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
Organization (S): EDF-R & D/AMA
Handbook 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 constraints 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 dilation coefficient.
Handbook of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
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
1
Problem of reference
1.1 Geometry
The studied structure is a section of cylinder, modelled into axisymmetric, (cf HPLA100)
Z
IH
Re
Interior radius IH = 19.5 mm
External radius Re = 20.5 mm
Not F
R = 20.0 mm
Thickness
H = 1.0 mm
Height
L = 10.0 mm
R
Z
J
D
C
H
+
R
With
B
F
1.2
Properties of materials
The material is homogeneous isotropic, thermoelastic linear. The mechanical coefficients are
The dilation coefficient 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.
Handbook of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
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
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.
2
Reference solution
2.1 Solution
thermo rubber band
The reference solution is numerical. It is obtained with Code_Aster for a fine grid (20
elements in the thickness). The TP is carried out with a very coarse grid (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 constraints 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) Température max
A number of nodes Température min Nombre of nodes
(Tmax) in °C
reached by Tmax
(Tmin) in °C
and numbers of
nodes
0.100 63
nodes 100 63
0,1
100
1 node: N26
69,5309
1 node: N62
4
100
1 node: N1
8,5 182
1 node: N62
10
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 constraints SIYY at the moments t=0s and t=11s
Case not attached
Moment (S)
Constraint
A number of meshs
Constraint
A number of meshs
maximum
attacks by
minimal
attacks by
SIYY max
SIYY max and
SIYY min
SIYY min and
number of the meshs
number of the meshs
11
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)
Constraint
A number of meshs
Constraint
A number of meshs
maximum
attacks by
minimal
attacks by
SIYY max
SIYY max and
SIYY min
SIYY min and
number of the meshs
number of the meshs
0
200
1 mesh: M40
200
1 mesh: M1
11
61,5003
1 mesh: M1
702,563
1 mesh: M22
Handbook of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
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
Case attached with MECA_STATIQUE and STAT_NON_LINE with TREF=100°C (and an initial state T=100°C),
Moment (S)
Constraint
A number of meshs
Constraint
A number of meshs
maximum
attacks by
minimal
attacks by
SIYY max
SIYY max and
SIYY min
SIYY min and
number of the meshs
number of the meshs
11
138,5
1 mesh: M21
502,563
1 mesh: M2
2.2 Reference
bibliographical
Documentation of validation [V7.01.100].
Handbook of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
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:
5/10
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 grid comprises 3 meshs QUAD4 in
the thickness (grid GIBI).
3.2
Characteristics of the grid
6 meshs
The useful edges for the boundary conditions are defined by the groups of meshs:
·
ECHANGE (left edge)
·
HAUT (higher edge)
·
BAS (lower edge)
3.3 Functionalities
tested
Commands
STAT_NON_LINE COMP_INCR RELATION
=
ELAS
DEFI_MATERIAU THER
ELAS_FO
THER_LINEAIRE
MECA_STATIQUE
Handbook of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
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
4
Results of modeling A
4.1 Values
tested
Temperature moment Identification Référence
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.
Handbook of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
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:
7/10
5 Modeling
B
5.1
Characteristics of modeling
This modeling corresponds to corrected TP. It implements all calculations suggested, in
commenting on the results obtained.
Appear 5.1-a
Appear 5.1-b
Handbook of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
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
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 step 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 grid, 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 steps of time (curve with marker cross on the figure [Figure 5.1-a] above).
In conclusion, for thermal calculation, it is necessary to use a THETA equal to or higher than 0.5, to have one
stable diagram some is the step of time. Moreover it is necessary to use a step of sufficiently small time
to apprehend the transient, but not too small to avoid the oscillations. If they appear,
either the grid 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 constraints 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 constraints 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 constraints, 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 constraint 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 constraints (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
constraints is different from the case not attached.
This modeling is correct, but is limited to the linear behaviors.
Handbook of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
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
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, constraints)
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 in
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 constraint.
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
commands 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 constraints are identical to the case
calculated with MECA_STATIQUE.
5.2
Characteristics of the grid
Even grid that for modeling A.
5.3 Functionalities
tested
Commands
STAT_NON_LINE COMP_INCR
RELATION
=
ELAS
DEFI_MATERIAU THER
ELAS_FO
PROJ_CHAMP
THER_LINEAIRE
MECA_STATIQUE
6
Results of modeling B
6.1 Values
tested
Modeling AXIS_DIAG
Temperature moment Identification Référence
Aster %
diff
maximum
4 temp
max 100 100
0
Handbook of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
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
7
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 (command STAT_NON_LINE) how to take into account
correctly the initial state.
Handbook of Validation
V7.20 booklet: Thermodynamic nonlinear statics of the axisymmetric structures
HT-66/03/008/A
Outline document