Fatigue Assessment of Fatigue Assessment of **** Weld Joints Using ANSYS, Weld Joints Using ANSYS,

Verity & FE-SafeVerity & FE-Safe

Zhichao Wang

Aditya Sakhalkar

5/8/2007

** Verity is a weld fatigue assessment software ** Verity is a weld fatigue assessment software developed by Battelle based on Structural developed by Battelle based on Structural Stress & Fracture Mechanics theory proposed Stress & Fracture Mechanics theory proposed by Dr. Dong et al, Battelleby Dr. Dong et al, Battelle

Part I: Key Points on Equivalent SS MethodPart I: Key Points on Equivalent SS Method

Part II: Example ApplicationPart II: Example Application

Part I: Key Points on Equivalent SS MethodPart I: Key Points on Equivalent SS Method

Part II: Example ApplicationPart II: Example Application

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Part I: Key Points on SS & Weld AssessmentsPart I: Key Points on SS & Weld AssessmentsPart I: Key Points on SS & Weld AssessmentsPart I: Key Points on SS & Weld Assessments

Zhichao WangSr. Lead Engineer

Emerson Climate Technology Inc.

Background

Why The Battelle’s Structure Stress Is Not Sensitive To FE Mesh Size?

How Could Multiple Joint S~N Curves Be Reduced to A Single S~N Curve, the Master S~N Curve?

Example Application (Part ii, Aditya)

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Background

Fatigue Assessment – Unwelded Structures

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Fatigue Assessment – Welded Structures

It’s been commonly recognized that the fatigue life of the polishedspecimen is dominated by fatigue crack initiation, whereas that of welded structures is dominated by small crack propagation from some pre-existing discontinuity.

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(i). Nominal Stress Method (BS,IIW)

The nominal stress range is used to develop the S~N curves using samples with actual weld joint geometry. The life curves refer to particular weld details, there is no need for the user to attempt to quantify the local stress concentration effect of the weld detail itself.

(ii). Hotspot Stress Approach (structural stress, geometric stress, BS, IIW, CEN,DNV)This procedure uses hot-spot stress range as a parameter. The S–N curves are obtained from tests of actual welded joints based on the hot-spot stress range rather than the nominal stress range.

(iii). Local Notch Stress Method (ASME, BS, IIW).The notch stress approach attempts to include all sources of stress concentration in the stress used with the design S–N curve. Thus a single S–N curve may be sufficient for a given type of material. The problem is that the local geometry of the toe or root of a weld is highly variable. It may be hard to achieve consistent results.

Fatigue Assessment – Welded Structures

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Fatigue Assessment – Welded Structures

(iv). The Fracture Mechanics Approach (For crack propagation life)

The parameter widely used is SIF, K. The fatigue resistance is represented by fatigue crack growth rate da/dN. Many crack propagation laws are available. The simplest one is Paris Law in which the crack growth law approximates to a linear relationship:

For a flaw size starts from a0 to a critical fatigue crack size af, the remaining fatigue life N under stress range S is obtained by integrating Eq (1):

(v) Verity Equivalent Structural Stress Method (Battelle)

Equivalent Structural Stress + Single Master S~N Curve

ndaC ( K) (1)

dN

f

0

a

na

daC N (2)

( K)

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Structural Stress & Mesh Sensitivity

(b) Comparison of SCF predicted by various modeling procedures and extrapolation based HSS at the weld toe [12].(b) Comparison of SCF predicted by various modeling procedures and extrapolation based HSS at the weld toe [12].

(c) Structural Stress Using Verity Method(c) Structural Stress Using Verity Method

Hot Spot Nomin a

Nomin al

l

FE

(Human Factor)

~

0

x

X~0.4 t

Hot SpotFE

Nomin al

(a) Normal Stress at the sharp corner

(Structural Stress)tσ

xσ sp

A

A

P

Y

X

0.4 t

A

A

t

Hot Spot Nomin a

Nomin al

l

FE

(Human Factor)

~

0

x

X~0.4 t

Hot SpotFE

Nomin al

(a) Normal Stress at the sharp corner

x

X~0.4 t

Hot SpotFE

Nomin al

(a) Normal Stress at the sharp corner

(Structural Stress)tσ

xσ sp

A

A

(Structural Stress)tσ

xσ sp

(Structural Stress)tσ

xσ sp

A

A

P

Y

X

0.4 t

A

A

tP

Y

X

0.4 t

A

A

A

A

t

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Why Structure Stress Is Not Sensitive To FE Mesh?

(a)

(b)

(c) Structural Stress Using Verity Method(c) Structural Stress Using Verity Method

N

P1P2

Q

m

P1 P2

P1 P2N/

Q/

m/

P1P2

t

X

Y

Fx

P1P2

Fy

Neutral axistσ t

mσ tbσ

)t(σ )tm(σ )t

b(σ

N

P1P2

Q

mN

P1P2

Q

m

P1 P2

P1 P2

P1 P2N/

Q/

m/ P1 P2N/

Q/

m/

P1P2

t

X

YP1

P2

P1P2

t

X

Y

Fx

P1P2

Fy

Neutral axis

Fx

P1P2

Fy

Fx

P1P2

Fy

Neutral axistσ t

mσ tbσtσ t

mσ tbσ

)t(σ )tm(σ )t

b(σ)t(σ )tm(σ )t

b(σ

Calculation of Structure Stress3-D Solid Element:i. Calculate nodal forceii. Transformation of nodal force to neutral

axis to obtain resultant forces (N, m).iii.Calculation of structural stress

Shell Element:i. Calculate nodal force ( N/, m/, Q/ )ii. Calculation of structural stressBecause equilibrium has to be satisfiedThus: m/=m

Q/=Q AndN/=N

tm

N (σ )=

Atb

m (σ )=

W

,/ /t t t t

m m b bσ =σ σ =σ

The equations in the calculation of structural stress are the same. Hence, the structural stress is mesh independent

Calculation of Structure Stress3-D Solid Element:i. Calculate nodal forceii. Transformation of nodal force to neutral

axis to obtain resultant forces (N, m).iii.Calculation of structural stress

Shell Element:i. Calculate nodal force ( N/, m/, Q/ )ii. Calculation of structural stressBecause equilibrium has to be satisfiedThus: m/=m

Q/=Q AndN/=N

tm

N (σ )=

Atb

m (σ )=

W

,/ /t t t t

m m b bσ =σ σ =σ

The equations in the calculation of structural stress are the same. Hence, the structural stress is mesh independent

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Master S~N Curve

Most codes divide weld joints into different types

Categorization of Weld Joints (BS 7608) Weld Joints (IIW)

Weld Joint Categorization

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Multiple S~N Curves Due to Weld Joint Categorization

Example Design S~N curves for welded joints: (a) Steel weld joint S~N curves (BS 7608); (b) Weld joint type and S~N curves (IIW recommendations); (c) Aluminum weld joint S~N curves (IIW recommendations)

(a)

(b)

(c)

Multiple S~N curves provide flexibility for the selection of life curves and increase difficulty to select the proper one due to the variation of actual joints

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How Could multiple joint S~N curves be merged into one - Master S~N curve?

Nominal Stress Method (BS) Hot Spot Stress Method (IIW)

Equivalent SS MethodWeld Joints (IIW)

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Small Crack Propagation Behavior

The data does not fall into one curve for the same specimen; Multiple da/dN curves obtained for the same or different specimens, which tells that the Paris Law does not hold for small crack growth. This is called anomalous crack growth behavior.

(g) K-correlated small crack vs. large crack growth, 7075-T6 AI [13]The curves show that small crack growth faster than corresponding large cracks at the same value of the driving force K.

Specimens for notch induced short crack growth test. (a) Compact tension (CT) with keyhole by Ramulu; (b) single edged notched (SEN) by Shin and Smith; (c) double edged notched (DEN) by Shin and Smith; (d) center notched (CB) by Tanaka and Nakai; (e) for CT specimen; (f) for three different specimens

daK

dN da

KdN

Specimens for notch induced short crack growth test. (a) Compact tension (CT) with keyhole by Ramulu; (b) single edged notched (SEN) by Shin and Smith; (c) double edged notched (DEN) by Shin and Smith; (d) center notched (CB) by Tanaka and Nakai; (e) for CT specimen; (f) for three different specimens

daK

dN da

KdN

Different factors may attribute to short crack anomalous growth such as the effect of crack closure, micro structure interaction and that of notch details.

A unified SIF formulation for both short and long crack and a two stage crack propagation model were proposed by Dr. Dong & his coworkers, Battelle, to use Equivalent Structural Stress as a parameter for weldments fatigue life assessment.

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A Unified Stress Intensity Factor (SIF) Formulation

(a) Weld geometry with a hypothetical crack l ; (b) Actual normal stress distribution; (c) Simplification; (d) Decomposition; (e) Equilibrium-equivalent structural stress or far-field stress; (f) Self-equilibrating stress (notch stress) with respect to a reference depth t1.

( b )

t

A

A

xσl 0

( b )

t

A

A

xσl 0

( a )

A

A

tl

( a )

A

A

tl

( c )

t1

t

1

2

3

1σ

2σ

3σA

AR1

R2

xσ

( c )

t1

t

1

2

3

1σ

2σ

3σ

1

2

3

1σ

2σ

3σA

AR1

R2

xσ

t1

t

1

2

3

A

A σ

tσ

A

A

tσt1

t

1

2

3

A

A

σ

( d )( e ) ( f )

t1

t

1

2

3

A

A σ

tσ

t1

t

1

2

3

A

A σ

tσ

A

A

tσ

A

A

tσ

A

A

tσt1

t

1

2

3

A

A

σt1

t

1

2

3

A

A

σ

( d )( e ) ( f )

/ tx= - / t

x = / tx= - / t

x =

t1/t=0.1

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A Unified Stress Intensity Factor

t ( )( ) (0 l t) sn KK=K

Notch Stress Structural Stress, Far field stress Notch Stress Structural Stress, Far field stress

The drive force for crack to start and grow is the crack tip stress, introduce crack

surface traction ps called self equilibrating surface traction due to (notch effect)

xt /

s( ) (p , (0 l t) )( ) s s sK K K

tl

tl

( a ) ( b )A

A

tσ

A

A

tσ

A

A

tσt1

t

1

2

3

A

A

σt1

t

1

2

3

A

A

σ

( c )

t

sp

l

( d )

t

sp

ltt

sp

l

( d )

x σt1t

3

A

Al

/s x

t p =f( Δσ)= σf( ,σ )( e )

x σt1t

3

A

Al

/s x

t p =f( Δσ)= σf( ,σ )( e )

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A Unified Stress Intensity Factor

ts(p( ) (0 l t) ) n sK= KK

Notch Effect Structural Stress, Far field stress

ts(p( ) (0 l t) ) n sK= KK

Notch Effect Structural Stress, Far field stress Notch Effect Structural Stress, Far field stress

tl

( d ) ( e )A

A

tσ

( f )

t

sp

lt

l

( d )

tl

( d ) ( e )A

A

tσ

( e )A

A

tσ

A

A

tσ

A

A

tσ

( f )

t

sp

l

( f )

t

sp

ltt

sp

l

Notch Effect Notch Effect

Far Field SIF

Far Field SIF

Notch Effect Notch Effect

Far Field SIF

Far Field SIF

Stress intensity solutions using published weight function results: (a) remote tension; (b) remote bending.

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SIF Magnification Factor Mkn

ts(p( ) (0 l t) ) n sK= KK

Introduction of notch induced SIF magnification factor Mkn :t

ts(p )( )

1.0 (0 l t)( )

knsn

n

KM =

KK

t( ) (0 l t) kn nK=M K

a/t a/ta/t a/t

Comparisons of stress intensity magnification factor Mkn at 135° sharp V notch for various specimen geometries and loading conditions: (a) Edge crack solutions; (b) Elliptical crack solutions for a/c = 0.4

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Mkn for 1350 V Notch Specimen

a/t a/t

Conclusions:• Mkn approaches unity as crack size a/t approaches 0.1 i.e., a/t=0.1 (short

crack correction factor) Thus a/t=0.1 can be taken as a characteristic parameter beyond which the notch effect is negligible

• The difference between edge crack and elliptical crack solutions are not significant.

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Modified Paris Law

mn

n mkn n

Paris Law :

daC K (a)

dNIntroduce t

daCM K

dN

heUnified SIF :

(b)

Figures showed the significant improvement for the application of Paris Law and its application

More important the crack starts from zero that covers crack initiation life

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Master S~N Curve

-msΔσ

f

m1

n m

2

nkn

kn n

a a

n ma 0

m b

n

m

kn

Using the Unified Paris Law,

daN (b)

CM KIntroduction of

S ~ N curve can be obtained

1N t I(r) (c)

Cd(a / t)

Where,

generallized SIF ra

daC

I(r)M {f (a

M K (a)dN

nge

/ t) r [f (a / t) f

, leads

(a

to,

/ t)]

a / t 1

ma / t 0(d)

}

1 2 m 1 1m 2m m m

2 m 1

2

1 1

m

m m

m

Then

C t I(r) N (e)

Introduce Equivalent Structrual Stress Range,

t I(r)

C N (f )

s

sss ΔS

Δσ

ΔσΔS

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Master S~N Curve

Nominal Stress Method Hot Spot Stress Method

Equivalent SS MethodWeld Joints (IIW)

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Summary

• The Structural Stress Method developed at Battelle is mesh insensitive that removes the uncertainty in the calculation of structural stress for weld joint fatigue assessment

• The nature of weld joint fatigue is considered through the introduction of Equivalent Structural Stress based on fracture mechanics, which enable most fatigue curves of weld joints merged into a narrow band, the Master S~N curve. Thus one S~N curve can be used for majority of weld joints

Note: I believe that the weld joints have to be stress concentration dominant to achieve consistent results with test data.

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References

[1]. BS PD 5500: , BSI Standards, London, 2000.[2]. European Standard for Unfired Pressure Vessels, EN 13445: 2002, BS EN 13445:2002, BSI, London, 2002 [3]. ASME Boiler and Pressure Vessel Code, Section VIII, Rules for construction of pressure vessels, Division 2-

Alternative rules, ASME, 2003. [4]. Carl E. Jaske, FSRF for WPVP, Journal of Pressure Vessel Technology, AUGUST 2000, Vol. 122, 297-304[5]. S.J.Maddox, Review of fatigue assessment procedures…, Int. J. of Fatigue, Vol. 25, 12, 2003, 1359-1378.[6]. Maddox S J: 'Fatigue aspects of pressure vessel design…, Spence J and Tooth A S, E & F N Spon, London, 1994.[7]. Harrison J D and Maddox S J: 'A critical examination of rules for the design of pressure vessels subject to fatigue

loading' in Proc. 4th Int. Conf. on 'Pressure Vessel Technology', Mech E, London, 1980.[8]. Taylor N (Ed): 'Current practices for design against fatigue in pressure equipment', EPERC Bulletin No.6, European

Commission, NL-1755ZG, Petten, The Netherlands, 2001. [9]. Dong, P., 2005, ‘‘A Robust Structural Stress Method for Fatigue Analysis of Offshore/Marine Structures’’, Journal of

Offshore Mechanics and Arctic Engineering , Vol. 127, pp. 68-74.[10]. Dong, P., 2001, ‘‘A Structural Stress Definition and Numerical Implementation for Fatigue Evaluation of Welded

Joints,’’ Int. J. Fatigue, 23/10, pp. 865–876.[11]. Dong, P., Hong, J. K, Osage, D., and Prager, M., ‘‘Assessment of ASME’s FSRF Rules for Pipe and Vessel Welds

Using A New Structural Stress Method,’’ Welding In the World, Vol. 47, No. 1/2, 2003, pp. 31–43.[12] Dong, P., Hong, J. K., Osage, D., Prager, M., 2002, ‘‘Master S-N Curve Method for Fatigue Evaluation of Welded

Components,’’ WRC Bulletin, No. 474, August.[13]. Lankford, J. , Fatigue of Eng Mater and Structures 5 (1982), pp233-248[14]. R. Craig McClung, et al, Behavior of Small Fatigue Cracks, ASME, Vol. 19, Fatigue & Fracture, P153[15]. Fricke W., 2001, ‘‘Recommended Hot-Spot Analysis Procedure for Structural Details of FPSO’s and Ships Based on

Round-Robin FE Analysis,’’ ISOPE Proceedings, Stavanger, Norway, June.

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Part II: Example ApplicationPart II: Example Application

Aditya SakhalkarSr. Applied Mechanics Engineer

Emerson Climate Technology Inc.

• Background• ANSYS, Verity, Fe-Safe Weld Assessment Procedure• ANSYS Preprocessing• Verity Analysis• Fe-Safe Analysis• ANSYS Results• Comparison of Analysis Results with the Test Results• Conclusions

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• Resistance welded suction fitting

• Three failures in the suction fitting weld during reliability testing

• Crack initiated at the weld toe (9 o’ clock) and propagated through the shell.

• Failure due to reverse bending fatigue.

BackgroundBackground

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ANSYS, Verity, Fe-Safe Weld Analysis Procedure

Verity, Fe-Safe Weld analysis

Ansys Preprocessing

Ansys Post processing

- Meshing per Verity requirements

- Linear material properties

- Apply load

- Solution

Verity Analysis (Eq. Structural Stress calculations along the weld line)

- Fe-Safe analysis (Weld life calculations using Master S-N curve)

- Import .rst file

- Post processing

Verity result validation and comparison

Reliability Testing

Calibration

Quantify loading relative to the test

for FEA

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Suction FittingShell

Weld Line

Element Type: Solid 186

Ansys Preprocessing- FE Model

Mesh Requirements• Shell Elements:

• 3D mid-surface element with no through-thickness dimension

• Solid Element: • Rectangular faces required along the through-thickness cut from the weld line• Regular mesh along the through thickness cut from weld line• Recommended elements: Hexahedral (brick) and Pentahedral (wedge)• Tetrahedral elements can be used. Requires special handling.

Hex elements along weld line Linear material properties (E = 29,000 Ksi, ν = 0.29)

Symmetry BCOn sides

Top & Bottom fixed

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ANSYS Results

eq1

Maximum Stress Equivalent Stress

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Verity Procedures

• Structural Stresses calculated along the weld line at each node

• Fe-Safe builds a connectivity table and maps the stresses to elemental stresses. These stresses are inserted into the stress matrix to be used for fatigue evaluation

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Fe-Safe Analysis – Weld life predictions using Master SN Curve

Fully reverse loading defined

Fe-Safe calculates weld fatigue life based on the Battelle’s Master SN curve

The weld life (log N) data at each node is written in the ANSYS .rst format

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ANSYS Post processing – Weld Life Results

Minimum life at element # 4436, node # 4212

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Comparison of Verity Predictions with Reliability Test Results

Conservative life estimate!Predicted Failure Location correlated well with the test failures!!

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• ANSYS could be used for the fatigue assessment of welded joints in conjunction with Verity & Fe-Safe

• Verity provides conservative estimate of the weld life

• Good correlation with the predicted and test failure locations

• Verity & Fe-Safe provides a excellent weld design tool in conjunction with ANSYS

Conclusions