ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules

Подождите немного. Документ загружается.

2010 SECTION VIII, DIVISION 2

5-19

()()

()

0.5

11, 22, 11, 33,

222

22, 33, 12, 13, 23,

kk kk

kk kkk

σσ σσ

σσ σσσ

⎡⎤

Δ−Δ +Δ−Δ +

⎢⎥

Δ=

⎢⎥

Δ−Δ +Δ+Δ+Δ

⎣⎦

(5.29)

d) STEP 4 – Determine the effective alternating equivalent stress amplitude for the

k cycle using the

results from STEP 3..

()

,, ,,,

ek Pk LT k vk LTk

alt k

KK S S K S

⋅⋅Δ−Δ +⋅Δ

(5.30)

1) If the local notch or effect of the weld is accounted for in the numerical model, then

1.0

Equations (5.30) and (5.36). If the local notch or effect of the weld is not accounted for in the

numerical model, then a fatigue strength reduction factor,

K , shall be included. Recommended

values for fatigue strength reduction factors for welds are provided in Tables 5.11 and 5.12.

2) The fatigue penalty factor,

,ek

K , in Equations (5.30) and (5.36) is evaluated using the following

equations where the parameters

m and n are determined from Table 5.13 and

S and

,nk

are

defined in paragraph 5.5.6.1. For

,ek

K values greater than 1.0, the simplified elastic-plastic criteria

of paragraph 5.5.6.2 shall be satisfied.

, ,

1.0

ek nk PS

KforSS=Δ≤

(5.31)

()

, ,

1.0 1

ek PS n k PS

KforSSmS

nm S

−

⎛⎞

=+ − <Δ<

⎜⎟

−

⎝⎠

(5.32)

, ,

ek nk PS

KforSmS

=Δ≥

(5.33)

3) The Poisson correction factor,

,vk

K in Equation (5.30) is computed using Equation (5.34).

⎛⎞

−

⎜⎟

−

⎝⎠

(5.34)

where

0.5 0.2 ,

max

⎡

⎤

⎛⎞

=−

⎢

⎥

⎜⎟

⎢

⎥

⎝⎠

⎣

⎦

(5.35)

4) The Poisson correction factor,

,vk

K , in Equation (5.34) need not be used if the fatigue penalty

factor,

,ek

, is used for the entire stress range (including

,LT k

). In this case, Equation (5.30)

becomes:

2010 SECTION VIII, DIVISION 2

5-20

ek Pk

alt k

KK S

⋅⋅Δ

(5.36)

e) STEP 5 – Determine the permissible number of cycles,

N , for the alternating equivalent stress

computed in STEP 4. Fatigue curves based on the materials of construction are provided in Annex 3.F,

paragraph 3.F.1.

f) STEP 6 – Determine the fatigue damage for the

k cycle, where the actual number of repetitions of the

cycle is

n .

(5.37)

g) STEP 7 – Repeat STEPs 3 through 6 for all stress ranges,

, identified in the cycle counting process

in STEP 2.

h) STEP 8 – Compute the accumulated fatigue damage using the following equation. The location in the

component is acceptable for continued operation if this equation is satisfied.

1.0

ffk

=≤

∑

(5.38)

i) STEP 9 – Repeat STEPs 2 through 8 for each point in the component subject to a fatigue evaluation.

5.5.3.3 In STEP 4 of paragraph 5.5.3.2,

,ek

may be calculated using one of the following methods.

a) Method 1 – The equivalent total strain range from elastic-plastic analysis and the equivalent total strain

range from elastic analysis for the point of interest as given below.

()

(5.39)

where,

()

()()

()

0.5

11, 22, 22, 33,

222

33, 11, 12, 23, 31,

1.5

kk kk

kk k k k

ee e e

ee eee

⎡⎤

Δ−Δ +Δ−Δ +

⎢⎥

Δ=

⎢⎥

Δ−Δ +Δ+Δ+Δ

⎣⎦

(5.40)

()

ya k

Δ=

(5.41)

The stress range

SΔ is given by Equation (5.29).

b) Method 2 – The alternate plasticity adjustment factors and alternating equivalent stress may be

computed using Annex 5.C.

5.5.3.4 In lieu of a detailed stress analysis, stress indices may be used to determine peak stresses

around a nozzle opening in accordance with Annex 5.D.

标准分享网 www.bzfxw.com 免费下载

2010 SECTION VIII, DIVISION 2

5-21

5.5.4 Fatigue Assessment – Elastic-Plastic Stress Analysis and Equivalent Strains

5.5.4.1 Overview

a) The Effective Strain Range is used to evaluate the fatigue damage for results obtained from an elastic-

plastic stress analysis. The Effective Strain Range is calculated for each cycle in the loading histogram

using either cycle-by-cycle analysis or the Twice Yield Method. For the cycle-by-cycle analysis, a cyclic

plasticity algorithm with kinematic hardening shall be used.

b) Twice Yield Method is an elastic-plastic stress analysis performed in a single loading step, based on a

specified stabilized cyclic stress range-strain range curve and a specified load range representing a

cycle. Stress and strain ranges are the direct output from this analysis. This method is performed in the

same manner as a monotonic analysis and does not require cycle-by-cycle analysis of unloading and

reloading. The Twice Yield Method can be used with an analysis program without cyclic plasticity

capability.

c) For the calculation of the stress range and strain range of a cycle at a point in the component, a

stabilized cyclic stress-strain curve and other material properties shall be used based on the average

temperature of the cycle being evaluated for each material of construction. The cyclic curve may be that

obtained by test for the material, or that which is known to have more conservative cyclic behavior to the

material that is specified. Cyclic stress-strain curves are also provided in paragraph 3.D.4 of Annex 3.D

for certain materials and temperatures. Other cyclic stress-strain curves may be used that are known to

be either more accurate for the application or lead to more conservative results.

5.5.4.2 Assessment Procedure

The following procedure can be used to evaluate protection against failure due to cyclic loading using elastic-

plastic stress analysis.

a) STEP 1 – Determine a load history based on the information in the User’s Design Specification and the

methods in Annex 5.B. The load history should include all significant operating loads and events that are

applied to the component.

b) STEP 2 – For a location in the component subject to a fatigue evaluation, determine the individual

stress-strain cycles using the cycle counting methods in Annex 5.B. Define the total number of cyclic

stress ranges in the histogram as

c) STEP 3 – Determine the loadings at the start and end points of the

cycle counted in STEP 2. Using

these data, determine the loading ranges (differences between the loadings at the start and end points of

the cycle).

d) STEP 4 – Perform elastic-plastic stress analysis for the

k cycle. For cycle-by-cycle analysis, constant-

amplitude loading is cycled using cyclic stress amplitude-strain amplitude curve (paragraph 5.5.4.1). For

the Twice Yield Method, the loading at the start point of the cycle is zero and the loading at the end point

is the loading range determined in STEP 3. The cyclic stress range-strain range curve is used

(paragraph 5.5.4.1). For thermal loading, the loading range in Twice-Yield Method may be applied by

specifying the temperature field at the start point for the cycle as an initial condition, and applying the

temperature field at the end point for the cycle in a single loading step.

e) STEP 5 – Calculate the Effective Strain Range for the

cycle.

eff k peq k

ya k

εε

Δ= +Δ

(5.42)

where, the stress range

SΔ is given by Equation (5.29)

2010 SECTION VIII, DIVISION 2

5-22

()()

()

0.5

11, 22, 22, 33,

222

33, 11, 12, 23, 31,

1.5

kk kk

peq k

kk k k k

pp p p

pp ppp

⎡⎤

Δ−Δ +Δ−Δ +

⎢⎥

Δ=

⎢⎥

Δ−Δ +Δ+Δ+Δ

⎣⎦

(5.43)

The component stress and plastic strain ranges (differences between the components at the start and

end points of the cycle) for the

k cycle are designated as

,ij k

and

,ij k

, respectively. However,

since a range of loading is applied in a single load step with the Twice Yield Method, the calculated

maximum equivalent plastic strain range,

,peq k

and the von Mises equivalent stress range

SΔ

defined above are typical output variables that can be obtained directly from a stress analysis.

f) STEP 6 – Determine the effective alternating equivalent stress for the

k cycle.

yf eff k

alt k

⋅Δ

(5.44)

g) STEP 7 – Determine the permissible number of cycles,

N , for the alternating equivalent stress

computed in STEP 6. Fatigue curves based on the materials of construction are provided in Annex 3.F,

paragraph 3.F.1.

h) STEP 8 – Determine the fatigue damage for the

cycle, where the actual number of repetitions of the

k cycle is

n .

(5.45)

i) STEP 9 – Repeat STEPs 3 through 8 for all stress ranges,

, identified in the cycle counting process

in STEP 2.

j) STEP 10 – Compute the accumulated fatigue damage using the following equation. The location in the

component is acceptable for continued operation if this equation is satisfied.

1.0

≤

∑

(5.46)

k) STEP 11 – Repeat STEPs 2 through 10 for each point in the component subject to a fatigue evaluation.

5.5.5 Fatigue Assessment of Welds – Elastic Analysis and Structural Stress

5.5.5.1 Overview

a) An equivalent structural stress range parameter is used to evaluate the fatigue damage for results

obtained from a linear elastic stress analysis. The controlling stress for the fatigue evaluation is the

structural stress that is a function of the membrane and bending stresses normal to the hypothetical

crack plane. This method is recommended for evaluation of welded joints that have not been machined

to a smooth profile. Weld joints with controlled smooth profiles may be evaluated using paragraphs 5.5.3

or 5.5.4.

b) Fatigue cracks at pressure vessel welds are typically located at the toe of a weld. For as-welded and

weld joints subject to post weld heat treatment, the expected orientation of a fatigue crack is along the

weld toe in the through-thickness direction, and the structural stress normal to the expected crack is the

stress measure used to correlate fatigue life data. For fillet welded components, fatigue cracking may

occur at the toe of the fillet weld or the weld throat, and both locations shall be considered in the

标准分享网 www.bzfxw.com 免费下载

2010 SECTION VIII, DIVISION 2

5-23

assessment. It is difficult to accurately predict fatigue life at the weld throat due to variability in throat

dimension, which is a function of the depth of the weld penetration. It is recommended to perform

sensitivity analysis where the weld throat dimension is varied.

c) This fatigue method may only be used when approved by the owner/user.

5.5.5.2 Assessment Procedure

The following procedure can be used to evaluate protection against failure due to cyclic loading using the

equivalent structural stress range.

a) STEP 1 – Determine a load history based on the information in the User’s Design Specification and the

histogram development methods in Annex 5.B. The load history should include all significant operating

loads and events that are applied to the component.

b) STEP 2 – For a location at a weld joint subject to a fatigue evaluation, determine the individual stress-

strain cycles using the cycle counting methods in Annex 5.B. Define the total number of cyclic stress

ranges in the histogram as

c) STEP 3 – Determine the elastically calculated membrane and bending stress normal to the assumed

hypothetical crack plane at the start and end points (time points

and

, respectively) for the

cycle

counted in STEP 2. Using this data, calculate the membrane and bending stress ranges between time

points

t and

t , and the maximum, minimum and mean stress.

,,,

emene

mk mk mk

σσ

Δ= − (5.47)

,,,

emene

bk bk bk

σσ

Δ= − (5.48)

()

(

)

,, ,,

max ,

me me ne ne

max,k m k b k m k b k

σσσσσ

⎡⎤

=+ +

⎣⎦

(5.49)

()

(

)

,, ,,

min ,

me me ne ne

min,k m k b k m k b k

σσσσσ

⎡⎤

=+ +

⎣⎦

(5.50)

max k min,k

mean,k

(5.51)

d) STEP 4 – Determine the elastically calculated structural stress range for the

cycle,

, using

Equation (5.52).

ee e

kmkbk

σσ

Δ=Δ +Δ (5.52)

e) STEP 5 – Determine the elastically calculated structural strain,

, from the elastically calculated

structural stress,

Δ , using Equation (5.53)

ya k

Δ=

(5.53)

The corresponding local nonlinear structural stress and strain ranges,

and

Δ , respectively, are

determined by simultaneously solving Neuber’s Rule, Equation (5.54), and a model for the material

hysteresis loop stress-strain curve given by Equation (5.55), see Annex 3.D, paragraph 3.D.4.

2010 SECTION VIII, DIVISION 2

5-24

kk kk

εσε

Δ⋅Δ=Δ⋅Δ (5.54)

css

ya k css

σσ

⎛⎞

ΔΔ

Δ= +

⎜⎟

⎝⎠

(5.55)

The structural stress range computed solving Equations (5.54) and (5.55) is subsequently modified for

low-cycle fatigue using Equation(5.56).

ya k

⎛⎞

Δ= Δ

⎜⎟

−

⎝⎠

(5.56)

NOTE: The modification for low-cycle fatigue should always be performed because the exact distinction

between high-cycle fatigue and low-cycle fatigue cannot be determined without evaluating the effects of

plasticity which is a function of the applied stress range and cyclic stress-strain curve. For high cycle

fatigue applications, this procedure will provide correct results, i.e. the elastically calculated structural

stress will not be modified.

f) STEP 6 – Compute the equivalent structural stress range parameter for the

k cycle using the following

equations. In Equation (5.57), for SI Units, the thickness,

t , stress range,

, and the equivalent

structural stress range parameter,

,ess k

SΔ , are in

, and

()

2/2

sss

MPa mm

−

, respectively,

and for US Customary Units, the thickness,

t , stress range,

, and the equivalent structural stress

range parameter,

,ess k

SΔ , are in inches , ksi , and

()

2/2

sss

ksi inches

−

, respectively.

ess k

ess M k

tIf

⎛⎞

−

⎜⎟

⎝⎠

Δ=

⋅⋅

(5.57)

where,

3.6

m = (5.58)

16 (0.625 .) 16 (0.625 .)

ess

tmmin fortmmin=≤ (5.59)

16 (0.625 .) 150 (6 .)

ess

tt for mm int mmin=<< (5.60)

150 (6 .) 150 (6 .)

ess

t mmin for t mmin=≥ (5.61)

1.23 0.364 0.17

1.007 0.306 0.178

bk bk

−−

(5.62)

mk bk

σσ

Δ+Δ

(5.63)

标准分享网 www.bzfxw.com 免费下载

2010 SECTION VIII, DIVISION 2

5-25

()

,,,

0.5 ,

10,

mean k y k

Mk k k

mk bk yk

S and

f R for R and

σσ

≥

=− >

Δ+Δ≤

(5.64)

,,,

0.5 ,

1.0 0,

mean k y k

Mk k

mk bk yk

Sor

fforRor

σσ

=≤

Δ+Δ>

(5.65)

min k

max k

= (5.66)

g) STEP 7 – Determine the permissible number of cycles,

N , based on the equivalent structural stress

range parameter for the

k cycle computed in STEP 6. Fatigue curves for welded joints are provided in

Annex 3.F, paragraph 3.F.2.

h) STEP 8 – Determine the fatigue damage for the

k cycle, where the actual number of repetitions of the

cycle is

n .

(5.67)

i) STEP 9 – Repeat STEPs 6 through 8 for all stress ranges,

, identified in the cycle counting process

in STEP 3.

j) STEP 10 – Compute the accumulated fatigue damage using the following equation. The location along

the weld joint is suitable for continued operation if this equation is satisfied.

1.0

ffk

=≤

∑

(5.68)

k) STEP 11 – Repeat STEPs 5 through 10 for each point along the weld joint that is subject to a fatigue

evaluation.

5.5.5.3 Assessment Procedure Modifications

The assessment procedure in paragraph 5.5.5.2 may be modified as shown below.

a) Multiaxial Fatigue – If the structural shear stress range is not negligible, i.e.

Δ>Δ , a

modification should be made when computing the equivalent structural stress range. Two conditions

need to be considered:

1) If

Δ and

Δ are out of phase, the equivalent structural stress range

,ess k

SΔ in Equation (5.57)

should be replaced by:

2010 SECTION VIII, DIVISION 2

5-26

0.5

()

ss ss

ess k

ess M k ess

tIf tI

στ

⎛⎞ ⎛⎞

−−

⎜⎟ ⎜⎟

⎝⎠ ⎝⎠

⎡⎤

⎛⎞

⎢⎥

⎜⎟

ΔΔ

⎢⎥

Δ= +

⎜⎟

⎢⎥

⎜⎟

⋅⋅ ⋅

⎢⎥

⎝⎠

⎣⎦

(5.69)

where

1.23 0.364 0.17

1.007 0.306 0.178

bk bk

ττ

−−

(5.70)

mk bk

Δ+Δ

(5.71)

kmkbk

ττ

Δ=Δ +Δ (5.72)

,,,

emene

mk mk mk

ττ

Δ= − (5.73)

,,,

emene

bk bk bk

ττ

Δ= − (5.74)

In Equation (5.69),

)(

F is a function of the out-of-phase angle between

and

Δ if both

loading modes can be described by sinusoidal functions, or:

[]

0.5

222

12 sin

() 1 1

στ δ

στ

⎡⎤

⋅Δ ⋅Δ ⋅

⎢⎥

=+−

⎢⎥

⎡⎤

Δ+Δ

⎣⎦

⎢⎥

⎣⎦

(5.75)

A conservative approach is to ignore the out-of-phase angle and recognize the existence of a

minimum possible value for

)(

F in Equation (5.75) given by:

()

= (5.76)

2) If

Δ and

Δ are in-phase the equivalent structural stress range

,ess k

is given by Equation

(5.69) with

() 1.0F

= .

b) Weld Quality – If a defect exists at the toe of a weld that can be characterized as a crack-like flaw, i.e.

undercut, and this defect exceeds the value permitted by Part 7, then a reduction in fatigue life shall

calculated by substituting the value of

in Equation (5.62) with the value given by Equation (5.77).

In this equation,

a is the depth of the crack-like flaw at the weld toe. Equation (5.77) is valid only

when

0.1at≤ .

标准分享网 www.bzfxw.com 免费下载

2010 SECTION VIII, DIVISION 2

5-27

,, ,

1.229 0.365 0.789 0.17 13.771 1.243

1 0.302 7.115 0.178 12.903 4.091

bk bk bk

aaa

RR R

ttt

aaa

RR R

ttt

⎛⎞ ⎛⎞ ⎛⎞

−+ −+ +

⎜⎟ ⎜⎟ ⎜⎟

⎝⎠ ⎝⎠ ⎝⎠

⎛⎞ ⎛⎞ ⎛⎞

−+ −+ −

⎜⎟ ⎜⎟ ⎜⎟

⎝⎠ ⎝⎠ ⎝⎠

(5.77)

5.5.6 Ratcheting Assessment – Elastic Stress Analysis

5.5.6.1 Elastic Ratcheting Analysis Method

a) To evaluate protection against ratcheting the following limit shall be satisfied.

,nk PS

SSΔ≤ (5.78)

b) The primary plus secondary equivalent stress range,

,nk

, is the equivalent stress range, derived from

the highest value across the thickness of a section, of the combination of linearized general or local

primary membrane stresses plus primary bending stresses plus secondary stresses

()

PPQ++ ,

produced by specified operating pressure and other specified mechanical loads and by general thermal

effects. The effects of gross structural discontinuities but not of local structural discontinuities (stress

concentrations) shall be included. Examples of this stress category for typical pressure vessel

components are shown in Table 5.6.

c) The maximum range of this equivalent stress is limited to

S . The quantity

S represents a limit on

the primary plus secondary equivalent stress range and is defined in paragraph 5.5.6.1.d. In the

determination of the maximum primary plus secondary equivalent stress range, it may be necessary to

consider the effects of multiple cycles where the total stress range may be greater than the stress range

of any of the individual cycles. In this case, the value of

S may vary with the specified cycle, or

combination of cycles, being considered since the temperature extremes may be different in each case.

Therefore, care shall be exercised to assure that the applicable value of

S for each cycle, or

combination of cycles, is used (see paragraph 5.5.3).

d) The allowable limit on the primary plus secondary stress range,

S , is computed as the larger of the

quantities shown below.

1) Three times the average of the

values for the material from Annex 3.A at the highest and lowest

temperatures during the operational cycle.

2) Two times the average of the

S values for the material from Annex 3.D at the highest and lowest

temperatures during the operational cycle, except that the value from paragraph 5.5.6.1.d.1 shall be

used when the ratio of the minimum specified yield strength to ultimate tensile strength exceeds

0.70 or the value of

S is governed by time-dependent properties as indicated in Annex 3.A.

5.5.6.2 Simplified Elastic-Plastic Analysis

The equivalent stress limit on the range of primary plus secondary equivalent stress in paragraph 5.5.6.1 may

be exceeded provided all of the following are true:

a) The range of primary plus secondary membrane plus bending equivalent stress, excluding thermal

bending stress, is less than

S .

b) The value of the alternating stress range in paragraph 5.5.3.2.d is multiplied by the factor

,ek

K (see

Equations (5.31) through (5.33), or paragraph 5.5.3.3) .

2010 SECTION VIII, DIVISION 2

5-28

c) The material of the component has a ratio of the specified minimum yield strength to specified minimum

tensile strength of less than or equal to 0.80.

d) The component meets the secondary equivalent stress range requirements of paragraph 5.5.6.3.

5.5.6.3 Thermal Stress Ratcheting Assessment

The allowable limit on the secondary equivalent stress range from thermal loading to prevent ratcheting,

when applied in conjunction with a steady state general or local primary membrane equivalent stress, is

determined below. This procedure can only be used with an assumed linear or parabolic distribution of a

secondary stress range (e.g. thermal stress).

a) STEP 1 – Determine the ratio of the primary membrane stress to the specified minimum yield strength

from Annex 3.D, at the average temperature of the cycle.

⎛⎞

⎜⎟

⎝⎠

(5.79)

b) STEP 2 – Compute the secondary equivalent stress range from thermal loading,

QΔ using elastic

analysis methods.

c) STEP 3 – Determine the allowable limit on the secondary equivalent stress range from thermal loading,

S .

1. For a secondary equivalent stress range from thermal loading with a linear variation through the wall

thickness:

00.5

SS for X

⎛⎞

=<<

⎜⎟

⎝⎠

(5.80)

()

4.0 1 0.5 1.0

SSX for X=− ≤≤ (5.81)

2. For a secondary equivalent stress range from thermal loading with a parabolic constantly increasing

or decreasing variation through the wall thickness:

0.0 0.615

0.1224 0.9944

SS for X

⎛⎞

=<<

⎜⎟

⎝⎠

(5.82)

()

5.2 1 0.615 1.0

SSX for X=− ≤≤ (5.83)

d) STEP 4 – To demonstrate protection against ratcheting, the following criteria shall be satisfied.

QSΔ≤ (5.84)

5.5.6.4 Progressive Distortion of Non-Integral Connections

Screwed-on caps, screwed-in plugs, shear ring closures, and breech lock closures are examples of non-

integral connections that are subject to failure by bell-mouthing or other types of progressive deformation. If

any combination of applied loads produces yielding, such joints are subject to ratcheting because the mating

members may become loose at the end of each complete operating cycle and may start the next cycle in a

new relationship with each other, with or without manual manipulation. Additional distortion may occur in

each cycle so that interlocking parts, such as threads, can eventually lose engagement. Therefore primary

plus secondary equivalent stresses that produce slippage between the parts of a non-integral connection in

标准分享网 www.bzfxw.com 免费下载