Meith, Panontin, and Hill on Compressed SE(B)`s

Analytical and Experimental Study of
Fracture in Locally Compressed Bend
Specimens
Wade Meith
Michael R. Hill
University of California, Davis
Tina L. Panontin
NASA-Ames Research Center
Local Compression (LC)
❏
Precracking weld samples is problematic
– From Towers and Dawes, STP 856, 1985
The Good …
(no weld)
The Bad …
(single-pass or restrained)
And The Ugly
(Multi-pass)
δ
❏
LC straightens precracks
◆
◆
◆
Plastically deform near-tip material
Reduce thickness by ~ 1%
Proposed Annex to E1290 suggests LC for welds
Slide 2
LC Reduces Measured Toughness
❏
Experimental results
7050 T7451 SE(B)’s
W=B=25mm, 1% LC
W=2B=25mm, 1%-2% LC
◆
◆
◆
◆
◆
110
B=W/2 (Experiment)
B=W (Experiment)
105
LC increases constraint
LC leaves positive
residual driving force
1.2
B=W/2, No LC
1
B=W/2, 2%LC
B=W, 1% LC
σ o) (10-3)
J/(Wσ
KQ , % of Plain Bx2B
Companion simulations
❏
100
0.8
95
0.6
90
0.4
85
σo/J = 4
at rσ
80
0
0.5
1
1.5
%LC applied
2
2.5
0.2
0.4
0.3
0.2
0.1
0
σyy - σyyssy)/σ
σo
Q = (σ
Slide 3
-0.1
Recent ASTM Round-robin Program
❏
Samples removed from seam
welded pipe
◆
◆
◆
Low hardening, pressure
vessel steel
SE(B) specimens, W = B = 25 mm
Crack samples weld depth
z
y
x
δ
❏
Procedures
◆
◆
◆
Locally compress 1%
Fatigue pre-crack
Fracture test at -192 C
Applied
Load
B
W
a ≈ 0.5W
S
Slide 4
Round-robin Local Compression
❏
Two labs responded to call for data
◆
Each implemented LC differently
d = 0.43W
d = 0.65W
Lab A
Lab B
Slide 5
Preliminary Round-robin Results
39.9
34.1
2 spec.
1 spec.
5 spec.
30
22.4
K, MPa*m1/2
40
36.5
RR instructions
Lab A
Lab B
5 spec.
20
10
0
0
1
2
%LC
◆
◆
Disparity at 1% LC due to procedural difference?
Lab A did side-study on amount of LC
●
●
Small effect on toughness
0% LC used to calibrate fracture model, then predict 1%, 2%
Slide 6
Goals of This Work
❏
Measure weld residual stress in SE(B) blanks
◆
❏
Measure transverse (opening) stress
Analyze test conditions in ASTM
round-robin
◆
Predict influence of LC on results
◆
Model range of test conditions
●
Vary %LC
●
Vary d/W
z
y
x
d/W
◆
Offer insight ?
Slide 7
Measure Residual Stress in Blank
❏
Measure RS using the
compliance method
◆
❏
Specimen Blank
Slot incrementally,
measure strain release
Express RS as polynomial
◆
σ RS ( x ) =
◆
◆
z
EDM Slot
∑ A P ( x)
i i
i = 2 ,m
◆
Strain Gages
y
x
Strain can be found for known stress (FEM)
Find strain for basis functions using FEM
ε = CA
Cij ≡ ε ( ai ) σ = P ( x )
j
❏
Find basis amplitudes
◆
(
A = C C) C T ε
T
−1
Slide 8
Residual Stress Due to Welding
Top gage
Bottom gage
Top (10th order)
Bottom (10th order)
600
500
Strain, µε
Opening Mode RS / Yield
700
400
300
200
100
0
0
0.2
0.4
0.6
0.8
1
0.15
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20
z/t
❏
❏
5
10
15
20
Depth, mm
Weld RS is small (< 15%Sy)
RS is tensile in center
◆
◆
❏
0
Restrained weld
Precracks would be tunneled
Approximate RS as symmetric, sinusoidal
Slide 9
25
Computational Fracture Prediction
❏
Elastic-plastic finite element modeling
◆
◆
❏
Employ micromechanical damage models
◆
◆
❏
Continuum material response assumed
Crack-tip state used directly to predict fracture
Include residual stresses
◆
◆
◆
❏
Incremental, J2 plasticity and finite strain
Resolve stress and strain close to the crack-tip
Eigenstrain for weld residual stress
Direct process simulation for LC
Residual and applied loadings interact
Analysis steps:
(1) Impose residual stress, (2) locally compress, (3) unload
compression platen, (4) extend crack (pre-cracking), (5) reduce
temperature, (6) fracture load
Slide 10
Brittle Fracture Models
❏
RKR model
◆
◆
FEM provides crack-tip stress
Calibration of σf* and l*
●
●
●
●
❏
σf*/σo
3.0
σyy/σo
2.0
r = l*
1.0
0.0
0
0.5
1
1.5
2
Distance from the crack-tip
J-integral (domain integral formulation)
◆
◆
❏
Use Lab A’s 0% LC result
Assume σf* = 2.0Sy
Computed crack-tip stress at
observed failure load gives l*
Repeat assuming σf* = 2.5Sy
σyy ≥ σ*
f
over 0 ≤ r ≤ l*
4.0
“Enriched” to obtain path independent
J’s with residual stress and prior plasticity
JDI includes effects of residual stress (unlike JLab)
RKR sensitive to constraint, JDI is not
◆
Testing at -196 C, do not expect constraint effects
Slide 11
Material Model
❏
ASTM RR instructions reported well-matched weld
Source
Material
Temp (C)
Sy (MPa)
Su (MPa)
E (GPa)
ν
n
❏
❏
❏
Round-robin instructions
Weld
Parent
21
-196
21
-196
548
888
514
848
593
989
593
960
206
218
206
218
0.3
0.3
0.3
0.3
25.2
20.4
16.8
18.5
Assume all-weld material
Power-law flow curve from Sy and Su
Paper investigates other models
◆
◆
Weld mismatch (bimaterial)
Low-hardening (yield plateau)
Slide 12
Fracture Model Calibration
❏
Impose residual stress
Eigenstrain distribution
Sinusoidal variation of opening stress through thickness
Stress approaches zero one thickness from weld center
◆
◆
◆
❏
❏
Extend crack, reduce temperature
Load model to K = 36.5 MPa.m1/2
3.0
σyy/S y
Calibration, 0% LC
2.5
2.0
l* 2
l* 1
• l* = 111µ (2.0 Sy)
• l* = 47µ (2.5 Sy)
• JDI = 7.1 kJ/m2
(JKQ = 5.56 kJ/m2)
1.5
0
0.001
0.002
0.003
0.004
0.005
x/W
Slide 13
Predictions: Amount of Local Compression
❏
Analysis steps
(1) Impose RS
(2) and (3) Locally compresses, remove compression load
(4) Extend crack to a/W = 0.5
(5) Reduce temperature, and (6) Load to fracture
LC predicted to drop fracture load (apparent toughness)
1.1
RKR σ* = 2.5S
1
c
K / Kcal
❏
0.9
RKR σ* = 2Sy
0.8
JDI
y
All weld material
d/W = 0.43
K
cal
= 36.5 MPa m1/2
0.7
0.6
0.5
0.4
0.3
0
0.5
1
1.5
2
%LC
Slide 14
Predictions: Effect on JDI
Concentrated opening stress following LC
◆
Large JDI at zero load
Main influence on apparent toughness decrease
1
0% LC
1% LC
0.8
cal
◆
0.6
J /J
DI
❏
0.4
All weld material
d/W = 0.43
Pcal = 13.6 kN
0.2
Jcal = 7.09 kJ/m2
0
0
0.2
0.4
0.6
0.8
1
P/Pcal
Slide 15
Predictions: Location of Platen
Lower apparent toughness when platen is further over
the ligament
May explain difference between Lab A and Lab B results
●
However, model is symmetric (platens from both sides)
Lab B application was non-symmetric
0.60
cal
◆
Kc /K
❏
RKR σ* = 2.5S
0.55
RKR σ* = 2Sy
0.50
JDI
y
d/W
0.45
0.40
0.35
0.30
0.25
All weld material
1% LC
Kcal = 36.5 MPa m1/2
0.20
0.40
0.45
0.50
0.55
0.60
d/W
Slide 16
Comparison with Round-robin Data
Predictions over estimate RR results
Especially those from Lab A
Lab A
1.20
1.00
1.00
1.00
DI
0.93
All weld material
d/W = 0.43
0.80
0.61
Kcal = 36.5 MPa m1/2
0.56
0.52
1 spec.
5 spec.
0.20
2 spec.
0.60
0.40
Lab B
Prediction (J )
1.09
cal
◆
K/K
❏
0.00
0
1
2
%LC
Slide 17
Open Questions
(Why do the model and experiments disagree?)
❏
Experiment related questions:
◆
◆
◆
❏
Were measured weld residual stresses representative?
Local compression procedure not ideal?
Precracking low enough?
Model related questions:
◆
◆
◆
◆
Flow curve?
Anisotropic properties?
Correct fracture model and parameters?
Does LC change the fracture parameters?
Slide 18
Predictions for 7050 SE(B)'s
❏
Similar approach
Fully characterized material
◆
◆
❏
❏
Flow curve
Calibrated fracture model
Ductile fracture model
(SMCS)
Good prediction
◆
Small over-estimate of
the effect of LC
110
B=W/2 (Experiment)
B=W (Experiment)
B=W/2 (SMCS)
B=W (SMCS)
105
KQ , % of Plain Bx2B
❏
100
95
90
85
80
75
0
0.5
1
1.5
2
%LC applied
Slide 19
2.5
Conclusions
❏
Weld RS in the round-robin blanks were small
◆
◆
❏
Simulations predict large effect of LC on toughness
◆
◆
◆
❏
Maximum ~ 0.15Sy
Tensile at mid-thickness, compressive at surfaces
Weakly dependent on fracture model assumed
Weakly dependent on amount of LC
Strongly dependent on position of platen
Simulations predict lower toughness when platen is
further over ligament
Slide 20