Code_Aster
®
Version
8.1
Titrate:
SSNP110 - Fissure edge in a plate in elastoplasticity
Date:
15/02/06
Author (S):
E. CRYSTAL
Key
:
V6.03.110-A
Page:
1/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-62/06/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.110
SSNP110 - Fissure edge in a plate
rectangular finished in elastoplasticity
Summary:
This test is a case test in nonlinear breaking process.
One calculates the rate of refund of energy G in a rectangular plate finished, fissured and subjected to one
loading of traction. The law of behavior used is an elastoplastic law of Von Mises without
work hardening.
This case test includes/understands two plane modelings in 2D forced in order to study the influence of the catch in
count or not terms of second command of the deformations (DEFORMATION = “SMALL” or “GREEN” in
operator STAT_NON_LINE). The stability of the result of the calculation of G by the method théta (CALC_G_THETA_T)
is also checked.
Code_Aster
®
Version
8.1
Titrate:
SSNP110 - Fissure edge in a plate in elastoplasticity
Date:
15/02/06
Author (S):
E. CRYSTAL
Key
:
V6.03.110-A
Page:
2/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-62/06/005/A
1
Problem of reference
1.1 Geometry
Length
L = 50 mm
Width
W = 16 mm
Depth of fissure
= 6 mm have
1.2
Properties of material
The material is rubber band-perfectly plastic of Von Mises type. Its properties are them
following:
Young modulus
E = 2,0601 105 MPa
Poisson's ratio
= 0.3
Yield stress
Y
= 808,34 MPa
Modulate work hardening
= 0
1.3
Boundary conditions and loading
The model will be limited to half of the structure, the plan of the vertical fissure being a plan of
symmetry.
Boundary conditions
They are thus defined for the half spaces y
0.
Vertical displacement UX = 0 at the point B
Horizontal displacement UY = 0 in ligament AB
Loading
Horizontal displacement imposed on the segment CD: UY =
2
Reference solution
No the reference solution. This is a test of not-regression.
L
W
has
Uy =
Uy = -
X
y
With
B
C
D
Code_Aster
®
Version
8.1
Titrate:
SSNP110 - Fissure edge in a plate in elastoplasticity
Date:
15/02/06
Author (S):
E. CRYSTAL
Key
:
V6.03.110-A
Page:
3/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-62/06/005/A
3 Modeling
With
3.1
Characteristics of modeling
It is about a calculation in elastoplasticity under the assumption of small displacements.
3.2
Characteristics of the mesh
The mesh, built with an automatic procedure gibi, consists of 400 elements
quadratic (1000 nodes). Cores are defined in bottom of fissure in order to improve the precision of
calculation in breaking process, cf [Figure 3.2-a] below. The radius of the largest core is of
1,5 Misters.
Appear 3.2-a: Mesh of the fissured rectangular plate
3.3
Functionalities tested
Calculation of the rate of refund of energy by the method THETA in elastoplasticity.
Controls
STAT_NON_LINE COMP_ELAS
RELATION
DEFORMATION
ELAS_VMIS_LINE
SMALL
CALC_THETA
CALC_G_THETA OPTION
COMP_ELAS
CALC_G
RELATION
ELAS_VMIS_LINE
Code_Aster
®
Version
8.1
Titrate:
SSNP110 - Fissure edge in a plate in elastoplasticity
Date:
15/02/06
Author (S):
E. CRYSTAL
Key
:
V6.03.110-A
Page:
4/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-62/06/005/A
4
Results of modeling A
4.1 Values
tested
The values of the rate of refund are tested for five values of imposed horizontal displacement
.
One compares the results obtained for three different crowns of integration:
· crown 1: R
inf
= 0,15 mm; R
sup
= 0,6 mm
· crown 2: R
inf
= 0,3 mm; R
sup
= 0,9 mm
· crown 3: R
inf
= 0,9 mm; R
sup
= 1,5 mm
Displacement
imposed
(mm)
G (NR/mm)
crown 1
G (NR/mm)
crown 2
G (NR/mm)
crown 3
0,02 3.29 3.20 3.20
0,04 13.60 13.24 13.24
0,06 31.97 31.22 31.24
0,08 58.99 57.74 57.76
0,1 91.42
89.64 89.71
The results are satisfactory: the maximum variation enters the values of G obtained on the three
crowns of integration is lower than 2%.
Code_Aster
®
Version
8.1
Titrate:
SSNP110 - Fissure edge in a plate in elastoplasticity
Date:
15/02/06
Author (S):
E. CRYSTAL
Key
:
V6.03.110-A
Page:
5/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-62/06/005/A
5 Modeling
B
5.1
Characteristics of modeling
It is about a calculation in elastoplasticity under the assumption of great displacements.
5.2
Characteristics of the mesh
The mesh is identical to that of modeling A.
5.3
Functionalities tested
Calculation of the rate of refund of energy by the method THETA in elastoplasticity.
Controls
STAT_NON_LINE COMP_ELAS
RELATION
DEFORMATION
ELAS_VMIS_LINE
GREEN
CALC_THETA
CALC_G_THETA OPTION
COMP_ELAS
CALC_G
RELATION
ELAS_VMIS_LINE
6
Results of modeling B
6.1 Values
tested
The values of the rate of refund are tested for the same crowns of integration as in
modeling A.
Displacement
imposed
(mm)
G (NR/mm)
crown 1
G (NR/mm)
crown 2
G (NR/mm)
crown 3
0,02 3.26 3.17 3.18
0,04 13.36 13.03 13.07
0,06 31.02 30.50 30.67
0,08 56.33 55.90 56.51
0,1 85.84
85.91 87.47
The results are satisfactory: the maximum variation enters the values of G obtained on the three
crowns of integration is lower than 2%.
The effect of the terms of second command in the deformation is relatively weak: the variation enters them
results of two modelings is increasing with imposed displacement
and is worth to the maximum 6%,
cf [Figure 6.1-a].
Code_Aster
®
Version
8.1
Titrate:
SSNP110 - Fissure edge in a plate in elastoplasticity
Date:
15/02/06
Author (S):
E. CRYSTAL
Key
:
V6.03.110-A
Page:
6/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-62/06/005/A
0
10
20
30
40
50
60
70
80
90
100
0
0,02
0,04
0,06
0,08
0,1
0,12
Imposed displacement (mm)
G (
NR
/
m
m
)
MODELING A
MODELING B
Appear 6.1-a: Comparison of the rates of refund of energy of two modelings
7
Summary of the results
This case test makes it possible to be ensured of the invariance of the calculation of the rate of refund of energy by
method théta according to the crowns of integration for laws of behavior of the type
plastic rubber band-perfectly.
The weak contribution of the terms of second command in the deformation is highlighted.