission to publish this paper. Many of the results
Prediction of linepipefracture behaviour
27
used in the analysis presented were obtained during the E C S C / E P R G pipeline fracture programme, and the helpful comments from E P R G members are acknowledged ( E P R G - - E u r o p e a n Pipe Research Group).
REFERENCES 1. Maxey, W. A., Fracture, initiation, propagation and arrest, Fifth Symposium in Linepipe Research, American Gas Association, 1974. 2. Maxey, W. A., Podlasek, R. J., Eiber, R. J. and Duffy, A. R., Observations on shear fracture behaviour, British Gas/IGE Symposium, Crack Propagation in Pipelines, Newcastle, March 1974. 3. Sub-committee of Large Diameter Linepipe Producers, Running shear fracture in linepipe, AISI, Technical Report, Sept. 1974. 4. Poynton, W. A., Shannon, R. W. E. and Fearnehough, G. D., The design and application of shear fracture propagation studies, Journal of Engineering Materials and Technology (Oct. 1974), pp. 323-9. 5. Fracture behaviour of gas transmission pipelines, full scale fracture tests, EPRG Report, ECSC Agreement no. 7210 KE 8/804, May 1980. 6. Priest, A. H. and Holmes, B., A multi-test piece approach to the fracture characterisation of linepipe steels, International Journal of Fracture, 17 (1981), pp. 277-99. 7. Fearnehough, G. D., Fracture propagation control in gas pipelines: a survey of relevant studies, International Journal of Pressure Vessels and Piping, 2 (1974), pp. 257-81. 8. Judy, R. W., Jr. and Goode, R. J., Fracture toughness evaluation of R-curve methods, American Society for Testing and Materials, STP527, pp. 48-61. 9. van Elst, H. C. et al., Fracture behaviour of linepipe steels, Progress Report no. 3 (EPRG Phase IV), Part 3, Appendix 1, 1975.
Prediction of Linepipe Fracture Behaviour from Laboratory Tests B. Holmes, A. H. Priest & E. F. Walker British Steel Corporation, SheffieldLaboratories, Swinden House, Moorgate, Rotherham, S. Yorks $60 3AR, Great Britain (Received: 22 January, 1982)
ABSTRACT Data obtained from full scale pipeline burst tests forming part of the American Iron and Steel Institute (AIS1) and the European Pipe Research Group (EPRG) programmes have been correlated with measurements of the shear fracture propagation energy and potential energy available. The former was obtained from the ~C, and Battelle energies using a previously derived two-parameter expression. For the combined A IS1 baseline and EPRG 'separated' and'non-separated" data, this expression explained considerably more of the variability than did the three generally used theories which only incorporate ~C,. values. There was also found to be no significant effect of pipe wall thickness when fracture occurred in the fully shear mode. Results from A ISl 'separated" materials did not generally fit the above two-parameter expression but they could be accommodated into a threeparameter expression which also incorporated values for yield stress and strain hardening exponent. The reason Jor this has been attributed to possible differences in the strain rate sensitivity of these materials and the presence of separations may not be significant.
INTRODUCTION Three well known relationships associated respectively with Battelle, 1'2 AISI 3 and British Gas 4 have been applied to the prediction of the outcome of full scale pipeline burst tests in terms of defining limiting 1
Int. J. Pres. Ves. & Piping0308-O161/83/O012-O001/$03.00 © Applied Science Publishers Ltd, England, 1983. Printed in Great Britain
2
B. Holmes, A. H. Priest, E. F. Walker
Charpy energy values to resist fracture propagation. Whilst these relationships were reasonably successful when applied to certain of the AISI test data, weaknesses were exposed in dealing with the results of the EPRG test programme. 5 Suggested reasons are as follows: (a)
The supposed effect of thickness is different in the three 'theories' and must be wrong in at least two of them. (b) Because of the small size of the Charpy test piece, no allowance is made for the plastic deformation accompanying fracture in a linepipe. (c) The existing relationships propose an agreement between terms which are expressed in unusual units which are not related to any known physical process and are difficult to relate to fracture energy. These difficulties have been known for some time and up to now considerable effort has been devoted to developing a better method of characterising the shear fracture resistance of linepipe steels. The twoparameter approach 6 appears to be a promising alternative since all of the above criticisms are resolved, and the total energy for fracture is governed by two constants, R c and So. An attempt has now been made to apply the approach, based on laboratory tests, to the practical results of full scale burst tests using the existing data. The main components of the proposed treatment are as follows: (a)
R~ and S~ values ideally determined from impact tests on at least two specimens with significantly different ligament length are used to define the fracture resistance from the original equation U B( W - a)
-2Rc+S~(W-a )
(1)
The term R~ is assumed to equate to the energy associated with the initiation and propagation of the shear fracture whilst Sc governs the energy absorbed as a consequence of associated plastic deformation. A value of 2R¢ is chosen to represent the condition during pipeline fracture as this is thought to be very similar to the situation which develops in a tension test. (b) In a pipeline, the extent of plastic deformation in eqn (1) is governed not by ( W - a) but by a simple function of the diameter of the pipe.
Prediction of linepipe fracture behaviour
3
(c) Fracture propagation energy is plotted against the total energy available for unit area of fracture which is virtually equal to the stored energy of the high pressure gas. This simple procedure ensures that the dimensions of both the energy available and the energy required for fracture are the same. (d) Linear boundaries are drawn through the lowest arrest data point and the highest propagate data point. These represent 100 per cent confidence limits in respect of the data available because it is felt that in the area of linepipe failure, a single unpredicted failure is unacceptable. The propagate boundary should therefore define minimum values of fracture propagation energy required to guarantee crack arrest.
FACTORS A F F E C T I N G E V A L U A T I O N OF Re A N D S c F R O M RESULTS OF T O U G H N E S S TESTS Before the concept expressed in eqn (1) could be used as a practical procedure, information was required on a number of factors which could have influenced the linearity of the relationship derived. For instance, as discussed below, data from small ligament lengths tend to fall below the linear relationship and it is, therefore, necessary to know the minimum ligament length required to avoid this. Other factors are thickness B, test piece geometry, notch acuity, strain rate and temperature. When the influence of the above factors is understood it should be possible to devise a standard testing procedure so that values of Re and S¢ can be determined unambiguously. Records of the ]Cv and Battelle fracture energies for burst test materials are documented and this should enable an estimate of the R¢ and S¢ values to be calculated and be used to quantify the resistance to fracture of pipelines more precisely than hitherto. The influence of the above variables on R¢ and S¢ has been assessed by performing appropriate tests on six samples of pipeline steel including normalised, controlled rolled, and quenched and tempered materials. An example of the data derived from slow rate tests on CT test pieces from several steels is shown in Fig. 1, where it can be seen there are linear relationships of the form shown in eqn (1). Data are also included which indicate that fracture energy increases with loading rate and that specimen geometry has little or no influence on the results. Controlled
4
B. Holmes, A. H. Priest, E. F. Walker
Energy per unit area, J/mm 2 L Controlled 2.0
/
/ / ' ~
rolled
!
,
~
e /
o
Controlled rolled
4.o
/ ~
a/. -'~a°/°a/"
°a/
o~
2.0
I
I
,/ Controlled rolled
4.o
/,/ •/~#~
..~/~0
~"
2.0
0
I
J
°/"
&j
Normalised
6.0
4.o
~
0~
0 ~"
2.0
I
0
Fig. 1.
50 Ligament
I
i00 length,
150
mm
Energy per unit area as a function of ligament length. • Impact rate; × C, type (notched); + ~C V(notched); (3 Slow rate CT; A Slow rate S E N B
Prediction of linepipe fracture behaviour Energy
per
unit
area,
5
J/mm 2
4.o
3.o
2.O
1.O
"/"
o/ O
Fig. 2.
l 50 Ligament
l ioo
length,
I 150
mm
Influence of temperature and small ligament sizes (cerium treated steel). • 20 °C; × 0°C; + - 2 5 ° C ; C) - 5 0 ° C
rolled, normalised, and also quenched and tempered materials assumed the same general relationship. For the quenched and tempered material, however, the Re and Sc values were significantly lower than for the original normalised material, probably because of the higher tensile properties of this material. Similar data were obtained at various test temperatures in the range 0 to - 5 0 eC for cerium treated steels and an example is shown in Fig. 2 where it can be seen that there was very little effect of temperature on the energy per unit area values. The deviation from linearity for ligament lengths of less than 30 mm is of significance. The effects of thickness on fully shear fracture are shown as a function of the ligament length for two of the materials in Fig. 3. No significant difference was observed in the results for test pieces machined from the surface or centre region of the material but nevertheless the average values were used. It can be seen that there was generally very little effect of thickness on the energy per unit area values for ligament lengths in the approximate range 30-60 m m where the data are obtained from test pieces machined from a single thick plate. Conflicting reports have been made on the influence of thickness on the shear fracture resistance of linepipe materials. Indeed several authors make different specific allowances for this in calculations for predicting the performance of pipelines using a power term for B in the range ¼to 1.
6
B. Holmes, A. H. Priest, E. F. Walker
For example, Fearnehough 7 and Judy and Goode 8 use a factor of B 1/2. The explanation for these different opinions becomes apparent when a comparison is made of U/A values for test pieces of different thickness at different ligament length. When, for instance, ( W - a) values are greater than 30 m m as in Fig. 3 there is no influence of thickness on U/A values, but when the ligament size is reduced to below about 2 0 m m then a significant difference is observed. The difference is particularly marked in Energy
per unit
area,
J/ram 2
4.0
Standard
3•O
\
2.O
~
i .0
/ /
++J
~
+
~
+/
+
1+$"
/ I 0
Cerium
Treated I
O
I
50 Ligament
Fig. 3. Influenceof thickness. • 3 m m ;
iOO length,
J
150
mm
× 6ram; + 12ram; O 25ram; • 35ram.
test pieces for the Charpy test which of course has been the standard test method for many years. The magnitude of the difference is clearly shown to be a function of the toughness of the material tested in Fig. 4 where a comparison is made between U/A values for full thickness (B = 12.7 or 16.0 mm) and ~Cv (B = 6.67 mm) nominal Charpy tests at different levels of toughness. F r o m Fig. 2 it is shown that below a ligament size of about 25 m m the data do not fit the linear relationship; a reduction in U/A occurs so that the values extrapolate to a value of zero at zero ligament length. The minimum ligament length necessary to avoid such deviations is related to the thickness and toughness of the steel so that this size probably varies with increasing thickness, yield stress and toughness. Consequently, Charpy type test pieces exhibit a greater influence of thickness for the tougher materials. Considerable detailed work would be required to prove this point; however, for thicknesses up to 16mm a
Prediction of linepipe fracture behaviour
7
minimum ligament size of about 30 mm would seem to be adequate in order for the data to fit the linear relationship. It has been shown that the difference between U/A values for machined notched and fatigue cracked test pieces is a function of Re. The values of U/A for the notched full thickness Charpy-type test pieces shown in Fig. 1 are, therefore, increased in proportion to their toughness so that they fit the linear relationship from pre-cracked large ligament impact test pieces A
UX , J/mm2 o.6-
o.4-
B = 16ram / , ¢ ' 0.2 0
I
2o Fig. 4.
I
40
I
Cv, J
60
I
80
i
100
Influence of thickness o n C h a r p y type values.
almost exactly (Fig. 1). This coincidence may be of use in avoiding the necessity for at least one large sized impact test. Whilst considerable effort has been put into elucidating the influence of crack velocity on the total energy available for fracture in pipelines, there is very little consistent information available on the influence of this factor on the actual fracture resistance of linepipe. The relationship illustrated in Fig. 5 shows that on increasing the displacement velocity from that of a conventional fracture toughness test (strain rate = 3 x 10 - 4 s - 1) to that of an impact test (strain rate = l 0 2 s - l ) , the total fracture energy is increased by approximately 40 per cent for a range of materials. Within the range of rates investigated, several interesting observations can be made. Comparison of the impact and slow rate data in Fig. 1 indicates that the greatest part of the increase in energy is due to the higher S c values at high rates. This increase in S c is accompanied by an increased level of strain in the plastic region indicated by the larger
8
B. Holmes, A. H. Priest, E. F. Walker Energy per unit ar~a (W-a) = 30mm, J/mm
4.0
for
--
! o
3.0
/
2.0 J
I
1.0 10 -4
i0
I
_9
~
1 Strain
Fig. 5.
I
rate,
s
-i
10 2
Influence of strain rate. Q , x , + Controlled rolled; O Normalised.
lateral contraction in impact tests. If small scale test results were used to assess the influence of rate then, because U/A values for these are closely related to R c, errors could be made in evaluating the rate sensitivity of low toughness materials. As strain rate behaviour is dominated by Sc the overall fracture resistance of larger structures will always increase with rate. It is desirable, if at all possible, to understand the relationship between the energy values obtained from fatigue and machined notch test pieces so that the latter can be used and a suitable allowance made to bring the values down to those obtained on fatigue cracked test pieces. The data shown in Fig. 6 indicate that the difference in energy per unit area A U/A
Prediction of linepipefracture behaviour U
9
J/mm 2 0.6
o.4
0.2
..~---~ 0
J
I
2O
I
I
/40
60
I
80
I
i00
~C v , J Fig. 6.
Influence of n o t c h acuity o n C h a r p y type values.
between machined and fatigue cracked Charpy test pieces increases with increasing ]Cv. From this work it has been established that within reasonable limits of accuracy, it is possible to calculate lower bound Re and S c values from relatively inexpensive tests on machined notched SENB test pieces, the relationship being: U B( W - a)
- 0-95R~ (machined notch) + S¢( W - a)
(2)
At the large ligament lengths likely to be related to the fracture of a pipeline the fracture propagation energy is dominated by plastic deformation governed by S c and any errors introduced by this approximation of Re will be small.
EVALUATION AND PREDICTION OF PIPELINE BURST TEST PERFORMANCE In order to compare the results of burst tests with laboratory fracture data it has been necessary to gather together data on pipeline burst tests and establish that sufficient information exists to permit an appropriate comparison to be made. Clearly any pipeline test for which insufficient data exists has had to be excluded from the selected results.
10
B. Holmes, A. H. Priest, E. F. Walker
Results were obtained from 66 AISI full scale burst tests, 3 including 30 tests which represented the baseline data, together with laboratory fracture and tensile properties. The pipe diameter varied from 406 to 1219mm and the wall thickness was in the range 7.92 to 18.29 mm. Tests were excluded from the baseline data for one of the following reasons: (a) No, or insufficient, backfill was used. (b) The pipe was used as a crack initiator and therefore was of insufficient length to allow for sufficient crack deceleration. (c) The pipe exhibited 'separated'* behaviour during fracture. (d) A reasonable judgement could not be made as to whether or not the crack arrested. Similarly, results were obtained from 25 E P R G full scale burst tests 5 together with laboratory fracture and tensile properties. The pipe diameter varied from 914 to 1219mm and the wall thickness was in the range 12-7 to 25-4mm. The tensile properties in most cases consisted of both yield stress and tensile strength and the values of work hardening exponent were derived from the following equation using an iterative procedure: =
F2"7183try] "
try trUE p/~
J
(3)
where O'y is the yield stress, a, the tensile strength, n the work hardening exponent and E Young's modulus. The yield stress values were mainly obtained from strip tensile specimens according to the API standard. It was found that the work hardening exponent was related to the tensile properties by the following equation: n=0.025+0"3L
~u
d
(4)
Where no tensile strength result was available, the value of n was estimated from the general inverse relationship between n and try, Fig. 7. Estimates for the parameters R c and Sc in eqn (1) were obtained from the * 'Separated' behaviour relates to the occurrenceof cleavagecracks normal to the fracture surface parallel to the rolling plane; they are caused by the triaxiality of stress when certain metallurgical features are present.
Prediction of linepipefracture behaviour
11
Work hardening exponent o.13
0.12
•
® ee
0.ii
O.iO
•
/xx X
o
® x x
ee
•
X
°e
O. 09
•
•• •
%.
•
X
ee •
0.08
e~ee 0.07
x
®
®®
®
®
®
® 0.06
0.05
I
I
4oo
5o0
I
26oo
1
7oo
Yield stress, N/mm Fig.
7.
Relationship between strain hardening exponent and yield stress. • AISI data; x EPRG data; © 'Separated'.
2C v and Battelle (DWTT) fracture energies using the procedure previously presented. The values of the total potential energy available per unit area, however, were obtained from the equation put forward by van Elst e t a l . 9 which was as follows: potential energy =
In P22 + 4
(5)
where D is the pipe diameter, P, the pressure in the pipe, P2 the ambient pressure, a the applied stress and E Young's modulus. Toughness requirements have been calculated using formulae from the
B. Holmes, A. H. Priest, E. F. Walker
12
three main 'theories' developed in recent years by Battelle, AIS1 and British Gas; these formulae are as follows: Battelle
Cv =2"38 x lO-5(~r~(Rt) 1/3)
J
(6)
where D = 2R is the pipe diameter (mm), t is the wall thickness (mm), a n is the hoop stress (N/mm 2) and C v is the required toughness (J) (2/3 Charpy V-notch specimen). AISI C v = 2"38 x 10-4(a~SD °5)
J
(7)
British Gas
( Cv=
R
1'713t~.5-0"2753
R 125) . ~ o"Hx 10 -3
J
(8)
The constants in the British Gas relationship are likely to change as more data are included in the analysis. It can be seen that the influence of wall thickness is particularly important in the interpretation of these relationships. The AISI relationship shows that there is no influence of wall thickness; Battelle requires higher toughness values at increasing wall thickness, whereas for the British Gas equation the required toughness decreases as the wall thickness increases. One of the problems in correlating shear fracture propagation energy, obtained from laboratory tests, with the data from full scale tests is in deciding what the ligament length ( W - a ) should correspond to in a pipeline. The size of the plastically deformed regions is governed by the diameter and not the ligament length as in a test piece. A further difference is that the hoop stress approximates to pure tension compared with the usual bending stress in laboratory tests. The value of R c is therefore increased by a factor of two due to the crack not having to pass through material previously deformed in compression as in the laboratory bend and compact tension tests. The shear fracture propagation energy per unit area (SFPE) can therefore be represented by an equation of the form: SFPE = 2Re + ZScD (9) where Z is a constant. In order to obtain the value for Z, an optimisation
Prediction of linepipefracture behaviour 2R
c
13
+ O.12SeD J/mm 2
12 x
8
AISI (Baseline)dala~
x
0
•
I
~
e °
I
I
12
EPRG ('Non-separated')d a t a
J
0 Fig. 8.
|
500 i000 Potentialenergyavailable~J/mm2
Propagation energy as a function of available potential energy. • × Arrest.
!
1500 Propagate;
technique was employed for the ratio (shear fracture propagation energy: potential energy available). This optimisation was carried out until the minimum ratio for an arrest point divided by the maximum ratio for a propagate point was at its maximum:. This is referred to as the gradient ratio. Z value > 1 would be ideal as this would indicate complete separation of the arrest and propagate data points whereas a value < 1 would indicate some region of overlap. As the existing AISI and Battelle relationships have been shown to predict the behaviour of the baseline AISI burst tests, these data were initially included in an optimisation analysis. The value obtained for Z in eqn (9) was 0.12 and the gradient ratio was 0.91. This measure of shear fracture propagation energy is plotted as a function of the available potential energy in Fig. 8 where it can be seen
B. Holmes, A. H. Priest, E. F. Walker
14
2R
c
+ 0.12S D c J/mm 2 12 A I SI
J 'Separated')
/ ~_ I / ~
data
/ /
-'t
8
4
-
5.-J
o/
I
I
I
12
EPRG
O Fig. 9.
('Separated')
data
x
500 I000 Potential energy available~ J/ram2
~
~
~'-
1500
Propagation energy as a function of available potentiaJ energy. • Propagate; x Arrest.
there was a small region of overlap for the arrest and propagate data points. It is now possible to compare the results from other test series with the expression in eqn (9) with Z = 0.12. The 'non-separated' EPRG data are presented in Fig. 8 with the overlap region for the AISI baseline data being represented by the broken lines. Only one arrest point was outside the region encompassing the baseline data and this was responsible for a reduction in the gradient ratio to 0.83. The material which exhibited 'separated' behaviour is similarly presented in Fig. 9 together with the overlap region for the AISI baseline data. For the AISI 'separated' material, there was considerable deviation of propagate data points from this overlap region, resulting in a gradient ratio of 0.64, whereas for the E PRG 'separated' material there were only minor deviations resulting in a gradient ratio of 0.86. The list of gradient ratios is presented in Table 1. A
15
Prediction of linepipe fracture behaviour
TABLE ! Gradient Ratios Data
AISI (baseline) AISI + EPRG ('non-separated') AISI + AISI Cseparated') AISI + EPRG ('separated') AISI + EPRG ('separated' and 'non-separated') AISI + AISI ('separated') + EPRG Cseparated' and 'non-separated')
P E - 2Rc + 0.12SoD
Battelle
A ISI
British Gas
0.91
0.95
0.94
0.78
0.83
0.74
0.59
0.64
0-64
0'64
0.58
0.45
0.86
0,77
0.66
0.55
0-81
0.62
0.53
0-48
0.58
0.52
0.44
0.39
further analysis of the AISI baseline data, together with all the EPRG data, resulted in a value for Z of 0-14 with a gradient ratio of 0.82. This small difference (0.12-0.14) supports the opinion that the basic expression could be used to predict fracture energy requirements to avoid propagation. However, if the AISI 'separated' data are also included in an optimisation a value of Z of 0-24 was obtained with a gradient ratio of only 0.59. Because data from both the 'separated' and 'non-separated' EPRG material showed only minor deviations from the overlap region for the AISI baseline data, it was decided to include them in an attempt to investigate if there was an effect which could be attributed to the thickness of the pipe. The shear fracture propagation energy as a function of the available potential energy is presented for the various thicknesses of pipe in Fig. 10; the lines shown indicate the boundary positions for both arrest and propagate data points. From the propagate data points it can be clearly seen that there is no real evidence of any effect due to pipe wall thickness. Figure 10 also illustrates quite clearly the linear relationship between both the propagate and arrest boundaries and the available potential energy. The analytical technique used in this investigation could have been rightly criticised if the optimisation analysis had been strongly
16
B. Holmes, A. H. Priest, E. F. Walker 2R
c
+ 0.12S
c
D
12 +
Arrest @
8
4
0
1
1
I
12 /
Propagate
8
0
1 500 Potential
I energy
i0oo available, J/mm 2
I 150o
Fig. 10. Propagation energy as a function of available potential energy for baseline AISI and combined EPRG data. Thickness: • 7-9-9-9mm; × 11.9-12.5mm; +14.215-9mm: ~ 18.3ram; [] 25-4mm.
influenced by individual data points which could have had a disproportionate effect on the gradient of the boundary. This is nullified by the data in Fig. 10 which show that numerous data points lie close to the boundary and are related to a wide range of potential energy values. The degree of overlap between these boundaries represented by their gradient ratio is probably largely accounted for by the inaccuracies in determining R c and Sc from the ~Cv value which is known to be in error. The AISI non-baseline data, excluding those where 'separations' occurred, are presented in a similar manner to the other data in Fig. 11. This consisted mainly of propagate data points, except where indicated, and it can be seen that they were generally in agreement with the AISI baseline data denoted by the broken lines, with a small number of exceptions; these include instances where propagation had occurred
Prediction of linepipefracture behaviour
17
2R c + 0 . 1 2 S c D J/mm 2 12
//
10
/
// /
,// 6
Arrest
4
lJ /
./D/ 2
/
x
+P ~
Arrest
,, o
o
// //
o
~ /
/ / /
/
o I 500 Potential
I i000 e n e r g y a v a i l a b l e , J/ram2
I 1500
Fig. 1 !. Propagation energy as a function of available potential energy for non-baseline AISI data. • Initiator pipe; + Crack arrested and reinitiated in special test section; x Normalised pipe; A Insufficient backfill on pipe; V Excursion in crack speed thought to be caused by instrumentation on pipe; [] No backfill on pipe.
because of insufficient or no backfill and also because it was an initiator pipe; the deviated arrest data point was associated with the material being in the normalised condition; however, when E P R G data are included the normalised material came within the general scatter of the combined data. Toughness requirements, in the form of 2C v values, calculated using formulae from the relationships proposed by Battelle, AISI and British Gas, are presented as a function of the actual ICy values in Figs 12 and 13; also included are the boundary positions for both arrest and propagate data points. For the AISI 'separated' material and the various E P R G materials, the boundary positions for the AISI baseline data are denoted by broken lines. Corresponding gradient ratios were obtained and are presented in Table 1 where it can be seen they were highest for Battelle and then generally followed by AISI and British Gas. For the AISI baseline
18
B. Holmes, A. H. Priest, E. F. Walker
~C v at J 80
O°C
/
AISI
(Baseline)
EPRG ( ' N o n - s e p a r a t e d ' )
data
Battelle
S)
. .d;~ /
x
4o
~n- o
/:i
data
L:;/" . I
I
I
|
|
AISI
80
4o
//// ////
}//
,i // !
/;C I
I
British
8o
-//j/
f?¢~/
4o
|
J
80
1
120 Calculated
Fig. 12.
I
Gas
.J 4o
I
0
I
I
QO
80
I
120
Cv , J
Relationship between observed and calculated ~C~ values. • x Arrest.
Propagate:
data, the Battelle and AISI theories are compatible and thus this data produced quite high values for the gradient ratios whereas the British Gas theory gave a somewhat lower value. The gradient ratio decreased upon the further addition of data and this appeared to be equally pronounced with either the AISI 'separated' data or the combined EPRG data. The main difference between these two sets of data, however, is that the inclusion of the combined EPRG data generally changed the boundary positions for both arrest and propagate data points equally, whereas the
Prediction of linepipefracture behaviour
AISI ]C v at J 120
('Separated')
EPRG
data
0°C
19
('Separated')
data
Battelle
.J
80
/ /,/,"".S" :
/>--
4o
I
0
I
12o
~/
80
I
I
/// //<~/
~
/ 40
/)
11
.
// 0
I
//////
- /,.2A" /z"
/-I
/.(
I
AISI
I
I B r i t i s h Gas
/ /
I I/I
/
/ /
/
40
0
I/:,¢" L /.// • 0
I
1
40
80
I
120 Calculated
Fig. 13.
0
4o
I
I
80
120
~ Cv, J
Relationships between observed and calculated ~Cv values. • × Arrest.
Propagate;
20
B. Holmes, A. H. Priest, E, F. Walker
AISI 'separated' data only changed the boundary position for the propagate data points. This effect of the combined E P R G data on the gradient ratio was very much greater than that observed when a measure of the shear fracture propagation energy was used; the effects due to the AISI 'separated' data, however, were very similar.
DISCUSSION
Comparison with previous relationships The values of R c and Sc are plotted as a function of the 2C v energy in Fig. 14 and as a function of the D W T T energy, corrected to a constant thickness, in Fig. 15. It can be seen that the only reliable relationships were between R c and 2C v energy, and Sc and D W T T energy. This is due to the scatter between D W T T and ~C v results as shown in Fig. 16 even though the general relationship is quite good. The indications therefore are that at least two measurements of energy are required in order to obtain a reasonably accurate value for the shear fracture propagation energy. This would appear to be confirmed when the AISI baseline data are considered together with the combined E P R G data as the gradient ratio was considerably higher for the shear fracture propagation energy approach as compared to the three other relationships which only incorporated 2C v values. In order to derive more accurate values for the shear fracture propagation energy, the two measurements of energy should be obtained fron SENB test pieces with widely different ligament lengths of not less than 30 ram.
Influence of pipe wall thickness Before the D W T T results on the 25.4 m m thick pipeline material were available it was thought that there could have been an effect associated with pipe wall thickness. It was therefore decided to use a parameter which included both pipe diameter and wall thickness and this was based on the length of a tangent to the inner surface within the wall thickness; the calculated value for the parameter was 1.75x/(Dt - fl) which approximates to the length of a tangent from the inner diameter to the outer diameter surface. This parameter, instead of pipe diameter, was incorporated into the optimisation analysis for the AISI baseline data and a value for Z of
Prediction of linepipe fracture behaviour
21
Rc, J/ram 2
/
/ I~XI
1.0
•
I
S , J/ram 3 c 0.06
I
I
@ @
@ @
x x
0.05
x
x
0.04
x x
e,
x
~x
"xx~
x
°~°° •
0.03
ee~ ee
x •
Xeneee • • •
@e ee~e °
0.O2
O. Ol
O
I 20
l 40
I I 60 80 3 C v at O°C, J
I i00
l 120
Fig. 14. Relationships between Re, S c and 2C v energy. • AISI data; x E P R G data.
B. Holmes, A. H. Priest, E. F. Walker
22
Rc, J/mm2
O O
,xx
1.0
I K X
I(
O0
A +"
•'..-'v "
~:-
o Sc , J/mm3 0.06
.
0.05
/ X
f e
x/
• •
o.o4 0.03
...~.. ~
x
0.02
0.01 o
Fig. 15.
O
I 2000
I i 4000 6000 DWTT (Corrected to thickness of 12.Smm), J
Relationships between Re, S c a n d D W T T energy. • AISI d a t a ; x E P R G data.
Prediction of linepipefracture behaviour DWTT (Corrected t o thickness of 12.5mm), J 50o0 /
[
23
®~@@ "
4000
/
®
®
."" x ~ "
3000
x
2000
I000
0
I
l
0
l
I
20
40
I
I
60 80 Cv at 0°C, J
I
i00
I
120
Fig. 16. Relationship between DWTT and ~CVenergies. • AISI data; x EPRG data; O 'Separated'.
0.28 with a gradient ratio of 0.99 was obtained as compared with a gradient ratio of 0.91 for pipe diameter alone. The EPRG data generally fitted this relationship, with the exception of the 25-4 mm thick material for which there was considerable over-estimation of the shear fracture propagation energy. It was therefore the results from these thicker materials which finally confirmed that there was no significant effect of wall thickness either on the basic parameters R c and S c or on the size of the plastic region emanating from the crack surface. Further assessment
Many of the results from AISI materials which exhibited 'separated' behaviour do not comply with either the AISI baseline data or with data from the EPRG materials, some of which were also 'separated', irrespective of whether the approach used a measurement of shear fracture propagation energy or the relationships incorporating 2C v values. Other factors which might have had an influence were therefore investigated. A plot of the strain hardening exponent as a function of the yield stress is
24
B. Holmes, A. H. Priest, E. F. Walker
presented in Fig. 7; the various AISI and E P R G materials are denoted and those which exhibited 'separated' behaviour are also identified. It can be clearly seen that within the range examined the AISI "separated" materials generally had a combination of low work hardening exponent together with a high yield stress value. This combination may in part be connected with the quite large amounts of warm working during controlled rolling which are associated with the 'separated' type of behaviour; however, this does not explain why the E P R G 'separated' material generally had somewhat higher work hardening exponents and lower yield stress values, unless there was a difference in the degree of 'separated' behaviour or microstructural differences contributed. The effects due to both yield stress and strain hardening exponent were incorporated into the two parameters R c and Sc in the previously derived equation, but very little improvement was obtained in the gradient ratio resulting from optimisation analyses. However, if an additional term incorporating yield stress (kN/mm 2) as a function of pipe diameter was introduced there was a significant improvement in the gradient ratio; this was further improved when the strain hardening exponent was also included. The shear fracture propagation energy (SFPE) obtained from an optimisation analysis of the AISI baseline, AISI 'separated' and combined E P R G data was: SFPE = 2R c + 0.12ScD + 0.08OynD
( l 0)
with a gradient ratio of 0.79. This was considerably higher than the value of 0"59 obtained using the two-parameter approach. If the same threeparameter approach was applied to the AISI baseline data, the equation obtained included only a small contribution from the additional term. SFPE = 2R~ + 0.10S~D + 0.008CrynD
(11)
The gradient ratio was 0.93 as compared to 0.91 for the two-parameter equation. From this analysis therefore it may be noted that for materials such as those represented by the AISI baseline or 'separated' and 'non-separated' E P R G data the use of a two-parameter approach would appear to be perfectly adequate in order to obtain a measurement of the shear fracture propagation energy. IfAISI 'separated' type material is also included then there would appear to be the need for a three-parameter approach in order to satisfactorily explain the variability. The reason for this difference between the AISI and E P R G 'separated' materials is not fully understood. It may be connected with factors which bear no relationship
Prediction of linepipe fracture behaviour
25
to the extent of separations. For instance higher strength steels may not demonstrate the same increase in fracture propagation energy with rate as do the lower strength steels (Fig. 1); consequently at the high rates associated with a running crack in a pipeline their fracture resistance may be over-estimated by laboratory impact tests in comparison with lower strength materials. The third term in eqn (10) may account for energy absorbed in a process not connected with crack propagation; for instance the energy absorbed in the buckling and ovalising deformation in front of the crack would be expected to be related to the tensile properties.
P R E D I C T I O N OF M I N I M U M F R A C T U R E ENERGY R E Q U I R E M E N T S F O R G U A R A N T E E OF ARREST As a result of these observations it should be possible to use this new approach to indicate the fracture requirements in order to prevent the occurrence of running shear fracture in pipelines. A measurement of the required shear fracture propagation energy can be derived from the relationship with the potential energy available and the R c and S¢ values can be obtained from their respective relationships with the 2C v or D W T T energy. This is illustrated by considering the fracture resistance required for a gas pipeline which will have a minimum diameter (D) of 914 m m at a thickness of 25 m m and support a gas pressure of 17.24 N / m m 2 (2500 psi). Measurements of shear fracture propagation energy (2R c + 0.12 ScD) derived for the AISI baseline and also the combined E P R G data are shown as a function of the potential energy available in Figs 8 and 9. The lines indicate the boundary positions for both arrest and propagate points and those for the AISI baseline data are compared with the E P R G data in the lower illustrations where the former boundaries are shown by broken lines. The upper line for the E P R G data therefore represents the boundary above which no propagation occurred. The available potential energy, which is in effect the stored energy in the gas, for the hypothetical pipeline is obtained from the equation put forward by van Elst et al. 9 This results in a value of 740 J/mm 2 and from Fig. 9 it is seen that the shear fracture propagation energy required to prevent propagation at this potential energy is 5.5J/mm 2. If a 2/3 Charpy specification value (joules) is now selected this can be compared with an equivalent R¢ value by use of Fig. 14. The Sc value may now be calculated from eqn (9), using the relationship between SFPE and
26
B. Holmes, d. H. Priest, E. F. Walker
PE at the upper limit boundary beyond which no propagation occurred. An equivalent DWTT energy (joules per mm 2) can then be obtained by reference to Fig. 15. The statistical expression which incorporates the above relationships is: PE = 1.86(3Cv) 2 1"16 + 0.179(DWTT)D (12) It should be recognised, however, that the accuracy of this equation is inferior to that of eqn (9) and is only marginally simpler to calculate. CONCLUSIONS It has been shown that laboratory fracture data, consisting of ~Cv and DWTT energies, may be used to provide a more useful prediction of shear fracture arrest in pipelines by using a two-parameter expression. It was found that the AISI baseline data together with the combined EPRG data could be better explained by the two-parameter approach than by previous relationships which only incorporated the 2Cv values. Examination of the data also confirmed that there was no significant effect of pipe wall thickness on shear fracture propagation behaviour. Results from AISI 'separated' materials generally do not comply with either the AISI baseline data or with data from the EPRG test programme some of which were also 'separated'. However, the addition of a further term incorporating yield stress and strain hardening exponent considerably improved the predictability; the addition of this further term had only a very small effect on the AISI baseline data alone. For materials such as those represented by the AISI baseline or EPRG 'separated' and 'non-separated' data, it is suggested that the use of a twoparameter approach would be perfectly adequate in order to obtain a measurement of the shear fracture propagation energy. It is concluded that the low work hardening exponent and high yield stress values of the AISI 'separated' materials may have affected their strain rate sensitivity and hence their shear fracture propagation resistance in full scale tests. ACKNOWLEDGEMENTS The authors wish to thank Dr K.J. Irvine, Manager, BSC Sheffield Laboratories for permission to publish this paper. Many of the results
Prediction of linepipefracture behaviour
27
used in the analysis presented were obtained during the E C S C / E P R G pipeline fracture programme, and the helpful comments from E P R G members are acknowledged ( E P R G - - E u r o p e a n Pipe Research Group).
REFERENCES 1. Maxey, W. A., Fracture, initiation, propagation and arrest, Fifth Symposium in Linepipe Research, American Gas Association, 1974. 2. Maxey, W. A., Podlasek, R. J., Eiber, R. J. and Duffy, A. R., Observations on shear fracture behaviour, British Gas/IGE Symposium, Crack Propagation in Pipelines, Newcastle, March 1974. 3. Sub-committee of Large Diameter Linepipe Producers, Running shear fracture in linepipe, AISI, Technical Report, Sept. 1974. 4. Poynton, W. A., Shannon, R. W. E. and Fearnehough, G. D., The design and application of shear fracture propagation studies, Journal of Engineering Materials and Technology (Oct. 1974), pp. 323-9. 5. Fracture behaviour of gas transmission pipelines, full scale fracture tests, EPRG Report, ECSC Agreement no. 7210 KE 8/804, May 1980. 6. Priest, A. H. and Holmes, B., A multi-test piece approach to the fracture characterisation of linepipe steels, International Journal of Fracture, 17 (1981), pp. 277-99. 7. Fearnehough, G. D., Fracture propagation control in gas pipelines: a survey of relevant studies, International Journal of Pressure Vessels and Piping, 2 (1974), pp. 257-81. 8. Judy, R. W., Jr. and Goode, R. J., Fracture toughness evaluation of R-curve methods, American Society for Testing and Materials, STP527, pp. 48-61. 9. van Elst, H. C. et al., Fracture behaviour of linepipe steels, Progress Report no. 3 (EPRG Phase IV), Part 3, Appendix 1, 1975.