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laws:vmvp
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Table of Contents
VMVP
Von Mises Visco-Plastic.
Description
3D isotropic viscoplastic damage law that enables the modeling of non-classical creep responses via Graham-Walles and a modified activation function-Norton viscosity function.
Numerical model
This law was implemented in the context of C.Rojas-Ulloa's PhD. project on the modeling of the non-classical long-term creep response of Incoloy 800H (see (C.Rojas-Ulloa et al., 2024) for more details). It is based in the law implemented by Hélène Morch (CHAB), a viscoplastic damage law combines the von Mises yield criterion with a Norton viscosity function, a complex backstress formulation, and Kachanov-Lemaitre creep-fatigue damage laws). VMVP includes
Input file
Parameters defining the type of constitutive law
| Line 01; format (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 271 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| Line 02; format (9I5) | ||
|---|---|---|
| 1:5 | TID | =1 if parameters are given for linear interpolation at different temperatures = 0 if not |
| 6:10 | ntemp | if TID=1, ntemp defines the number of temperatures at which parameters are given |
| 11:15 | ianisoth | =1 if anisothermal loadings = 0 otherwise |
| 16:20 | MAXIT | =maximum number of Newton-Raphson iterations within the colaw (25 default) |
| 21:25 | nintv | =Number of sub-intervals (substeps); if 0, no substeps |
| 26:30 | ilcf | indicator for low-cycle fatigue |
| 31:35 | mat_interp | indicator for interpolation method (XX) for material parameters $(E, \nu)$ |
| 36:40 | tdilc_interp | indicator for interpolation method (XX) for temp. dilatation coefficient |
| 41:45 | iso_interp | indicator for interpolation method (XX) for isotropic hardening parameters $(b, Q)$ |
| Line 03; format (10I5) | ||
| 1:5 | nAFX | Number of Armstrong-Fredericks equations used to define the back-stress X (minimum value=1) |
| 6:10 | NAFC | Number of Armstrong-Fredericks equations taking into account cyclic hardening |
| 11:15 | NAFY | Number of Armstrong-Fredericks equations taking into account evolution of the mean stress |
| 16:20 | iarrh | ID for interpolation method of AD equations (see XXX) |
| 21:25 | ivp | ID for type of viscoplastic law 1=Norton law (after CHAB); 2=Graham-Walles; 4=AFN |
| 26:30 | vpinterp | ID for interpolation method for viscoplastic law parameters. if ivp=2, vpinterp defines the number of Graham-Walles equations |
| 31:35 | type_dam | ID for damage type. 0=no damage; 1=uncoupled damage; 3=semi-coupled damage; 4=fully-coupled damage(not working yet) |
| 36:40 | idam | ID for damage law. 1 = Kachanov(creep) + Lemaitre(fatigue) (after CHAB); 2 = IfW (PhD. thesis from Narayana K. Karthik, RWTH Aachen university) |
| 41:45 | dam_interp | ID for interpolation of damage law parameters |
| 46:50 | daminit | ID for damage initiation criterion |
Real parameters
case TID = 0
→ IF (mat_interp=1) THEN
| Line 04; format (1G10.0) | ||
|---|---|---|
| 1:10 | $E$ | Young modulus (MPa) |
| Line 05; format (1G10.0) | ||
| 1:10 | $\nu$ | Poisson ratio (-) |
→ ELSEIF (mat_interp=2) THEN
| Line 04; format (3G10.0) | ||
|---|---|---|
| 1:10 | $A_E$ | Single Arrhenius fit $E(T)=A_E\cdot[1+B_E\cdot exp(T/C_E)]$ |
| 11:20 | $B_E$ | |
| 21:30 | $C_E$ | |
| Line 05; format (3G10.0) | ||
| 1:10 | $A_\nu$ | Single Arrhenius fit $\nu(T)=A_\nu\cdot[1+B_\nu\cdot exp(T/C_\nu)]$ |
| 11:20 | $B_\nu$ | |
| 21:30 | $C_\nu$ | |
→ ELSEIF (mat_interp=3) THEN
| Line 04; format (5G10.0) | ||
|---|---|---|
| 1:10 | $A_E$ | Double Arrhenius fit $E(T)=A_E\cdot[1+B_E\cdot exp(T/C_E)] + A_E\cdot[1+D_E\cdot exp(T/E_E)]$ |
| 11:20 | $B_E$ | |
| 21:30 | $C_E$ | |
| 31:40 | $D_E$ | |
| 41:50 | $E_E$ | |
| Line 05; format (5G10.0) | ||
| 1:10 | $A_\nu$ | Double Arrhenius fit $E(T)=A_\nu\cdot[1+B_\nu\cdot exp(T/C_\nu)] + A_\nu\cdot[1+D_\nu\cdot exp(T/E_\nu)]$ |
| 11:20 | $B_\nu$ | |
| 21:30 | $C_\nu$ | |
| 31:40 | $D_\nu$ | |
| 41:50 | $E_\nu$ | |
→ ELSEIF (mat_interp=4) THEN
| Line 04; format (5G10.0) | ||
|---|---|---|
| 1:10 | $X_E$ | Polynomial fit $E(T)=X_E\cdot[1+A_E\cdot (T-T_0)+B_E\cdot (T-T_0)^2+C_E\cdot (T-T_0)^3]$ |
| 11:20 | $A_E$ | |
| 21:30 | $B_E$ | |
| 31:40 | $C_E$ | |
| 41:50 | $T_0$ | |
| Line 05; format (5G10.0) | ||
| 1:10 | $X_\nu$ | Polynomial fit $\nu(T)=X_\nu\cdot[1+A_\nu\cdot (T-T_0)+B_\nu\cdot (T-T_0)^2+C_\nu\cdot (T-T_0)^3]$ |
| 11:20 | $A_\nu$ | |
| 21:30 | $B_\nu$ | |
| 31:40 | $C_\nu$ | |
| 41:50 | $T_0$ | |
→ ELSEIF (mat_interp=5) THEN
| Line 04; format (5G10.0) | ||
|---|---|---|
| 1:10 | $X_E$ | Polynomial fit $E(T)=X_E\cdot[1+A_E\cdot (T-T_0)+B_E\cdot (T-T_0)^2+C_E\cdot (T-T_0)^3]$ |
| 11:20 | $A_E$ | |
| 21:30 | $B_E$ | |
| 31:40 | $C_E$ | |
| 41:50 | $T_0$ | |
| Line 05; format (5G10.0) | ||
| 1:10 | $X_\nu$ | Polynomial fit $\nu(T)=X_\nu\cdot[1+A_\nu\cdot (T-T_0)+B_\nu\cdot (T-T_0)^2+C_\nu\cdot (T-T_0)^3]$ |
| 11:20 | $A_\nu$ | |
| 21:30 | $B_\nu$ | |
| 31:40 | $C_\nu$ | |
| 41:50 | $T_0$ | |
Other things
| Interpolation methods included within VMVP: | |
|---|---|
| 1 | Unique value, no interpolation |
| 2 | Single Arrhenius fit $P(T)=A_P\cdot[1+B_P\cdot exp(T/C_P)]$ Parameters $A_P$, $B_P$ & $C_P$ are introduced in format 3G10.0 |
| 3 | Double Arrhenius fit $P(T)=A_P\cdot[1+B_P\cdot exp(T/C_E)] D_P\cdot exp(T/E_P)]$ Parameters $A_P$, $B_P$, $C_P$, $D_P$ & $E_P$ are introduced in format 3G10.0 |
| List of state variables | |
|---|---|
| Q(1) | Equiv. plastic (creep) strain (-) |
| Q(2) | Equiv. plastic (creep) strain rate $(s^{-1})$ |
| Q(3) | Equiv. thermal strain (-) |
| Q(4:9) | Plastic strain vector (-) |
| Q(10:15) | Total strain vector (-) |
| Q(16) | Isotropic/cyclic hardening R (MPa) |
| Q(17) | Plastic memory surface radius (-) |
| Q(18:23) | Plastic memory surface center $\zeta$ |
| Q(24) | Total accumulated damage |
| Q(25) | Accumulated creep damage |
| Q(26) | Accumulated fatigue damage |
| Q(27) | Accumulated plastic energy $w_D$ |
| Q(28:28+6$\times$nAFX-1) | Kinematic hardening components $\underline{X}$ |
laws/vmvp.1730995363.txt.gz · Last modified: 2024/11/07 17:02 by carlos
