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

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2010 SECTION VIII, DIVISION 2

5-49

Table 5.7 – Uniaxial Strain Limit for use in Multiaxial Strain Limit Criterion

Material

Maximum

Temperature

Uniaxial Strain Limit (1), (2), (3)

Elongation

Specified

Reduction of

Area Specified

Ferritic Steel

480°C (900°F)

(

)

0.60 1.00

−

2ln1

100

⎡

⎤

⋅+

⎢

⎥

⎣

⎦

100

⎡⎤

⎢⎥

−

⎣⎦

2.2

Stainless Steel

and Nickel

Base Alloys

480°C (900°F)

(

)

0.75 1.00

−

3ln1

100

⎡

⎤

⋅+

⎢

⎥

⎣

⎦

100

⎡⎤

⎢⎥

−

⎣⎦

0.6

Duplex

Stainless Steel

480°C (900°F)

(

)

0.70 0.95

−

2ln1

100

⎡

⎤

⋅+

⎢

⎥

⎣

⎦

100

⎡⎤

⎢⎥

−

⎣⎦

2.2

Super Alloys

(4)

480°C (900°F)

(

)

1.90 0.93

−

ln 1

100

⎡

⎤

⎢

⎥

⎣

⎦

100

⎡⎤

⎢⎥

−

⎣⎦

2.2

Aluminum

120°C (250°F)

(

)

0.52 0.98

−

1.3 ln 1

100

⎡

⎤

⋅+

⎢

⎥

⎣

⎦

100

⎡⎤

⎢⎥

−

⎣⎦

2.2

Copper

65°C (150°F)

(

)

0.50 1.00

−

2ln1

100

⎡

⎤

⋅+

⎢

⎥

⎣

⎦

100

⎡⎤

⎢⎥

−

⎣⎦

2.2

Titanium and

Zirconium

260°C (500°F)

(

)

0.50 0.98

−

1.3 ln 1

100

⎡

⎤

⋅+

⎢

⎥

⎣

⎦

100

⎡⎤

⎢⎥

−

⎣⎦

2.2

Notes:

1. If the elongation and reduction in area are not specified, then

2Lu

. If the elongation or

reduction in area is specified, then

is the maximum number computed from columns 3, 4 or 5,

as applicable.

is the ratio of the minimum specified yield strength divided by the minimum specified ultimate

tensile strength.

is the % elongation and

A is the % reduction in area determined from the applicable material

specification.

4. Precipitation hardening austenitic alloys

2010 SECTION VIII, DIVISION 2

5-50

Table 5.8 – Temperature Factors For Fatigue Screening Criteria

Metal temperature Differential

Temperature Factor For Fatigue Screening

Criteria

°C °F

28 or less 50 or less 0

29 to 56 51 to 100 1

57 to 83 101 to 150 2

84 to 139 151 to 250 4

140 to 194 251 to 350 8

195 to 250 351 to 450 12

Greater than 250 Greater than 450 20

Notes:

1. If the weld metal temperature differential is unknown or cannot be established, a value of 20 shall be

used.

2. As an example illustrating the use of this table, consider a component subject to metal temperature

differentials for the following number of thermal cycles.

Temperature Differential Temperature Factor Based On

Temperature Differential

Number Of Thermal

Cycles

28 °C (50 °F)

0 1000

50 °C (90 °F)

1 250

222 °C (400 °F)

12 5

The effective number of thermal cycles due to changes in metal temperature is:

() ()

(

)

1000 0 250 1 5 12 310

Ncycles

=++=

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2010 SECTION VIII, DIVISION 2

5-51

Table 5.9 – Fatigue Screening Criteria For Method A

Description

Integral

Construction

Attachments and nozzles in the knuckle

region of formed heads

350

FP PO TE T

NNNN

ΔΔ ΔΔ

++≤

All other components

1000

FP PO TE T

NNNN

ΔΔ ΔΔ

++≤

Non-integral

construction

Attachments and nozzles in the knuckle

region of formed heads

FP PO TE T

NNNN

ΔΔ ΔΔ

++≤

All other components

400

FP PO TE T

NNNN

ΔΔ ΔΔ

++≤

Table 5.10 – Fatigue Screening Criteria Factors For Method B

Description

Integral

Construction

Attachments and nozzles in the knuckle

region of formed heads

2.7

All other components

Non-integral

construction

Attachments and nozzles in the knuckle

region of formed heads

5.3 3.6

All other components

2.7

Table 5.11 – Weld Surface Fatigue-Strength-Reduction Factors

Weld

Condition

Surface

Condition

Quality Levels (see Table 5.12)

1 2 3 4 5 6 7

Full penetration

Machined 1.0 1.5 1.5 2.0 2.5 3.0 4.0

As-welded 1.2 1.6 1.7 2.0 2.5 3.0 4.0

Partial

Penetration

Final Surface

Machined

NA 1.5 1.5 2.0 2.5 3.0 4.0

Final Surface

As-welded

NA 1.6 1.7 2.0 2.5 3.0 4.0

Root NA NA NA NA NA NA 4.0

Fillet

Toe machined NA NA 1.5 NA 2.5 3.0 4.0

Toe as-welded NA NA 1.7 NA 2.5 3.0 4.0

Root NA NA NA NA NA NA 4.0

2010 SECTION VIII, DIVISION 2

5-52

Table 5.12 – Weld Surface Fatigue-Strength-Reduction Factors

Fatigue-Strength-Reduction

Factor

Quality

Level

Definition

1.0 1

Machined or ground weld that receives a full volumetric examination,

and a surface that receives MT/PT examination and a VT examination.

1.2 1

As-welded weld that receives a full volumetric examination, and a

surface that receives MT/PT and VT examination

1.5 2

Machined or ground weld that receives a partial volumetric

examination, and a surface that receives MT/PT examination and VT

examination

1.6 2

As-welded weld that receives a partial volumetric examination, and a

surface that receives MT/PT and VT examination

1.5 3

Machined or ground weld surface that receives MT/PT examination

and a VT examination (visual), but the weld receives no volumetric

examination inspection

1.7 3

As-welded or ground weld surface that receives MT/PT examination

and a VT examination (visual), but the weld receives no volumetric

examination inspection

2.0 4

Weld has received a partial or full volumetric examination, and the

surface has received VT examination, but no MT/PT examination

2.5 5

VT examination only of the surface; no volumetric examination nor

MT/PT examination.

3.0 6 Volumetric examination only

4.0 7 Weld backsides that are non-definable and/or receive no examination.

Notes:

1. Volumetric examination is RT or UT in accordance with Part 7.

2. MT/PT examination is magnetic particle or liquid penetrant examination in accordance with Part 7

3. VT examination is visual examination in accordance with Part 7.

4. See WRC Bulletin 432 for further information.

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2010 SECTION VIII, DIVISION 2

5-53

Table 5.13 – Fatigue Penalty Factors For Fatigue Analysis

Material

K (1)

max

T (2)

m n

(

C) (

Low alloy steel 2.0 0.2 371 700

Martensitic stainless steel 2.0 0.2 371 700

Carbon steel 3.0 0.2 371 700

Austenitic stainless steel 1.7 0.3 427 800

Nickel-chromium-iron 1.7 0.3 427 800

Nickel-copper 1.7 0.3 427 800

Notes:

1. Fatigue penalty factor

2. The fatigue penalty factor should only be used if all of the following are satisfied:

• The component is not subject to thermal ratcheting, and

• The maximum temperature in the cycle is within the value in the table for the material.

2010 SECTION VIII, DIVISION 2

5-54

5.15 Figures

1.5S

+ P

+ Q

+ P

+ Q + F

Use design loads

Use operating loads

Primary

General

Membrane

Local

Membrane

Bending

Secondary

Membrane

plus Bending

Peak

Stress

Category

Descrip-

tion (For

examples,

see Table

5.2)

Average primary

stress across

solid section.

Excludes dis-

continuities and

concentrations.

Produced only

by mechanical

loads.

Average stress

across any solid

section.

Considers dis-

continuities but

not concentra-

tions. Produced

only by mech-

anical loads.

Component of

primary stress

proportional to

distance from

centroid of solid

section.

Excludes dis-

continuities and

concentrations.

Produced only

by mechanical

loads.

Self-equilibrating

stress necessary

to satisfy contin-

uity of structure.

Occurs at struc-

tural discontinui-

ties. Can be

caused by

mechanical load

or by differential

thermal

expansion.

Excludes local

stress

concentrations.

1. Increment

added to

primary or

secondary

stress by a

concentration

(notch).

2. Certain ther-

mal stresses

which may

cause fatigue

but not distor-

tion of vessel

shape.

Symbol P

1.5S

Figure 5.1

Stress Categories and Limits of Equivalent Stress

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2010 SECTION VIII, DIVISION 2

5-55

Girth Weld

External Loads Acting

Circumferentially Around

Shell

Figure 5.2

Example of Girth Weld Used to Tie Layers for Solid Wall Equivalence

Conical Section

Figure 5.3

Example of Circumferential Butt Weld Attachment Between Layered Sections in Zone of Discontinuity

2010 SECTION VIII, DIVISION 2

5-56

Circle Weld

External Loads Acting

Around Circle of

Spherical Shell

Figure 5.4

An Example of Circle Weld Used to Tie Layers for Solid Wall Equivalence

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2010 SECTION VIII, DIVISION 2

5-57

ANNEX 5.A

LINEARIZATION OF STRESS RESULTS FOR STRESS

CLASSIFICATION

(INFORMATIVE)

5.A.1 Scope

This Annex provides recommendations for post-processing of the results from an elastic finite element stress

analysis for comparison to the limits in paragraph 5.2.2.

5.A.2 General

a) In the finite element method, when continuum elements are used in an analysis, the total stress

distribution is obtained. Therefore, to produce membrane and bending stresses, the total stress

distribution shall be linearized on a stress component basis and used to calculate the equivalent

stresses. If shell elements (shell theory) are used, then the membrane and bending stresses shall be

obtained directly from shell stress resultants.

b) Membrane and bending stresses are developed on cross sections through the thickness of a component.

These sections are called stress classification planes (SCPs). In a planar geometry, a Stress

Classification Line (SCL) is obtained by reducing two opposite sides of a SCP to an infinitesimal length.

SCPs are flat planes that cut through a section of a component and SCLs are straight lines that cut

through a section of a component. SCLs are surfaces when viewed in an axisymmetric or planar

geometry. Examples of an SCP and SCL are given in Figure 5.A.1 and Figure 5.A.2.

c) The following three approaches are provided for linearization of finite element results.

1) Stress Integration Method – This method can be used to linearize stress results from continuum

finite element models [Ref. WRC-429].

2) Structural Stress Method Based on Nodal Forces – This method is based on processing of nodal

forces, and has been shown to be mesh insensitive and correlate well with welded fatigue data [Ref.

WRC-474].

3) Structural Stress Method Based on Stress Integration – This method utilizes the Stress Integration

Method, but restricts the set of elements that contribute to the line of nodes being processed.

d) The Structural Stress Method based on Stress Integration is recommended unless another method can

be shown to produce a more accurate assessment for the given component and loading condition. This

method matches the Structural Stress Method Based on Nodal Forces, which is insensitive to mesh

refinement. In addition, this method can be performed with post-processing tools typically provided by

commercial finite element analysis software.

5.A.3 Selection of Stress Classification Lines

a) Pressure vessels usually contain structural discontinuity regions where abrupt changes in geometry,

material or loading occur. These regions are typically the locations of highest stress in a component.

For the evaluation of failure modes of plastic collapse and ratcheting, Stress Classification Lines (SCLs)

are typically located at gross structural discontinuities. For the evaluation of local failure and fatigue,

SCLs are typically located at local structural discontinuities.

2010 SECTION VIII, DIVISION 2

5-58

b) For SCLs that span a material discontinuity (e.g. base metal with cladding), the SCL should include all

materials and associated loadings. If one of the materials, such as cladding, is neglected for strength

calculations, then only the base metal thickness should be used to calculate the membrane and bending

stresses from the linearized forces and moments across the full section for the evaluation of plastic

collapse.

c) To most accurately determine the linearized membrane and bending stresses for comparison to elastic

stress limits, the following guidelines should be followed. These guidelines can be used as a qualitative

means to evaluate the applicability of different SCLs. Failure to comply with any of these criteria may not

produce valid membrane and/or bending stresses. Application of the limit load or elastic-plastic analysis

methods in Part 5 is recommended for cases where elastic stress analysis and stress linearization may

produce ambiguous results.

1) SCLs should be oriented normal to contour lines of the stress component of highest magnitude.

However, as this may be difficult to implement, similar accuracy can be obtained by orienting the

SCL normal to the mid-surface of the cross section. SCL orientation guidelines are shown in Figure

5.A.3.

2) Hoop and meridional component stress distributions on the SCL should be monotonically increasing

or decreasing, except for the effects of stress concentration or thermal peak stresses, see Figure

5.A.3.b.

3) The distribution of the through-thickness stress should be monotonically increasing or decreasing.

For pressure loading the through-thickness stress should be equal to the compressive pressure on

the applied surface, and approximately zero on the other surface defining the SCL (see Figure

5.A.3.c). When the SCL is not perpendicular to the surfaces, this requirement will not be satisfied.

4) The shear stress distribution should be parabolic and/or the stress should be low relative to the

hoop and meridional stresses. Depending on the type of loading, the shear stress should be

approximately zero on both surfaces defined by the SCL. Guidelines are provided in Figure 5.A.3.d.

i) The shear stress distribution along an SCL will approximate a parabolic distribution only when

the inner and outer surfaces are parallel and the SCL is normal to the surfaces. If the surfaces

are not parallel or an SCL is not normal to the surfaces, the appropriate shear distribution will

not be obtained. However, if the magnitude of shear stress is small as compared to the hoop

or meridional stresses, this orientation criterion can be waived.

ii) When the shear stress distribution is approximately linear, the shear stress is likely to be

significant.

5) For pressure boundary components, the hoop or meridional stresses typically are the largest

magnitude component stresses and are the dominant terms in the equivalent stress. Typically the

hoop or meridional stresses deviate from a monotonically increasing or decreasing trend along an

SCL if the SCL is skewed with respect to the interior, exterior, or mid surfaces. For most pressure

vessel applications, the hoop or meridional stresses due to pressure should be nearly linear.

5.A.4 Stress Integration Method

5.A.4.1 Continuum Elements

5.A.4.1.1 Overview

Stress results derived from a finite element analysis utilizing two-dimensional or three-dimensional continuum

elements may be processed using the stress integration method. Stress components are integrated along

SCLs through the wall thickness to determine the membrane and bending stress components. The peak

stress components can be derived directly using this procedure by subtracting the membrane plus bending

stress distribution from the total stress distribution. Using these components, the equivalent stress shall be

computed per Equation (5.1).

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