laws:evp-nh
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
laws:evp-nh [2019/03/18 18:00] chantal |
laws:evp-nh [2020/08/25 15:46] (current) |
||
|---|---|---|---|
| Line 2: | Line 2: | ||
| ===== Description ===== | ===== Description ===== | ||
| ELASTO VISCO PLASTIC CONSTITUTIVE LAW FOR SOLID ELEMENTS AT VARIABLE TEMPERATURE (Norton-Hoff)\\ | ELASTO VISCO PLASTIC CONSTITUTIVE LAW FOR SOLID ELEMENTS AT VARIABLE TEMPERATURE (Norton-Hoff)\\ | ||
| - | Implemented by: PASCON F (1998), Charles JF (1997 - 1999)\\ | + | Implemented by: Pascon F (1998), Charles JF (1997 - 1999)\\ |
| Project: continuous casting research for ARBED (RW2748)\\ | Project: continuous casting research for ARBED (RW2748)\\ | ||
| ==== The model ==== | ==== The model ==== | ||
| - | Coupled dynamic recrystallisation-thermo mechanical analysis of elasto visco plastic solids undergoing large strains.\\ | + | Coupled dynamic recrystallisation-thermo-mechanical analysis of elasto-visco-plastic solids undergoing large strains.\\ |
| JAUMANN stress rate is used\\ | JAUMANN stress rate is used\\ | ||
| __IANA= 2, 3, 5:__\\ | __IANA= 2, 3, 5:__\\ | ||
| - | See report RW2748 (1, 8, 17, 24) and intermediate report of April '98 \\ | + | See intermediate report RW2748 (1, 8, 17, 24) and intermediate report of April 1998 \\ |
| For details on equations used in analytical compliance matrix computation, see appendix D of April 1998\\ | For details on equations used in analytical compliance matrix computation, see appendix D of April 1998\\ | ||
| __IANA= 4:__\\ | __IANA= 4:__\\ | ||
| Line 17: | Line 17: | ||
| Lagamine: NHIC2E.F (IANA= 2, 3 or 5) or NHIC3D.F (IANA= 4) | Lagamine: NHIC2E.F (IANA= 2, 3 or 5) or NHIC3D.F (IANA= 4) | ||
| ==== Subroutines ==== | ==== Subroutines ==== | ||
| - | In the following table, fill in the file (*.F) and the names of the subroutines used by the law. Generic subroutines such as ‘ANNULD’ (putting a vector to zero) or ‘MST_SOLVE’ (computing the solution to a system of linear equations) do not need to be listed here. | + | |
| ^File^Subroutine^Description^ | ^File^Subroutine^Description^ | ||
| - | |XXX.F| XXX|Main subroutine of the law | | + | |CALMAT.F | CALMAT|Computes material data at temperature T | |
| + | |NHIMAT.F |CALSIGY | | | ||
| + | |:::|MATMSGS2|Used for analytical compliance matrix| | ||
| + | |:::|MATMSGL2|Used for analytical compliance matrix| | ||
| + | |:::|MATMSGS|Used for analytical compliance matrix (3D case)| | ||
| + | |:::|MATMSGL|Used for analytical compliance matrix (3D case)| | ||
| + | |:::|EIGVECT| Computes eigen vectors| | ||
| + | |:::|CMATINV| Inverse complex matrix| | ||
| + | |:::|VGMOYEN |Computes the constant velocities gradient matrix | | ||
| + | |CALPNH.F| CALPNH|Computes $K_0, P_1, P_2, P_3, P_4$ at temperature T | | ||
| + | |RECRYDYN.F|RECRYDYN |Dynamic recrystallization computation | | ||
| ===== Availability ===== | ===== Availability ===== | ||
| |Plane stress state| NO | | |Plane stress state| NO | | ||
| Line 37: | Line 48: | ||
| |IDYN| = 1: if recrystallisation computation| | |IDYN| = 1: if recrystallisation computation| | ||
| |:::| = 0: else| | |:::| = 0: else| | ||
| - | |ICHP2| = 2: if parameters K0, P1, P2, P3, P4 are given at several temperatures| | + | |ICHP2| = 2: if parameters $K_0, P_1, P_2, P_3, P_4$ are given at several temperatures| |
| - | |:::| = 1: if p2= FORMULE 1 (**__only if nodes temperature in Kelvin !!!__**)| | + | |:::| = 1: if $P_2= e^{-(\frac{T-C_4}{C_5})}.T^{C_6}$ (**__only if nodes temperature in Kelvin !!!__**)| |
| - | |:::| any other value if p2= FORMULE 2 (**__only if nodes temperature in Kelvin !!!__**)| | + | |:::| any other value if $P_2= (\frac{C_4}{T})^2 - \frac{C_5}{T} + C_6$ (**__only if nodes temperature in Kelvin !!!__**)| |
| |IALG| = 1: if enthalpic formulation for ALPHA| | |IALG| = 1: if enthalpic formulation for ALPHA| | ||
| |:::| = 0: if classical formulation for ALPHA | | |:::| = 0: if classical formulation for ALPHA | | ||
| |MAXITER| maximum number of iteration in elastic field \\ ≤ 0: set default value = 50 | | |MAXITER| maximum number of iteration in elastic field \\ ≤ 0: set default value = 50 | | ||
| - | |NTEMP2| number of temperatures at which parameters K0, P1, P2, P3, P4 are given (only if ICHP2 = 2)| | + | |NTEMP2| number of temperatures at which parameters $K_0, P_1, P_2, P_3, P_4$ are given (only if ICHP2 = 2)| |
| ==== Real parameters ==== | ==== Real parameters ==== | ||
| Line 50: | Line 61: | ||
| |E| YOUNG’s elastic modulus at temperature T| | |E| YOUNG’s elastic modulus at temperature T| | ||
| |ANU| POISSON’s ratio at temperature T| | |ANU| POISSON’s ratio at temperature T| | ||
| - | |ALPHA| Thermal expansion coefficient (α) at temperature T. \\ Even if IALG = 1, ALPHA must be introduced at temperature T. \\ In this case, FORMULE will be automatically computed | | + | |ALPHA| Thermal expansion coefficient (α) at temperature T. \\ Even if IALG = 1, ALPHA must be introduced at temperature T. \\ In this case, $\int_0^T\alpha(T).dT$ will be automatically computed | |
| ^ If ICHP2 = 2: 1 Line repeated NTEMP2 times (6G10) \\ Note: parameters introduced by increasing temperature order^^ | ^ If ICHP2 = 2: 1 Line repeated NTEMP2 times (6G10) \\ Note: parameters introduced by increasing temperature order^^ | ||
| |T| Temperature| | |T| Temperature| | ||
| - | |K0| See X for formula| | + | |$K_0$| See further| |
| - | |P1| A ADAPTER| | + | |$P_1$| See "Information about EVP-NH"| |
| - | |P2| see 4.4 for more information| | + | |$P_2$| | |
| - | |P3| | | + | |$P_3$| | |
| - | |P4| | | + | |$P_4$| | |
| ^ If ICHP2 ≠ 2: 2 Lines (5G10/4G10) (**__only if nodes temperature in Kelvin !!!__**) ^^ | ^ If ICHP2 ≠ 2: 2 Lines (5G10/4G10) (**__only if nodes temperature in Kelvin !!!__**) ^^ | ||
| - | |AK0| See X for formula| | + | |$AK_0$| | |
| - | |C1| A ADAPTER| | + | |$C_1$| See further| |
| - | |C2| see 4.4 for more information| | + | |$C_2$| See "Information about EVP-NH"| |
| - | |C3| | | + | |$C_3$| | |
| - | |C4| | | + | |$C_4$| | |
| - | |C5| | | + | |$C_5$| | |
| - | |C6| | | + | |$C_6$| | |
| - | |P3| (be careful: 0 < P3 < 1)| | + | |$P_3$| (be careful: 0 < $P_3$ < 1)| |
| - | |P4| | | + | |$P_4$| | |
| ^ 1 Line (4G10) ^^ | ^ 1 Line (4G10) ^^ | ||
| |TQ| Taylor-Quinney’s coefficient. Absolute value between 0 and 1 :\\ < 0: when thermal analysis within a semi-coupled analysis\\ > 0: for other cases (total coupled analysis or mechanical analysis within a semi-coupled analysis)| | |TQ| Taylor-Quinney’s coefficient. Absolute value between 0 and 1 :\\ < 0: when thermal analysis within a semi-coupled analysis\\ > 0: for other cases (total coupled analysis or mechanical analysis within a semi-coupled analysis)| | ||
| - | |PRECVG| precision in VGMOY calculation (3D state only)\\ ≤ 0: set default value = 1.10-5| | + | |PRECVG| precision in VGMOY calculation (3D state only)\\ ≤ 0: set default value = $1.10^{-5}$| |
| - | |PRECELA| precision in elastic computation\\ ≤ 0: set default value = 1.10-4| | + | |PRECELA| precision in elastic computation\\ ≤ 0: set default value = $1.10^{-4}$| |
| - | |EPSINC| increment of deformation for the automatic computation of NINTV\\ ≤ 0: set default value = 1.10-3| | + | |EPSINC| increment of deformation for the automatic computation of NINTV\\ ≤ 0: set default value = $1.10^{-3}$| |
| ^ If IDYN = 1: 4 Lines (3I5/4G10.0/4G10.0/2G10.0) ^^ | ^ If IDYN = 1: 4 Lines (3I5/4G10.0/4G10.0/2G10.0) ^^ | ||
| |ICOUPL| = 1: the recrystallisation is coupled | | |ICOUPL| = 1: the recrystallisation is coupled | | ||
| |:::| = 0: the recrystallisation is uncoupled | | |:::| = 0: the recrystallisation is uncoupled | | ||
| - | |ITYPEPS| = 0: the equations defining the beginning and the end of the recryst. have the form : FORMULE | | + | |ITYPEPS| = 0: the equations defining the beginning and the end of the recryst. have the form : $\varepsilon= Q_1. Q_4^{Q_2} . [LN(Zener)]^{Q_3}$ | |
| - | |:::| = 1: the equations defining the beginning and the end of the recryst. have the form : FORMULE | | + | |:::| = 1: the equations defining the beginning and the end of the recryst. have the form : $\varepsilon= Q_1.ATAN[Q_3.[LN(Zener)-Q_2]]+ Q_4$ | |
| - | |:::| = 2: the equations defining the beginning and the end of the recryst. have the form : FORMULE | | + | |:::| = 2: the equations defining the beginning and the end of the recryst. have the form : $\varepsilon= Q_1.[LN(Zener)]^{Q_2}+ Q_3.LN(Zener) + Q_4$ | |
| |NSSMAX| used if ICOUPL = 1: Maximum number of sub-structures\\ The precision on the recryst. fraction is 1/NSSMAX | | |NSSMAX| used if ICOUPL = 1: Maximum number of sub-structures\\ The precision on the recryst. fraction is 1/NSSMAX | | ||
| - | |Q1| parameters for the __beginning__ of the recrystallisation: εc | | + | |$Q_1$| parameters for the __beginning__ of the recrystallisation: $\varepsilon_c$ | |
| - | |Q2| parameters for the __beginning__ of the recrystallisation: εc | | + | |$Q_2$| parameters for the __beginning__ of the recrystallisation: $\varepsilon_c$ | |
| - | |Q3| parameters for the __beginning__ of the recrystallisation: εc | | + | |$Q_3$| parameters for the __beginning__ of the recrystallisation: $\varepsilon_c$ | |
| - | |Q4| parameters for the __beginning__ of the recrystallisation: εc | | + | |$Q_4$| parameters for the __beginning__ of the recrystallisation: $\varepsilon_c$ | |
| - | |Q1| parameters for the __end__ of the recrystallisation: εs | | + | |$Q_1$| parameters for the __end__ of the recrystallisation: $\varepsilon_s$ | |
| - | |Q2| parameters for the __end__ of the recrystallisation: εs | | + | |$Q_2$| parameters for the __end__ of the recrystallisation: $\varepsilon_s$ | |
| - | |Q3| parameters for the __end__ of the recrystallisation: εs | | + | |$Q_3$| parameters for the __end__ of the recrystallisation: $\varepsilon_s$ | |
| - | |Q4| parameters for the __end__ of the recrystallisation: εs | | + | |$Q_4$| parameters for the __end__ of the recrystallisation: $\varepsilon_s$ | |
| - | |ACTIV| Activation energy for Zener computation : FORMULE \\ with T the temperature and R the Boltzman gas constant| | + | |ACTIV| Activation energy for Zener computation : $Z=\dot{\varepsilon}.EXP(\frac{ACTIV}{R.T})$ \\ with T the temperature and R the Boltzman gas constant| |
| - | |EXPO| Exponent for the AVRAMI law : FORMULE | | + | |EXPO| Exponent for the AVRAMI law : $X= 1- EXP[-3.(\frac{\bar{\varepsilon}-\varepsilon_c}{\varepsilon_s-\varepsilon_c})^{expo}]$ | |
| __**NOTE:**__ ISTRA(3) parameter of the execution file:\\ **Units:** \\ = 0: analytical compliance matrix used (default value) \\ = 1: perturbation method \\ **Tens:** \\ = 0: mean velocities gradient (default value) \\ = 1: initial velocities gradient \\ **Hundreds:** \\ = 0: yield limit given by intersection between N-H curve and Young’s straight line \\ = 1: yield limit given by K0 (given parameter – see below) \\ | __**NOTE:**__ ISTRA(3) parameter of the execution file:\\ **Units:** \\ = 0: analytical compliance matrix used (default value) \\ = 1: perturbation method \\ **Tens:** \\ = 0: mean velocities gradient (default value) \\ = 1: initial velocities gradient \\ **Hundreds:** \\ = 0: yield limit given by intersection between N-H curve and Young’s straight line \\ = 1: yield limit given by K0 (given parameter – see below) \\ | ||
| + | |||
| \\ __**Information about EVP-NH:**__ \\ | \\ __**Information about EVP-NH:**__ \\ | ||
| For the 1D case, we have: \\ | For the 1D case, we have: \\ | ||
| - | FORMULE \\ | + | $\bar{\sigma}= A. K_0. \bar{\varepsilon}^{P_4}. exp(-P_1.\bar{\varepsilon}). P_2. \sqrt{3}. (\sqrt{3}. \bar{\dot{\varepsilon}})^{P_3}$ with $P_1 \geq 0$ \\ |
| - | The parameters K0, P1, P2, P3, P4 can be given at several temperatures (ICHP2 = 2) \\ | + | The parameters $K_0, P_1, P_2, P_3, P_4$ can be given at several temperatures (ICHP2 = 2) \\ |
| - | Otherwise: (ICHP2 ≠ 2) \\ | + | Otherwise, if ICHP2 ≠ 2: (see the law in section: "integer parameters") \\ |
| - | Formule 1 \\ | + | $P_1= (\frac{T}{C_1})^{C_2} + C_3$ \\ |
| - | Formule 2 \\ | + | $P_2= f(C_4, C_5, C_6, T)$ \\ |
| - | Formule 3 \\ | + | $P_3, P_4, K_0= constants$ \\ |
laws/evp-nh.1552928438.txt.gz · Last modified: 2020/08/25 15:35 (external edit)
Page Tools
