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EVP-NH
Description
ELASTO VISCO PLASTIC CONSTITUTIVE LAW FOR SOLID ELEMENTS AT VARIABLE TEMPERATURE (Norton-Hoff)
Implemented by: Name of developer + approximate date of implementation
Project:
The model
Coupled dynamic recrystallisation-thermo mechanical analysis of elasto visco plastic solids undergoing large strains.
JAUMANN stress rate is used
IANA= 2, 3, 5:
PASCON F (1998), Charles JF (1999)
See report RW2748 (1, 8, 17, 24) and intermediate report of April '98 on continuous casting research for ARBED.
For details on equations used in analytical compliance matrix computation, see appendix D of April '98 report on continuous casting research for ARBED.
IANA= 4:
Charles JF (1997)
See intermediate report RW2748 (17, 24)
Files
Prepro: LNHC2.F
Lagamine: NHIC2E.F (IANA= 2, 3 or 5) or NHIC3D.F (IANA= 4)
Subroutines
In the following table, fill in the file (*.F) and the names of the subroutines used by the law. Generic subroutines such as ‘ANNULD’ (putting a vector to zero) or ‘MST_SOLVE’ (computing the solution to a system of linear equations) do not need to be listed here.
| File | Subroutine | Description |
|---|---|---|
| XXX.F | XXX | Main subroutine of the law |
Availability
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | YES |
| Generalized plane state | YES |
Input file
The following section indicates the parameters to be written in the *.lag file. The parameters should be listed in tables. For better understanding, the table should indicate the line numer and the format in the headline, then the list of parameters (see example below). Sub-sections can be used to separate different categories of parameters (integer, real).
Parameters defining the type of constitutive law
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 270 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| 1 Line (7I5) | |
|---|---|
| NINTV | number of sub-steps used to integrate numerically the constitutive equation in a time step. If NINTV < 0 or = 0, then the number of sub-steps will be computed automatically |
| NTEMP | number of temperatures at which material data (E, ANU and ALPHA) are given |
| IDYN | = 1: if recrystallisation computation |
| = 0: else | |
| ICHP2 | = 2: if parameters K0, p1, p2, p3, p4 are given at several temperatures |
| = 1: if p2= FORMULE 1 (only if nodes temperature in Kelvin !!!) | |
| any other value if p2= FORMULE 2 (only if nodes temperature in Kelvin !!!) | |
| IALG | = 1: if enthalpic formulation for ALPHA |
| = 0: if classical formulation for ALPHA | |
| MAXITER | = maximum number of iteration in elastic field |
| ≤ 0: set default value = 50 | |
| NTEMP2 | number of temperatures at which parameters K0, p1, p2, p3, p4 are given (only if ICHP2 = 2) |
Real parameters
| 1 Line repeated NTEMP times (4G10) Note: parameters introduced by increasing temperature order |
|
|---|---|
| T | Temperature |
| E | YOUNG’s elastic modulus at temperature T |
| ANU | POISSON’s ratio at temperature T |
| ALPHA | Thermal expansion coefficient (α) at temperature T. Even if IALG = 1, ALPHA must be introduced at temperature T. In this case, FORMULE will be automatically computed |
| If ICHP2 = 2: 1 Line repeated NTEMP2 times (6G10) Note: parameters introduced by increasing temperature order |
|
| T | Temperature |
| K0 | See X for formula |
| P1 | A ADAPTER |
| P2 | see 4.4 for more information |
| P3 | |
| P4 | |
| If ICHP2 ≠ 2: 2 Lines (5G10/4G10) (only if nodes temperature in Kelvin !!!) | |
| AK0 | See X for formula |
| C1 | A ADAPTER |
| C2 | see 4.4 for more information |
| C3 | |
| C4 | |
| C5 | |
| C6 | |
| P3 | (be careful : 0 < P3 < 1) |
| P4 | |
| 1 Line (4G10) | |
| TQ | Taylor-Quinney’s coefficient. Absolute value between 0 and 1 : < 0 when thermal analysis within a semi-coupled analysis > 0 for other cases (total coupled analysis or mechanical analysis within a semi-coupled analysis) |
| PRECVG | precision in VGMOY calculation (3D state only) ≤ 0 set default value = 1.10-5 |
| PRECELA | precision in elastic computation ≤ 0 set default value = 1.10-4 |
| EPSINC | increment of deformation for the automatic computation of NINTV ≤ 0 set default value = 1.10-3 |
| If IDYN = 1: 4 Lines (3I5/4G10.0/4G10.0/2G10.0) | |
| ICOUPL | = 1 : the recrystallisation is coupled |
| = 0: the recrystallisation is uncoupled | |
| ITYPEPS | = 0 : the equations defining the beginning and the end of the recryst. have the form : FORMULE |
| = 1 : the equations defining the beginning and the end of the recryst. have the form : FORMULE | |
| = 2 : the equations defining the beginning and the end of the recryst. have the form : FORMULE | |
| NSSMAX | used if ICOUPL = 1: Maximum number of sub-structures The precision on the recryst. fraction is 1/NSSMAX |
| Q1 | parameters for the beginning of the recrystallisation: εc |
| Q2 | parameters for the beginning of the recrystallisation: εc |
| Q3 | parameters for the beginning of the recrystallisation: εc |
| Q4 | parameters for the beginning of the recrystallisation: εc |
| Q1 | parameters for the end of the recrystallisation: εs |
| Q2 | parameters for the end of the recrystallisation: εs |
| Q3 | parameters for the end of the recrystallisation: εs |
| Q4 | parameters for the end of the recrystallisation: εs |
| ACTIV | Activation energy for Zener computation : FORMULE with T the temperature and R the Boltzman gas constant |
| EXPO | Exponent for the AVRAMI law : FORMULE |
NOTE: ISTRA(3) parameter of the execution file:
Units:
= 0 analytical compliance matrix used (default value)
= 1 perturbation method
Tens:
= 0 mean velocities gradient (default value)
= 1 initial velocities gradient
Hundreds:
= 0 yield limit given by intersection between N-H curve and Young’s straight line
= 1 yield limit given by K0 (given parameter – see below)
Information about EVP-NH:
For the 1D case, we have:
FORMULE
The parameters K0, P1, P2, P3, P4 can be given at several temperatures (ICHP2 = 2)
Otherwise: (ICHP2 ≠ 2)
Formule 1
Formule 2
Formule 3
Stresses
Number of stresses
6 for 3D state
4 for the other cases
Meaning
The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates.
For the 3-D state:
| SIG(1) | $\sigma_{xx}$ |
| SIG(2) | $\sigma_{yy}$ |
| SIG(3) | $\sigma_{zz}$ |
| SIG(4) | $\sigma_{xy}$ |
| SIG(5) | $\sigma_{xz}$ |
| SIG(6) | $\sigma_{yz}$ |
For the other cases:
| SIG(1) | $\sigma_{xx}$ |
| SIG(2) | $\sigma_{yy}$ |
| SIG(3) | $\sigma_{xy}$ |
| SIG(4) | $\sigma_{zz}$ |
State variables
Number of state variables
27
List of state variables
| Q(1) | thickness |
| Q(2) | equivalent stress (effective if icoupl=1) |
| Q(3) | equivalent strain |
| Q(4) | equivalent strain rate |
| Q(5) | instantaneous thermal flow (effective if icoupl=1) |
| Q(6) | plastic dissipation (effective if icoupl=1) |
| Q(7) | ΔT |
| Q(8) | RHOC capacity |
| Q(9) | LN (ZENER) |
| Q(10) | recrystallised fraction since the beginning of the simulation |
| Q(11) | recrystallised fraction on this step |
| Q(12) | elastic part on this step – in percent (>0 : loading ; <0 : unloading) (effective if icoupl=1) |
| Q(13) | number of sub-structures |
| Q(14) | volumic fraction of the unrecrystallised sub-structure |
| Q(15) | effective equivalent strain |
| Q(16) | equivalent strain standard deviation |
| Q(17) | = 0 if always elastic state since the beginning = 1 if any previous step has been performed in visco-plastic domain |
| Q(18) | recrystallised fraction during previous step |
| Q(19) | |
| Q(20) | |
| Q(21) | |
| Q(22) | |
| Q(23) | |
| Q(24) | |
| Q(25) | triaxiality (BLZ2T) |
| Q(26) | shape parameter of the element (BLZ2T) |
| Q(27) | Remeshing parameter (BLZ2T) |
