Anisotropic elasto-plastic law based on texture for solid elements at constant temperature combined with the microstructure hardening model of C. TEODOSIU.
Microscopic INTerpolated Yield locus 3D KInematic
This law is used for mechanical analysis of elasto-plastic anisotropic solids undergoing large strains. Isotropic or Isotropic & Kinematic (Teodosiu) hardening are assumed.
Prepro: LMINTY_KI.F
Lagamine: MINTY3_KI.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 | 511 |
| 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 (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 |
| VOCE | |
Thus, the number of sub-steps = MAX(NINTV; NINTEPS*DELTA EPSILON).
| Line 1 (1I5) | |
|---|---|
| NTEO | = 0 : Classic hardening |
| = 1 : Teodosiu hardening | |
If NTEO = 1 :
| Line 1 (3I5) | |
|---|---|
| NREAD | = 1 : Read the 58 state variables in .f72 (in column) |
| KREAD | = 1 : Changes hardening parameters if fitted with a Von Mises yield locus and shear tests |
| = 2 : Automatically performed in Lagamine | |
| IOPTEO | = 10 : Hofferlin type. $S_L$ only activated if a path change with an elastic transition occurs |
| = 20 : Alves type. $S_L$ activated for any path change (continuous path change or even local path change, for example simple shear where material frame rotates) | |
| = 21 : Alves type but $S_L$ activated only if a sufficiently strong path change occurs $\rvert\Delta\hat{\varepsilon}_{n+1}^p-\Delta\hat{\varepsilon}_n^p\rvert\geq prec$, where $n$ and $n+1$ are two successive steps and $\Delta\hat{\varepsilon}^p$ is the increment of the local plastic strain | |
Only if KREAD=1 :
| Line 1 (1G10.0) | |
|---|---|
| COEFK | Value to correct Teodosiu's parameters |
| Line 1 (3G10.0) | |
|---|---|
| E | YOUNG's elastic modulus |
| ANU | POISSON's ratio |
| THETA$\phi$ | Angle between stress nodes for the yield locus interpolation |
If NTEO=1, the 3 following parameters can be equal to 0 :
| Line 1 (3G10.0) | |
|---|---|
| CK | Hardening factor K (see below) |
| GAMMA$\phi$ | Hardening GAMMA$\phi$ coefficient ($\Gamma^{\circ}$) (see below) |
| CN | Hardening exponent (see below) |
If IMETH=9 or 10 :
| Line 1 (1G10.0) | |
|---|---|
| H | Visco-plastic parameter (=1/$m$ with $m$ the strain rate sensitivity parameter) |
Only if NTEO=1 : Theodosius hardening parameters :
| Line 1 (2G10.0) | |
|---|---|
| CP | Polarity saturation rate |
| NP | Polarity exponent |
| Line 1 (5G10.0) | |
| CSD | Orientation saturation rate for $S_D$ |
| CSL | Orientation saturation rate for $\underline{\underline{S_L}}$ |
| SSAT0 | Initial orientation saturation value |
| NL | Orientation exponent |
| R0 | Initial yield limit |
| Line 1 (2G10.0) | |
| CX | Back stress saturation rate |
| XSAT0 | Initial back stress saturation value |
| Line 1 (2G10.0) | |
| M | Influence of $\underline{\underline{S}} on kinematic ($m=0$) - isotropic ($m=1$) hardening |
| Q | $S_D-\underline{\underline{S_L}}$ balance on $X_{sat}$ |
| Line 1 (2G10.0) | |
| CR | Isotropic hardening : saturation rate |
| RSAT | Isotropic hardening : saturation value |
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 if NTEO=0
= 62 if NTEO=1
If NTEO=0 :
| Q(1) | Accumulated plastic strains |
| Q(2) | GAMMA hardening parameter ($\Gamma$) |
| Q(3)$\rightarrow$Q(7) | 5 components of the plastic strain rate direction |
If NTEO=1 :
| Q(1) | IYIELD |
| = 0 : Elastic | |
| = 1 : Plastic | |
| Q(2) | pd (for printing) |
| Q(3:7) | 5 components of the plastic strain rate direction |
| Q(8:13) | 6 components back stress X |
| Q(20) | SD (for printing) |
| Q(21:56) | 36 components of $S_L$ |
| Q(57) | $\rvert$S$\rvert$ (for printing) |
| Q(58) | R |
| Q(59:62) | Internal parameters (for printing) |
NTEO=0 : - 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 $\sigma_{eq}$ : \[\sigma = K(\varepsilon_0+\varepsilon)^n\]
NTEO=1 :
Depicted in internal report
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 |