Code_Aster
®
Version
5.0
Titrate:
SSNP102 Rate of refund of energy for a notched plate
Date:
22/03/99
Author (S):
G. DEBRUYNE,
E. SCREWS
Key
:
V6.03.102-A
Page:
1/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/01/010/A
Organization (S):
EDF/IMA/MN
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
V6.03.102 document
SSNP102 - Rate of refund of energy
for a plate notched in elastoplasticity
Summary:
This test makes it possible to validate the calculation of the rate of refund of energy G for an elastoplastic problem in
plane deformations [R7.02.06].
This test contains a modeling in plane deformations and the results are compared with values
numerical obtained by WATANABE by another method of calculation of G in elastoplasticity. Variations
are considered to be satisfactory.
Caution:
The defect is modelized by a notch and not by a fissure like usually in
breaking process (cf [R7.02.07]).
Code_Aster
®
Version
5.0
Titrate:
SSNP102 Rate of refund of energy for a notched plate
Date:
22/03/99
Author (S):
G. DEBRUYNE,
E. SCREWS
Key
:
V6.03.102-A
Page:
2/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/01/010/A
1
Problem of reference
1.1 Geometry
F
C
D
E
X
y
With
30
0.25
4
10
B
1.2
Material properties
The law of behavior of material constituting the notched plate is a law of plasticity with criterion
of von Mises and isotropic linear work hardening. It is described in the control
DEFI_MATERIAU
[U4.23.01].
y
E
E = 205800 MPa
= 0.3
y
= 480.2 MPa
E
T
= 20.58 MPa
E
T
1.3
Boundary conditions and loadings
The plate is locked:
·
according to
OX
along side AB
·
according to
OY
along the side OF
It is subjected to a cyclic traction on side AF.
F
0
196 NR
F
1.0
2.0
3.0
T (S)
Code_Aster
®
Version
5.0
Titrate:
SSNP102 Rate of refund of energy for a notched plate
Date:
22/03/99
Author (S):
G. DEBRUYNE,
E. SCREWS
Key
:
V6.03.102-A
Page:
3/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/01/010/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution results from an article of K. WATANABE [bib1]. To calculate the rate of
restitution of energy in elastoplasticity K. WATANABE uses an integral
J
who is detailed in
[bib1] and [bib2].
The reference solution is numerical:
T (S)
0.
0.5
1.0.1.5.2.0 2.5
3.0
G 0. 2.769
3.183 4.276 4.651 5.691
6.052
It should be noted that:
·
the theoretical method used in the reference is different from the method established in
Code_Aster,
·
the geometry of the test and the reference are identical, but the mesh of the Aster test is more
refined that that of the reference.
2.2 References
bibliographical
[1]
K. WATANABE: Application off
J
- integral to elasto-plastic Ace, Bulletion off JSME, Flight.
28, n°242, August 1985
[2]
G. DEBRUYNE: Proposal for an energy parameter of ductile rupture in
thermo plasticity HI-74/95/027/0
Code_Aster
®
Version
5.0
Titrate:
SSNP102 Rate of refund of energy for a notched plate
Date:
22/03/99
Author (S):
G. DEBRUYNE,
E. SCREWS
Key
:
V6.03.102-A
Page:
4/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/01/010/A
3 Modeling
With
The plate is modelized by 243 TRIA6 and 39 SEG3.
3.1
Characteristics of the mesh
A number of nodes: 527
A number of meshs and types: 243 TRIA6
3.2 Functionalities
tested
Controls
Keys
DEFI_MATERIAU TRACTION
SIGM
[U4.23.01]
STAT_NON_LINE COMP_INCR RELATION
VMIS_ISOT_TRAC
[U4.32.01]
CALC_THETA THETA_2D
[U4.63.02]
CALC_G_THETA_T COMP_INCR
RELATION
VMIS_ISOT_TRAC
[U4.63.03]
Code_Aster
®
Version
5.0
Titrate:
SSNP102 Rate of refund of energy for a notched plate
Date:
22/03/99
Author (S):
G. DEBRUYNE,
E. SCREWS
Key
:
V6.03.102-A
Page:
5/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/01/010/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
Tolerance
T = 0.5 S
G (crown A)
2.769
2.863 3.39
3.5
G (crown B)
2.769
2.860 3.29
3.5
G (crown C)
2.769
2.859 3.27
3.5
G (crown D)
2.769
2.858 3.25
3.5
T = 1.0 S
G (A)
3.183
3.208 0.81
1.0
G (B)
3.183
3.212 0.93
1.0
G (C)
3.183
3.212 0.93
1.0
G (D)
3.183
3.212 0.93
1.0
T = 1.5 S
G (A)
4.2760
4.204 1.66
2.0
G (B)
4.2760
4.201 1.75
2.0
G (C)
4.2760
4.199 1.78
2.0
G (D)
4.2760
4.199 1.80
2.0
T = 2.0 S
G (A)
4.6510
4.640 0.22
1.0
G (B)
4.6510
4.645 0.13
1.0
G (C)
4.6510
4.645 0.13
1.0
G (D)
4.6510
4.645 0.13
1.0
T = 2.5 S
G (A)
5.691
5.570 2.12
3.0
G (B)
5.691
5.565 2.20
3.0
G (C)
5.691
5.564 2.22
3.0
G (D)
5.691
5.563 2.25
3.0
T = 3.0 S
G (A)
6.052
6.048 0.06
1.0
G (B)
6.052
6.052 0.01
1.0
G (C)
6.052
6.052 0.01
1.0
G (D)
6.052
6.052 0.01
1.0
4.2 Remarks
WITH B C D
R
inf
0.55 1.0
1.5
2.0
R
sup
1.0.1.5.2.0 3.0
4.3 Parameters
of execution
Version: 4.03
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
175 seconds
Code_Aster
®
Version
5.0
Titrate:
SSNP102 Rate of refund of energy for a notched plate
Date:
22/03/99
Author (S):
G. DEBRUYNE,
E. SCREWS
Key
:
V6.03.102-A
Page:
6/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/01/010/A
5
Summary of the results
The comparison of the results resulting from the test Aster and those obtained numerically by another
method by WATANABE are satisfactory (the maximum change is 3.4%).
It should be noted that the numerical results are sensitive to the mesh in the vicinity of the notch and to
form this notch. In particular if one modelizes a fissure the values obtained are false. In
revenge, starting from a sufficient smoothness of the mesh and radius of the notch, results
numerical are stable. For more information, it is advised to consult the document [R7.02.07]
and bibliographical references.