SSLV311 - Murakami 9.39. Fissure in quarter dellipse with the corner dun thick disc in rotation

Code_Aster

Version

8.2

Titrate:

SSLV311 - Murakami 9.39. Fissure in quarter of ellipse to the corner of a disc

Date:

15/02/06

Author (S)

E. CRYSTAL

Key:

V3.04.311-A

Page:

1/8

Manual of Validation

V3.04 booklet: Linear statics of the voluminal structures

HT-62/06/005/A

Organization (S)

: EDF-R & D/AMA

Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
V3.04.311 document

SSLV311 - Murakami 9.39. Fissure in quarter of ellipse
with the corner of a thick disc in rotation

Summary:

This test results from the validation independent of the version in breaking process.

Applicability:

Linear breaking process

Type of analysis:

Statics

Type of behavior:

Isotropic linear rubber band

Type of model:

Three-dimensional

A number of modelings:

Objective:

Basic test into three-dimensional for isotropic elastic materials, in
field limited in three directions, in the presence of a voluminal loading.

Explored parameters:

Fixed parameters:

Reports/ratios has/T, B/has, R2/R1, T/R1

Precision of the results:

Average standard deviation of 3% with the analytical reference solution

Code_Aster

Version

8.2

Titrate:

SSLV311 - Murakami 9.39. Fissure in quarter of ellipse to the corner of a disc

Date:

15/02/06

Author (S)

E. CRYSTAL

Key:

V3.04.311-A

Page:

2/8

Manual of Validation

V3.04 booklet: Linear statics of the voluminal structures

HT-62/06/005/A

Problem of reference

1.1 Geometry

Internal radius:

R1 = 0,1 m

External radius:

R2 = 0,6 m

Thickness:

T = 0,2 m

Half large axis:

= 0,05 m have

Small half centers:

B = 0,0125 m

1.2

Properties of material

Young modulus

E = 2.105 MPa

Poisson's ratio

= 0.3

Density

= 7800 kg/m3

1.3

Boundary conditions and loading

The model will be limited to the part of the thick disc located in the half space Y

0, the plan of

fissure vertical being a symmetry plane.

In the absence of nodes on the axis of revolution, a rigid mode will be locked by a linear relation
between degrees of freedom.

That is to say points:

With (R1,0, T) B

(- R1,0, T)

Blocking of the translation in X: UX (A) + UX (B) = 0
Blocking of the translation in Y: UY = 0 in plan XOZ, except for the lips of the fissure.
Blocking of the translation in Z: UZ (A) = 0

Blocking of rotation around OX: ensured by the C.L of symmetry in plan XOZ
Blocking of rotation around OY: UZ (B) = 0
Blocking of rotation around OZ: ensured by the C.L of symmetry in plan XOZ

Loading: stationary angular velocity

= 500 radians/second

With

Code_Aster

Version

8.2

Titrate:

SSLV311 - Murakami 9.39. Fissure in quarter of ellipse to the corner of a disc

Date:

15/02/06

Author (S)

E. CRYSTAL

Key:

V3.04.311-A

Page:

3/8

Manual of Validation

V3.04 booklet: Linear statics of the voluminal structures

HT-62/06/005/A

Reference solution

2.1

Method of calculation used for the reference solution

Method of integral equation of border.

2.2

Results of reference

B F

= + ·

+ - +

1
3

where the geometrical factor of correction is given,

according to the parametric angle of the ellipse

, with the figure below.

The report/ratio has/T selected corresponds to the higher curve (squares).

2.3

Uncertainty on the solution

The maximum change enters the points marked and the curve being of 2%, the misreading on the curve
is lower than the announced maximum error (5%).

2.4 References

bibliographical

[1]

Y. MURAKAMI: Stress Intensity Factors Handbook, box 9.39, pages 786-791. The Society
off Materials Science, Japan, Pergamon Near, 1987.

Code_Aster

Version

8.2

Titrate:

SSLV311 - Murakami 9.39. Fissure in quarter of ellipse to the corner of a disc

Date:

15/02/06

Author (S)

E. CRYSTAL

Key:

V3.04.311-A

Page:

5/8

Manual of Validation

V3.04 booklet: Linear statics of the voluminal structures

HT-62/06/005/A

3.2

Characteristics of the mesh

The initial mesh consists of 8890 nodes and 2203 elements, including 1264 elements CU20 and
939 elements PR15.
After the conversion of the mesh of quadratic to linear, the number of nodes is reduced to 2230.
This conversion is made essential by the use of the operator DEFI_FISS_XFEM, who

function for the moment that with linear elements.

3.3

Functionalities tested

Calculation of the factors of intensity of the stresses buildings, in all the nodes of the bottom of fissure, by
method THETA.

The factors of intensity of the stresses buildings are calculated on a crown of lower radius
Rinf=0,00075 m and of radius higher Rsup = 0,0025 Mr.

Controls

CREA_MAILLAGE QUAD_LINE

AFFE_CHAR_MECA FORCE_INTERN

FORMULATE

DEFI_FISS_XFEM

CALC_G_LOCAL_T' CALC_K_G”

SYME_CHAR

EXCIT

Code_Aster

Version

8.2

Titrate:

SSLV311 - Murakami 9.39. Fissure in quarter of ellipse to the corner of a disc

Date:

15/02/06

Author (S)

E. CRYSTAL

Key:

V3.04.311-A

Page:

6/8

Manual of Validation

V3.04 booklet: Linear statics of the voluminal structures

HT-62/06/005/A

Results of modeling A

4.1 Values

tested

Identification

Reference (AP.

Aster (AP.

% difference

KI, = 0 degrees

5,657E+07 5,789E+07 - 2,33

KI, = 1,4 degrees

5,945E+07 5,360E+07 9,84

KI, = 2,8 degrees

6,292E+07 6,596E+07 - 4,84

KI, = 4,3 degrees

6,638E+07 6,606E+07 0,48

KI, = 5,9 degrees

6,984E+07 6,902E+07 1,18

KI, = 7,6 degrees

7,273E+07 7,289E+07 - 0,22

KI, = 9,5 degrees

7,562E+07 7,597E+07 - 0,47

KI, = 11,6 degrees

7,908E+07 8,053E+07 - 1,83

KI, = 14,4 degrees

8,197E+07 8,261E+07 - 0,78

KI, = 16,9 degrees

8,543E+07 8,695E+07 - 1,78

KI, = 20,5 degrees

8,889E+07 8,785E+07 1,17

KI, = 25,1 degrees

9,178E+07 9,190E+07 - 0,13

KI, = 31,1 degrees

9,466E+07 9,173E+07 3,09

KI, = 39,5 degrees

9,640E+07 9,562E+07 0,81

KI, = 51,5 degrees

9,755E+07 9,510E+07 2,51

KI, = 68,5 degrees

9,755E+07 9,824E+07 - 0,71

KI, = 90 degrees

9,640E+07 9,720E+07 - 0,83

The parametric angles of the values tested correspond to the position of the 17 points of the bottom of
fissure. The figure below makes it possible to compare the result of calculation with the reference solution.
The average standard deviation is very satisfactory:

Average standard deviation =

(

)

()

ref.

Aster

ref.

= 3,11%

100

Angle (°)

K1 (MPa/m^

0.5)

K1 - Reference
K1 - Aster

Note:

The voluminal loading is introduced here using the key word

FORCE_INTERN

(control

AFFE_CHAR_MECA) and of

FORMULATE

. The results are equivalent if the key word is used

ROTATION

Code_Aster

Version

8.2

Titrate:

SSLV311 - Murakami 9.39. Fissure in quarter of ellipse to the corner of a disc

Date:

15/02/06

Author (S)

E. CRYSTAL

Key:

V3.04.311-A

Page:

7/8

Manual of Validation

V3.04 booklet: Linear statics of the voluminal structures

HT-62/06/005/A

Summary of the results

Within sight of the precision announced on the results of reference (5%) and the average standard deviation
obtained (3,11%), the results provided by Code_Aster are satisfactory.