fatigue life assessment by haagensen

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Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 1

Professor P J Haagensen

Norges teknisk-naturvitenskapelige universitet

Fakultet for ingeniørvitenskap og teknologi Institutt for konstruksjonsteknikk

Trondheim

[email protected]

Utmattingsberegninger for stålkonstruksjoner

ihht NORSOK og Eurokode 3

Fatigue life assessment

Tirsdag 13 desember 2011


Approaches to fatigue life estimation

1. Nominal stress

2. Hot spot stress

3. Notch stress

4. Fracture mechanichs

Loads and stress calculations

Damage accumulation

Comparisons of standards

Fatigue life assessment

•

Topics

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Fatigue life assessment.

Fatigue life predictions analysis should be

performed according to standards in order to avoid

uncertainties regarding assumptions for loads and

component capacity.


Fatigue life assessment approaches

- S-N curves, nominal stress

- S-N curves, hot spot stress

- S-N curves, notch stress

- Crack growth curves

(da/dN - K diagram

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Loading data – load spectra

Cumulative load spectra obtained by stress range counting

(rainflow) is converted to histogram to give stress ranges Sr vs.

number of cycles ni per stress interval


Narrow band vs. broad band load time

histories:

Frequency

Narrow band PSD

Time

Stress

Stress

Time

Broad band

Frequency

PSD

PSD = Power Spectrum Density

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Fatigue damage

accumulation

Damage at stress level Sri :

i

ii

N

nd

0.11

k

i i

i

N

nD

Cumulative damage at fracture

(Miner-Palmgren rule:

If damage due to loads in spectrum = DT (during time T )

then:

Fatigue life L = T/DT

i

k

Log n, Log N

Stress range bin #

Number of stress range

occurrences, ni

Experimental

S-N curve

Number of cycles

to failure, Nfi

Design


Uncertainties in calculated fatigue life are

caused by: 1. Uncertainties in load spectra

2. Uncertainties in S-N curves - extrapolation

3. Uncertainties in Miner-Palmgren damage

summation rule (sequence effects)

Fatigue tests with representative load–time histories show

that the damage sum

at failure varies typically in the range 0.1 < D < 10

k

i

i=1 i

nD =

N

Some tests indicate that D decreases with increasing

irregularity, i.e. more than one peak in the power density

spectrum (PSD)

IIW design guidance recommends D ≤ 0.5 instead of 1.0 at failure

DNV: D ≤ where is the usage factor. 0.5 < <0.1 depending on

inspectability and consequences of failure.

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Sequence effects gives variations in Miner-

Palmgren damage sum

Cycles

Cra

ck length

Overloads in tension

blunt the crack tip and

introduce compressive

stresses that slow

down crack growth


Uncertainties in extrapolation of S-N curves A major source of uncertainty is related to the extrapolation of

the S-N curve below the constant amplitude fatigue limit. In

most current codes, e.g. Norsok, DNV and IIW the knee point

is now at N =107 cycles. However, an increasing amount of test

data indicate that the knee point should be at N =108, or a

straight line extrapolation should be used.

Fisher, 1993 Dahle, 1994

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Extrapolation of S-N curves

New test data indicate that the knee point should be at N =108, or a

straight line extrapolation should be used.

Sonsino, Maddox & Haagensen

IIW 2004

EXXON data, OMAE 2003

107 108

107


Fatigue life calculation – nominal stress method

1. Choose weld class

2. Calculate nominal stress range

3. Correct stress range for thickness effect and ?

3. Determine cycles to failure from S-N curve

4. Use Miner rule to calculate damage and life

misalignment

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What loads and stresses to consider?

All types of fluctuating load acting on the component and the

resulting stresses at potential sites for fatigue have to be

considered. Stresses or stress intensity factors then have to be

determined according to the fatigue assessment procedure

applied.

The actions originate from live loads, dead weights, snow, wind,

waves, pressure, accelerations, dynamic response etc. Actions

due to transient temperature changes should be considered.

Improper knowledge of fatigue actions is one of the major sources

of fatigue problems.

Tensile residual stresses due to welding decrease the fatigue

resistance, however, the influence of residual weld stresses is

already included in the fatigue resistance data given in S-N curves



Separation of stress components

The membrane stress mem is equal to the average stress calculated

through the thickness of the plate. It is constant through the thickness.

The shell bending stress bend is linearly distributed through the

thickness of the plate. It is found by drawing a straight line through the

point O where the membrane stress intersects the mid-plane of the plate.

The gradient of the shell bending stress is chosen such that the

remaining non-linearly distributed component is in equilibrium.

The non-linear stress peak nlp is the remaining component of the stress.

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Nominal stress is the stress calculated in the sectional area

under consideration, disregarding the local stress raising effects

of the welded joint, but including the stress raising effects of the

macro-geometric shape of the component in the vicinity of the

joint, such as e.g. large cut-outs. Overall elastic behaviour is

assumed.

Nominal stress calculations


Effects of macrogeometric features of the component as well

as stress fields in the vicinity of concentrated loads must be

included in the nominal stress:

Nominal stress calculations

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Local effects occur in the vicinity of concentrated loads or

reaction forces. Significant shell bending stress may also be

generated, as in curling of a flange, or distortion of a box section.


The secondary bending stress caused by axial or angular misalignment

must be considered if the misalignment exceeds the amount which is

already covered by fatigue resistance S-N curves for the structural detail.

This is done by the application of an additional stress concentration factor

(SCF). Intentional misalignment (e.g. allowable misalignment specified in

the design stage) is considered when assessing the stress by multiplying

by SCF.

Effects of misalignment (eccentricity

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In other cases, finite element method (FEM) modelling may be used.

This is primarily the case in:

a) complicated statically over-determined (redundant) structures

b) structural components incorporating macro-geometric

discontinuities, for which no analytical solutions are available

Using FEM, meshing can be simple and coarse. However, care must

be taken to ensure that all stress raising effects of the structural

detail of the welded joint are excluded when calculating the

modified (local) nominal stress.

Calculation of nominal stress In simple components the nominal stress can be determined

using elementary theories of structural mechanics based on

linear-elastic behaviour.


• Misalignment, axial and angular

• Effects of stress relief

• Plate thickness, for t > 25 mm

• Effects of corrosion

• Temperature

• Effects of high and low stresses in the spectrum

Modification of basic S-N curves

The basic S-N curves may need to be modified for the following

influencing factors:

Material: Different S-N curves for steel, aluminium,

titanium

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Butt welds: 0 = 0.1t (10% of plate thickness)

Effects of misalignment (DNV & Norsok 004)

In the test data on which the design cures are based, some axial

misaligment (eccentricity) 0 is included as follows:

The effect of axial misaligment for butt welds e0 is accounted for

by applying a stress concentration factor SCF:

where m is the measured eccentricity

m 03 δ -δSCF =1-

t


Cruciform joints

Axial misalignment included in S-N curves:

e0 = 0.5t (15% of plate thickness)

where

δ = (δm + δt) is the total eccentricity.

δ0 = 0.3t is misalignment inherent in the

S-N data for cruciform joints

ti = thickness of the considered plate

(i = 1, 2)

li = length of considered plate (i = 1, 2)

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Effect of thickness (DNV & Norsok)

For plate thickness t > 25 mm the thickness correction is included in the

equation for the S-N curve

The thickness exponent k is listed as follows:


Thickness effects in welded

connections:

Exponent k depends on weld class:

0.1< n <0.4 (IIW design guidance)

0 < n <0.25 (0.3 for tubular joints with high SCF’s

0.25 for bolts) (DNV-RP-C203)

0 0/ ( / )kS S t t

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Biaxial loading

1. Use the equivalent normal stress range is less than 10% of the equivalent

shear stress range, or if the damage sum due to shear stress range is

lower than 10% of that due to normal stress range, the effect of shear

stress may be neclected.

2. If the normal and shear stress vary simultaneously in phase, or if the

plane of maximum principal stress is not changed significantly, the

maximum principal stress range should be used.

IIW recommendations:


IIW verification procedures for combined normal and

shear stress using S-N curves

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Norsok 004, NS 3472 and DNV RP-C203

Weld classes - 1 unwelded components


DNV RP-C203 Weld classes – example welded components

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DNV RP-C203- Aug. 2005

S-N curves – welded structures in air


S-N curves – welded structures in air -details


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1. Choose weld class

2. Calculate nominal stress range

3. Correct stress range for thickness effect and ?

3. Determine cycles to failure from S-N curve

4. Use Miner rule to calculate damage and life

misalignment


DNV RP-C203

S-N curve for high strength steel – unwelded material

YS > 500 Mpa, machined surface with Ra < 3.2 m

FAT 235 MPa

S-N curve

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New S-N curve – small diameter umbilical pipes

in super duplex steel

Equations for S-N curve:



The hot spot stress method

The hot spot stress is a local stress at the weld toe, taking

into account the overall geometry of the joint, except the

shape of the weld. It is therefore sometimes called the

structural or geometrical stress.

It is used when it is difficult to define a nominal stress, e.g. in

complicated plate structures.

Originally (in the 60’s), the stress was measured at a single spot. In

the AWS/API at a distance of 1/8” (3.2mm) from the weld toe, while

Haibach recommended 2mm.

In recent versions the stress at the weld toe is extrapolated from two or

three points near the weld toe. The method is included in DNV’s RP-C203,

also and IIW (International Institute of Welding)

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Definition of the hot spot stress (DNV)

The hot spot stress is a linear extrapolation at distances 0.5t an 1.5t from

the weld toe.

In the IIW guidance the to points are at 0.4 and 1.0t. The stress at these

two points are obtained from FE analysis or from strain gauge

measurements.


Failure locations in welded joints

The structural hot spot stress method is normally applicable to surface cracks

only, but it is also possible to define a stress in a weld, e.g. by stress linearisation

over the weld throat or weld leg. Examples: Fillet weld subjected to local bending,

e.g. one-sided welds or welds around cover plates subjected to lateral loads

(Fricke et al.,2006)

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Types of hot spot stress

The stresses obtained in FE analyses must include any

misalignments or by an appropriate stress concentration factor,

SCF.

Two or three types of hot spot stress are usully defined:


FE modeling - hot spot stress

The stresses obtained in FE analyses must include any

misalignments or an appropriate stress concentration factor, SCF.

Shell or solid elements are used in the FE meshing depending on

the shape and size of the structure

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Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 39 39 Utmatting - grunnlag Oslo, 8. nov. 2010 P J Haagensen

FE stress analysis – ship structure


Meshing rules and determination of hot spot stress

The IIW and DNV fatigue design rules give detailed advice regarding

meshing and determination of the hot spot stress

At the extrapolation procedures for structural hot spot

stress of type “b”, a wall thickness

correction exponent of n=0.1 shall be applied.

Reference points for different

types of meshing

Recommended meshing and extrapolation

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Calculation of hot spot stress

Since the stresses obtained in FE analyses depend strongly on the

type of element and the mesh that are used, detailed guidance is

given in the design rules. The degree of bending influences life.

The DNV RP C-203 correction:

In IIW the FAT 90 curve is used for load carrying welds and FAT 100

for non-load carrying welds.

A single hot spot S-N curve is used by DNV (in air). This is the T-

curve = the D-curve = the FAT 90 curve. This is the S-N curve for a

“good” butt weld, welded from both sides.


The hot spot stress method – tubular joints

The hot spot stress method is used for tubular structures, and

parametric equations are given for stress concentration factors

(SCFs) for simple joint configurations. The hot spot stress to be

used when entering the S-N curve is given by:

HS nomSCF

An example of SCFs for a simple tubular joint:

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Example of FE analysis

- out of plane loading of brace


S-N curves to use with the hot spot stress

In air: Use the T-curve (= the D-curve)

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Effective notch stress method

The effective notch stress is the total stress at the root

of a notch, obtained assuming linear-elastic material

behaviour. For structural steels an effective notch root

radius of r = 1 mm in the FE analysis gives consistent

results. For fatigue assessment, the effective notch

stress is compared with a common fatigue resistance

curve.)The method is valid for plate thickness t> 5 mm

The FAT 225 (m=3) S-N curve is to be used in this

method. For t < 5 mm a radius o

The method is included in DNV’s revised RP-C203, April 2010

For t < 5 mm a radius of 0.05 has been proposed

(Sonsino 2002) with an S-N curve with FAT 630


Effective notch stress method

An effective notch radius of 1 mm is assumed in the FE

analysis

Main advantages:

Only one S-N curve is required, the FAT 225 curve.

Can be used to assess fatigue life for root cracks

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Example of stress analysis of cover plate

which can fail from the weld toe or the root


Example from 2D FE analysis

50 mm

Ref. Stress

= 100 MPa

225 MPa 142 MPa

50 mm long plate

Small risk of root cracking

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Comparison with nominal stress method

Effective notch

stress S-N curve

FAT 225 225

L = 51 mm

51 mm long plate gives the F curve


Alternative local stress methods

In recent years several local stress based methods have

been proposed as follows:

Battelle/Dong “mesh insensitive” method (Dong, et al. 2000)

Xiao and Yamada 1 mm method (2004)

Notch stress intensity factor approach (Lazzarin et al. 2006)

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The Battelle/Dong method

In this method the through-thickness stress distribution

is used to obtain an equivalent stress surface stress SS

based on equilibrium of nodal forces and moments.

A large number of test data can from many types of test

specimens be correlated on the basis of SS in a single

master curve.


Master S-N curve according to Dong (2003)

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The Xiao-Yamada method

Xiao and Yamada found that the influence of various

sharpness of the notch practically disapears at at dept

of 1 mm, and proposed to use this as a structural stress

SS .

A large number of test data can from many types of test

specimens be correlated on the basis of SS in a single

master curve.


Stress distribution at the surface and in the

depth direction (Xiao and Yamada)

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Test data correlated on the stress at 1 mm

below the surface

The data indicate that the FAT100 curve can be used for design.


The fracture mechanics method

Useful for:

Calculating residual strength

Calculting remaining life spent in crack growth

under cyclic loading

- describing the behaviour of cracked components

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Stresses at the crack tip


Stresses at the crack tip

for = 0 i.e. in the plane directly ahead of the crack the

trigonometric function = 1

When r 0 all stresses infinity

Use K as a loading parameter

23sin

2sin1

2cos

2

r

KX

23sin

2sin1

2cos

2

r

KY

23cos

2sin

2cos

2

r

KXY

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The Stress Intensity Factor K (SIF)

= global stress

Y = geometry factor

a = crack depth,

or crack half length

for interior crack

The stress intensity factor K is a scaling factor

for the stress field at the crack tip, i.e. all

stresses are proportional to K

aYK

2a

a


The critical value of the stress intensity

factor is the fracture toughness of the

material, i.e. fracture occurs when

K KIC

The fracture toughness KIC can be used to:

a) determine failure stress, when the crack size is known

b) determine critical crack size, when the stress is known

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Fracture mechanics - fatigue

When the speed at which a crack grows is

known, then the fatigue life can be

estimated if the stress intensity factor is

known for the particular load the part is

subjected to.

The crack growth rate can be determined in

tests on standardized specimens (ASTM, BS).


Testing to determine crack growth rate

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Influence of R Ratio on crack growth

-1

1

0

R=0.5 R=0 R=-1

• Largest Influence near the

threshold

• Decreasing threshold with

increasing R ratio.


Integrating the crack growth law

gives the fatigue life N

K=Yσ πa

mKCdNda )(/

mCN 0

This is the equation for an S-N curve with slope - 1/m

Assume that Y = const.

By inputting values of ai and af:

1

Stress

range,

Δ

N Log C0

m

1 / 2 1 / 2

( 2)( ) (1 / 2)

f f

i i

a a m m

f i

m mm

a a

a ada daN m

C K C Y a C Y m

SmCN logloglogOr:

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Relationship between the crack growth

diagram and the S-N curve

logdadN

log KKth

KmaxKc

dadN

= C(K)m

m

1

Paris:

log

m

1

o

o= f(Kth, ai)

log N

Fatigue limit

Fatigue limit: th EΔK =YΔσ πa th

E

i

ΔKσ

πa


Example 1 Crack growth prediction

Crack in a Finite Width Plate K= (sec(a/W))

Smin=0, Smax=50 MPa,

W=100 mm

t=10 mm

ai=4 mm

Material 355 YS Yield =370 MPa, KIC= 55 MPam

Crack Growth Data C=1.37x10-14

m=3.3

2ai

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Example 1 Crack length development

0

5

10

15

20

25

30

35

40

45

50

0.0E+00 2.0E+06 4.0E+06 6.0E+06 8.0E+06

Cycles

Cra

ck

Le

ng

th a

(m

m)

da/dN=C Km

a= (C Km) dN

Fatigue life ?


0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50

Crack Length (mm)

Ligament(M

Pa)

05101520253035404550

K (

MP

a m

1/2

)

Example 1 Failure mode

Ligσ =355MPa =YS

Yield Strength = 355 MPa

Critical Crack Length = ~ 42 mm

K

Failure occurs by

plastic collapse when Lig

i

Fσ =

W - 2a t

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Structural implications

Actions:

Establish failure criteria, apply safety factor (SF) to the critical crack length (ac) i.e. 42 mm / SF of 2.0; which gives allowable crack length = 21 mm

Establish inspection and maintenance schedules up to the allowable crack length.

When the crack length (a) reaches 21 mm: Remove component from service

Slow growth up to 10 mm, fast growth beyond 20 mm


Fracture mechanics - summary

Disadvantages:

Requires detailed information of structure geometry

Cycles to failure dependent on initial flaw geometry

Implementation at the design stage difficult

Determining SIFs can be involved and require special

numerical techniques

Advantages: Applicable to any type of structure with life dominated by crack growth

FEM, BEM or formulas can be used to determine SIF

Prediction of tolerable crack sizes in structure

Provide maintenance and inspection intervals

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The BS 7910

standard


The critical value of the crack tip opening

displacement (CTOD = ) is C i.e. ductile

fracture occurs for when

The critical value of the stress intensity

factor for brittle materials is the fracture

toughness of the material, i.e. fracture

occurs when

K KIC

C

37


Guidance assessing the risk for unstable

fracture: • Methods for calculating stresses, external

and interior (or residual stresses)

• Calculation of SIFs for defect in question

• Materials data Use Level 1 or 2 fracture assessment


Guidance needed for fatigue crack

growth calculations:

Methods for calculating stresses, external

and interior (residual stresses)

Calculation of SIFs

Materials data (crack growth curves)

Acceptable flaw sizes

Remaining life

Inspection planning – length of inspection periods

Objectives

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Stress calculations – BS 7910


Crack growth data - schematic

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Crack growth data - schematic

Environmental effects


Crack growth data, BS 7910

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Crack growth data constants, BS 7910


SIF

calculations

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Quality category S-N curves


Symmary – Fracture mechanics

BS 7910 gives comprehensive guidance for assessing

the criticality of cracks or crack-like defects in welded

structures with respect to fracture and fatigue

The assessment can be made at different levels of

complexity

The effects of environment can be included in the

assessments

fatigue life assessment by haagensen

Design

nominal stress s

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