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Mismatch Limit Load Solutions for Circumferential Cracked Pipes

ESIS TC1 Autumn Meeting December 5-6, Freiburg Yun-Jae Kim Mechanical Engineering Dept Korea University Seoul, Korea

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Significance of Mis-Match Limit Loads  Elastic-plastic J estimates for mismatched structures  use of mismatch limit loads important

Through-wall cracked welded plates under tension

Normalized by homogeneous limit loads

Normalized by Mismatch limit loads

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Existing Works: Mismatch Limit Loads (1)  Planar geometry (2-D plane strain and plane stress)

• Mismatch Effect on Plastic Yield Loads in Idealised Weldments: Part I – Weld Metal Cracks, EFM, 68(2), 2001, 163-182. • Mismatch Effect on Plastic Yield Loads in Idealised Weldments: Part II – HAZ Cracks. EFM 68(2), 2001, 183-199. • Compendium of Yield Load Solutions for Strength Mis-matched DE(T), SE(B) and C(T) Specimens. EFM 68(9), 2001, 1137-1151.

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Existing Works: Mismatch Limit Loads (2)  Planar geometry (3-D plates)

 Pipe geometry

Mismatch limit loads for tensile plates with constant-depth surface cracks in the center of welds. IJF 148(4), 343-360, 2007

Strength mis-match effect on limit loads for surface cracked pipes. EFM 76(8), 1074-1086, 2009.

 Existing solutions are for idealized cases: rectangular weld shapes  The weld shape effect on mismatch limit load solutions need to be quantified

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Scope of Presentation  Review essence of existing solutions  M(T) solutions: 2-D plane strain and plane stress  Report intermediate results:  Effect of the V-groove weld shape  Summary of on-going works

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Mismatched M(T) Plate: Variables

 Normalized mismatch limit load

FLM FLB

 Mismatch limit loads depend on

σYW

weld

 strength mismatch ratio M=

 weld slenderness

σYB

base

ψ=(w-c)/h Effect of weld shape

σ YW σ YB

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Characteristics of Mismatch Limit Loads Plastic deformation patterns

M·FYB

FYB

FYB

M·FYB

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Mismatch Limit Loads for Plane Strain M(T)

overmatching

ψ1 depends on M and geometry

Undermatching

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Plane Strain vs Plane Stress: M(T)

• Plane strain and plane stress different mainly for under-matching  due to different plastic deformation patterns

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Mismatch Limit Loads for 3-D M(T) Plates Mismatch limit loads for tensile plates with constant-depth surface cracks in the center of welds. IJF 148(4), 343-360, 2007

Through-wall crack

Surface crack

• For overmatching, solutions for plane strain and plane stress similar  2-D solutions can be used for 3-D plates • For undermatching, solutions are different  Mismatch limit loads should be in between plane strain and plane stress depending on w/t ratio

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Finite Element Limit Analyses weld stress

base strain

ABAQUS • Elastic-perfectly plastic material • Small strain option • Limit analysis

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Through-Wall Cracks

w/t=1- close to plane strain

w/t=20 - close to plane stress

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Through-Wall Cracks

w/t=5- closer to plane stress

w/t=10 - close to plane stress

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Surface Cracks Definition of the slenderness parameter ψ ? Two limiting cases

ψ =

(w − c) h

ψ

t − a) ( = h

 The slenderness parameter for surface crack should include (w-c)/h and (t-a)/h

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Choice of ψ: Examples

• Neither ψ=(w-c)/h nor ψ=(t-a)/h could correlate mismatch limit load data for surface cracked plates

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Calibrated Parameter ψeff for Surface Cracks 1  ( t − a) ( w − c )  + ψ eff =   f h h    w  a  w 2 g − 1 − 0.5 + g        t        t   t f= −2  g  w  − 1   a − 0.5  + g  w     t     t      t   w w g   = 0.13   + 2.37  t   t 

0≤

a ≤ 0.5 t

0.5 ≤

a ≤ 1.0 t

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Mismatch Limit Loads for Surface Cracks

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Mismatch Limit Loads for Circumferential Cracked Pipes Strength mis-match effect on limit loads for surface cracked pipes. EFM 76(8), 1074-1086, 2009.

• Based on plastic deformation patterns, mismatch limit load solutions should be similar to those of M(T) plates • For through-wall cracks, plane stress solutions may be relevant • For surface cracks, plane strain solutions may be more relevant

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Finite Element Limit Analyses weld stress

base strain

ABAQUS • Elastic-perfectly plastic material • Small strain option • Limit analysis

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Through-Wall Cracks

ψ=

r (π − θ ) h

Plane stress M(T)

(

)

ψ 1 = 1 + 0.43exp −5( M −1) exp−( M −1) / 5

for plane stress M(T)  M − 5.2   3  

ψ 1 = exp  −

for TWC pipes

Normalized mismatch limit loads Similar to plane stress M(T)

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Fully Circumferential Surface Cracks

ψ=

(t − a ) h

Plane strain M(T)

 Normalized mismatch limit loads similar to plane strain M(T)  ( M − 1)  ψ 1 = exp  −  5    2 ( M − 1)   5  

ψ 1 = exp  −

for plane strain M(T)

for fully circumferential cracked pipes

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Surface Cracks Fully circumferential crack solutions Through-wall crack solutions

t − a) ( ψ= h

ψ=

( t − a ) + 5 cos  θ  − sin θ  h

 

  2

2 

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Surface Cracks t − a) (   θ  sin θ  ψ= + 5 cos   −  h



2

2 

Fully circumferential crack solutions Through-wall crack solutions

 Using a proper definition of ψ, fully circumferential crack solutions can be used for surface cracks

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Surface Cracks

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Effect of V-Groove on Mismatch Limit Loads  Circumferential Cracked Pipes with V-Groove Butt Welds • Parametric Study: Matrix V-Groove

Cases Φ

45, 90

r/t

5, 20

M

0.5, 2.0

a/t

0.35, 0.5, 0.8, 1

θ/π

0.25, 0.5, 0.8, 1

h/t

0.125, 0.5

• Circumferential through-wall crack under axial tension (N) or bending (M) • Fully circumferential surface crack under axial tension (N) • Surface crack under axial tension (N)

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Circumferential Through-Wall Cracks

Φ r/t M a/t θ/π h/t

• Slenderness parameter

CASE 45, 90 5, 20 0.5, 2.0 1 0.25, 0.5, 0.8 0.125, 0.5

r (π − θ ) ψ eff = heff

h eff = h+(t × tan(φ /2))/2 Mean weld width

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Results  Effect of slenderness parameter: Groove angle= 90°

ψ = f ( h)

ψ = f (heff )

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Results: Effect of r/t

r/t=5

r/t=10

r/t=20

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On-Going Works  Circumferential cracked pipes with V-groove welds  Surface crack  Effect of crack location

 Effect of V-groove for plates  Mismatch limit loads for plates under bi-axial loading

Thank You Very Much

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Kim et al

Mismatch Limit Load Solutions for Circumferential Cracked Pipes ESIS TC1 Autumn Meeting December 5-6, Freiburg Yun-Jae Kim Mechanical Engineering Dep...

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