FORMA09 - TP of the formation thermoplasticity

Code_Aster

Version

6.4

Titrate:

FORMA09 - TP formation thermoplasticity

Date:

11/06/03

Author (S):

J.M. PROIX, F.WAECKEL

Key

V7.20.101-A

Page:

1/10

Manual of Validation

V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures

HT-66/03/008/A

Organization (S):

EDF-R & D/AMA

Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the structures
axisymmetric
V7.20.101 document

FORMA09 - TP of the formation thermoplasticity

Summary:

This test in quasi-static axisymmetric 2D makes it possible to illustrate on a simple case the questions relative to
elastoplastic thermo modelings:

for thermal calculation, it highlights the effects of going beyond of maximum, of instability of
diagram clarifies and shows the contribution of the diagonalisation of the thermal matrix of mass,

For mechanical calculation, it highlights the stresses due to the incompatibility of the deformations
thermics, even if the cylinder is free, then incrémentaux aspects of calculation with
STAT_NON_LINE. One shows also the influence of the temperature of reference and the temperature of

definition of the thermal expansion factor.

Code_Aster

Version

6.4

Titrate:

FORMA09 - TP formation thermoplasticity

Date:

11/06/03

Author (S):

J.M. PROIX, F.WAECKEL

Key

V7.20.101-A

Page:

2/10

Manual of Validation

V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures

HT-66/03/008/A

Problem of reference

1.1 Geometry

The studied structure is a section of cylinder, modelized into axisymmetric, (cf HPLA100)

With

Interior radius

19.5 mm

External radius

20.5 mm

Not F

R =

20.0 mm

Thickness

H =

1.0 mm

Height

L =

10.0 mm

H
+

1.2

Properties of materials

The material is homogeneous isotropic, thermoelastic linear. The mechanical coefficients are

The expansion factor is a function of the temperature:

The temperature of reference is worth 0°C. The thermal coefficients are worth:

1.3

Boundary conditions and loadings of thermal calculation

The cylinder is subjected on its internal edge to an exchange with a fluid which passes brutally from
100°C with 0°C:

null flow on edges AB, BC, CD

on the edge AD, condition of convectif exchange, with:
H = 100 W/mm ²/°C
Text = 100°C with T = 0s, then 0°C with T = 0.01s, and then maintained constant.

Code_Aster

Version

6.4

Titrate:

FORMA09 - TP formation thermoplasticity

Date:

11/06/03

Author (S):

J.M. PROIX, F.WAECKEL

Key

V7.20.101-A

Page:

3/10

Manual of Validation

V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures

HT-66/03/008/A

1.4

Boundary conditions and loadings of mechanical calculation

Conditions of symmetry
Case not attached: null displacement following OY along side AB.
Attached case: null displacement following OY along sides AB and CD.
Loading: thermal dilation.

Reference solution

2.1 Solution

thermo rubber band

The reference solution is numerical. It is obtained with Code_Aster for a fine mesh (20
elements in the thickness). The TP is carried out with a very coarse mesh (3 elements in
the thickness), one thus should not be astonished to obtain results rather far away from the solution from
reference.

Indeed, the goal of the TP is to show:

for thermal calculation, the effects of going beyond of maximum, instability of the diagram
explicit and the contribution of the diagonalisation of the thermal matrix of mass,

for mechanical calculation, the stresses due to the incompatibility of the deformations
thermics, even if the cylinder is free, then incrémentaux aspects of calculation with
STAT_NON_LINE.

The values tested are:

Moment (S) Temperature max

(Tmax) in °C

A number of nodes

reached by Tmax

and numbers of

nodes

Temperature min

(Tmin) in °C

A number of nodes

0.100 63

nodes 100 63

0,1

100

1 node: N26

69,5309

1 node: N62

100

1 node: N1

8,5 182

1 node: N62

100

1 node: N2

5,56755

1 node: N62

100

95,1712

1 node: N3

1,81091

1 node: N62

The values maximum and minimum of stresses SIYY at the moments t=0s and t=11s

Case not attached

Moment (S)

Stress

maximum
SIYY max

A number of meshs

attacks by

SIYY max and

number of the meshs

Stress

minimal
SIYY min

A number of meshs

attacks by

SIYY min and

number of the meshs

364,875

1 mesh: M21

 320,094

1 mesh: M2

Case attached with MECA_STATIQUE and STAT_NON_LINE with TREF=0 (and an initial state T=0°C),

Moment (S)

Stress

maximum
SIYY max

A number of meshs

attacks by

SIYY max and

number of the meshs

Stress

minimal
SIYY min

A number of meshs

attacks by

SIYY min and

number of the meshs

 200

1 mesh: M40

 200

1 mesh: M1

 61,5003

1 mesh: M1

 702,563

1 mesh: M22

Code_Aster

Version

6.4

Titrate:

FORMA09 - TP formation thermoplasticity

Date:

11/06/03

Author (S):

J.M. PROIX, F.WAECKEL

Key

V7.20.101-A

Page:

4/10

Manual of Validation

V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures

HT-66/03/008/A

Case attached with MECA_STATIQUE and STAT_NON_LINE with TREF=100°C (and an initial state T=100°C),

Moment (S)

Stress

maximum
SIYY max

A number of meshs

attacks by

SIYY max and

number of the meshs

Stress

minimal
SIYY min

A number of meshs

attacks by

SIYY min and

number of the meshs

138,5

1 mesh: M21

 502,563

1 mesh: M2

2.2 Reference

bibliographical

Documentation of validation [V7.01.100].

Code_Aster

Version

6.4

Titrate:

FORMA09 - TP formation thermoplasticity

Date:

11/06/03

Author (S):

J.M. PROIX, F.WAECKEL

Key

V7.20.101-A

Page:

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Manual of Validation

V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures

HT-66/03/008/A

3 Modeling

With

3.1

Characteristics of modeling

Modeling A corresponds to the statement of the TP. It comprises only the first thermal calculation
(without diagonalisation of the thermal mass).

The mesh comprises 3 meshs QUAD4 in

the thickness (mesh GIBI).

3.2

Characteristics of the mesh

6 meshs

The useful edges for the boundary conditions are defined by the groups of meshs:

EXCHANGE (left edge)

HIGH (higher edge)

LOW (lower edge)

3.3 Functionalities

tested

Controls

STAT_NON_LINE COMP_INCR RELATION

ELAS

DEFI_MATERIAU THER

ELAS_FO

THER_LINEAIRE

MECA_STATIQUE

Code_Aster

Version

6.4

Titrate:

FORMA09 - TP formation thermoplasticity

Date:

11/06/03

Author (S):

J.M. PROIX, F.WAECKEL

Key

V7.20.101-A

Page:

6/10

Manual of Validation

V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures

HT-66/03/008/A

Results of modeling A

4.1 Values

tested

Temperature moment Identification Reference

Aster %

diff

maximum

4 temp

max

126.314

126.314 0

Note:

This modeling comprises only one test of nonregression. It is the starting point of
TP, intended to improve modeling (cf modeling B). On the change of the temperature
in the middle of the cylinder according to time, and the distribution of temperature to t=4s. One
note (see curved reds, with square marker on the following figure), that one exceeds
the temperature of 100°C, which is not physical. This characterizes nona respect of
principle of the maximum.

Code_Aster

Version

6.4

Titrate:

FORMA09 - TP formation thermoplasticity

Date:

11/06/03

Author (S):

J.M. PROIX, F.WAECKEL

Key

V7.20.101-A

Page:

8/10

Manual of Validation

V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures

HT-66/03/008/A

5.1.1 Calculation

thermics

To improve the results of modeling A, therefore to mitigate these goings beyond of the temperature
maximum (cf [R3.06.07]), several solutions are possible:

one can increase the pitch of time, which is not always compatible with the maid
apprehension of the speed of the transient (as in this case),

or to refine the mesh, which is a good solution, but expensive in time calculation,

one can finally use the diagonalisation of the thermal matrices of mass, i.e. here
modeling AXIS_DIAG. One then obtains the curves marked of circles on the figures

[Figure 5.1-a] and [Figure 5.1-b] Ci above. The temperature remains always lower than 100°C.
It is the simplest solution.

If one seeks to use an explicit diagram (THETA = 0), one sees appearing a clear instability for
great pitches of time (curve with marker cross on the figure [Figure 5.1-a] above).

In conclusion, for thermal calculation, it is necessary to use THETA equal to or higher than 0.5, to have one
stable diagram some is the pitch of time. Moreover it is necessary to use a pitch of sufficiently small time
to apprehend the transient, but not too small to avoid the oscillations. If they appear,
either the mesh should be refined, or to use modeling AXIS_DIAG, (or PLAN_DIAG, or 3d_DIAG).

5.1.2 Thermoelastic calculation in free dilation

One carries out calculation with MECA_STATIQUE, using for only loading thermal dilation.

With the boundary conditions of the case not attached: null displacement following OY along side AB.

For mechanical calculation, it will be enough to calculate at the moment T = 0s, and T = 11s for example.

The stresses at the moment t=0s are null, because the field of temperature is uniform (T = 200°C) and
remain compatible. On the other hand the deformations obtained are not null since the temperature of
reference is equal to 200°C.

With T = 11s, or any other positive mechanical moment, one sees appearing stresses known as of
compatibility thermics. Indeed, the field of temperature is not uniform any more but varies according to R.
This produced of the incompatible deformations, which thus generate stresses, even for one
roll not attached. This situation occurs even for a linear field of temperature by report/ratio
with the radius. On the other hand (cf exposed) a linear field of temperature compared to the co-ordinates
total does not produce stress for a not attached structure.

5.1.3 Thermoelastic calculation with fastening

Calculation with MECA_STATIQUE of the attached case shows the contribution of fastening on stresses (SIYY in

private individual): at the moment T = 0s, the temperature of reference being equal to 0°C, the uniform field of
temperature causes a uniform state of stress SIYY of 200MPa, and with T = 11s, the state of
stresses is different from the case not attached.

This modeling is correct, but is limited to the linear behaviors.

Code_Aster

Version

6.4

Titrate:

FORMA09 - TP formation thermoplasticity

Date:

11/06/03

Author (S):

J.M. PROIX, F.WAECKEL

Key

V7.20.101-A

Page:

9/10

Manual of Validation

V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures

HT-66/03/008/A

5.1.4 Thermoplastic calculation with fastening

One seeks to carry out same calculation as previously, but this time with

STAT_NON_LINE

with

COMP_INCR=_F (RELATION=' ELAS')

, not to complicate the problem (another

behavior would lead to the same observations). The list of moments provided to

STAT_NON_LINE

is:

t=0s, and t=11s.

Since an incremental calculation is made, moment 0 is regarded as initial moment. It is not
thus not calculated, and at the next moment (t=11s), one calculates the solution due to the increase in load
(thermics here) between 0s and 11s. One notes whereas the solution obtained (displacements, stresses)
is different from calculation with

MECA_STATIQUE

. It is logical and coherent with the definition of calculation

incremental, but it is a trap for the use. To retain: implicitly,

STAT_NON_LINE

incremental supposes that at the initial moment, the structure is not forced, not deformed. This implies
that the field of temperature must be uniform and equal to the temperature of reference.

It is not the case here: with t=0s, TREF=0°C, and T=200°C. By not calculating this thermal dilation,
it is supposed here that with t=0s, there is no deformation, and no stress.

5.1.5 Thermoplastic calculation with fastening and addition of initial conditions

One modifies the list of moments: one adds one preliminary moment t=1s for example. In this moment, one
a field of uniform temperature, equal to the temperature of reference defines. One uses for this purpose them
controls

CREA_CHAMP

, then

CREA_RESU

to enrich the structure of data thermics results

with this uniform field. One carries out then mechanical calculation, by providing the list of moments:
t=1s, t=0s, and t=11s
It is noted whereas the moment t=0s is well calculated, and that the stresses are identical to the case
calculated with

MECA_STATIQUE

5.2

Characteristics of the mesh

Even mesh that for modeling A.

5.3 Functionalities

tested

Controls

STAT_NON_LINE COMP_INCR

RELATION

ELAS

DEFI_MATERIAU THER

ELAS_FO

PROJ_CHAMP

THER_LINEAIRE

MECA_STATIQUE

Results of modeling B

6.1 Values

tested

Modeling AXIS_DIAG

Temperature moment Identification Reference

Aster %

diff

maximum

4 temp

max 100 100

Code_Aster

Version

6.4

Titrate:

FORMA09 - TP formation thermoplasticity

Date:

11/06/03

Author (S):

J.M. PROIX, F.WAECKEL

Key

V7.20.101-A

Page:

10/10

Manual of Validation

V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures

HT-66/03/008/A

Summary of the results

This test relates to the formation thermoplasticity. It shows the utility of the choice of modeling DIAG

(thermal matrix of diagonalized mass) for thermal calculations, and illustrates in
incremental thermomechanics (control STAT_NON_LINE) how to take into account

correctly the initial state.