Anisotropic elasto-plastic law based on texture for solid elements at constant temperature.
MIcroscopic PArt Yield law 3D
This law is used for mechanical analysis of elasto-plastic anisotropic solids undergoing large strains. Isotropic hardening is assumed.
Prepro: LMIPAY.F
Lagamine: MIPAY3.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 | 501 |
| COMMNT | Any comment (up to 60 characters) that will be reproduced on the output listing |
| Line 1 (6I5) | |
|---|---|
| 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 (=65) |
| IMETH | Type of anisotropic yield surface to be used |
| = -1 : No updated HILL without discretized yield locus | |
| = +1 : No updated HILL with discretized yield locus | |
| = -2 : No updated J. WINTERS no discretized yield locus (6 order series in stresses space) | |
| = +2 : No updated B. van BAEL 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 plasticity with no yield locus | |
| IKAP | = 0 : Analytical compliance matrix (available only for IMETH=-2) |
| = 1 : Perturbation compliance matrix (general case) | |
| = 2 : Compliance matrix always the elastic one (available only for IMETH =-5) | |
| Line 1 (5G10.0) | |
|---|---|
| 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) |
| Line 2 (6G10.0) | |
| THETA$\phi$ | = 10 |
| THETAMAX | = 85 |
| CMIN | = 0,2 |
| FLIMIT | = 0,05 |
| SLIMIT | = 0,025 |
| TOL | = 1.10-7 |
The last 6 parameters are temporary values. See report 11 of research Micro-Macro (RW 2748).
Only if IMETH=1 (HILL) :
| Line 1 (6G10.0) : HILL's coefficient | |
|---|---|
| ALPHA12 | $\alpha_{12}$ |
| ALPHA13 | $\alpha_{13}$ |
| ALPHA23 | $\alpha_{23}$ |
| ALPHA44 | $\alpha_{44}$ |
| ALPHA55 | $\alpha_{55}$ |
| ALPHA66 | $\alpha_{66}$ |
| Line 2 (1G10.0) | |
| SIG$\phi$ | Uniaxial yield stress in a reference direction |
6 for 3D state
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) | $\sigma_{yz}$ |
2
| Q(1) | Yield indicator |
| = 0 : Current state is elastic | |
| = 1 : Current state is elasto-plastic | |
| Q(2) | GAMMA hardening parameter ($\Gamma$) |
- 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 $\sigma_{eq}$ : \[\sigma = K(\varepsilon_0+\varepsilon)^n\]
for META=4 , IMETH=-5.
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 |