Development and Implementation of the Abaqus Subroutines and

19 Pages·2012·1.24 MB·English

Development and Implementation of the Abaqus
Subroutines and Plug-in for Routine Structural
Integrity Assessment using the Linear Matching
Method.
James Urea, Haofeng Chena, David Tipping b
a Dept of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow, Scotland, G1 1XJ
b Engineering Division, EDF Energy Nuclear Generation, Barnwood, Gloucester, GL4 3RS
Introduction
• How the Linear Matching Method (LMM) works
• Verification of method and results
• Implementation of LMM in Abaqus through user
subroutines
• Development of a plug-in
• Conclusions and future work
Responses to Cyclic Loading
σ σ
σ σ
Y Y
ε
ε
d
ao Global -σ
L Y
-σ c Shakedown
Y ilc Ratcheting
y
C
d
e
s
σ ilam Strict σ σ
σ ro Shakedown Y
Y N
Elastic
Normalised Constant Load
ε
ε
-σ
-σ Y
Y
Responses to Cyclic Loading
σ σ
σ σ
Y Y
ε
ε
d
ao Global -σ
L Y
-σ c Shakedown
Y ilc Ratcheting
y
C
d
e
s
σ ilam Strict σ σ
σ ro Shakedown Y
Y N
Elastic
Normalised Constant Load
ε
ε
-σ
-σ Y
Y
The Linear Matching Method
• At present, simplified methods (i.e. R5), cyclic elastic-plastic
FEA or Direct Cyclic Analysis (DCA) are used to determine
the stabilised response
• These methods cannot determine proximity to the shakedown
limit directly
• The LMM is a direct method which assesses the steady state
response of a structure, including the shakedown and ratchet
limits
• Uses linear elastic solutions and spatially varying modulus to
emulate plastic behaviour
The Linear Matching Method
• Uses linear elastic solutions and spatially varying
modulus to emulate plastic behaviour
σ
Ei
Ei+1
σ
y
εi ε
The Linear Matching Method
• Uses linear elastic solutions and spatially varying
modulus to emulate plastic behaviour
σ
Ei
Ei+1
Ei+2
σ
y
εi+1 ε
The Linear Matching Method
• Uses linear elastic solutions and spatially varying
modulus to emulate plastic behaviour
• Equilibrium and compatibility maintained at each stage
σ
Ei
Ei+1
Ei+2
Ei+3
σ
y
εi+2 ε
The Linear Matching Method
• In addition to the modulus adjustment, a load multiplier is
calculated
– Energy balance between external work done and internal energy
dissipation
• Between both of these, the solution is convergent
towards the shakedown/ratchet limit
Results Verification
SA508
Temp Dependent Upper Bound
4.5
0
Inconel 82/182 Temp Dependent Lower Bound
4
316 3.5 Temp depednent Reverse Plasticity Limit
3 Temp Dependent Reverse Plasticity Limit
Lower Bound
2.5 D
C
2
Ratcheting
1.5 Global Shakedown
1
P
0.5 B
Strict Shakedown
A P
0
0
0 0.5 1 1.5 2 2.5 3
10
9 Normalised Plastic Strain Range
Cyclic Loading % Difference
8
D Level Step by Step LMM
7
%
,n6 1.5 1.26E-03 1.27E-03 0.24
ia
r
tS5 B 2 2.71E-03 2.71E-03 0.08
c
its4
a 2.5 6.24E-03 6.19E-03 -0.74
lP
3
3 9.54E-03 9.52E-03 -0.17
2
C
3.5 1.31E-02 1.31E-02 -0.09
1
0 A 4 1.69E-02 1.68E-02 -0.62
0 2 4 6 8 10 12 14 16 18 20
Cycle Number