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V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
Organization (S)
: EDF-R & D/AMA, CS IF
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
V6.03.312 document
SSNP312 - DMT94.132 Fissures parallel with the interface
in a bimetallic test-tube CT
Summary:
This test results from the validation independent of version 3 in breaking process.
It is about a two-dimensional test in statics (plane deformations) which relates to the calculation of a parallel fissure
with the interface between two materials, for a noncommonplace geometry in limited field.
The structure has an elastoplastic behavior of Von Mises with isotropic work hardening.
The objective of this case test is the study of the sensitivity of G to the choice of the crowns.
It includes/understands two plane modelings 2D in which one studies the influence of an incremental displacement
imposed. The first modeling uses linear elements, the other of the quadratic elements.
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V6.03 booklet: Nonlinear statics of the plane systems
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1
Problem of reference
1.1 Geometry
All the dimensions are expressed in Misters the fissure is to 0,2 mm of the interface, in the part
higher of the test-tube.
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V6.03 booklet: Nonlinear statics of the plane systems
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1.2
Properties of materials
Material n° 1: austenitic steel
Elastoplastic of von Mises type to isotropic work hardening
Young modulus E1 = 2.105 MPa, Poisson's ratio
1 = 0,3
Yield stress
y1 = 310 MPa
Uniaxial traction diagram:
(MPa)
0.310.600 700
(%)
0 0,155 40 100
Material n° 2: ferritic steel
Elastoplastic of von Mises type to isotropic work hardening
Young modulus E2 = 2.105 MPa, Poisson's ratio
2 = 0,3
Yield stress
y2 = 442 MPa
(MPa)
0.442.600 650
(%)
0 0,221 40 100
Material n° 3: quasi indeformable pins
Isotropic linear rubber band
Young modulus E3 = 6 1010 MPa, Poisson's ratio
3 = 0,3
1.3
Boundary conditions and loading
Being given the dissymmetry of materials, the totality of the test-tube is modelized.
Blockings:
UX = UY = 0
at the point B (center of the lower pin)
UX = 0
at point A (center of the higher pin)
Loading by imposed displacement:
0
UY
1 mm at point A, by equal increments of 0,02 mm
The loading is thus monotonous growing.
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V6.03 booklet: Nonlinear statics of the plane systems
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2
Reference solution
2.1
Method of calculation used for the reference solution
Calculation by finite elements with CASTEM2000 and the method theta.
2.2
Results of reference
Response curve force-displacement to point A
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V6.03 booklet: Nonlinear statics of the plane systems
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Vertical displacement of the two lips of the fissure
Rate of refund of energy G according to displacement in A
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Semi-empirical formula of ASTM [bib2]
JASTM = (2 + 0,522 * b0/W) * A/b0 where b0 = W - a0 is the initial length of the ligament and where A is the surface
under the curve load-displacement at point A, i.e. the work of the load applied.
2.3
Uncertainty on the solution
The maximum change between results CASTEM2000 and the formula of ASTM is approximately 9% for
first crown (nearest to the fissure) and the maximum loading. This variation decreases when
one takes crowns further away from the bottom of fissure.
2.4 References
bibliographical
[1]
X.Z. SUO and J. BROCHARD: Elastoplastic calculation of a bimetallic test-tube CT with
a fissure close to the interface. Report ECA DMT/94-132
[2]
American Society for Testing and Materials. Annual Book off ASTM Standard, flight 3.01,
Section 3, Metals Test Methods and Analytical Procedures, E813 article, page 711, 1990.
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3 Modeling
With
3.1
Characteristics of modeling
The totality of the test-tube is with a grid in quadrangular with 4 nodes or triangular elements to 3
nodes.
It comprises 799 nodes, 624 quadrangles, 185 triangles and 261 segments.
3.2
Characteristics of the mesh
Very small elements (0,02 mm) with the point of the fissure.
The first crown is located in only one material, the 4 other crowns cross the interface
between two materials.
X
Y
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Lip of the fissure
Interface between
2 materials
Melts of
fissure
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3.3 Functionalities
tested
Calculation of the rate of refund of energy G by the method THETA for various crowns.
Controls
STAT_NON_LINE
COMP_INCR
VMIS_ISOT_TRAC
NEWTON
TANGENT
DEFI_FOND_FISS
MELTS
GROUP_NO
NORMAL
CALC_THETA
THETA_2D
GROUP_NO
CALC_G_THETA_T
COMP_ELAS
ELAS_VMIS_TRAC
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V6.03 booklet: Nonlinear statics of the plane systems
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4
Results of modeling A
The rate of refund of energy G is calculated by the method THETA for the 5 following crowns:
·
Crown 0: Rinf = 0,02 mm Rsup = 0,18 mm
·
Crown 1: Rinf = 0,2 mm Rsup = 1 mm
·
Crown 2: Rinf = 1 mm Rsup = 2 mm
·
Crown 3: Rinf = 2 mm Rsup = 3 mm
·
Crown 4: Rinf = 3 mm Rsup = 5 mm
4.1 Values
tested
Identification Reference
J ASTM
Aster %
difference
G (NR/mm) Crown n°0 UY=0,2 mm
5,82
5,76
-
1,02
G (NR/mm) Crown n°0 UY=0,4 mm
22,60
21,97
-
2,80
G (NR/mm) Crown n°0 UY=0,6 mm
47,24
48,32
2,291
G (NR/mm) Crown n°0 UY=0,8 mm
74,70
79,03
5,786
G (NR/mm) Crown n°0 UY=1,0 mm
103,74
111,3
7,305
G (NR/mm) Crown n°1 UY=0,2 mm
5,82
6,10
4,82
G (NR/mm) Crown n°1 UY=0,4 mm
22,60
22,79
0,84
G (NR/mm) Crown n°1 UY=0,6 mm
47,24
46,51
-
1,54
G (NR/mm) Crown n°1 UY=0,8 mm
74,70
72,88
-
2,44
G (NR/mm) Crown n°1 UY=1,0 mm
103,74
100,4
-
3,202
G (NR/mm) Crown n°2 UY=0,2 mm
5,82
6,07
4,28
G (NR/mm) Crown n°2 UY=0,4 mm
22,60
23,43
3,69
G (NR/mm) Crown n°2 UY=0,6 mm
47,24
47,97
1,54
G (NR/mm) Crown n°2 UY=0,8 mm
74,70
74,95
0,32
G (NR/mm) Crown n°2 UY=1,0 mm
103,74
103,44
-
0,28
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Identification
Reference
J ASTM
Aster
% difference
G (NR/mm) Crown n°3 UY=0,2 mm
5,82
6,08
4,39
G (NR/mm) Crown n°3 UY=0,4 mm
22,60
23,46
3,82
G (NR/mm) Crown n°3 UY=0,6 mm
47,24
48,37
2,40
G (NR/mm) Crown n°3 UY=0,8 mm
74,70
75,56
1,14
G (NR/mm) Crown n°3 UY=1,0 mm
103,74
104,35
0,59
G (NR/mm) Crown n°4 UY=0,2 mm
5,82
6,09
4,52
G (NR/mm) Crown n°4 UY=0,4 mm
22,60
23,42
3,63
G (NR/mm) Crown n°4 UY=0,6 mm
47,24
48,43
2,53
G (NR/mm) Crown n°4 UY=0,8 mm
74,70
75,69
1,32
G (NR/mm) Crown n°4 UY=1,0 mm
103,74
104,53
0,77
Stability of G to the choice of the crowns
Identification
Crown 2
Crown 3
Crown 4
% maximum variation.
G (NR/mm) UY=0,2 mm
6,07
6,08
6,08
0,16
G (NR/mm) UY=0,4 mm
23,43
23,46
23,42
0,17
G (NR/mm) UY=0,6 mm
47,97
48,37
48,43
0,85
G (NR/mm) UY=0,8 mm
74,95
75,56
75,69
0,53
G (NR/mm) UY=1,0 mm
103,44
104,35
104,53
0,60
4.2 Remarks
The calculation of reference (Castem 2000) and Aster calculation use the same mesh strictly.
The absolute value of the variation on the calculation of G for crowns 0 and 1 grows according to
displacement to reach a value from approximately 5%.
For the other crowns, the variation decreases to reach a quasi null value.
Stability on crowns 2, 3 and 4 is very good, the difference between crowns is always lower than
1%.
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5 Modeling
B
5.1
Characteristics of modeling
The totality of the test-tube is with a grid in quadrangular with 8 nodes or triangular elements to 6
nodes.
It comprises 2416 nodes, 625 quadrangles, 185 triangles and 264 segments.
5.2
Characteristics of the mesh
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5.3 Functionalities
tested
Calculation of the rate of refund of energy G by the method THETA for various crowns.
Controls
STAT_NON_LINE
COMP_INCR
VMIS_ISOT_TRAC
NEWTON
TANGENT
DEFI_FOND_FISS
MELTS
GROUP_NO
NORMAL
CALC_THETA
THETA_2D
GROUP_NO
CALC_G_THETA_T
COMP_ELAS
ELAS_VMIS_TRAC
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6
Results of modeling B
The rate of refund of energy G is calculated by the method THETA for the 5 following crowns:
·
Crown 0: Rinf = 0,02 mm Rsup = 0,18 mm
·
Crown 1: Rinf = 0,2 mm Rsup = 1 mm
·
Crown 2: Rinf = 1 mm Rsup = 2 mm
·
Crown 3: Rinf = 2 mm Rsup = 3 mm
·
Crown 4: Rinf = 3 mm Rsup = 5 mm
6.1 Values
tested
Identification
Reference
J ASTM
Aster
% difference
G (NR/mm) Crown n°0 UY=0,2 mm
5,82
6,0
3,18
G (NR/mm) Crown n°0 UY=0,4 mm
22,60
21,63
-
4,29
G (NR/mm) Crown n°0 UY=0,6 mm
47,24
46,14
-
2,32
G (NR/mm) Crown n°0 UY=0,8 mm
74,70
73,06
-
2,20
G (NR/mm) Crown n°0 UY=1,0 mm
103,74
100,85
-
2,782
G (NR/mm) Crown n°1 UY=0,2 mm
5,82
5,33
-
8,43
G (NR/mm) Crown n°1 UY=0,4 mm
22,60
20,41
-
9,71
G (NR/mm) Crown n°1 UY=0,6 mm
47,24
43,22
-
8,52
G (NR/mm) Crown n°1 UY=0,8 mm
74,70
68,13
-
8,80
G (NR/mm) Crown n°1 UY=1,0 mm
103,74
93,94
-
7,34
G (NR/mm) Crown n°2 UY=0,2 mm
5,82
5,39
-
7,35
G (NR/mm) Crown n°2 UY=0,4 mm
22,60
21,18
-
6,29
G (NR/mm) Crown n°2 UY=0,6 mm
47,24
44,18
-
6,48
G (NR/mm) Crown n°2 UY=0,8 mm
74,70
68,64
-
8,11
G (NR/mm) Crown n°2 UY=1,0 mm
103,74
93,90
-
9,48
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Identification
Reference
J ASTM
Aster
% difference
G (NR/mm) Crown n°3 UY=0,2 mm
5,82
5,27
-
9,51
G (NR/mm) Crown n°3 UY=0,4 mm
22,60
20,31
-
10,11
G (NR/mm) Crown n°3 UY=0,6 mm
47,24
42,81
-
9,37
G (NR/mm) Crown n°3 UY=0,8 mm
74,70
67,19
-
10,06
G (NR/mm) Crown n°3 UY=1,0 mm
103,74
92,35
-
10,98
G (NR/mm) Crown n°4 UY=0,2 mm
5,82
5,36
-
7,96
G (NR/mm) Crown n°4 UY=0,4 mm
22,60
20,82
-
7,88
G (NR/mm) Crown n°4 UY=0,6 mm
47,24
43,95
-
6,97
G (NR/mm) Crown n°4 UY=0,8 mm
74,70
68,53
-
8,27
G (NR/mm) Crown n°4 UY=1,0 mm
103,74
93,84
-
9,54
Stability of G to the choice of the crowns
Identification
Crown 2
Crown 3
Crown 4
% maximum variation.
G (NR/mm) UY=0,2 mm
5,39
5,27
5,36
2,27
G (NR/mm) UY=0,4 mm
21,17
20,31
20,82
4,23
G (NR/mm) UY=0,6 mm
44,18
42,81
43,95
3,20
G (NR/mm) UY=0,8 mm
68,64
67,19
68,53
2,30
G (NR/mm) UY=1,0 mm
93,90
92,34
93,84
1,86
6.2 Remarks
The value of G of the Aster model is logically lower than that of the reference.
The variation is approximately 10% for crowns 1 2 3 and 4. For crown 0, the average deviation is
approximately 3%.
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7
Summary of the results
It should initially be announced that the reference solution is not an exact solution and
that it does not apply, in general, in the case of the Bi-materials. Moreover it is based on one
calculation of the linear elements. It is however exploitable for this study because the fissure is not
located at the interface of two materials.
Modeling A (degree 1) gives results in conformity with those of the reference.
Modeling B (degree 2) revealed a variation from approximately 8% on the value of G.
One can notice that the crowns far away from the fissure provide more precise results and
more stable than those close to the bottom of fissure. The low-size crowns give
results worse than those whose radii are important. Consequently, it seems judicious
to use large-sized crowns for a modeling 2D.