SSLP313 - Fissure inclined in an unlimited plate, subjected to a uniform traction with linfini

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Titrate:

SSLP313 - Fissure inclined in an unlimited plate

Date:

15/10/01

Author (S):

J.M. PROIX, I. CORMEAU, E. LECLERE

Key

V3.02.313-A

Page:

1/10

Manual of Validation

V3.02 booklet: Linear statics of the plane systems

HI-75/01/010/A

Organization (S):

EDF/MTI/MN, CS IF

Manual of Validation
V3.02 booklet: Linear statics of the plane systems
Document

SSLP313 - Fissure inclined in a plate
unlimited, subjected to a uniform traction ad infinitum

Summary:

This test results from the validation independent of version 3 in breaking process.

K is calculated

, K

and the rate of refund of energy for a right fissure, tilted of an angle

, in one

large-sized plate subjected to a uniform traction. The model is two-dimensional in stresses
plane. The material is elastic linear isotropic. This test of reference in 2D makes it possible to check separability
K

and K

in a mixed mode.

The reference solution, given for a theoretically unlimited field, is analytical.

In addition to the energy method (CALC_G_THETA), one tests the method of calculation of the factors of intensity

stresses by extrapolation of displacements (POST_K1_K2_K3). Modeling B makes it possible to test

this last method with a type of mesh recommended (nodes mediums with the quarter) to obtain a solution
precise.

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Version

5.3

Titrate:

SSLP313 - Fissure inclined in an unlimited plate

Date:

15/10/01

Author (S):

J.M. PROIX, I. CORMEAU, E. LECLERE

Key

V3.02.313-A

Page:

2/10

Manual of Validation

V3.02 booklet: Linear statics of the plane systems

HI-75/01/010/A

Problem of reference

1.1 Geometry

has

One allots an unspecified value to the slope,

= 37 degrees.

One chooses has = 1.E-3 Mr.

1.2

Properties of material

The material is elastic linear isotropic, of Young E and Poisson's ratio modulus

E = 2.E11 AP,

= 0.3.

Assumption of the plane stresses

1.3

Boundary conditions and loadings

Arbitrary limits of the field with a grid:
- xmax X xmax with xmax = 10a
- ymax y ymax with ymax = 20a

Boundary conditions:
In order to lock the 3 plane rigid modes exclusively.
UX = UY = 0 with the left lower corner of the complete model.
UY = 0 with the corner lower right of the complete model.
On the lower edge, we impose UY = 0

Loading: uniform voltage

yy = 0 on the higher edge:

The value of

0 are worth 100MPa, in plane stresses.

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Version

5.3

Titrate:

SSLP313 - Fissure inclined in an unlimited plate

Date:

15/10/01

Author (S):

J.M. PROIX, I. CORMEAU, E. LECLERE

Key

V3.02.313-A

Page:

3/10

Manual of Validation

V3.02 booklet: Linear statics of the plane systems

HI-75/01/010/A

Reference solution

2.1

Method of calculation used for the reference solution

Function of stress of Airy.

2.2

Results of reference

has

E K

ref.

cos

sin cos

(

)

in plane stresses

2.3

Uncertainty on the solution

Exact analytical solution (Irwin) in unlimited medium.

2.4 References

bibliographical

[1]

Y. MURAKAMI Stress intensity factors handbook, box 4.2, page 188. The Society off
Materials Science, Japan, Pergamon Near, 1987.

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Titrate:

SSLP313 - Fissure inclined in an unlimited plate

Date:

15/10/01

Author (S):

J.M. PROIX, I. CORMEAU, E. LECLERE

Key

V3.02.313-A

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Manual of Validation

V3.02 booklet: Linear statics of the plane systems

HI-75/01/010/A

Initial block 2D

radius

center

The radius is worth 7,5E-5 m

3.2

Characteristics of the mesh

The mesh consists of 14888 nodes and 6674 elements, including 1392 elements QUA8 and 5282
elements TRI6.

3.3

Functionalities tested

Controls

MECHANICAL AFFE_MODELE

C_PLAN

ALL

AFFE_CHAR_MECA FORCE_CONTOUR

MECA_STATIQUE

CALC_THETA THETA_2D

CALC_G_THETA_T OPTION

CALC_G

CALC_G_THETA_T OPTION

CALC_K_G

POST_K1_K2_K3

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Titrate:

SSLP313 - Fissure inclined in an unlimited plate

Date:

15/10/01

Author (S):

J.M. PROIX, I. CORMEAU, E. LECLERE

Key

V3.02.313-A

Page:

7/10

Manual of Validation

V3.02 booklet: Linear statics of the plane systems

HI-75/01/010/A

Results of modeling A

4.1 Values

tested

4.1.1 Results obtained with CALC_G_THETA_T

Identification Reference

Aster

% difference

G 1.0019E+02

1.0126E+02

1.07

KI 3,5750E+6

3,6038E+6

0,81

KII 2,6939E+6

2,7003E+6

0,24

4.1.2 Results obtained with POST_K1_K2_K3

Identification Method Reference

Aster %

difference

K1_MAX 1

3.57E+06

3.54E+06

 1.04

K1_MIN 1

3.57E+06

3.19E+06

 10.72

K2_MAX 1

2.69E+06

2.62E+06

 2.82

K2_MIN 1

2.69E+06

1.92E+06

 28.62

G_MAX 1

1.00E+02

9.69E+01

 3.33

G_MIN 1

1.00E+02

6.94E+01

 30.70

K1_MAX 2

3.57E+06

3.51E+06

 1.76

K1_MIN 2

3.57E+06

3.33E+06

 6.79

K2_MAX 2

2.69E+06

2.61E+06

 3.12

K2_MIN 2

2.69E+06

2.25E+06

 16.49

G_MAX 2

1.00E+02

9.57E+01

 4.50

G_MIN 2

1.00E+02

8.08E+01

 19.32

4.2

Remarks on the 2 methods of POST_K1_K2_K3:

Two methods are programmed in POST_K1_K2_K3:

Method 1: one calculates the jump of the field of displacements squared and one divides it by R.
Various values of K1 (resp. K2, K3) are obtained (except for a factor) by extrapolation
in R =0 of the segments of straight lines thus obtained. If the solution were perfect (field
asymptotic analytical everywhere), one should obtain a line. Actually, one is obtained
curve, therefore values different of K1, K2, K3. In order to give an indication of
quality of the result, one lists the values maximum and minimum obtained on the unit of
discussed items (that one names here K1_MAX, K1_MIN, etc…)

Method 2: one traces the jump of the field of displacements squared according to R. Them
approximations of K1 are (always except for a factor) equal to the slope of the segments connecting
the origin at the various points of the curve. There still, one obtains various values of K1,
K2, K3.et one lists the values maximum and minimum obtained on the unit of the points
treaties (named K1_MAX, K1_MIN, etc…)

To provide to compare the solution obtained with that provided by CALC_G_THETA_T, one

calculate G starting from K1 and K2 by the formula of Irwin, which gives G_MAX and G_MIN.

4.3 Parameters

of execution

Version: 5.3

Machine: SGI/ORIGIN 2000

Overall dimension memory:

128 Mo

Time CPU To use: 22 seconds

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Titrate:

SSLP313 - Fissure inclined in an unlimited plate

Date:

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J.M. PROIX, I. CORMEAU, E. LECLERE

Key

V3.02.313-A

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Manual of Validation

V3.02 booklet: Linear statics of the plane systems

HI-75/01/010/A

5 Modeling

5.1

Characteristics of modeling

Even form of mesh that previously, but amendment of the co-ordinates of the nodes mediums
edges touching the bottom of fissure, to move them with the quarter of these edges (method of
Barsoum).

This amendment of the co-ordinates of the nodes is carried out by an accessible procedure GIBI in
to card-index data of mesh (

SSLP313B.datg

5.2

Characteristics of the mesh

The mesh consists of 14888 nodes and 6674 elements, including 1392 elements QUA8 and 5282
elements TRI6.

5.3

Functionalities tested

Controls

MECHANICAL AFFE_MODELE

C_PLAN

ALL

AFFE_CHAR_MECA FORCE_CONTOUR

MECA_STATIQUE

CALC_THETA THETA_2D

CALC_G_THETA OPTION

CALC_G

CALC_G_THETA OPTION

CALC_K_G

POST_K1_K2_K3

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Version

5.3

Titrate:

SSLP313 - Fissure inclined in an unlimited plate

Date:

15/10/01

Author (S):

J.M. PROIX, I. CORMEAU, E. LECLERE

Key

V3.02.313-A

Page:

9/10

Manual of Validation

V3.02 booklet: Linear statics of the plane systems

HI-75/01/010/A

Results of modeling B

6.1 Values

tested

6.1.1 Results obtained with CALC_G_THETA_T

Identification Reference

Aster

% difference

G 1.0019E+02

1.0135E+02

1.16

KI 3,5750E+6

3.6033E+06

0.79

KII 2,6939E+6

2.6996E+06

0.21

6.1.2 Results obtained with POST_K1_K2_K3

Identification Method Reference

Aster %

difference

K1_MAX 1

3.57E+06

3.6089E+06

0.95

K1_MIN 1

3.57E+06

3.5995E+06

0.69

K2_MAX 1

2.69E+06

2.7035E+06

0.36

K2_MIN 1

2.69E+06

2.6944E+06

0.02

G_MAX 1

1.00E+02

1.0142E+02

1.23

G_MIN 1

1.00E+02

1.0120E+02

1.01

K1_MAX 2

3.57E+06

3.6027E+06

0.78

K1_MIN 2

3.57E+06

3.5344E+06

 1.14

K2_MAX 2

2.69E+06

2.6927E+06

 0.05

K2_MIN 2

2.69E+06

2.6478E+06

 1.71

G_MAX 2

1.00E+02

1.0115E+02

0.96

G_MIN 2

1.00E+02

9.7512E+01

 2.67

6.2

Remarks on the 2 methods of POST_K1_K2_K3:

Two methods are programmed in POST_K1_K2_K3:

To provide to compare the solution obtained with that provided by CALC_G_THETA_T, one

calculate G starting from K1 and K2 by the formula of Irwin, which gives G_MAX and G_MIN.

6.3 Parameters

of execution

Version: 5.3

Machine: SGI/ORIGIN 2000

Overall dimension memory:

128 Mo

Time CPU To use:19 seconds

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Version

5.3

Titrate:

SSLP313 - Fissure inclined in an unlimited plate

Date:

15/10/01

Author (S):

J.M. PROIX, I. CORMEAU, E. LECLERE

Key

V3.02.313-A

Page:

10/10

Manual of Validation

V3.02 booklet: Linear statics of the plane systems

HI-75/01/010/A

Summary of the results

With this choice of the limits of the field of calculation, we obtain variations of about 1% on
coefficients KI and KII, and on the rate of refund of energy G.

With regard to method POST_K1_K2_K3, the results are further away from the reference with

a standard mesh (of 1% with 30% of variation), on the other hand, with a mesh of the type Barsoum (nodes
mediums with the quarter on the sides), recommended for this type of method, the differences are included/understood between 3% and
+1.2%, which is relatively precise.