Idea Transcript
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
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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