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The effect of proof testing on the behaviour of two stainless steel pressure vessel drumheads
Int. J. Pres. Ves. & Piping 48 (1991) 321-330
The Effect of Proof Testing on the Behaviour of Two Stainless Steel Pressure Vessel Drumheads D. N. M o r e t o n & D. G. M o f f a t Department of Mechanical Engineering, University of Liverpool, PO Box 147, Liverpool L69 3BX, UK (Received 20 March 1991; accepted 5 April 1991)
ABSTRACT Two torispherical drumheads which had previously been used for shakedown testing, have been used to determine the effect of proof testing. One drumhead was pressure cycled at its design pressure prior to undergoing a proof test and subsequent pressure cycling. The second drumhead was subjected to a proof test and subsequently pressure cycled at its design pressure. For the first drumhead, significant incremental strain was evident prior to the proof test but not after the proof test. For the second drumhead, no incremental strain was evident after the proof test.
1 INTRODUCTION The results of a study of the shakedown behaviour of stainless steel pressure vessel c o m p o n e n t s have previously been presented by the authors, t The three c o m p o n e n t s used in the tests were two different stainless steel type 321 torispherical d r u m h e a d s and a nozzle/sphere junction, the latter being located in the crown of one of the drumheads. Subsequent to the previously published work the authors have investigated the behaviour of the two torispherical heads in the postshakedown range. Of particular concern was the fact that the BS 55002 design pressures for the two heads were both of the order of twice the experimental shakedown pressures. The specific objectives of the study were therefore to first determine 321 Int. J. Pres. Ves. & Piping 0308-0161/91/$03-50 (~ 1991 Elsevier Science Publishers Ltd, England. Printed in Northern Ireland
322
D. N. Moreton, D. G. Moffat
the rate of incremental growth at the design pressure, and then to examine the effect of over-pressure tests on subsequent cycling at the design pressures. Some later work 3 has indicated that this failure to shakedown is perhaps associated with cold creep rather than a true incremental collapse (ratcheting) mechanism. However, it remains an incremental growth of significant magnitude. 2 NOTATION D e
f h he P eproof
es F
R Re Rm
Outside diameter of the cylindrical section of the drumhead Wall thickness of the cylindrical and torispherical sections of the drumhead BS 5500 design stress Outside head height The smallest of h, D2/4(R + e) and V'D(r + e)/2 BS 5500 design pressure BS 5500 proof test pressure Experimental shakedown pressure Inside knuckle radius of the drumhead Inside spherical radius of the drumhead Minimum value of specified yield strength for the grade of steel concerned Minimum tensile strength specified for the grade of material concerned at room temperature 3 T H E P R E S S U R E VESSEL C O M P O N E N T S T E S T E D
Both vessels were machined from a forged billet of stainless steel type 321 to 1.6mm oversize on thickness and then heat treated. This consisted of a 1-h soak at 850 °C followed by an oven quench using nitrogen gas with circulator fans. Following this heat treatment, both vessels were final machined and again vacuum heat treated. Test specimens cut from the billet, and similarly oversize, accompanied the vessels throughout machining and heat treatment. After final machining and strain gauging the tensile test specimens were loaded by two techniques: (a) by slow loading in a dead weight testing machine where cold creep could be allowed to run its course at each load step. Stress/strain curves obtained by this technique are given in Ref. 1 and were useful in the understanding of the vessel shakedown test results;
Effect of proof testing on pressure vessel drumheads
(b)
323
by conventional 'fast' loading where no allowance was made for cold creep. The stress/strain curve for this type of loading is given in Fig. 1. It is this curve that is the relevant one in the present context of considering design code procedures.
The two torispherical heads were geometrically similar to two of the mild steel heads (referred to as heads 31 and 32) tested by Findlay et al. 4 and the shape parameters are as follows:
Head
e/D
hc/D
r/D
r/e
R/D
31 32
0.0146 0.0146
0-161 0.216
0-089 0.068
6.13 4.67
1-496 0.789
For both components D = 180.5 mm and e = 2-68 mm. A comparison of the above parameters with the shape limitations listed in BS 5500 for torispherical heads shows that head 32 meets the limitations, whereas the crown radius of head 31 is unacceptably large. However, notwithstanding this, the parameters fall within the range of the code design chart and hence this has been used to determine the 'design' pressures for the two heads.
300
%
~.200 -a 100
o'-s
1.o Axiol strain %
Fig. 1. Uniaxial stress/strain curve of the S/S 321 used to manufacture heads 31 and 32.
324
D. N. Moreton, D. G. Moffat
4 D E S I G N P R E S S U R E BY BS 5500 The design pressure/design stress ratios P/f for heads 31 and 32 are found from the code design chart to be 0-0150 and 0.0235 respectively, and it now remains to quantify the design stress f . The nominal design strength for austenitic steels is given by Appendix K of BS 5500, for temperatures up to and including 50 °C, as =
f
-
Re 1.5 -
or
Rm 2.5
whichever is the lower. Re is the proof stress for the material and Appendix K of BS 5500 stipulates that the Re value should correspond to the 1% proof stress for austenitic steels. The 1% proof stress is found from Fig. 1 to be 321 M N / m 2. From Table 2.3 of the design code, the quoted value for Rm varies between 510 and 540 M N / m 2 for a thickness up to 20 mm depending upon product form. From the tensile tests conducted on this material, the figure of 540 M N / m 2 appears most suitable. Thus f =321/1.5 or 540/2-5MN/m 2 whichever is the lesser. The design stress value is therefore derived in this case from the 1% proof stress, and is 214 M N / m 2. The relevant design and proof test pressures for the two heads are thus
Head
P/f
P(MN/m2)
PPaOOF( M N / m 2)
31 32
0.0150 0.0235
3.21 5.03
4.02 6.29
The proof test pressures are taken to be 1.25 × design pressures, as specified by BS 5500 at the time the work was done. (BS 5500 now stipulates a proof test for stainless steel vessels of 1.3 x design pressure.)
5 S E Q U E N C E OF TESTING A N D RESULTS For both pressure vessel components the shakedown testing sequence is outlined in Ref. 1. The subsequent testing sequence, to satisfy the present obiectives , is described below for each component.
Effect of proof testing on pressure vessel drumheads
325
5.1 Head 31
Previously head 31 had been subjected to many pressure cycles with the objective of establishing the shakedown pressure P,. The maximum pressure achieved in this exercise was 2.55 M N / m 2. After reconnecting and balancing of the strain gauges, the pressure was raised to the BS 5500 design pressure of 3.21 M N / m 2 (see Fig. 2). This pressure was maintained until the 'cold creep' rate had reduced to less than 1 #/h. Pressure cycling between zero and the design pressure was then continued for 25 cycles, with the same allowance for cold creep at both ends of each cycle. The rate of accumulation of strain at the design pressure is indicated in Fig. 3. The proof test pressure of 1.25 P (4-02 MN/m2), was now applied and maintained for 30 min. During this hold time, considerable cold creep was recorded (see Fig. 2) prior to reducing the pressure to zero. Following the proof test, the vessel was cycled between zero and the design pressure P. The first of these pressure/strain cycles is shown in Fig. 2, and the peak strain variation over nine cycles at the design pressure is presented in Fig. 4. 5.2 Head 32
Previously, head 32 had been subjected to a maximum pressure of 2-41 MN/m 2. The sequence of testing used for head 31 raised some
creepsfroi~..,~1
__•old 4/IL//I~ iI Pr°°f fesf pre~ure p 3 Z
'
1st cycle of
~2
P= BS5500design pressure Ps=The experimentalshakedown pressure
J 1st cycle of ~ Poffer the proof fesi-~/ /J -251hcycle/T _
t3..
1' /
/
~
f
Permanentstrain from previoustests i
ooo
i
8obo
2ooo
Strain of first yietding location I-L Fig. 2. Pressure/strain history of head 31.
D. N. Moreton, D. G.
326
Moffat
500 --I
~. 300
2"B
Slope of
steady sfnfe=15plcycle
"-5 200
100
'
~.
'
8
'
1'2 '
1L6 '
2'0
'
~6
'
Cycle No. Fig°
Rate of accumulation of strain at design pressure P for head 31.
3,
doubt that the initial pressure cycling at the design pressure may have influenced the subsequent performance. Consequently, this part of the testing sequence was omitted in the testing of head 32. After reconnecting and balancing the strain gauges, an attempt was made to conduct a proof test, but it was not possible to continue beyond 4.14 M N / m 2 due to a leak in the vessel flange. After rectifying the leak, the proof pressure of 6.29 M N / m 2 was achieved, and for this test, the hold time was not observed. (For vessels of less than 500 mm diameter and 10 mm thickness, BS 5500 stipulates that a hold period is unnecessary.) The pressure/peak-strain history for head 32 is given in Fig. 5.
10560 10550
& ios4o ¢/J
o, 10530
4[=
CI
._c 10520 10510
I i
i
I
L
I
I
Cycle No.
I
9
Decay of peak strain at design pressure P following the proof test for head
Fig. 4.
31.
Effect of proof testing on pressure vessel drumheads
327
Proof test pressure
6 5 __P
~3 2
1 0
t,000 8000 12000 Strain of first yielding location LI
Fig. 5. Pressure/strain history of head 32.
Following the proof test, the component was subjected to five pressure cycles between zero and the design pressure (5.03 MN/m 2) with due allowance for cold creep. The decay in peak strain with pressure cycling is shown in Fig. 6 and the hysteresis loop for the fifth cycle is plotted in Fig. 7.
13200
"~ 13150 ._=
c~ 131000
Cycle No
Fig. 6. Decay of peak strain at design pressure P following the proof test for head 32.
328
D. N. Moreton, D. G. Moffat
4~5p -'h
I-
5
Z
~3 t_ r~
2
1
9000
i I 11000 r-----i._,/~5~lh
13000 Stf'0il'l ~L
.L~
Fig. 7. Pressure/strain hysteresis loop for the fifth cycle at design pressure P after the proof test for head 32.
6 DISCUSSION The shakedown tests discussed in Ref. 1 showed that, beyond the experimental shakedown pressures, each of the components tested experienced an apparently steady incremental growth with continued pressure cycling. The situation indicated in Fig. 3 for head 31 was therefore not unexpected. The results show that after only two cycles at the design pressure, the incremental strain rate settles down to a steady value of 15 #/cycle over the 25 cycles applied. This is shown on a plot of strain accumulation rate against pressure in Fig. 8, together with the data obtained from the previously reported results. It appears that the incremental strain rate is rising sharply in the region of the BS 5500 'design' pressure for this head. Equivalent data is not available for head 32, since as explained previously, cycling was not conducted at the design pressure prior to proof test. On the application of the proof pressure, heads 31 and 32 experienced peak strains of about 1.2% and 1.4% respectively. (The latter figure would have been higher had time been allowed for cold creep at the proof pressure.) On subsequent cycling at the design pressure, head 31 experienced a form of 'reversed' shakedown as indicated in Fig. 4--over the 9 cycles applied, there was a strain recovery of about 40 microstrain. Head 32 behaved in a similar fashion
Effect of proof testing on pressure vessel drumheads
Design pressure(SSSSO0)
f
329
~
%
~ d o w n
0
pressure
I
I
S 10 15 Steady-state accumulatedcyclic strain/cycle-i.1.
]~° 8° Steady-state incremental growth versus pressure for head 31.
(Fig. 6), although in this case, only the five cycles stipulated by BS 5500 were applied following the proof test. The above results are important in that they allow the conclusion to be drawn that, 'proof testing, prior to cycling at design pressure, ensures shakedown'--insofar as incremental growth is concerned. However, if shakedown is taken to be the avoidance of both incremental growth and cyclic plasticity, then strictly speaking, shakedown does not occur at the design pressure after proof testing. The hysteresis loop widths at design pressure are approximately 250 and 445 # for heads 31 and 32 respectively, and it is a matter for debate how significant these figures are. It is appreciated that further discussion is required on the above results. In particular, the following questions arise: (1)
(2)
(3)
Would the incremental strain rate indicated in Fig. 3 have continued at the level indicated, or would the value have levelled off after say some hundreds of cycles? From the work reported in Ref. 3, it is probable that this strain accumulation would have decayed logarithmically with pressure cycling. A Pproof/Pdesign ratio of 1"25 prevents incremental growth, but will lower values have the same effect? Is it possible that normal fluctuations of pressure above the design pressure in service will have the required effect? Can the behaviour be explained? Is it a material or a structural phenomenon, or a combination of both?
The writers are currently considering these questions, and are
330
D. N. Moreton, D. G. Moffat
conducting tests on stainless steel type 316 branch junctions. It is hoped that results from these tests will be reported in the near future.
7 CONCLUSIONS From the testing of two machined and annealed stainless steel type 321 drumheads the following may be concluded. Cyclic incremental strains which were observed when operating the vessels at the design pressure were not present after subjecting the vessels to a proof test.
REFERENCES 1. Moreton, D. N. & Moffat, D. G. Shakedown of three stainless steel pressure vessel components. 3rd Int. Conf. on J. Pressure Vessel Technology, Tokyo, ASME, 1977, pp. 233-245. 2. British Standard 5500, Specification for unfired fusion welded pressure vessels, 1976. 3. Brookfield, D. J., Moreton, D. N. & Moffat, D. G., Shakedown and cold creep of stainless steel type 316 torispherical drumheads subjected to internal pressure. J. Pressure Vessel Technology, ASME 108 (1986) 289-96. 4. Findlay, G. E., Moffat, D. G. & Stanley, P., Torispherical drumheads: a limit pressure and shakedown investigation. J. Strain Analysis, I. Mech. E., 3 (1971) 147.
The Effect of Proof Testing on the Behaviour of Two Stainless Steel Pressure Vessel Drumheads D. N. M o r e t o n & D. G. M o f f a t Department of Mechanical Engineering, University of Liverpool, PO Box 147, Liverpool L69 3BX, UK (Received 20 March 1991; accepted 5 April 1991)
ABSTRACT Two torispherical drumheads which had previously been used for shakedown testing, have been used to determine the effect of proof testing. One drumhead was pressure cycled at its design pressure prior to undergoing a proof test and subsequent pressure cycling. The second drumhead was subjected to a proof test and subsequently pressure cycled at its design pressure. For the first drumhead, significant incremental strain was evident prior to the proof test but not after the proof test. For the second drumhead, no incremental strain was evident after the proof test.
1 INTRODUCTION The results of a study of the shakedown behaviour of stainless steel pressure vessel c o m p o n e n t s have previously been presented by the authors, t The three c o m p o n e n t s used in the tests were two different stainless steel type 321 torispherical d r u m h e a d s and a nozzle/sphere junction, the latter being located in the crown of one of the drumheads. Subsequent to the previously published work the authors have investigated the behaviour of the two torispherical heads in the postshakedown range. Of particular concern was the fact that the BS 55002 design pressures for the two heads were both of the order of twice the experimental shakedown pressures. The specific objectives of the study were therefore to first determine 321 Int. J. Pres. Ves. & Piping 0308-0161/91/$03-50 (~ 1991 Elsevier Science Publishers Ltd, England. Printed in Northern Ireland
322
D. N. Moreton, D. G. Moffat
the rate of incremental growth at the design pressure, and then to examine the effect of over-pressure tests on subsequent cycling at the design pressures. Some later work 3 has indicated that this failure to shakedown is perhaps associated with cold creep rather than a true incremental collapse (ratcheting) mechanism. However, it remains an incremental growth of significant magnitude. 2 NOTATION D e
f h he P eproof
es F
R Re Rm
Outside diameter of the cylindrical section of the drumhead Wall thickness of the cylindrical and torispherical sections of the drumhead BS 5500 design stress Outside head height The smallest of h, D2/4(R + e) and V'D(r + e)/2 BS 5500 design pressure BS 5500 proof test pressure Experimental shakedown pressure Inside knuckle radius of the drumhead Inside spherical radius of the drumhead Minimum value of specified yield strength for the grade of steel concerned Minimum tensile strength specified for the grade of material concerned at room temperature 3 T H E P R E S S U R E VESSEL C O M P O N E N T S T E S T E D
Both vessels were machined from a forged billet of stainless steel type 321 to 1.6mm oversize on thickness and then heat treated. This consisted of a 1-h soak at 850 °C followed by an oven quench using nitrogen gas with circulator fans. Following this heat treatment, both vessels were final machined and again vacuum heat treated. Test specimens cut from the billet, and similarly oversize, accompanied the vessels throughout machining and heat treatment. After final machining and strain gauging the tensile test specimens were loaded by two techniques: (a) by slow loading in a dead weight testing machine where cold creep could be allowed to run its course at each load step. Stress/strain curves obtained by this technique are given in Ref. 1 and were useful in the understanding of the vessel shakedown test results;
Effect of proof testing on pressure vessel drumheads
(b)
323
by conventional 'fast' loading where no allowance was made for cold creep. The stress/strain curve for this type of loading is given in Fig. 1. It is this curve that is the relevant one in the present context of considering design code procedures.
The two torispherical heads were geometrically similar to two of the mild steel heads (referred to as heads 31 and 32) tested by Findlay et al. 4 and the shape parameters are as follows:
Head
e/D
hc/D
r/D
r/e
R/D
31 32
0.0146 0.0146
0-161 0.216
0-089 0.068
6.13 4.67
1-496 0.789
For both components D = 180.5 mm and e = 2-68 mm. A comparison of the above parameters with the shape limitations listed in BS 5500 for torispherical heads shows that head 32 meets the limitations, whereas the crown radius of head 31 is unacceptably large. However, notwithstanding this, the parameters fall within the range of the code design chart and hence this has been used to determine the 'design' pressures for the two heads.
300
%
~.200 -a 100
o'-s
1.o Axiol strain %
Fig. 1. Uniaxial stress/strain curve of the S/S 321 used to manufacture heads 31 and 32.
324
D. N. Moreton, D. G. Moffat
4 D E S I G N P R E S S U R E BY BS 5500 The design pressure/design stress ratios P/f for heads 31 and 32 are found from the code design chart to be 0-0150 and 0.0235 respectively, and it now remains to quantify the design stress f . The nominal design strength for austenitic steels is given by Appendix K of BS 5500, for temperatures up to and including 50 °C, as =
f
-
Re 1.5 -
or
Rm 2.5
whichever is the lower. Re is the proof stress for the material and Appendix K of BS 5500 stipulates that the Re value should correspond to the 1% proof stress for austenitic steels. The 1% proof stress is found from Fig. 1 to be 321 M N / m 2. From Table 2.3 of the design code, the quoted value for Rm varies between 510 and 540 M N / m 2 for a thickness up to 20 mm depending upon product form. From the tensile tests conducted on this material, the figure of 540 M N / m 2 appears most suitable. Thus f =321/1.5 or 540/2-5MN/m 2 whichever is the lesser. The design stress value is therefore derived in this case from the 1% proof stress, and is 214 M N / m 2. The relevant design and proof test pressures for the two heads are thus
Head
P/f
P(MN/m2)
PPaOOF( M N / m 2)
31 32
0.0150 0.0235
3.21 5.03
4.02 6.29
The proof test pressures are taken to be 1.25 × design pressures, as specified by BS 5500 at the time the work was done. (BS 5500 now stipulates a proof test for stainless steel vessels of 1.3 x design pressure.)
5 S E Q U E N C E OF TESTING A N D RESULTS For both pressure vessel components the shakedown testing sequence is outlined in Ref. 1. The subsequent testing sequence, to satisfy the present obiectives , is described below for each component.
Effect of proof testing on pressure vessel drumheads
325
5.1 Head 31
Previously head 31 had been subjected to many pressure cycles with the objective of establishing the shakedown pressure P,. The maximum pressure achieved in this exercise was 2.55 M N / m 2. After reconnecting and balancing of the strain gauges, the pressure was raised to the BS 5500 design pressure of 3.21 M N / m 2 (see Fig. 2). This pressure was maintained until the 'cold creep' rate had reduced to less than 1 #/h. Pressure cycling between zero and the design pressure was then continued for 25 cycles, with the same allowance for cold creep at both ends of each cycle. The rate of accumulation of strain at the design pressure is indicated in Fig. 3. The proof test pressure of 1.25 P (4-02 MN/m2), was now applied and maintained for 30 min. During this hold time, considerable cold creep was recorded (see Fig. 2) prior to reducing the pressure to zero. Following the proof test, the vessel was cycled between zero and the design pressure P. The first of these pressure/strain cycles is shown in Fig. 2, and the peak strain variation over nine cycles at the design pressure is presented in Fig. 4. 5.2 Head 32
Previously, head 32 had been subjected to a maximum pressure of 2-41 MN/m 2. The sequence of testing used for head 31 raised some
creepsfroi~..,~1
__•old 4/IL//I~ iI Pr°°f fesf pre~ure p 3 Z
'
1st cycle of
~2
P= BS5500design pressure Ps=The experimentalshakedown pressure
J 1st cycle of ~ Poffer the proof fesi-~/ /J -251hcycle/T _
t3..
1' /
/
~
f
Permanentstrain from previoustests i
ooo
i
8obo
2ooo
Strain of first yietding location I-L Fig. 2. Pressure/strain history of head 31.
D. N. Moreton, D. G.
326
Moffat
500 --I
~. 300
2"B
Slope of
steady sfnfe=15plcycle
"-5 200
100
'
~.
'
8
'
1'2 '
1L6 '
2'0
'
~6
'
Cycle No. Fig°
Rate of accumulation of strain at design pressure P for head 31.
3,
doubt that the initial pressure cycling at the design pressure may have influenced the subsequent performance. Consequently, this part of the testing sequence was omitted in the testing of head 32. After reconnecting and balancing the strain gauges, an attempt was made to conduct a proof test, but it was not possible to continue beyond 4.14 M N / m 2 due to a leak in the vessel flange. After rectifying the leak, the proof pressure of 6.29 M N / m 2 was achieved, and for this test, the hold time was not observed. (For vessels of less than 500 mm diameter and 10 mm thickness, BS 5500 stipulates that a hold period is unnecessary.) The pressure/peak-strain history for head 32 is given in Fig. 5.
10560 10550
& ios4o ¢/J
o, 10530
4[=
CI
._c 10520 10510
I i
i
I
L
I
I
Cycle No.
I
9
Decay of peak strain at design pressure P following the proof test for head
Fig. 4.
31.
Effect of proof testing on pressure vessel drumheads
327
Proof test pressure
6 5 __P
~3 2
1 0
t,000 8000 12000 Strain of first yielding location LI
Fig. 5. Pressure/strain history of head 32.
Following the proof test, the component was subjected to five pressure cycles between zero and the design pressure (5.03 MN/m 2) with due allowance for cold creep. The decay in peak strain with pressure cycling is shown in Fig. 6 and the hysteresis loop for the fifth cycle is plotted in Fig. 7.
13200
"~ 13150 ._=
c~ 131000
Cycle No
Fig. 6. Decay of peak strain at design pressure P following the proof test for head 32.
328
D. N. Moreton, D. G. Moffat
4~5p -'h
I-
5
Z
~3 t_ r~
2
1
9000
i I 11000 r-----i._,/~5~lh
13000 Stf'0il'l ~L
.L~
Fig. 7. Pressure/strain hysteresis loop for the fifth cycle at design pressure P after the proof test for head 32.
6 DISCUSSION The shakedown tests discussed in Ref. 1 showed that, beyond the experimental shakedown pressures, each of the components tested experienced an apparently steady incremental growth with continued pressure cycling. The situation indicated in Fig. 3 for head 31 was therefore not unexpected. The results show that after only two cycles at the design pressure, the incremental strain rate settles down to a steady value of 15 #/cycle over the 25 cycles applied. This is shown on a plot of strain accumulation rate against pressure in Fig. 8, together with the data obtained from the previously reported results. It appears that the incremental strain rate is rising sharply in the region of the BS 5500 'design' pressure for this head. Equivalent data is not available for head 32, since as explained previously, cycling was not conducted at the design pressure prior to proof test. On the application of the proof pressure, heads 31 and 32 experienced peak strains of about 1.2% and 1.4% respectively. (The latter figure would have been higher had time been allowed for cold creep at the proof pressure.) On subsequent cycling at the design pressure, head 31 experienced a form of 'reversed' shakedown as indicated in Fig. 4--over the 9 cycles applied, there was a strain recovery of about 40 microstrain. Head 32 behaved in a similar fashion
Effect of proof testing on pressure vessel drumheads
Design pressure(SSSSO0)
f
329
~
%
~ d o w n
0
pressure
I
I
S 10 15 Steady-state accumulatedcyclic strain/cycle-i.1.
]~° 8° Steady-state incremental growth versus pressure for head 31.
(Fig. 6), although in this case, only the five cycles stipulated by BS 5500 were applied following the proof test. The above results are important in that they allow the conclusion to be drawn that, 'proof testing, prior to cycling at design pressure, ensures shakedown'--insofar as incremental growth is concerned. However, if shakedown is taken to be the avoidance of both incremental growth and cyclic plasticity, then strictly speaking, shakedown does not occur at the design pressure after proof testing. The hysteresis loop widths at design pressure are approximately 250 and 445 # for heads 31 and 32 respectively, and it is a matter for debate how significant these figures are. It is appreciated that further discussion is required on the above results. In particular, the following questions arise: (1)
(2)
(3)
Would the incremental strain rate indicated in Fig. 3 have continued at the level indicated, or would the value have levelled off after say some hundreds of cycles? From the work reported in Ref. 3, it is probable that this strain accumulation would have decayed logarithmically with pressure cycling. A Pproof/Pdesign ratio of 1"25 prevents incremental growth, but will lower values have the same effect? Is it possible that normal fluctuations of pressure above the design pressure in service will have the required effect? Can the behaviour be explained? Is it a material or a structural phenomenon, or a combination of both?
The writers are currently considering these questions, and are
330
D. N. Moreton, D. G. Moffat
conducting tests on stainless steel type 316 branch junctions. It is hoped that results from these tests will be reported in the near future.
7 CONCLUSIONS From the testing of two machined and annealed stainless steel type 321 drumheads the following may be concluded. Cyclic incremental strains which were observed when operating the vessels at the design pressure were not present after subjecting the vessels to a proof test.
REFERENCES 1. Moreton, D. N. & Moffat, D. G. Shakedown of three stainless steel pressure vessel components. 3rd Int. Conf. on J. Pressure Vessel Technology, Tokyo, ASME, 1977, pp. 233-245. 2. British Standard 5500, Specification for unfired fusion welded pressure vessels, 1976. 3. Brookfield, D. J., Moreton, D. N. & Moffat, D. G., Shakedown and cold creep of stainless steel type 316 torispherical drumheads subjected to internal pressure. J. Pressure Vessel Technology, ASME 108 (1986) 289-96. 4. Findlay, G. E., Moffat, D. G. & Stanley, P., Torispherical drumheads: a limit pressure and shakedown investigation. J. Strain Analysis, I. Mech. E., 3 (1971) 147.