Topics in Ship Structures

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OPen INteractive Structural Lab

Topics in Ship Structures

04 Low Cycle Fatigue for Welded Joint – Design Rules

Reference : DNV30.7

2017. 9

by Jang, Beom Seon

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Strain-Life Approach

Fundamentals of Metal Fatigue Analysis

A S  P

Nominal Stress range

∆S

Strain-life Curve True Stress range ∆

True Strain range ∆ε

N_f : fatigue life Applied Load P

Neuber’s rule

Cyclic Stress- Strain Curve

2

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Stress-Life Approach

DNV 30.7 Appendix I Low Cycle Fatigue

Linear elastic stress by FEA ∆_elastic(=K_t∆S)

Stress-life Curve Stress redistribution factor

Pseudo Stress range

∆_pseudo(E∆ε_hs)

N_f : fatigue life

Neuber’s rule True Stress range ∆_hs

True Strain range ∆ε_hs Cyclic Stress-

Strain Curve

∆_elastic from FEA

∆_hs

∆_pseudo

∆ε_hs

∆ε_elastic

from FEA

3

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Tank Arrangement

⁴

DNV 30.7 Appendix I Low Cycle Fatigue

Internal Turret Ballast Tanks

Cargo Tanks

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Midship Part

DNV 30.7 Appendix I Low Cycle Fatigue

Deck

Bottom Long bhd

2.5

Long BHD

Hopper

Long stiffener

Side shell Long bhd stiff

Inner skin

Stringer Deck trans Web

Long stiffener

Web plate

inner bottom

Web plate

5

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Midship Part

⁶

DNV 30.7 Appendix I Low Cycle Fatigue

Transverse Bulkheads Longitudinal

Bulkheads

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Midship Part

⁷

DNV 30.7 Appendix I Low Cycle Fatigue

Transverse Bulkheads Longitudinal

Bulkheads

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Horizontal Stringers

⁸

DNV 30.7 Appendix I Low Cycle Fatigue

Transverse Bulkheads

Stringers

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Midship Part

⁹

DNV 30.7 Appendix I Low Cycle Fatigue

Stringers

Transverse Bulkhead

Web section

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Web Sections

¹⁰

DNV 30.7 Appendix I Low Cycle Fatigue

Web Section Ordinary Section

Ba llast T ank

Ba llast T ank Ca rgo T ank Ca rgo T ank Cargo T ank Ca rgo T ank

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Critical locations for low cycle fatigue

 Heel and toe of horizontal stringer of transverse bulkhead

DNV 30.7 Appendix I Low Cycle Fatigue

Trans Bulkhead Stringer

Stringer Toe

Stringer Heel

11

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Critical locations for low cycle fatigue

DNV 30.7 Appendix I Low Cycle Fatigue

Full load condition Ballast condition

Alternate 2 Alternate 1

12

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Critical locations for low cycle fatigue

DNV 30.7 Appendix I Low Cycle Fatigue

13

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Critical locations for low cycle fatigue

 Web stiffener on top of inner bottom longitudinal.

DNV 30.7 Appendix I Low Cycle Fatigue

LCF LCF

HCF HCF

Transverse Web Longitudinal

stiffener

Inner Bottom

Typical Elevation

14

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Critical locations for low cycle fatigue

DNV 30.7 Appendix I Low Cycle Fatigue

Full load condition Ballast condition

LCF LCF

HCF HCF

Transverse Web Longitudinal

stiffener

Inner Bottom

15

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Critical locations for low cycle fatigue

 Inner bottom connection to transverse bulkhead

DNV 30.7 Appendix I Low Cycle Fatigue

16

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General

DNV 30.7 Appendix I Low Cycle Fatigue

17

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Load conditions for assessment

 Low cycle fatigue is mainly due to mainly loading and unloading of cargoes and ballast. Quasi-static load.

(HCF is caused by Wave loading n

_HCF

=10

⁸

, number of waves encountered during 20 years, average period = 7 sec)

 The number of design cycles may vary depending on the ship in operation

DNV 30.7 Appendix I Low Cycle Fatigue

Ship Type Recommended Cycle, n_LCF

Tankers over 120,000 TDW 500

Tankers below 120,000 TDW 600

Chemical tankers 1,000

LNG carriers 800

LPG carriers 800

Shuttle tankers 1,200

18

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Hot spot stress range for low cycle fatigue

 Static elastic hot spot stress range for load combination k for low cycle fatigue

DNV 30.7 Appendix I Low Cycle Fatigue

19

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Combined hot spot stress range

 A peak to peak stress

= static stress induced by static hull girder and static pressure loads during loading and unloading

+ elastic dynamic hot spot stress amplitude at 10

^-4

probability level due to wave actions

DNV 30.7 Appendix I Low Cycle Fatigue

k

comb



20

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General

DNV 30.7 Appendix I Low Cycle Fatigue

21

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Plasticity correction factor (K

_e

)

 Method 1 : from 1) Cyclic stress-strain curve and 2) Neuber's rules

DNV 30.7 Appendix I Low Cycle Fatigue

' / 1 '

2 n

hs hs

hs E K 



 



 



  





' / 1 '

n hs hs

hs E K 



 







 



' / 1 ' 2

2

2 n

hs hs

hs n

K E

E

K 



 



 





   



 Se K_t²

E K ⁿ K

n n elastic

elastic hs

hs

2 2

2















  

constant



 _elastic _elastic

hs

  



_elastic

=K_n

_hs

_pseudo

_n(S)

①

②

③

' / 1 '

n hs hs

hs E K 



 







 



σ_hs can be obtained from an iterative way.

22

①

②

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Plasticity correction factor

 K(≈K

_t

) = theoretical stress concentration factor

 σ

_hs,

ε

_hs

= actual hot spot stress and strain in hot spot

 σ

_elastic,

ε

_elastic

= linear elastic hot spot stress and strain by FEA

 σ

_n

(=S) = nominal stress

 E = Young’s modulus

 n', K' = material coefficients

 σ

_pseudo

= Pseudo linear elastic hot spot stress=E 

_hs

DNV 30.7 Appendix I Low Cycle Fatigue

23

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Plasticity correction factor

 Method 2 : from an empirical formula

 Plasticity correction factor is proportional to Δσ

_comp

. If Δσ

_comp

is below 2.0 σ

_Y

, the factor =1 since it remains within elastic limit.

DNV 30.7 Appendix I Low Cycle Fatigue

0 . 2 10 for

0 . max 1

0 . 2 for

1.0

factor correction

plasticity :

K

Y comb 3

comb Y comb e

 











 

 



 



b

a _Y :yieldstress

Stress range ^∆𝝈^{𝒄𝒐𝒎𝒃}

𝝈_𝒇 >2.0 Mild steel a = 1.16

b = 0.524 NV-32 and NV-36 a = 1.0

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Plasticity correction factor

 Method 3 : a non-linear finite element analysis

 ε

_hs

can be directly obtained form a non-linear FE analysis.

 Cyclic stress-strain curve should be provided to non-linear FE analysis.

 σ

_elastic

can be linear elastic hot spot stress and strain by FEA.

DNV 30.7 Appendix I Low Cycle Fatigue

elastic pseudo

K

e



 

hs pseudo

E 

 

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General

DNV 30.7 Appendix I Low Cycle Fatigue

26

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Effective pseudo stress range

 Factor due to stress redistribution.

 Stress redistribution factor is applied when Δσ

_comp

goes beyond elastic limit.

 Effective pseudo stress range

DNV 30.7 Appendix I Low Cycle Fatigue





K_e factor

correction linearity

- non



:

0 . 2

if steel NV36

or NV32 for

8 . 0

0 . 2 if

steel mild for .9 0

0 . 2 if

1.0

tion redistribu stress

to due Factor :

Y comb Y

comb Y

comb

 



 



 







k comb k

eff

 

   



NV : High tensile steel.

NV32 : yield stress =315MPa NV32 : yield stress = 355 MPa

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General

DNV 30.7 Appendix I Low Cycle Fatigue

28

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Fatigue damage calculations for LCF

 One-slope S-N curve for low cycle fatigue strength

N

_k

: number of cycles to failure for low cycle fatigue stress range σ

^k_eff

: effective stress range for the k-th load combination

 This design curve is applicable to both welded joints and base metal for LCF region.

DNV 30.7 Appendix I Low Cycle Fatigue

k eff

k

a m Log

N  log     log

Welded joint with cathodic protection

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Fatigue damage calculations for LCF

 The damage due to low cycle fatigue is calculated as follows,

n

_LC

: total number of design load condition L

_k

: fraction of load combinations

DNV 30.7 Appendix I Low Cycle Fatigue

k LCF n

k k

LCF n

k

LCF

N

L n D

L D

LC



 



1 1

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Low Cycle Fatigue Factors

 Thickness effect : not accounted

 Mean stress effect : not accounted

 Environmental reduction factor : not considered

 Weld Improvement : Benefit of weld improvement methods like grinding, hammer peening and TIG-dressing should not be applied

 Fabrication tolerance : are assumed applicable .

DNV 30.7 Appendix I Low Cycle Fatigue

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General

DNV 30.7 Appendix I Low Cycle Fatigue

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Combined fatigue damage due to HCF and LCF

 Combined damage ratio due to high cycle fatigue and low cycle fatigue shall be satisfied when D

_LCF

≥ 0.25 .

 For low cycle fatigue damage below 0.25, fatigue damage due to HCF shall be satisfied.

D

_HCF

≤1 for D

_LCF

≤0.25

DNV 30.7 Appendix I Low Cycle Fatigue

D_HCF = damage due to high cycle fatigue based on design life

D_LCF = damage due to low cycle fatigue based on the design cycles

The combined fatigue criteria

0 . 1 25

. 0 0

. 1 75 )

. 0

25 .

( 0

²

2

   





_HCF ^HCF _LCF

f

D for D

D D

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Example

DNV 30.7 Appendix I Low Cycle Fatigue

Location to be checked

Hot spot stress components at HS1, N/mm²

Combined stress range for low cycle fatigue strength assessment, N/mm²

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Example

DNV 30.7 Appendix I Low Cycle Fatigue

Low cycle fatigue strength assessment

0 . 2 10 for

0 . max 1

0 . 2 for

1.0

factor correction

plasticity :

K

Y comb 3

comb Y comb e

 











 

 



 



b a

35

NV-32 and NV-36 steels

a = 1.0 b = 0.53

0 . 2

if steel NV36 or NV32 for 8 . 0

0 . 2 if

steel mild for .9 0

0 . 2 if

1.0

tion redistribu stress

to due Factor :

Y comb Y

comb Y

comb

 



 



 





