7.6.6.1 Specific symbols and units
Table 7.6-3 lists further specific symbols and units.
Table 7.6-3 — Specific symbols and units
Symbol Characteristics Unit
i Subscript of load level -
j Subscript of individual test -
k Gradient of stress-number curve in limited endurance area - l Number of individual tests per load level -
m Number of load levels -
NS Maximum allowable number of cycles for ∆P -
n Median number of cycles -
Pfa Probability of failure -
∆PS Maximum allowable pressure fluctuation range in service. MPa a
R Ratio of load -
RS Ratio of load during service -
s Standard deviation -
Tn Scatter range -
z Quantile of a probability of distribution of standard deviation -
a MPa for calculation purposes only, otherwise the unit should be bar (1 MPa = 10 bar).
7.6.6.2 General conditions
The procedure for interpreting and evaluating cyclic pressure tests shall be based on a component stress-number curve. The evaluation leads to an allowable pressure fluctuation range to which the pressure-containing envelope of the accumulator may be exposed.
The following restrictions shall apply to the procedure described here:
⎯ the pressure-retaining parts consist of a ferritic steel which has been qualified in accordance with EN 14359 for pressure-containing envelopes;
⎯ where the pressure-retaining parts have been qualified for limited life with regard to a maximum allowable pressure fluctuation range, a crack-examination of those parts shall be performed when no more than 50 % of the maximum allowable number of cycles has been achieved. The accumulator shall be taken out of service when the cycle number limit has been reached. The end-user of the accumulator has to guarantee a safe monitoring of the relevant number of cycles. The end-user shall be responsible for carrying out above mentioned examination steps. The manufacturer of the accumulator shall give the maximum allowable number of cycles, the number of cycles for the intermediate examination and the responsibility of the end-user, expressly within the operating instructions.
NOTE National regulations may apply.
7.6.6.3 Evaluation of the fatigue test results
Cyclic pressure tests on representative parts of pressure equipment shall be performed. Such parts are exposed to loads that lead to failure by cracks. These tests are performed at a minimum of two load levels and are statistically evaluated. The gradient of the stress-number curve is calculated from the mean values of the number of cycles at those load levels. Taking into account the distribution of the number of cycles to failure and the number of test specimens, an allowable stress-number curve is defined which is related to a certain probability of failure.
NOTE If the gradient of the stress-number curve is known from previous tests with similar parts (comparison proven by stress analysis) a test at one load level may be sufficient.
The value of the probability of failure shall be defined by the manufacturer depending on the number of pressure equipment of the qualified type that is planned to be put into service. A failure under service conditions has to be excluded under reasonable judgement.
On Figure 7.2, at the point of intersection of the allowable stress-number curve with a line corresponding to two million (2 × 106) load cycles, the pressure fluctuation range for unlimited lifetime can be determined.
Psv = 10%
Psv = 50%
Psv = 90%
Psv = 99,9%
X Y
103 104 105 106 107
2,106 TN
Key
X number of cycles Y pressure MPa (bar)
Figure 7.2 — Scatter ranges in fatigue tests (schematic) 7.6.6.4 Upper and lower cyclic test pressures
The pressure fluctuation range between upper PU and lower PL cyclic pressure in these tests shall be determined in a way that leads to failure of the accumulator used for verification testing. Experience, estimations and stress analysis may be taken into account.
Upper cyclic test pressure:
U PS
P ≥ (7.6-1)
Pressure fluctuation range in test:
L U
test P P
P = −
∆ (7.6-2)
With i load levels:
Li Ui testi P P
P = −
∆ (7.6-3)
Number of load levels:
m ≥ 2
In order to take the influence of the level of mean stresses into account, R, the ratio of load between upper and lower cyclic test pressure, shall be greater than or equal to that in service.
i RS
R ≥ (7.6-4)
Li i PUi
R = P (7.6-5)
7.6.6.5 Number of accumulators for verification testing
The number of test accumulators shall be determined in a way which allows a realistic estimation of fatigue strength through statistical evaluation of test results. Previous manufacturing experience and results from comparable tests are valuable support.
A number of at least five test accumulators per load level is necessary.
Using the well-known statistical devices of quality assurance, the significance and plausibility of test results has to be evaluated by statistical means. Additionally it has to be taken into account as to what extent the accumulators are representative with regard to material properties, geometry and surface roughness.
Taking into account the limited number of accumulators, only an applicable estimation of mean values is possible. Scatter ranges gained from tests shall be examined critically in case they estimated on series with less than 25 individual results. Scatter ranges from test results have to be compared to values found in literature. A value of TN = 1:10 shall be used unless another value has been statistically verified. The larger (see note) values apply if the test results are statistically not sufficient.
NOTE 'larger' means MAX [TNTEST; TNLITERATURE] 7.6.6.6 Statistical evaluation
The numbers of cycles to failure shall be assumed to have a log-normal distribution. The mean values at the different load levels correspond to a probability of survival of 50 %.
( )
∑=
⋅
= i
1 lgnij i
i 1 n lg
l
l j (7.6-6)
The standard deviation of the log-normal distribution shall be calculated as follows:
( )2
i
1lgn ij lgn i i 1
i 1 ∑
= −
− ⋅
= l
l j
s (7.6-7)
The scatter range shall be defined with the numbers of cycles corresponding to probabilities of survival of 10 % and 90 %.
2,56 10si 1 = 10%i = ⋅
n n
T (7.6-8)
For an estimation of the realistic scatter range see 7.6.6.5.
The load cycle safety factor is a function of the scatter range and the probability of failure.
2,564ni lg 1 Ni 10
⎟⎟
⎟
⎠
⎞
⎜⎜
⎜
⎝
⎛
= ⋅ z T
S (7.6-9)
with z = f (Pfl)
Table 16
Pfa z
0,1 % 3,09
0,01 % 3,72 0,001 % 4,27 0,000 1 % 4,75
The manufacturer shall define an allowable probability of failure depending on his risk analysis. Even with a small number of equipment put into service, values above 0,1 % are not recommended.
In order to take into account the drawbacks of experimentally determined mean values a risk factor is introduced which is based on a statistical certainty of 95 %:
1,56 i 1
ni 1 Ni
l
j T ⋅
= ⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛ (7.6-10)
The product of SNi and JNi determines the distance between the mean value of the test and the allowable number of cycles. This distance shall be set equally at all load levels. If no other applicable values apply:
( Ni Ni)
N max
N j S j
S ⋅ = ⋅ (7.6-11)
The allowable number of cycles on the load levels of the performed tests is:
N N i i
S S j
N n
= ⋅ (5.6-12)
The gradient of the stress-number curve is calculated with the median number of cycles from two chosen load levels (i = 1, 2):
test2 test1 g
1 g 2
∆P l ∆P
n l n
k= (7.6-13)
with
∆Ptest2 < ∆Ptest1
7.6.6.7 Determination of cyclic operating limits
In order to determine the cyclic operating limits the stress-number curve as given in Figure 7.3 shall be divided into zones of limited and unlimited lifetime.
X Y
1
2
100 101 102 103 104 105 106 107
ND
Key
1 limited life 2 unlimited life
X number of cycles, n (log)
Y pressure fluctuation range, ∆P MPa (bar) (log)
Figure 7.3 — Stress-number curve ((S-N) curve) 7.6.6.8 Limited life
In case of qualifying for a limited life the allowable number of cycles with a given pressure fluctuation is determined by the intersection of a parallel line with the distance ∆P from the abscissa and the allowable stress-number curve.
( ) k
∆P NS ∆P
∆P NS
−
⋅
= ⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
i i (7.6-14)
7.6.6.9 Unlimited life
In case of qualifying for an unlimited life the allowable pressure fluctuation range is determined by the intersection of a parallel line with the distance ND from the ordinate and the allowable stress-number curve. Where there are no extraordinary aspects to be taken into account ND is assumed to equal 2 million (2 × 106) load cycles.
k N
∆P NS
∆PS
1 testi i ⎟ ⎟ ⎞
⎜ ⎜
⋅⎛
= (7.6-15)