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EVP-NH
Description
ELASTO VISCO PLASTIC CONSTITUTIVE LAW FOR SOLID ELEMENTS AT VARIABLE TEMPERATURE (Norton-Hoff)
Implemented by: PASCON F (1998), Charles JF (1997 - 1999)
Project: continuous casting research for ARBED (RW2748)
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:
See report RW2748 (1, 8, 17, 24) and intermediate report of April '98
For details on equations used in analytical compliance matrix computation, see appendix D of April 1998
IANA= 4:
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
| 1 Line (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) |
