background image
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A.M. DONORE
Key
:
U4.83.02-F1
Page:
1/20
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Organization (S):
EDF-R & D/AMA















Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
Document: U4.83.02



Operator
CALC_FATIGUE

1 Goal
To calculate a field of damage of fatigue undergone by a structure and to determine the plan criticize in
which shearing is maximum.
Calculation of a field of damage: starting from a history of equivalent stresses (forced
von Mises signed) or of deformations equivalent (invariant of the second signed command) calculated to
nodes or at the points of Gauss and stored in a concept result of the type
evol_elas
,
evol_noli
or
dyna_trans
, one calculates a field of size which contains the damage undergone by the structure in
each node or in each point of Gauss.
With this intention, in each node or each point of Gauss,
CALC_FATIGUE
:
·
reads in the structure of data result the equivalent stress of von Mises signed
(
VMIS_SG
) or the second signed invariant (
INVA_2SG
),
·
extract by a method of counting of cycles (method RAINFLOW) elementary cycles
of loading (history of the equivalent stress or equivalent deformation) undergone
by the structure,
·
determine the elementary damage associated with each elementary cycle,
·
determine the total damage undergone by the structure by a linear rule of office plurality while summoning
elementary damage.
Critical plan and maximum shearing: starting from a history of stresses calculated at the points of
Gauss (
SIEF_ELGA
, or SIEF_ELGA_DEPL) or with nodes (SIEF_NOEU_ELGA or SIGM_NOEU_DEPL)
and stored in a concept result of the type
evol_elas
or
evol_noli
,
D
years the case where the loading
is periodic, we calculate a field of size which contains inter alia: the half amplitude of
maximum shearing, the associated normal vector, the number of cycles to the rupture and the damage
corresponding to the points of Gauss or the nodes. If the loading is not periodical the field of
sizes contains the maximum damage and the normal vector associated the points of Gauss or
with the nodes.
Product a concept of the cham_elem_DOMMAG type or cham_elem_FACY_R or cham_no_FACY_R.
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Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A.M. DONORE
Key
:
U4.83.02-F1
Page:
2/20
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
2 Syntax
CHAM [cham_elem *] = CALC_FATIGUE
(
TYPE_CALCUL =/“CUMUL_DOMMAGE”,
/
“FATIGUE_MULTI”,
# If TYPE_CALCUL = “CUMUL_DOMMAGE” - > calculation of the damage
# Choice of the option of calculation
OPTION
=/“DOMA_ELNO_SIGM”
,
/
“DOMA_ELGA_SIGM”
,
/
“DOMA_ELNO_EPSI”
,
/
“DOMA_ELGA_EPSI”
,
/
“DOMA_ELNO_EPME”
,
/
“DOMA_ELGA_EPME”
,
# Reading of the history of stress or deformation
HISTORY = _F
(
RESULT
=
LMBO,/
[evol_elas]
/
[evol_noli]
/
[dyna_trans]
EQUI_GD =
/
“VMIS_SG”, [DEFECT]
/
“INVA_2_SG”,
)
# Calculation of the damage
DAMAGE =/“WOHLER”,
/
“MANSON_COFFIN”,
/
“TAHERI_MANSON”,
/
“TAHERI_MIXTE”
,
MATER
=
to subdue,
[to subdue]
TAHERI_NAPPE
=
tablecloth,
/
[tablecloth]
/
[formula]
TAHERI_FONC
=
fonc,
/
[function]
/
[formula]
),
# Finsi
# If TYPE_CALCUL = “FATIGUE_MULTI” - > Calculation of the maximum shearing or of
maximum damage
TYPE_CHARGE =/“PERIODIC”,
/
“NON_PERIODIQUE”,
OPTION
=
/
“DOMA_ELGA”,
/
“DOMA_NOEUD”,
RESULT
=
LMBO,/
[evol_elas]
/
[evol_noli]
CHAM_MATER =
cham_mater,
[cham_mater]
# If TYPE_CHARGE = “PERIODIC”
CRITERION =/“MATAKE”,
/“DANG_VAN_MODI_AC”,
METHOD =/“CERCLE_EXACT”,
# Finsi
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Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A.M. DONORE
Key
:
U4.83.02-F1
Page:
3/20
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
# If TYPE_CHARGE = “NON_PERIODIQUE”
CRITERION =/“DOMM_MAXI”,
/
“DANG_VAN_MODI_AV”,
/
“FATEMI_SOCIE”,
PROJECTION =/“UN_AXE”,
/
“DEUX_AXES”,
DELTA_OSCI =
/
delta,
[R]
/
0.,
[DEFECT]
# Finsi
/
MESH
=
mesh,
[mesh]
/
GROUP_MA
=
grma,
[l_gr_maille]
/
NET
=
my,
[l_maille]
/
GROUP_NO
=
grno,
[l_gr_noeud]
/
NODE
=
No,
[l_noeud]
COEF_PREECROU
=
/
coef_pre,
[R]
/
1.0, [DEFECT]
# If (GROUP_MA!= None gold NETS!= Nun gold \
GROUP_NO!= Nun gold NODE!= Nun)

# Finsi
# Finsi
# Level
of impression
INFORMATION =
/
1,
[DEFECT]
/2,
)
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Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A.M. DONORE
Key
:
U4.83.02-F1
Page:
4/20
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
3 Operands
3.1 Word
key
TYPE_CALCUL
This key word makes it possible to calculate is a field of damage of fatigue undergone by a structure, if
TYPE_CALCUL = “CUMUL_DOMMAGE”, is the critical plan in which shearing is maximum, if
TYPE_CALCUL = “FATIGUE_MULTI”.
The following table indicates the key words which are usable according to the type of selected calculation.
TYPE_CALCUL
Key word
Paragraph
“CUMUL_DOMMAGE”
OPTION
3.2
“CUMUL_DOMMAGE”
HISTORY
3.3
“CUMUL_DOMMAGE”
TOO BAD
3.4
“CUMUL_DOMMAGE”
MATER
3.5
“CUMUL_DOMMAGE”
TAHERI_NAPPE
3.6
“CUMUL_DOMMAGE”
TAHERI_FONC
3.7
“FATIGUE_MULTI”
TYPE_CHARGE
3.8
“FATIGUE_MULTI”
OPTION
3.9
“FATIGUE_MULTI”
RESULT
3.10
“FATIGUE_MULTI”
CHAM_MATER
3.11
“FATIGUE_MULTI”
CRITERION
3.12
“FATIGUE_MULTI”
METHOD
3.13
“FATIGUE_MULTI”
PROJECTION
3.14
“FATIGUE_MULTI”
DELTA_OSCI
3.15
“FATIGUE_MULTI”
GROUP_MA/MESH/GROUP_NO/NODE
3.16
“FATIGUE_MULTI” COEF_PREECROU
3.17
“FATIGUE_MULTI”
MESH
3.18

3.2 Word
key
OPTION
This key word factor makes it possible to specify the type of damage to be calculated:
·
“DOMA_ELNO_SIGM”
for the calculation of the damage to the nodes starting from a field of
stresses.
The structure of data result specified under the key word factor
RESULT
must contain it
field of reference symbol
EQUI_ELNO_SIGM
(calculable by CALC_ELEM), which defines between
other the value of the equivalent stress of von Mises signed (component
VMIS_SG
)
calculated with the nodes.
·
“DOMA_ELGA_SIGM”
for the calculation of the damage at the points of Gauss starting from a field of
stresses.
The structure of data result specified under the key word factor
RESULT
must contain it
field of reference symbol
EQUI_ELGA_SIGM
(calculable by CALC_ELEM), which defines between
other the value of the equivalent stress of von Mises signed (component
VMIS_SG
)
calculated at the points of Gauss.
·
“DOMA_ELNO_EPSI”
for the calculation of the damage to the nodes starting from a field of
deformations.
The structure of data result specified under the key word factor
RESULT
must contain it
field of reference symbol
EQUI_ELNO_EPSI
, which defines the value of the invariant amongst other things
of a signed nature 2 (component
INVA_2SG
) calculated with the nodes.
·
“DOMA_ELGA_EPSI”
for the calculation of the damage at the points of Gauss starting from a field of
deformations.
The structure of data result specified under the key word factor
RESULT
must contain it
field of reference symbol
EQUI_ELGA_EPSI
, which defines the value of the invariant amongst other things
of a signed nature 2 (component
INVA_2SG
) calculated at the points of Gauss.
background image
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A.M. DONORE
Key
:
U4.83.02-F1
Page:
5/20
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
·
“DOMA_ELNO_EPME”
for the calculation of the damage to the nodes starting from a field of
mechanical deformations, out-thermics:
=
-
B U
HT
.
.
The structure of data result specified under the key word factor RESULT must contain it
field of reference symbol EQUI_ELNO_EPME (calculable by CALC_ELEM), which defines between
other the value of the invariant of a signed nature 2 (component INVA_2SG) calculated with the nodes.
·
“DOMA_ELGA_EPME”
for the calculation of the damage at the points of Gauss starting from a field of
mechanical deformations, out-thermics:
=
-
B U
HT
.
.
The structure of data result specified under the key word factor RESULT must contain it
field of reference symbol EQUI_ELGA_EPME, which defines the value of the invariant amongst other things
of a signed nature 2 (component INVA_2SG) calculated at the points of Gauss.
3.3
Key word factor
HISTORY
This key word factor gathers all the phase of definition of the history of loading.
The history of loading is the evolution of a value of the stress or deformation during
time.
3.3.1 Operand
RESULT
RESULT = LMBO
Name of the concept result containing the stress fields or the fields of deformation
defining the history of loading. More precisely, the concept result must contain one of
fields of reference symbol
EQUI_ELNO_SIGM
,
EQUI_ELGA_SIGM
,
EQUI_ELNO_EPSI
,
EQUI_ELGA_EPSI
, EQUI_ELNO_EPME or EQUI_ELGA_EPME according to the desired option of calculation.
3.3.2 Operand
EQUI_GD
EQUI_GD =/“VMIS_SG”,
/
“INVA_2_SG”
To be able to calculate the damage undergone by a structure, a method of Wöhler, Manson-
Whetstone sheath or a method of Taheri, it is necessary to have a history of loading in stresses or in
deformations “uniaxial”. With this intention it is necessary to transform the tensor of stresses or the tensor of
deformations in a uniaxial field (scalar) “equivalent”.
“VMIS_SG”
to calculate the damage starting from a history of loading of the type
stress of von Mises signed,
“INVA_2_SG”
to calculate the damage starting from a history of loading of the type
invariant of a nature 2 signed of the deformation.
3.4 Operand
TOO BAD
To be able to calculate the damage undergone by a structure, the cycles should beforehand be extracted
elementary of the history of loading.
For that of many methods are available. Method available in Code_Aster for
calculation of the damage by the Wöhler method or Manson-Whetstone sheath, is the method of counting of
extended in cascade or method of Rainflow [R7.04.01].
For the calculation of the damage by the methods
TAHERI_MANSON
and
TAHERI_MIXTE
, one uses
method of counting known as natural which consists in generating cycles in the order of their application.
Once the extracted elementary cycles, this operand makes it possible to specify the method of calculation of
damage for each elementary cycle.
DAMAGE =/“WOHLER”
For a history of loading of the type forced, the number of cycles to the rupture is
determined by interpolation of the curve of Wöhler of material for a level of stress
alternated given (to each elementary cycle a level of amplitude of stress corresponds
=
-
max
min
and an alternate stress
S
alt
= 1 2
/
).
background image
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A.M. DONORE
Key
:
U4.83.02-F1
Page:
6/20
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
One cannot use the method
WOHLER
that for the options '
DOMA_ELNO_SIGM
'or
'
DOMA_ELGA_SIGM
'. Moreover, it is necessary that the concept specified result contains it respectively
field of reference symbol
EQUI_ELNO_SIGM
or
EQUI_ELGA_SIGM
(calculable by
CALC_ELEM).
The curve of Wöhler of material must be introduced into the operator
DEFI_MATERIAU
[U4.43.01],
under one of the three possible forms [R7.04.02]:
·
point by point discretized function (key word
TIRE
, operand
WOHLER
),
·
analytical form of Basquin (key word
TIRE
, operands
A_BASQUIN
and
BETA_BASQUIN
),
·
form “current area” (key word
TIRE
, operands
E_REFE
,
A0
,
A1
,
A2
,
A3
and
SSL
and word
key
ELAS
operand
E
).
Notice on the curves of fatigue:
For the small amplitudes, the problem of the prolongation of the curve of fatigue can
to pose: for example, for the curves of fatigue of the RCC-M beyond 10
6
cycles,
corresponding stress 180 MPa is regarded as limit of endurance, i.e.
that very forced lower than 180 MPa must produce a factor of null use, or one
an infinite number of cycles acceptable.
The method adopted here corresponds to this concept of limit of endurance: if the amplitude of
stress is lower than the first X-coordinate of the curve of fatigue, then one takes one
factor of null use i.e. a number of infinite acceptable cycle.
DAMAGE =/“MANSON_COFFIN”
For a history of loading of the deformations type, the number of cycles to the rupture is
determined by interpolation of the curve of Manson-Whetstone sheath of material for a level of
alternate deformation given (to each elementary cycle corresponds a level of amplitude of
deformation
=
-
max
min
and an alternate deformation
E
alt
= 1 2
/
).
One cannot use the method
MANSON_COFFIN
that for the options '
DOMA_ELNO_EPSI
'or
'
DOMA_ELGA_EPSI
', “DOMA_ELNO_EPME” or “DOMA_ELGA_EPME”. Moreover, it is necessary that it
concept specified result contains respectively the field of reference symbol
EQUI_ELNO_EPSI
,
EQUI_ELGA_EPSI
, EQUI_ELNO_EPME or EQUI_ELGA_EPME (calculable by
CALC_ELEM).
The curve of Manson-Whetstone sheath must be introduced into the operator
DEFI_MATERIAU
[U4.43.01] (word
key
TIRE
, operand
MANSON_COFFIN
).
DAMAGE =/“TAHERI_MANSON”
This method of calculation of the damage applies only to loadings of the deformation type,
i.e. for the options
“DOMA_ELNO_EPSI”
,
“DOMA_ELGA_EPSI”
,
“DOMA_ELNO_EPME”
or
“DOMA_ELGA_EPME”
. Moreover, it is necessary that the concept specified result contains it respectively
field of reference symbol
EQUI_ELNO_EPSI
,
EQUI_ELGA_EPSI
, EQUI_ELNO_EPME or
EQUI_ELGA_EPME (calculable by CALC_ELEM).
Are
N
elementary cycles of half amplitude
1
2
2
,
N
.
The calculation of the elementary damage of the first cycle is determined by interpolation on the curve
of Manson-Whetstone sheath of material.
background image
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A.M. DONORE
Key
:
U4.83.02-F1
Page:
7/20
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
The calculation of the elementary damage of the following cycles is determined by the algorithm described
below:
·
If
I
I
+
1
2
2
the calculation of the elementary damage of the cycle
(
)
I
+1
is determined by interpolation on
curve of Manson-Whetstone sheath.
·
If
I
I
+
<
1
2
2
one determines:
I
I
J I
J
I
I
Max
+
+
<
+
+
=










=




1
1
1
1
2
2
2
2
2
F
F
TABLECLOTH
FONC
,
*
where F
TABLECLOTH
is a tablecloth introduced under the operand
TAHERI_NAPPE
.
F
FONC
is
a function introduced under the operand
TAHERI_FONC
.
The value of the damage of the cycle
(
)
I
+1
is obtained by interpolation of
I
+1
2
*
on the curve of
Manson-whetstone sheath of material (
Nrupt
I
+1
= a number of cycles to the rupture for the cycle
(
)
I
I
+ =






+
1
2
1
MANSON_ WHETSTONE SHEATH
*
and
Dom
I
+1
= damage of the cycle
(
)
I
Nrupt
I
+ =
+
1
1
1
).
The curve of Manson-Whetstone sheath must be introduced into the operator
DEFI_MATERIAU
[U4.43.01] (word
key
TIRE
, operand
MANSON_COFFIN
).
Note:
1) Tablecloth or the formula introduced under the operand
TAHERI_NAPPE
is in fact
cyclic curve of work hardening with prestressed material.
2) The function or the formula introduced under the operand
TAHERI_FONC
is in fact
cyclic curve of work hardening of material.
3) Tablecloth or the formula introduced under the operand
TAHERI_NAPPE
, must have
“X”
and
“EPSI”
like parameters.
4) The function or the formula introduced under the operand
TAHERI_FONC
, must have for
parameter
“SIGM”
.
DAMAGE =/“TAHERI_MIXTE”
This method of calculation of the damage applies only to loadings of the deformation type,
i.e. for the options
“DOMA_ELNO_EPSI”
,
“DOMA_ELGA_EPSI”
,
“DOMA_ELNO_EPME”
or
“DOMA_ELGA_EPME”
. Moreover, it is necessary that the concept specified result contains it respectively
field of reference symbol
EQUI_ELNO_EPSI
,
EQUI_ELGA_EPSI
, EQUI_ELNO_EPME or
EQUI_ELGA_EPME (calculable by CALC_ELEM).
background image
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A.M. DONORE
Key
:
U4.83.02-F1
Page:
8/20
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Are
N
elementary cycles of half amplitude
1
2
2
,
N
.
The calculation of the elementary damage of the first cycle is determined by interpolation on the curve
of Manson-Whetstone sheath of material.
The calculation of the elementary damage of the following cycles is determined by the algorithm described
below:
·
If
I
I
+
1
2
2
the calculation of the elementary damage of the cycle
(
)
I
+1
is determined by interpolation on
curve of Manson-Whetstone sheath.
·
If
I
I
+
<
1
2
2
one determines:
I
I
J I
J
Max
+
+
<
=










1
1
2
2
2
F
TABLECLOTH
,
where F
TABLECLOTH
is a tablecloth introduced under the operand
TAHERI_NAPPE
.
The value of the damage of the cycle
(
)
I
+1
is obtained by interpolation of
I
+1
2
on the curve of
Wöhler of material (
Nrupt
I
+1
= a number of cycles to the rupture for the cycle
(
)
I
I
+ =




+
1
2
1
WOHLER
and
Dom
I
+1
= damage of the cycle
(
)
I
Nrupt
I
+ =
+
1
1
1
).
This method requires the data of the curves of Wöhler and Manson-Whetstone sheath of the material, which
must be introduced into the operator
DEFI_MATERIAU
[U4.43.01] (key word factor
TIRE
).
Note:
1) Tablecloth or the formula introduced under the operand
TAHERI_NAPPE
is in fact
cyclic curve of work hardening with prestressed material.
2) Tablecloth or the formula introduced under the operand
TAHERI_NAPPE
, must have
“X”
and
“EPSI”
like parameters.
3.5 Operand
MATER
MATER = to subdue
Allows to specify the name of material
to subdue
created by
DEFI_MATERIAU
[U4.43.01].
The material
to subdue
must contain the definition of the curve of Wöhler of material for the calculation of
damage by the methods
“WOHLER”
and
“TAHERI_MIXTE”
and the definition of the curve of
Manson-whetstone sheath of material for the calculation of the damage by the methods
“MANSON_COFFIN”
,
“TAHERI_MANSON”
and
“TAHERI_MIXTE”
.
background image
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A.M. DONORE
Key
:
U4.83.02-F1
Page:
9/20
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
3.6 Operand
TAHERI_NAPPE
This operand makes it possible to specify the name of a tablecloth F
TABLECLOTH
2,
MAX




necessary to the calculation of
damage by the methods
“TAHERI_MANSON”
and
“TAHERI_MIXTE”
.
The tablecloth must have
“X”
and
“EPSI”
like parameters.
Note:
This tablecloth is in fact the cyclic curve of work hardening with prestressed material.
3.7 Operand
TAHERI_FONC
This operand makes it possible to specify the name of a function F
FONC
2




necessary to the calculation of
damage by the method
“TAHERI_MANSON”
.
The parameter of this function must be '
SIGM'
.
Note:
This function is in fact the cyclic curve of work hardening of material.
3.8 Operand
TYPE_CHARGE
This operand makes it possible to specify the type of loading applied to the structure:
·
PERIODIC, the loading is periodic;
·
NON_PERIODIQUE, the loading are not periodical.
3.9 Operand
OPTION
This operand makes it possible to specify the place where postprocessing will be made:
·
DOMA_ELGA, postprocessing are made at the points of Gauss of the mesh;
·
DOMA_NOEUD, postprocessing are made with the nodes of the mesh or part of the mesh, cf.
operands: GROUP_MA, MESH, GROUP_NO and NO.
3.10 Operand
RESULT
RESULT = LMBO
Name of the concept result containing the stress fields defining the history of loading.
More precisely, the concept result must contain the field of reference symbol
SIEF_ELGA
and/or
SIEL_ELGA_DEPL
and/or
SIEF_NOEU_ELGA
and/or
SIGM_NOEU_DEPL
.
3.11 Operand
CHAM_MATER
CHAM_MATER = cham_mater
Allows to specify the name of the field of material
cham_mater
created by
AFFE_MATERIAU
[U4.43.03].
The material
to subdue
defined with the control
DEFI_MATERIAU
and which is used for the assignment of
material with the mesh with the control
AFFE_MATERIAU
must contain the definition of the curve
of Wöhler as well as information necessary to the implementation of the criterion, to see the key words
factors TIRES and CISA_PLAN_CRIT of control DEFI_MATERIAU [U4.43.01].
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3.12 Operand
CRITERION
CRITERION =/“MATAKE”,
/“DANG_VAN_MODI_AC”,
/“DOMM_MAXI”,
/“DANG_VAN_MODI_AV”,
/“FATEMI_SOCIE”,
Allows to specify the name of the criterion which half amplitude of shearing will have to satisfy to it
maximum.
()
() ()
.
elasticity
of
limit
;
wise
préécrouis
possible
one
count
in
to take
with
being useful
T
coeffician
;
that
hydrostati
pressure
;
alternated
pure
N
compressio
-
traction
in
endurance
of
limit
;
alternated
pure
NT
cisailleme
in
endurance
of
limit
;
normal
of
plan
on
normal
maximum
stress
;
normal
of
plan
one
in
N
déformatio
in
NT
cisailleme
of
amplitude
;
normal
of
plan
one
in
stress
in
NT
cisailleme
of
amplitude
;
maximum
is
NT
cisailleme
of
amplitude
which
in
plan
with
normal
:
Notation
:
:
:
:
:
:
:
:
:
*
0
0
max
y
p
C
P
D
NR
N
N
N
N
N
N
N
Criterion of MATAKE
()
()
B
NR
has
+
*
*
2
max
N
N
éq
3.12-1
where
has
and
B
are two constant data by the user under key words MATAKE_A and
MATAKE_B of the key word factor CISA_PLAN_CRIT of DEFI_MATERIAU, they depend on
characteristics materials and are worth:
.
2
2
0
0
0
0
=


-
=
B
D
D
has
If the user has the results of two tensile tests compression, alternated and the other
not, the constant ones
has
and
B
are given by:
(
)
(
)
(
)
,
2
2
,
2
1
1
2
2
1
1
2
×
+
-
=
-
-
-
=
m
m
m
B
has
with
1
the amplitude of loading for the alternate case
(
)
0
=
m
and
2
the amplitude of
loading for the case where the mean stress is nonnull
(
)
0
m
.
Moreover, we define an equivalent stress within the meaning of MATAKE, noted
()
*
N
eq
:
()
()
()
,
*
*
2
*
max
T
F
NR
has
C
p
eq


+
=
N
N
N
where
T
F
/
represent the report/ratio of the limits of endurance in bending and alternating torsion, and must be
informed under key word COEF_FLEX_TORS of the key word factor CISA_PLAN_CRIT of
DEFI_MATERIAU.
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Page:
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Criterion DANG_VAN_MODI_AC
()
B
P
has
+
*
2 N
éq
3.12-2
where
has
and
B
are two constant data by the user under key words D_VAN_A and D_VAN_B
key word factor CISA_PLAN_CRIT of DEFI_MATERIAU, they depend on the characteristics
materials. If the user has two tensile tests compression, alternate
the other not constants
has
and
B
are worth:
(
)
(
)
(
)
,
2
2
2
2
3
1
1
2
2
1
1
2
×
+
-
=
-
-
-
×
=
m
m
m
B
has
with
1
the amplitude of loading for the alternate case
(
)
0
=
m
and
2
for the case where
mean stress is nonnull
(
)
0
m
.
Moreover, we define an equivalent stress within the meaning of DANG VAN, noted
()
*
N
eq
:
()
()
,
*
2
*
T
C
P
has
C
p
eq


+
=
N
N
where
T
C/
represent the report/ratio of the limits of endurance in alternated shearing and traction, and must
to be well informed under key word COEF_CISA_TRAC of the key word factor CISA_PLAN_CRIT of
DEFI_MATERIAU.
For more information, to consult the document [R7.04.04].
Criterion DOMM_MAXI
Criterion DOMM_MAXI is an evolution of the criterion of MATAKE. Contrary to the two criteria
precedents, this criterion selects the critical plan according to the damage calculated in each
plan. It is the plan in which the damage is maximum which is retained. This criterion is adapted to
nonperiodic loadings, which induces the use of a method of counting of cycles so
to calculate the elementary damage. To count the cycles, we use the method
RAINFLOW.
The once known elementary damage is cumulated linearly to determine it
too bad.
To calculate the elementary damage we project the history of the stresses of
shearing on one or two axes in order to reduce the aforementioned to a unidimensional function time
()
T
F
p
=
. After having extracted the elementary under-cycles from
p
with method RAINFLOW
we define an elementary equivalent stress for any elementary under-cycle
I
:
()
()
()
(
)
()
()
(
)
()
()
(
)
,
0
,
,
2
,
,
2
max
1
max
2
1
2
1




+
-
=
N
N
N
N
N
N
N
I
I
IP
IP
IP
IP
p
ieq
NR
NR
aMax
Min
Max
C
éq 3.12-3
with
N
the normal of the plan running,
()
N
ip1
and
()
N
ip2
values of shear stresses
projected under-cycle
I
and
()
N
I
NR
1
max
and
()
N
I
NR
2
max
maximum normal stresses of
under-cycle
I
. From
()
N
ieq
and of a curve of fatigue we determine the number of cycles
with the elementary rupture
()
N
I
NR
and corresponding damage
()
()
N
N
I
I
NR
D
/
1
=
. In
[éq 3.12-3]
is a corrective term which makes it possible to use a curve of fatigue in
traction and compression. Constants
and
has
must be well informed under the key words
DOMM_A and COEF_CISA_TRAC of the key word factor CISA_PLAN_CRIT of DEFI_MATERIAU.
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We use a linear office plurality of damage. That is to say
K
the number of elementary under-cycles, for
a normal
N
fixed, the cumulated damage is equal to:
()
()
.
1
=
=
K
I
I
D
D
N
N
éq
3.12-4
To determine the normal vector
*
N
corresponding to the maximum cumulated damage we make
to vary
N
, the normal vector
*
N
corresponding to the maximum cumulated damage is then given by:
()
()
(
)
.
*
N
N
N
D
Max
D
=
Criterion DANG_VAN_MODI_AV
The step and the techniques implemented to calculate this criterion are identical to those
used for criterion DOMM_MAXI. The only difference lies in the definition of the stress
equivalent elementary where hydrostatic pressure
p
replace the maximum normal stress
max
NR
:
()
()
()
(
)
()
()
(
)
() ()
(
)
.
0
,
,
2
,
,
2
1
2
1
2
1




+
-
=
N
N
N
N
N
N
N
I
I
IP
IP
IP
IP
p
ieq
P
P
aMax
Min
Max
C
Constants
and
has
are to be informed by the user under key words D_VAN_A and
COEF_CISA_TRAC of the key word factor CISA_PLAN_CRIT of DEFI_MATERIAU.
For more information to consult the document [R7.04.04].
Criterion of FATEMI_SOCIE
The criterion of FATEMI and SOCIE is defined by the relation:
()
()
()




+
=
y
eq
N
NR
K
N
N
max
1
2
where
K
is a constant which depends on the characteristics materials. Contrary to the others
criteria, it uses shearing in deformation instead of shearing in stress. Moreover, them
various quantities which contribute to the criterion are multiplied and not added. The criterion of
FATEMI and SOCIE are usable after an elastic design or elastoplastic. This criterion selects
the plan criticizes according to the damage calculated in each plan. It is the plan in which
damage is maximum which is retained.
This criterion is adapted to the nonperiodic loadings, which leads us to use the method
of counting of cycles RAINFLOW to calculate the elementary damage. Damage
elementary are then cumulated linearly to determine the damage.
In order to calculate the elementary damage we project the history of shearing in
deformation on one or two axes in order to reduce the aforementioned to a unidimensional function time
()
T
F
p
=
. After having extracted the elementary under-cycles with method RAINFLOW us
let us define an elementary equivalent deformation for any elementary under-cycle
I
:
()
()
()
(
)
()
()
(
)
()
()
(
)
(
)
0
,
,
1
2
,
,
2
max
1
max
2
1
2
1
N
N
N
N
N
N
N
I
I
IP
IP
IP
IP
p
ieq
NR
NR
aMax
Min
Max
C
+




-
=
éq 3.12-5
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with
N
,
y
K
has
=
the normal in the plan running,
()
()
N
N
IP
IP
2
1
and
values of shearings in
deformation projected of the under-cycle
I
,
()
()
N
N
I
I
NR
NR
2
max
1
max
and
being two values of the stress
maximum normal of the under-cycle
I
. From
()
N
ieq
and of a curve of Manson-Whetstone sheath us
let us determine the number of cycles to the elementary rupture
()
N
I
NR
and corresponding damage
()
()
N
N
I
I
NR
D
/
1
=
.
In the equation [éq 3.12-5]
is a corrective term which to use a curve of Manson-Whetstone sheath obtained
in traction compression.
p
C
is a coefficient which makes it possible to take into account possible
préécrouissage.
Constants
has
and
must be well informed under key words FATSOC_A and COEF_CISA_TRAC
key word factor CISA_PLAN_CRIT of control DEFI_MATERIAU.
As we use a linear office plurality of damage, if
m
is the number of under-cycles
elementary, then for a normal
N
fixed, the cumulated damage is equal to:
()
()
=
=
m
I
I
D
D
1
N
N
To find the vector normal
*
N
corresponding to the maximum cumulated damage we vary
N
.
The normal vector
*
N
associated the maximum cumulated damage is then given by:
()
()
(
)
N
N
N
D
Max
D
=
*
3.13 Operand
METHOD
METHOD = “CERCLE_EXACT”
Allows to specify the name of the method which will be used to calculate to it half amplitude of
maximum shearing.
The method of the “CERCLE_EXACT” is used to determine the circle circumscribed at the points which are
in plans of shearing. This method rests on the process which consists in obtaining it
ring which passes by three points, cf document [R7.04.04].
3.14 Operand
PROJECTION
If the loading is not periodical, it is necessary to project the history of
shearing on one or two axes, cf document [R7.04.04].
·
UN_AXE, the history of shearing are projected on an axis;
·
DEUX_AXES, the history of shearing are projected on two axes.
3.15 Operand
DELTA_OSCI
DELTA_OSCI =/delta,
/
0.0,
Filtering of the history of the loading. In all the cases, if the function remains constant or
decreasing on more than two consecutive points one removes the intermediate points for
to keep that two extreme points. Then, one removes history of loading the points for
which the variation of the value of the stress is lower than the value
delta
. By defect
delta
is equal to zero, which amounts keeping all the oscillations of the loading, even those of weak
amplitude. For more information to see the documentation of the control
POST_FATIGUE
,
[U4.83.01], even operand.
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3.16 Operands
GROUP_MA/MESH/GROUP_NO/NODE
GROUP_MA = lgma,
The options are calculated on the groups of meshs contained in the list lgma.
NET = lma,
The options are calculated on the meshs contained in the list lgma.
GROUP_NO = lgno,
The options are calculated on the groups of nodes contained in the list lgno.
NODE = lno,
The options are calculated on the nodes contained in the list lno.
3.17 Operand
COEF_PREECROU
COEF_PREECROU =/coef_pre,
/
1.0,
This coefficient is used to take into account the effect of possible a préécrouissage.
3.18 Operand
MESH
MESH = mesh,
Allows to specify the name of the mesh given by the user.

3.19 Operand
INFORMATION
INFORMATION =
/
1
Impression:
·
no impression

/2
Impression:
·
parameters of the calculation of the damage (a number of the sequence numbers, numbers
points of calculation, type of the calculation of the damage (forced, deformations), localization
damage (nodes or points of Gauss), type of the equivalent component
(
VMIS_SG
or
INVA_2SG
), method of extraction of cycles (RAINFLOW) and method
of calculation of the damage (
WOHLER
or
MANSON_COFFIN
or
TAHERI_MANSON
or
TAHERI_MIXTE
).
·
point by point of the history of loading, of the cycles extracted and the value from
too bad.
·
field of damage.

The impressions are made in the file
MESSAGE
.
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4 Example
One will be able to refer to test SZLZ105 concerning the damage and the office plurality of damage, with
tests SSLV135a and SSLV135b as regards relating to the periodic loadings like with the tests
SSLV135c and SSLV135d for the case where the loading is not periodical.

4.1
Calculation of the equivalent history of loading
DEPL
=
CALC_ELEM
(
reuse
=
DEPL,
MODEL
=
CPLAN,
CHAM_MATER =
CHECHMATE,
OPTION
=
(
“SIEF_ELGA_DEPL”,
“EPSI_ELGA_DEPL”,
“EQUI_ELGA_SIGM”,
“EQUI_ELGA_EPSI”,
“EQUI_ELNO_SIGM”,
“EQUI_ELNO_EPSI”,
),
RESULT
=
DEPL
)

4.2
Definition of the curve of Wöhler of material and associated damage
WOHL = DEFI_FONCTION (
NOM_PARA
=
“SIGM”,
VALE =
(
0.
,
1000.,
10.
, 0.,
),
PROL_DROITE
=
“LINEAR”,
PROL_GAUCHE
=
“LINEAR”,
TITRATE
=
'FUNCTION
OF
WOHLER'
)

# Definition of material

= DEFI_MATERIAU SUBDUE (FATIGUE = _F (WOHLER = WOHL))

# Calculation of the damage to the nodes starting from the history of stress of von
Settings signed (the loading being homogeneous with stresses, damage
calculate by interpolation on a curve of Wöhler of material).

DMG_WOHL = CALC_FATIGUE (
TYPE_CALCUL = “CUMUL_DOMMAGE”,
OPTION
=
“DOMA_ELNO_SIGM”,
HISTORY
=_F
(RESULT = DEPL,
EQUI_GD
=
“VMIS_SG”,
)
DAMAGE =
“WOHLER”,
MATER
=
SUBDUE,
INFORMATION =
2
)
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4.3 Definition of the curve of
Manson_Coffin
material and damage
associated
MANS = DEFI_FONCTION (
NOM_PARA
=
“EPSI”,
VALE =
(
0.
,
1000.,
10.
, 0.,
),
PROL_DROITE
=
“LINEAR”,
PROL_GAUCHE
=
“LINEAR”,
TITRATE
=
'FUNCTION
OF
MANSON
COFFIN'
)
# Definition of material
MAT1 = DEFI_MATERIAU (FATIGUE = _F (MANSON_COFFIN = MANS))
# Calculation of the damage to the nodes starting from the history of the value of
the invariant of a nature 2 signed (the loading being homogeneous with deformations,
the damage is calculated by interpolation on a curve of Manson_Coffin of
material).
DMG_MCOF = CALC_FATIGUE (
TYPE_CALCUL = “CUMUL_DOMMAGE”,
OPTION
=
“DOMA_ELNO_EPSI”,
HISTORY
=_F (RESULT
=
DEPL,
EQUI_GD
=
“INVA_2_SG”,
),
DAMAGE =
“MANSON_COFFIN”,
MATER
=
MAT1,
INFORMATION =
2
)

4.4 Definition of the curves of cyclic work hardening and work hardening
cyclic with prestressing
F_NAPPE = DEFI_NAPPE (
NOM_PARA = “X”,
PROL_DROITE
=
“LINEAR”,
PROL_GAUCHE
=
“LINEAR”,
PARA = (0.5, 1.,),
NOM_PARA_FONC
=
“EPSI”,
DEFI_FONCTION
=_F (
PROL_DROITE
=
“LINEAR”,
PROL_GAUCHE
=
“LINEAR”,
VALE
=
(
0.,
25.,
10., 525.,),
)
_F (
PROL_DROITE
=
“LINEAR”,
PROL_GAUCHE
=
“LINEAR”,
VALE
=
(
0. , 50.,
10., 550.,))),
TITRATE
=
'TABLECLOTH
of
TAHERI'
)
F_FONC = DEFI_FONCTION (
NOM_PARA
= “SIGM”,
PROL_DROITE
=
“LINEAR”,
PROL_GAUCHE
=
“LINEAR”,
PARA =
(
0.,
0.,
100.,
10.,),
TITER=' FUNCTION
of
TAHERI')
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4.5 Calculation of the damage by the methods
“TAHERI_MANSON”
and
“TAHERI_MIXTE”
MAT2 = DEFI_MATERIAU (
TIRE = _F (
WOHLER = WOHL,
MANSON_COFFIN
=
MANS
)
)
DMG_TMA = CALC_FATIGUE (
TYPE_CALCUL = “CUMUL_DOMMAGE”,
OPTION
=
“DOMA_ELNO_EPSI”,
HISTORY
=_F (RESULT
=
DEPL,
EQUI_GD
=
“INVA_2_SG”
)
DAMAGE =
“TAHERI_MANSON”,
MATER
=
MAT2,
TAHERI_NAPPE
=
F_NAPPE,
TAHERI_FONC
=
F_FONC,
INFORMATION =
2
)
DMG_TMI = CALC_FATIGUE (
TYPE_CALCUL = “CUMUL_DOMMAGE”,

OPTION
=
“DOMA_ELNO_EPSI”,
HISTORY
=_F (RESULT
=
DEPL,
EQUI_GD
=
“INVA_2_SG”
),
DAMAGE =
“TAHERI_MIXTE”,
MATER
=
MAT2,
TAHERI_NAPPE
=
F_NAPPE,
INFORMATION =
2
)
4.6
Calculation of the half amplitude of maximum shearing by the method:
“CERCLE_EXACT”
This example is drawn from the case test SSLV135a. Ici the loading is periodic and the damage is calculated
at the points of Gauss.
STEEL = DEFI_MATERIAU (ELAS =_F (E = 200000.,
NAKED = .3,
ALPHA = 0. ),
TIRE =_F (WOHLER = WHOL,),
CISA_PLAN_CRIT =_F (CRITERION = “MATAKE”,
COEF_FLEX_TORS = 1.5,
MATAKE_A = 1.0,
MATAKE_B = 2.0,)
)
CHECHMATE = AFFE_MATERIAU (MESH = CUBIC,
AFFE =_F (ALL = “YES”,
MATER = STEEL,
TEMP_REF = 20. )
)
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SOL_NL = STAT_NON_LINE (TITLE =
“TEST ALTERNATE TRACTION AND COMPRESSION - CRITICAL PLAN”,
MODEL = TROISD,
CHAM_MATER = CHECHMATE,
EXCIT =_F (LOAD = TR_CS,
FONC_MULT = COEFF,
TYPE_CHARGE = “FIXE_CSTE”),
COMP_ELAS =_F (RELATION = “ELAS”,
DEFORMATION = “SMALL”,
ALL = “YES”),
INCREMENT =_F (LIST_INST = LINST,),
NEWTON =_F (MATRIX = “ELASTIC”,
REAC_INCR = 0))
FATI_NL=CALC_FATIGUE (TYPE_CALCUL = “FATIGUE_MULTI”,
OPTION = “DOMA_ELGA”,
TYPE_CHARGE = “PERIODIC”,
RESULT = SOL_NL,
CHAM_MATER = CHECHMATE,
CRITERION = “MATAKE”,
COEF_PREECROU = 1.0,
METHOD = “CERCLE_EXACT”
)
4.7
Calculation of the damage when the loading is not periodical
This example is drawn from the case test SSLV135d. Ici the loading is not periodic, the damage is
calculated at the points nodes on part of the whole of the mesh:
“FACE1”
,
“FACE3”
and
“FACE5”
.
STEEL = DEFI_MATERIAU (ELAS =_F (E = 200000.,
NAKED = .3,
ALPHA = 0. ),
TIRE =_F (WOHLER = WHOL,),
CISA_PLAN_CRIT =_F (CRITERE= “DANG_VAN_MODI_AV”,
D_VAN_A = 1.0,
D_VAN_B = 2.0,
COEF_CISA_TRAC = 1.5)
)
CHECHMATE = AFFE_MATERIAU (MESH = CUBIC,
AFFE =_F (ALL = “YES”,
MATER = STEEL,
TEMP_REF = 20. ))
SOL_L = MECA_STATIQUE (TITLE =
“TEST ALTERNATE TRACTION AND COMPRESSION - DANG_VAN_MODI_AV”,
MODEL = TROISD,
CHAM_MATER = CHECHMATE,
EXCIT =_F (LOAD = TR_CS,
FONC_MULT = COEFF),
LIST_INST = LINST,
)
SOL_L = CALC_ELEM (reuse = SOL_L,
RESULT = SOL_L,
OPTION = “SIGM_ELNO_DEPL”,
)
SOL_L = CALC_NO (reuse = SOL_L,
RESULT = SOL_L,
OPTION = “SIGM_NOEU_DEPL”
)
background image
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A.M. DONORE
Key
:
U4.83.02-F1
Page:
19/20
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
FATI_LNO2=CALC_FATIGUE (TYPE_CALCUL = “FATIGUE_MULTI”,
OPTION = “DOMA_NOEUD”,
TYPE_CHARGE = “NON_PERIODIQUE”,
RESULT = SOL_L,
CHAM_MATER = CHECHMATE,
GROUP_MA = (“FACE1”, “FACE3”, “FACE5”),
MESH = CUBIC,
CRITERION = “DANG_VAN_MODI_AV”,
COEF_PREECROU = 1.0,
PROJECTION = “DEUX_AXES”,
)
4.8
Calculation of the damage with criterion FATEMI_SOCIE
This example is drawn from the case SSLV135e test. Here the loading is not periodic, the damage is
calculated with the nodes on part of the whole of the mesh:
“FACE1”
,
“FACE2”
and
“FACE3”
.
STEEL = DEFI_MATERIAU (ELAS =_F (E = 200000.,
NAKED = 0.3,
ALPHA = 0.0),
TIRE =_F (MANSON_COFFIN = MANCOF,),
CISA_PLAN_CRIT =_F (CRITERION = “FATEMI_SOCIE”,
FATSOC_A = 1.0,
COEF_CISA_TRAC = 1.5)
)
CHECHMATE = AFFE_MATERIAU (MESH = CUBIC,
AFFE =_F (ALL = “YES”,
MATER = STEEL,
TEMP_REF = 20. ))


# CALCULATION WITH STAT_NON_LINE
# -------------------------
SOL_NL = STAT_NON_LINE (TITLE =
“TEST ALTERNATE TRACTION AND COMPRESSION - FATEMI_SOCIE”,
MODEL = TROISD,
CHAM_MATER = CHECHMATE,
EXCIT =_F (LOAD = TR_CS,
FONC_MULT = COEFF,
TYPE_CHARGE = “FIXE_CSTE”),
COMP_ELAS =_F (RELATION = “ELAS”,
DEFORMATION = “SMALL”,
ALL = “YES”),
INCREMENT =_F (LIST_INST = LINST,),
NEWTON =_F (MATRIX = “ELASTIC”,
REAC_INCR = 0))
SOL_NL = CALC_ELEM (reuse = SOL_NL,
RESULT = SOL_NL,
OPTION = (“EPSI_ELGA_DEPL”,
“SIEF_ELNO_ELGA”,
“EPSI_ELNO_DEPL”)
)
SOL_NL = CALC_NO (reuse = SOL_NL,
RESULT = SOL_NL,
ALL = “YES”,
GROUP_MA_RESU = (“FACE1”, “FACE2”, “FACE3”),
OPTION = (“SIEF_NOEU_ELGA”, “EPSI_NOEU_DEPL”)
)
background image
Code_Aster
®
Version
8.2
Titrate:
Operator
CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A.M. DONORE
Key
:
U4.83.02-F1
Page:
20/20
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
F_NLNO2A=CALC_FATIGUE (TYPE_CALCUL = “FATIGUE_MULTI”,
OPTION = “DOMA_NOEUD”,
TYPE_CHARGE = “NON_PERIODIQUE”,
RESULT = SOL_NL,
CHAM_MATER = CHECHMATE,
COEF_PREECROU = 1.0,
GROUP_MA = (“FACE1”, “FACE2”, “FACE3”),
MESH = CUBIC,
CRITERION = “FATEMI_SOCIE”,
PROJECTION = “DEUX_AXES”,
)