Anisotropic elasto-plastic law based on texture for solid elements at constant temperature.
Microscopic INTerpolated Yield locus 3D
This law is used for mechanical analysis of elasto-plastic anisotropic solids undergoing large strains. Isotropic hardening is assumed.
Prepro: LMINTY.F
Lagamine: MINTY3.F
| Plane stress state | NO |
| Plane strain state | NO |
| Axisymmetric state | NO |
| 3D state | YES |
| Generalized plane state | NO |
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number Texture data being read as metallurgical data, this constitutive law MUST BE THE FIRST one (IL=1) |
| ITYPE | 502 |
| COMMNT | Any comment (up to 60 characters) that will be reproduced on the output listing |
| Line 1 (8I5) | |
|---|---|
| NINTV | Number of sub-steps used to integrate numerically the constitutive equation in a time step |
| NCRI | Number of crystals for each integration point (400 or 1600) (to be in accordance with *.MET) |
| NNLP | Maximum number of steps without re-actualisation of the yield locus |
| NTEMPO | Number of TEMPO variables per integration point (NTEMPO=100 for IMETH=5, 7, 9 or 11 and NTEMPO=109 for IMETH=6, 8, 10 or 12) |
| IMETH | Type of anisotropic yield surface to be used |
| = -1 : No updated HILL with no discretized yield locus | |
| = +1 : No updated HILL with discretized yield locus | |
| = -2 : No updated J. WINTERS with no discretized yield locus (6 order series in stresses space) | |
| = +2 : No updated B. van BAEL with discretized yield locus (6 order series in strains space) | |
| = +3 : No updated U.L.G. yield locus | |
| = +4 : Updated U.L.G. yield locus | |
| = +5 : Taylor model without updating | |
| = +6 : Taylor model with updating | |
| = +7 : Bishop-Hill model without updating | |
| = +8 : Bishop-Hill model with updating | |
| = +9 : Visco-plastic Taylor model without updating | |
| = +10 : Visco-plastic Taylor model with updating | |
| = +11 : ALAMEL model without updating | |
| = +12 : ALAMEL model with updating | |
| IKAP | = 0 : Analytical compliance matrix |
| = 1 : Perturbation compliance matrix | |
| MAXIT | |
| NINTEPS | Number of sub-intervals per unit of delta epsilon |
Thus, the number of sub-steps = MAX(NINTV; NINTEPS*DELTA EPSILON).
| Line 1 (6G10.0) | |
|---|---|
| E | YOUNG's elastic modulus |
| ANU | POISSON's ratio |
| CK | Hardening factor K (see below) |
| GAMMA$\phi$ | Hardening GAMMA$\phi$ coefficient ($\Gamma^{\circ}$) (see below) |
| CN | Hardening exponent (see below) |
| THETA$\phi$ | Angle between stress nodes for the yield locus interpolation |
If IMETH=9 or 10 :
| Line 1 (1G10.0) | |
|---|---|
| H | Visco-plastic parameter (=1/$m$ with $m$ the strain rate sensitivity parameter) |
Only if IMETH=$\pm$1 (HILL) :
| Line 1 : HILL's coefficient | |
|---|---|
| ALPHA12 | $\alpha_{12}$ |
| ALPHA13 | $\alpha_{13}$ |
| ALPHA23 | $\alpha_{23}$ |
| ALPHA44 | $\alpha_{44}$ |
| ALPHA55 | $\alpha_{55}$ |
| ALPHA66 | $\alpha_{66}$ |
| Line 2 | |
| SIG$\phi$ | Uniaxial yield stress in a reference direction |
6
The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates.
| SIG(1) | $\sigma_{xx}$ |
| SIG(2) | $\sigma_{yy}$ |
| SIG(3) | $\sigma_{zz}$ |
| SIG(4) | $\sigma_{xy}$ |
| SIG(5) | $\sigma_{xz}$ |
| SIG(6) | $\sigma_{yz}$ |
7
| Q(1) | Accumulated plastic strains |
| Q(2) | GAMMA hardening parameter ($\Gamma$) |
| Q(3)$\rightarrow$Q(7) | 5 components of the plastic strain rate direction |
- For IMETH$\neq$1 : in this case, the yield surface is scaled by the critical resolved shear stress $\tau$ : \[\tau=K(\Gamma^{\circ}+\Gamma)^N\] - For IMETH=1 : in this case, the yield surface is scaled by $\sigma_{eq}$ : \[\sigma = K(\varepsilon_0+\varepsilon)^n\]
File *.MET for META=4 , IMETH=5 to 12.
For each material :
| Line 1 (1I5) | |
|---|---|
| NGLI | Number of slip system in the crystal |
| Line 2-3-4-… (NGLI lines) (8G10.0) | |
| NORMAL(3) | Vector $\perp$ to the slip plane |
| DIRECTION(3) | Vector direction of the slip |
| CRSS+ | Critical resolved shear stress + if slip in positive direction |
| CRSS- | Critical resolved shear stress - otherwise |
| Line 2 + NGLI and following ones (NCRI lines) (I5,4(1F13.5) | |
| ICRI | Crystal number (increasing order from 1 to NCRI) |
| WEIGHT | Crystal weight |
| EULER | Euler angles to define crystal orientation Phi_1 / Phi / Phi _2 |