laws:evp-nh
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laws:evp-nh [2019/03/18 16:22] chantal [List of state variables] |
laws:evp-nh [2020/08/25 15:46] (current) |
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| ===== 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: Name of developer + approximate date of implementation\\ | + | Implemented by: Pascon F (1998), Charles JF (1997 - 1999)\\ |
| - | Project: | + | 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.\\ |
| - | If available, give a reference paper/phD thesis to which the law is associated. | + | JAUMANN stress rate is used\\ |
| + | __IANA= 2, 3, 5:__\\ | ||
| + | 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\\ | ||
| + | __IANA= 4:__\\ | ||
| + | See intermediate report RW2748 (17, 24) | ||
| ==== Files ==== | ==== Files ==== | ||
| - | Write here the names of the main subroutines of the law (those called by loi2 for Lagamine) | + | Prepro: LNHC2.F \\ |
| - | Prepro: XXX.F \\ | + | Lagamine: NHIC2E.F (IANA= 2, 3 or 5) or NHIC3D.F (IANA= 4) |
| - | Lagamine: XXX.F | + | |
| ==== 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 22: | Line 38: | ||
| |Generalized plane state| YES | | |Generalized plane state| YES | | ||
| ===== Input file ===== | ===== Input file ===== | ||
| - | The following section indicates the parameters to be written in the *.lag file. The parameters should be listed in tables. For better understanding, the table should indicate the line numer and the format in the headline, then the list of parameters (see example below). | + | ^ 1 Line (2I5, 60A1)^^ |
| - | Sub-sections can be used to separate different categories of parameters (integer, real). | + | |
| - | ==== Parameters defining the type of constitutive law ==== | + | |
| - | ^ Line 1 (2I5, 60A1)^^ | + | |
| |IL|Law number| | |IL|Law number| | ||
| |ITYPE| 270| | |ITYPE| 270| | ||
| Line 35: | 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 | | + | |MAXITER| maximum number of iteration in elastic field \\ ≤ 0: set default value = 50 | |
| - | |:::| ≤ 0: set default value = 50 | | + | |NTEMP2| number of temperatures at which parameters $K_0, P_1, P_2, P_3, P_4$ are given (only if ICHP2 = 2)| |
| - | |NTEMP2| number of temperatures at which parameters K0, p1, p2, p3, p4 are given (only if ICHP2 = 2)| | + | |
| ==== Real parameters ==== | ==== Real parameters ==== | ||
| Line 49: | 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 !!!__) ^^ | + | |
| - | |AK0| See X for formula| | + | ^ If ICHP2 ≠ 2: 2 Lines (5G10/4G10) (**__only if nodes temperature in Kelvin !!!__**) ^^ |
| - | |C1| A ADAPTER| | + | |$AK_0$| | |
| - | |C2| see 4.4 for more information| | + | |$C_1$| See further| |
| - | |C3| | | + | |$C_2$| See "Information about EVP-NH"| |
| - | |C4| | | + | |$C_3$| | |
| - | |C5| | | + | |$C_4$| | |
| - | |C6| | | + | |$C_5$| | |
| - | |P3| (be careful : 0 < P3 < 1)| | + | |$C_6$| | |
| - | |P4| | | + | |$P_3$| (be careful: 0 < $P_3$ < 1)| |
| + | |$P_4$| | | ||
| ^ 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:|**//A COMPLETER//** | | + | |
| + | __**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:**__ \\ | ||
| + | For the 1D case, we have: \\ | ||
| + | $\bar{\sigma}= A. K_0. \bar{\varepsilon}^{P_4}. exp(-P_1.\bar{\varepsilon}). P_2. \sqrt{3}. (\sqrt{3}. \bar{\dot{\varepsilon}})^{P_3}$ with $P_1 \geq 0$ \\ | ||
| + | The parameters $K_0, P_1, P_2, P_3, P_4$ can be given at several temperatures (ICHP2 = 2) \\ | ||
| + | Otherwise, if ICHP2 ≠ 2: (see the law in section: "integer parameters") \\ | ||
| + | $P_1= (\frac{T}{C_1})^{C_2} + C_3$ \\ | ||
| + | $P_2= f(C_4, C_5, C_6, T)$ \\ | ||
| + | $P_3, P_4, K_0= constants$ \\ | ||
| Line 128: | Line 155: | ||
| |Q(10)|recrystallised fraction since the beginning of the simulation| | |Q(10)|recrystallised fraction since the beginning of the simulation| | ||
| |Q(11)|recrystallised fraction on this step| | |Q(11)|recrystallised fraction on this step| | ||
| - | |Q(12)|elastic part on this step – in percent \\(>0 : loading ; <0 : unloading) (effective if icoupl=1)| | + | |Q(12)|elastic part on this step – in percent \\ (>0 : loading ; <0 : unloading) (effective if icoupl=1)| |
| |Q(13)|number of sub-structures| | |Q(13)|number of sub-structures| | ||
| |Q(14)|volumic fraction of the unrecrystallised sub-structure| | |Q(14)|volumic fraction of the unrecrystallised sub-structure| | ||
| |Q(15)|effective equivalent strain| | |Q(15)|effective equivalent strain| | ||
| |Q(16)|equivalent strain standard deviation| | |Q(16)|equivalent strain standard deviation| | ||
| - | |Q(17)|= 0 if always elastic state since the beginning \\= 1 if any previous step has been performed in visco-plastic domain| | + | |Q(17)|= 0 if always elastic state since the beginning| |
| + | |:::| = 1 if any previous step has been performed in visco-plastic domain| | ||
| |Q(18)|recrystallised fraction during previous step| | |Q(18)|recrystallised fraction during previous step| | ||
| |Q(19)|| | |Q(19)|| | ||
laws/evp-nh.1552922559.txt.gz · Last modified: 2020/08/25 15:35 (external edit)
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