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Titrate
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SSNP311 Biblio_131. Cracking in mode II of a test-tube
Date:
05/11/02
Author (S):
S. GRANET, I. CORMEAU, E. LECLERE
Key:
V6.03.311-A
Page:
1/8
Manual deValidation
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
V6.03.311 document
SSNP311 - Biblio_131. Cracking in mode II of one
elastoplastic test-tube
Summary:
This test results from the validation independent of version 3 in breaking process.
It is about a two-dimensional test in statics which aims at the validation of the calculation of G, and its not
dependence with respect to the crown, in elastoplastic mode in an incremental calculation, on a geometry
noncommonplace. The law of behavior used is an elastoplastic law of Von Mises with isotropic work hardening.
This case test includes/understands only one modeling 2D planes in which one studies the influence of a load
incremental.
The results obtained with Code_Aster are compared with the calculations carried out using code ADINA.
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:
SSNP311 Biblio_131. Cracking in mode II of a test-tube
Date:
05/11/02
Author (S):
S. GRANET, I. CORMEAU, E. LECLERE
Key:
V6.03.311-A
Page:
2/8
Manual deValidation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
The test-tube in the shape of twin wheel, represented in (A), is fixed at the system of loading (b) by six
pins equivalent to hinges.
Dimensions of the parts are expressed in Misters.
Test-tube:
thickness B variable
6,36; 6,39; 6,44 mm
overall width
98 mm
outdistance between the axes of the pins
74 mm
width of the central part
6 mm
overall height
84 mm
outdistance between centers of the pins
31 mm
height in the center W
30 mm
length of the fissure has
15, 18 or 21 mm
ligament B = W - has
15, 12 or 9 mm
bore of pins
8 mm
Carry-test-tube:
thickness 25
mm
external diameter
190 mm
outdistance between the center of the part and them
centers of the circular cavities
40,3 mm
radius of the cavities
20 mm
diameter of the 2 holes where they are applied
loads
10 mm
Code_Aster
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Version
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Titrate
:
SSNP311 Biblio_131. Cracking in mode II of a test-tube
Date:
05/11/02
Author (S):
S. GRANET, I. CORMEAU, E. LECLERE
Key:
V6.03.311-A
Page:
3/8
Manual deValidation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
1.2
Properties of materials
Test-tube:
The material is elastoplastic, of Von Mises type, with isotropic work hardening, defined by a curve of
uniaxial traction.
Young modulus: E = 74,2 GPa
Poisson's ratio:
= 0,32
E tangent
(GPa)
(
uniaxial)
(MPa)
T
(
uniaxial)
(%)
72,74 334,6 0,46
50,69 410,7 0,61
15,00 431,6 0,75
4,75 443,5 1,00
1,82 480,0 3,00
0,80 500,1 5,50
0,0017 505,2 300,0
Carry-test-tube:
The material is elastic linear isotropic.
Young modulus: E = 206 GPa
Poisson's ratio:
= 0,3
1.3
Boundary conditions and loading
The carry-test-tube has a fixed point UX = UY = 0 with the lower clamp hole and is subjected to one
vertical specific loading applied to the higher clamp hole UX = 0, FY = P variable.
For a length of fissure/W has = 0,5:
P varies:
0 NR with 11772 NR in 12 pitches of 981 NR
11772 NR with 19620 NR in 16 pitches of 490,5 NR
19620 NR with 23544 NR in 20 pitches of 196,2 NR
23544 NR with 25114 NR in 16 pitches of 98,1 NR
Code_Aster
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Version
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Titrate
:
SSNP311 Biblio_131. Cracking in mode II of a test-tube
Date:
05/11/02
Author (S):
S. GRANET, I. CORMEAU, E. LECLERE
Key:
V6.03.311-A
Page:
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Manual deValidation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Calculation in finite elements with ADINA. Update of the matrix of tangent stiffness by the method
BFGS (BROYDEN, FLETCHER, GOLDFARB and SHAMNO). Calculation of J per integral of Rice in
which the density of deformation energy is evaluated according to the theory of plasticity of Hencky
(reversible elastic model nonlinear equivalent with the incremental theory of plasticity for one
monotonous radial loading growing in the space of the main stresses)
2.2
Results of reference
Response curve charges/displacement
P/1000
D/20
Response curve giving the load P/1000 according to displacement D/20. Higher curve
calculated in plane deformations, curves lower calculated in plane stresses. Curves in feature
stopped are experimental results. Stress of reference
ref. = 334,6 MPa (first point
on the traction diagram). Thickness of test-tube B = 6,36 or 6,39 Misters Longueur of fissure
a/W = 0,5.
Code_Aster
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Version
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Titrate
:
SSNP311 Biblio_131. Cracking in mode II of a test-tube
Date:
05/11/02
Author (S):
S. GRANET, I. CORMEAU, E. LECLERE
Key:
V6.03.311-A
Page:
5/8
Manual deValidation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
Integral J according to the load
P/1000
Standardized integral E * JII/(has *
ref2) according to the stress P/1000, where
ref. = 334,6 MPa, for
a test-tube thickness B=6,44 mm
One also has some tabulées values, for a length of fissure has/W=0,5 and one
calculation in plane deformations; the dispersion of JII is related to the choice of the contour of integration around
melts of fissure.
No the loading
P (KN)
E * JII/(has *
ref2)
22
27,66
0,292 to 0,295
36
35,11
0,540 to 0,543
50
38,83
0,798 to 0,813
64
41,49
1,065 to 1,190
2.3
Uncertainty on the solution
The difference between experimental measurements and calculation does not exceed 7%, with regard to the curve of
answer charges/displacement.
The precision of the calculation of J is unknown; the error seems to grow with the level of load, like
show the increasing dependence of J compared to the contour, which reaches a margin of variation of
12% with the pitch n° 64.
2.4 References
bibliographical
[1]
LESLIE BANKS-SILLS and DOV SHERMAN: Elasto-plastic analysis off has mode II fractures
specimen. Int.J.Fracture, 46, 105-122, 1993.
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:
SSNP311 Biblio_131. Cracking in mode II of a test-tube
Date:
05/11/02
Author (S):
S. GRANET, I. CORMEAU, E. LECLERE
Key:
V6.03.311-A
Page:
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Manual deValidation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
3.1.1 Mesh of the test-tube and the gate test-tube
Mesh of the test-tube and the gate test-tube
Zoom on the bottom of fissure
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Version
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:
SSNP311 Biblio_131. Cracking in mode II of a test-tube
Date:
05/11/02
Author (S):
S. GRANET, I. CORMEAU, E. LECLERE
Key:
V6.03.311-A
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Manual deValidation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
3.1.2 Definition of the radii of the crowns
We define the values of the higher and lower radii, to specify in the control
CALC_THETA
:
1 era crowns
2nd crown
3rd crown
4th crown
rinf (mm)
1
2
3
4
rsup (mm)
2
3
4
5
3.2
Characteristics of the mesh
The mesh consists of two objects:
·
the gate test-tube consists of 718 nodes and 200 elements QUA8.
·
the test-tube consists of 1741 nodes and 576 elements including 496 QUA8 and 80 TRI6.
3.3 Functionalities
tested
Controls
AFFE_MODELE
MECHANICS
D_PLAN
ALL
AFFE_CHAR_MECA
FORCE_NODALE
STAT_NON_LINE
CALC_THETA
THETA_2D
MODULE_F0
CALC_G_THETA
CALC_G_THETA_T
Code_Aster
®
Version
5.0
Titrate
:
SSNP311 Biblio_131. Cracking in mode II of a test-tube
Date:
05/11/02
Author (S):
S. GRANET, I. CORMEAU, E. LECLERE
Key:
V6.03.311-A
Page:
8/8
Manual deValidation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
Increment of load n° 22
G, crown n°1 (kN/mm)
6,7451
7,005
3,868
G, crown n°2 (kN/mm)
6,7451
6,99728
3,739
G, crown n°3 (kN/mm)
6,7451
6,9964
3,726
G, crown n°4 (kN/mm)
6,7451
6,998
3,75
Increment of load n°36
G, crown n°1 (kN/mm)
12,473
13,069
4,786
G, crown n°2 (kN/mm)
12,473
13,094
4,977
G, crown n°3 (kN/mm)
12,473
13,083
4,887
G, crown n°4 (kN/mm)
12,473
13,071
4,795
Increment of load n°50
G, crown n°1 (kN/mm)
18,433
19,49
5,744
G, crown n°2 (kN/mm)
18,433
19,573
6,184
G, crown n°3 (kN/mm)
18,433
19,577
6,204
G, crown n°4 (kN/mm)
18,433
19,574
6,194
Increment of load n°64
G, crown n°1 (kN/mm)
24,601
26,84
9,105
G, crown n°2 (kN/mm)
24,601 26,977
9,657
G, crown n°3 (kN/mm)
24,601
26,981
9,672
G, crown n°4 (kN/mm)
24,601
26,983
9,684
5
Summary of the results
The results concerning the rate of refund of energy give 1 maximum change of 9,7% by
report/ratio with the reference solution on the last crown, for an announced precision of 12%.
results are excellent taking into account the non-linear character of the test-tube.