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laws:arbth
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ARBTH
Description
Elasto-plastic constitutive law with thermal effects for solid elements at variable temperature
Developed from 1985 to 2005 by AM Habraken, F. Libon, De Montleau - 3D version by C. Lequesne (2005)
Project:
Use
Coupled thermo-mechanical analysis of elasto-plastic solids undergoing large strains
Files
Prepro: LARBTN.F
Lagamine: ARBC2N.F (plane strain, axissymetric, generalized plane state)
ARB3C (3D state)
Subroutines
| File | Subroutine | Description |
|---|---|---|
| ARBC2N.F | ARBC2N | Main subroutine of the law for plane strain, axissymetric, or generalized plane state |
| ARB3C.F | ARB3C | Main subroutine of the law for 3D state |
| CALMAT.F | CALAMAT | Linear interpolation of parameters at a given temperature |
| CALDER.F | CALDER | Computation of $\frac{dE}{dT}$, $\frac{d\nu}{dT}$, and $\frac{d\alpha}{dT}$ |
| CALSYT.F | CALSYT | Computes actualized plastic limit |
| CONCAT.F | CONCAT | Concatenation of 2 vectors |
| CALMU2.F | CALMU2 | Computation of the plastic modulus |
Availability
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | YES |
| Generalized plane state | YES |
Input file
Parameters defining the type of constitutive law
| 1 line (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 250 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| 1 line (6I5) | |
|---|---|
| NTEMP | number of temperatures at which material data are given |
| NINTV | number of sub-steps used to integrate numerically the constitutive equation in a time step if NINTV ⇐ 0 : number of sub-steps is based on the norm of the deformation increment and on DIV=1.D-04 |
| IENTH | = 0 to use the classical formulation for $\alpha$ |
| = 1 to use $\int \alpha dT$ | |
| NPOINT | number of points (eps,sig) to define the law |
| =0 if parabolic or bilinear law | |
| IZENER | =0 if $\sigma$-$\varepsilon$ curves do not depend on strain rate |
| = 1 if $\sigma$-$\varepsilon$ curves depend on strain rate (Not available) | |
| IDYN | = 1 if recrystallisation |
| = 0 else | |
Real parameters
| Line 1 (2G10.0) | |
|---|---|
| ACTIVE | energy activation (not used) |
| EPSRATE | epsilon rate (not used) |
Note: This first line was implemented in the prepro but these parameters are not used in the law - probably a development that was never completed…
If NPOINT=0 - repeat NTEMP times
Not available in ARBC2N ?
| Line 1 (9G10.0) | |
|---|---|
| T | temperature |
| E | Young's elastic modulus at temperature T |
| Nu | Poisson's ratio at temperature T |
| ALPHA | Thermal expansion coefficient $\alpha$ at temperature T |
| SIGY1 | Lower yield limit ($\sigma_{y1}$) at temperature T |
| SIGY2 | Upper yield limit ($\sigma_{y2}$) at temperature T (SIGY2<SIGY1 bilinear case) (parabolic case wrong very often AMH - better use bilinear case or npoint>0) |
| EPS2 | upper yield strain ($\varepsilon_2$) at temperature T |
| ET | Elasto-plastic tangent modulus (Et) at temperature T |
| COEFTQ | TAYLOR-QUINNEY's coefficient (q) at temperature T |
If NPOINT>0
| Lines 1:NPOINT - (G10.0) | |
|---|---|
| EPS | Strain for which stress will be given at each temperature |
Repeat NTEMP times
| Line 1 (3G10.0) | |
|---|---|
| T | temperature |
| Nu | Poisson's ratio at temperature T |
| ALPHA | Thermal expansion coefficient $\alpha$ at temperature T |
| Line 2:NPOINT+1 | |
| SIGY | Stress for strain defined here above at temperature T |
| Line NPOINT+2 | |
| COEFTQ | TAYLOR-QUINNEY's coefficient (q) at temperature T |
If IDYN=1
Recrystallisation function $\varepsilon = C_1 * atan((ln(Z)-C_2)*C_3)+C_4$
| Line 1 (4G10.0) | |
|---|---|
| C1 | for $\varepsilon_C$ |
| C2 | |
| C3 | |
| C4 | |
| Line 2 (4G10.0) | |
| C1 | for $\varepsilon_S$ |
| C2 | |
| C3 | |
| C4 | |
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
13
List of state variables
| Q(1) | = element thickness (t) in plane stress state and generalized plane state |
| =1 in plane strain state | |
| = circumferential strain rate ($\dot{\varepsilon}_\theta$) in axisymmetric state | |
| = 0 in 3D state | |
| Q(2) | Current yield limit in tension; its initial value is $\sigma_{yl}$ |
| Q(3) | = 0 if the current state is elastic |
| = 1 if the current state is elasto-plastic | |
| Q(4) | Equivalent plastic strain |
| Q(5) | Instantaneous thermal flow at the end of the step |
| Q(6) | adiabatic temperature increase due to plastic dissipation since the beginning (coupled analysis) since the preceding thermomechanical meeting (semi-coupled analysis) |
| Q(7) | Initial temperature |
| Q(8) | Capacity $\rho C$ (used in semi-coupled analysis) |
| Q(9) | epsilon rate for idyn=1 |
| Q(10) | Ln(Z) Zener parameter for idyn=1 |
| Q(11) | $T_{eq}$ equivalent temperature for izener=1 |
| Q(12) | Xdyn = recrystallisation fraction for all step |
| Q(13) | Xdy2 = recrystallisation fraction for actual step |
laws/arbth.txt · Last modified: 2020/08/25 15:46 (external edit)
