phase#

phase is a dictionary of arbitrarily labeled keys. Each phase entry requires a key lattice that specifies the lattice structure in Pearson notation. At least the type of the employed constitutive model for each active field (mechanical/elastic, mechanical/plastic, mechanical/eigen, thermal/source(s), or damage) is required; any further configuration details depend on the selected constitutive model. It is recommended to construct phase entries based on the Reference Examples (also included in config.tar.xz) rather than from scratch.

The basic layout is sketched in the following:

phase:

 label_1:
   lattice: lattice_1
   mechanical:
     elastic:
       type: tbd
       ...:
     plastic:
       type: tbd
       ...:
     eigen:
       type: tbd
       ...:
   damage:
     type: tbd
     ...:
   thermal:
     source:
       - type: tbd
         ...:
       - type: tbd
         ...:

 label_2:
   lattice: lattice_2
   mechanical:
     elastic:
       type: tbd
       ...:
     plastic:
       type: tbd
       ...:
     eigen:
       type: tbd
       ...:
   damage:
     type: tbd
     ...:
   thermal:
     source
       - type: tbd
         ...:
       - type: tbd
         ...:

 label_N:
   ...

Reference Examples#

AISI304#

references:
  - H.M. Ledbetter,
    physica status solidi (a) 85(1):89-96, 1984,
    https://doi.org/10.1002/pssa.2210850111

lattice: cF
rho: 7937.0

Ag#

references:
  - https://en.wikipedia.org/wiki/Silver

lattice: cF
rho: 10490.0

Al#

references:
  - https://en.wikipedia.org/wiki/Aluminium

lattice: cF
rho: 2700.0

Au#

references:
  - https://en.wikipedia.org/wiki/Gold

lattice: cF
rho: 19300.0

Cu#

references:
  - https://en.wikipedia.org/wiki/Copper

lattice: cF
rho: 8960.0

Fe#

references:
  - https://en.wikipedia.org/wiki/Iron

lattice: cI
rho: 7874.0

Mg#

references:
  - D. Tromans,
    International Journal of Recent Research and Applied Studies 6(4):462-483, 2011,
    https://www.arpapress.com/Volumes/Vol6Issue4/IJRRAS_6_4_14.pdf

lattice: hP
c/a: 1.62350
rho: 1740.0

Ni#

references:
  - https://en.wikipedia.org/wiki/Nickel

lattice: cF
rho: 8908.0

Pt#

references:
  - https://en.wikipedia.org/wiki/Platinum

lattice: cF
rho: 21450.0

Sn-beta#

references:
  - J.A. Rayne and B.S. Chandrasekhar,
    Physical Review 120(5):1658-1663, 1960,
    https://doi.org/10.1103/PhysRev.120.1658
  - https://en.wikipedia.org/wiki/Tin

lattice: tI
c/a: 0.5458 # T=300K (c=31.83nm, a=5.832nm)
rho: 7265.0

Ti#

references:
  - https://www.totalmateria.com/page.aspx?ID=CheckArticle&site=ktn&NM=221
  - https://en.wikipedia.org/wiki/Titanium

lattice: hP
c/a: 1.587
rho: 4506.0

W#

references:
  - https://en.wikipedia.org/wiki/Tungsten

lattice: cI
rho: 19300.0

bcc#

lattice: cI

bct#

lattice: tI
c/a: 0.55

fcc#

lattice: cF

hcp#

lattice: hP
c/a: 1.6333

damage#

anisobrittle_cubic#

type: anisobrittle

output: [f_phi]

N_cl: [3]

g_crit: [0.5e+7]
s_crit: [0.006666]
dot_o: 1.e-3
q: 20

l_c: 1.0
mu: 0.001

isobrittle_generic#

type: isobrittle

output: [f_phi]

G_crit: 1400000.0
l_c: 1.0
mu: 0.001

mechanical#

eigen#

thermalexpansion_AISI304#
type: thermalexpansion

references:
  - R.H. Bogaard et al.,
    Thermochimica Acta 218:373-393, 1993,
    https://doi.org/10.1016/0040-6031(93)80437-F,
    fit to Fig. 6 (T_min=100K, T_max=1400K)

A_11: 2.068e-08
A_11,T: 1.579e-09
A_11,T^2: 3.449e-13

T_ref: 293.15
thermalexpansion_Al#
type: thermalexpansion

references:
  - https://en.wikipedia.org/wiki/Thermal_expansion,
    293.15K

A_11: 23.1e-6
thermalexpansion_Au#
type: thermalexpansion

references:
  - https://en.wikipedia.org/wiki/Thermal_expansion,
    293.15K

A_11: 14.e-6
thermalexpansion_C35E#
type: thermalexpansion

references:
  - https://commons.wikimedia.org/wiki/File:Coefficient_dilatation_lineique_aciers.svg,
    fit to image description (Scilab code)

A_11: 12.70371e-6
A_11,T: 7.54e-9
A_11,T^2: -1.0e-11

T_ref: 273.0
thermalexpansion_Cu#
type: thermalexpansion

references:
  - https://en.wikipedia.org/wiki/Thermal_expansion,
    293.15K

A_11: 17.e-6
thermalexpansion_Fe#
type: thermalexpansion

references:
  - https://en.wikipedia.org/wiki/Thermal_expansion,
    293.15K

A_11: 11.8e-6
thermalexpansion_Sn-beta#
type: thermalexpansion

references:
  - V.T. Deshpande and D.B. Sirdeshmukh,
    Acta Crystallographica 15:294-295, 1962,
    https://doi.org/10.1107/S0365110X62000742,
    fit to Tab. 2 (T_min=30ºC, T_max=210ºC)

A_11: 1.639e-05
A_11,T: 1.799e-08
A_11,T^2: 1.734e-10

A_33: 3.263e-05
A_33,T: 1.387e-08
A_33,T^2: 5.794e-10

T_ref: 293.15
thermalexpansion_W#
type: thermalexpansion

references:
  - https://en.wikipedia.org/wiki/Thermal_expansion,
    293.15K

A_11: 4.5e-6
thermalexpansion_X20Cr13#
type: thermalexpansion

references:
  - https://commons.wikimedia.org/wiki/File:Coefficient_dilatation_lineique_aciers.svg,
    fit to image description (Scilab code)

A_11: 11.365e-6
A_11,T: 5.0e-9

T_ref: 273.0

elastic#

Hooke_AISI304#
type: Hooke

references:
  - H.M. Ledbetter,
    physica status solidi (a) 85(1):89-96, 1984,
    https://doi.org/10.1002/pssa.2210850111

C_11: 204.6e+9
C_12: 137.7e+9
C_44: 126.2e+9
Hooke_Ag#
type: Hooke

references:
  - J.R. Neighbours and G.A. Alers,
    Physical Review 111:707-712, 1958,
    https://doi.org/10.1103/PhysRev.111.707
  - Y.A. Chang and L. Himmel,
    Journal of Applied Physics 37:3567-3572, 1966,
    https://doi.org/10.1063/1.1708903

C_11: 122.9e+9
C_11,T: -313.5e+5
C_11,T^2: -107.3e+2

C_12: 91.55e+9
C_12,T: -164.1e+5
C_12,T^2: -681.6e+1

C_44: 42.63e+9
C_44,T: -180.5e+5
C_44,T^2: -353.8e+1

T_ref: 300
Hooke_Al#
type: Hooke

references:
  - G.N. Kamm and G.A. Alers,
    Journal of Applied Physics 35:327-330, 1964,
    https://doi.org/10.1063/1.1713309,
    fit to Tab. I (T_min=100K, T_max=300K)
  - D. Gerlich and E.S. Fisher,
    Journal of Physics and Chemistry of Solids 30:1197-1205, 1969
    https://doi.org/10.1016/0022-3697(69)90377-1,
    fit to Tab. 2 (T_min=293K, T_max=900K)

C_11: 106.9e+9
C_11,T: -3.685e+7
C_11,T^2: -1.016e+4

C_12: 60.55e+9
C_12,T: -8.307e+6
C_12,T^2: -4.353e+3

C_44: 28.37e+9
C_44,T: -1.418e+7
C_44,T^2: -3.253e+3

T_ref: 293.15
Hooke_Au#
type: Hooke

references:
  - J.P. Hirth and J. Lothe,
    Theory of Dislocations, 1982,
    John Wiley & Sons,
    page 837

C_11: 186.e+9
C_12: 157.e+9
C_44: 42.e+9
Hooke_Cu#
type: Hooke

references:
  - W.C. Overton, Jr. and J. Gaffney,
    Physical Review 98(4):969-977, 1955,
    https://doi.org/10.1103/PhysRev.98.969,
    fit to Tab. I (T_min=100K, T_max=300K)

C_11: 168.6e+9
C_11,T: -3.779e+7
C_11,T^2: -2.536e+4

C_12: 121.5e+9
C_12,T: -1.632e+7
C_12,T^2: -1.116e+4

C_44: 75.59e+9
C_44,T: -2.912e+7
C_44,T^2: -1.669e+4

T_ref: 293.15
Hooke_Fe#
type: Hooke

references:
  - D.J. Dever,
    Journal of Applied Physics 43(8):3293-3301, 1972,
    https://doi.org/10.1063/1.1661710
    fit to Tab. II (T_min=25ºC, T_max=880ºC)

C_11: 232.1e+9
C_11,T: -4.678e+7
C_11,T^2: -5.762e+4

C_12: 135.9e+9
C_12,T: -1.695e+7
C_12,T^2: 1.555e+3

C_44: 117.0e+9
C_44,T: -2.047e+7
C_44,T^2: -2.814e+2

T_ref: 293.15
Hooke_IN625#
type: Hooke

references:
  - Wang et al.,
    Materials Science and Engineering:A 674:406-412, 2016,
    https://doi.org/10.1016/j.msea.2016.08.010,
    fitted to Tab. 2 (last 3 rows)

C_11: 243.3e+9
C_11,T: -6.380e+5
C_11,T^2: -8.362e+4

C_12: 156.7e+9
C_12,T: 2.091e+7
C_12,T^2: -4.675e+4

C_44: 117.8e+9
C_44,T: -3.800e+7
C_44,T^2: 1.587e+4

T_ref: 293.15
Hooke_Mg#
type: Hooke

references:
  - L.J. Slutsky and C.W. Garland,
    Physical Review 107(4):972-976, 1957,
    https://doi.org/10.1103/PhysRev.107.972,
    fit to Tab. I (T_min=100K, T_max=300K)

C_11: 59.50e+9
C_11,T: -1.930e+7
C_11,T^2: -1.215e+4

C_33: 61.72e+9
C_33,T: -2.175e+7
C_33,T^2: -5.624e+3

C_44: 16.46e+9
C_44,T: -1.006e+7
C_44,T^2: -7.692e+3

C_12: 25.62e+9
C_12,T: -2.216e+6
C_12,T^2: -4.138e+3

C_13: 21.46e+9
C_13,T: -1.921e+6
C_13,T^2: -4.283e+3

T_ref: 293.15
Hooke_Ni#
type: Hooke

references:
  - G.A. Alers,
    Journal of Physics and Chemistry of Solids 13(1-2):40-55, 1960,
    https://doi.org/10.1016/0022-3697(60)90125-6,
    fit to Tab. 2 (T_min=100K, T_max=700K)

C_11: 251.0e+9
C_11,T: -4.998e+7
C_11,T^2: -2.952e+4

C_12: 150.0e+9
C_12,T: -4.269e+6
C_12,T^2: -6.429e+3

C_44: 123.7e+9
C_44,T: -3.618e+7
C_44,T^2: -7.024e+3

T_ref: 293.15
Hooke_Pt#
type: Hooke

references:
   - S.M. Collard and R.B. McLellan,
     Acta Metallurgica et Materialia 40:699-702, 1992,
     https://doi.org/10.1016/0956-7151(92)90011-3

C_11: 373.42e+9
C_11,T: -8.929e+7
C_11,T^2: -1.298e+5
C_11,T^3: 1.2807e+2
C_11,T^4: -4.6114e-2

C_12: 241.74e+9
C_12,T: 5.705e+7
C_12,T^2: 0.4511e+5
C_12,T^3: -0.4860e+2
C_12,T^4: 1.446e-2

C_44: 77.65e+9
C_44,T: -1.342e+7
C_44,T^2: -0.1493e+5
C_44,T^3: 0.1260e+2
C_44,T^4: -0.6470e-2

T_ref: 0
Hooke_SAE1050-martensite#
type: Hooke

references:
  - S.A. Kim and W.L. Johnson,
    Materials Science & Engineering A 452-453:633-639, 2007,
    https://doi.org/10.1016/j.msea.2006.11.147

C_11: 268.1e+9
C_12: 111.2e+9
C_44: 79.06e+9
Hooke_Sn-beta#
type: Hooke

references:
  - J.A. Rayne and B.S. Chandrasekhar,
    Physical Review 120(5):1658-1663, 1960,
    https://doi.org/10.1103/PhysRev.120.1658,
    fit to Fig. 2 (T_min=100K, T_max=300K) and Tab. IV (C_13, T_min=77K, T_max=300K)

C_11: 72.90e+9
C_11,T: -4.399e+7
C_11,T^2: -2.645e+4

C_12: 59.27e+9
C_12,T: 1.058e+7
C_12,T^2: 1.002e+4

C_13: 35.80e+9
C_13,T: -2.870e+6

C_33: 88.78e+9
C_33,T: -5.250e+7
C_33,T^2: 3.546e+3

C_44: 22.26e+9
C_44,T: -1.982e+7
C_44,T^2: -8.711e+3

C_66: 24.18e+9
C_66,T: -1.806e+7
C_66,T^2: -4.112e+3

T_ref: 293.15
Hooke_TWIP-steel#
type: Hooke

references:
  - D. Music et al.,
    Applied Physics Letters 99(19):191904, 2007,
    https://doi.org/10.1063/1.2807677
  - S.L. Wong et al.,
    Acta Materialia 118:140-151, 2016,
    https://doi.org/10.1016/j.actamat.2016.07.032

C_11: 175.0e+9
C_12: 115.0e+9
C_44: 135.0e+9
Hooke_Ti#
type: Hooke

references:
  - E.S. Fisher and C.J. Renken,
    Physical Review 135(2A):A482-A494, 1964,
    https://doi.org/10.1103/PhysRev.135.A482,
    fit to Tab. IV (T_min=150K, T_max=250K)
  - H. Ogi et al.,
    Acta Materialia 52(7):2075-2080, 2004,
    https://doi.org/10.1016/j.actamat.2004.01.002,
    fit to Fig. 3 (T_min=300K, T_max=900K)

C_11: 162.6e+9
C_11,T: -6.150e+7
C_11,T^2: -5.557e+2

C_33: 183.3e+9
C_33,T: -1.655e+07
C_33,T^2: -1.022e+04

C_44: 45.80e+9
C_44,T: -2.936e+07
C_44,T^2: 7.120e+02

C_12: 89.97e+9
C_12,T: 2.776e+6
C_12,T^2: -2.389e+4

C_13: 69.53e+9
C_13,T: 1.057e+7
C_13,T^2: -2.966e+3

T_ref: 293.15
Hooke_W#
type: Hooke

references:
  - F.H. Featherston and J.R. Nieghbours,
    Physical Review 130(4):1324-1333,
    https://doi.org/10.1103/PhysRev.130.1324,
    fit to Tab. III (T_min=100K, T_max=300K)

C_11: 523.6e+9
C_11,T: -7.607e+7
C_11,T^2: -1.551e+5

C_12: 205.1e+9
C_12,T: -2.843e+6

C_44: 160.8e+9
C_44,T: -1.057e+7
C_44,T^2: 9.933e+3

T_ref: 293.15
Hooke_vanishing-Poisson-ratio#
type: Hooke

references:
  - T. Maiti and P. Eisenlohr,
    Scripta Materialia 145:37-40, 2018,
    https://doi.org/10.1016/j.scriptamat.2017.09.047

C_11: 1.e+8
C_12: 1.e+6
C_44: 4.95e+7

plastic#

dislotungsten_W#
type: dislotungsten

references:
  - D. Cereceda et al.,
    International Journal of Plasticity 78:242-265, 2016,
    http://dx.doi.org/10.1016/j.ijplas.2015.09.002
  - R. Gröger et al.,
    Acta Materialia 56(19):5412-5425, 2008,
    https://doi.org/10.1016/j.actamat.2008.07.037

output: [Lambda_sl]

N_sl: [12]

b_sl: [2.72e-10]
rho_mob_0: [1.0e+9]  # estimated from section 3.2
rho_dip_0: [1.0]     # not given
Q_s: [2.61154e-19]   # 1.63 eV, Delta_H0
B: [8.3e-5]
omega: [9.1e+11]     # nu_0
p_sl: [0.86]
q_sl: [1.69]
tau_Peierls: [2.03e+9]
h: [2.566e-10]
h_sl-sl: [0.009, 0.72, 0.009, 0.05, 0.05, 0.06, 0.09]
w: [2.992e-09] # 11b

##values in Cereceda et al. are high, using parameters from Gröger et al.
a_nonSchmid: [0.0, 0.56, 0.75] # Table 2

##(almost) no annhilation, adjustment needed for simulations beyond the yield point
i_sl: [1]  # c, eq. (25)
D: 1.0e+20 # d_g, eq. (25)
D_a: 1.0 # d_edge = D_a*b

##disable climb (not discussed in Cereceda et al.)
D_0: 0.0
f_at: 1
Q_cl: 1.0
dislotwin_IF-steel#
type: dislotwin

references:
  - K. Sedighiani et al.,
    International Journal of Plasticity 134:102779, 2020,
    https://doi.org/10.1016/j.ijplas.2020.102779
  - K. Sedighiani et al.,
    Mechanics of Materials, 164:104117, 2022,
    https://doi.org/10.1016/j.mechmat.2021.104117

output: [rho_dip, rho_mob]

N_sl: [12, 12]

b_sl: [2.49e-10, 2.49e-10]
rho_mob_0: [2.81e12, 2.8e+12]
rho_dip_0: [1.0, 1.0] # not given
v_0: [1.4e+3, 1.4e+3]
Q_sl: [1.57e-19, 1.57e-19] # Delta_F
tau_0: [454.e+6, 454.e+6]
p_sl: [0.325, 0.325]
q_sl: [1.55, 1.55]
i_sl: [23.3, 23.3]
D_a: 7.4 # C_anni
B: [0.001, 0.001]
h_sl-sl: [0.1, 0.72, 0.1, 0.053, 0.053, 0.073, 0.137, 0.72, 0.72, 0.053, 0.053, 0.053, 0.053, 0.073, 0.073, 0.073, 0.073, 0.073, 0.073, 0.137, 0.073, 0.073, 0.137, 0.073]
Q_cl: 5.4e-19 # no recovery!
D: 40.e-6 # estimated
dislotwin_alpha-Brass-shearbanding#
type: dislotwin

references:
  - N. Jia et al.,
    Acta Materialia 60(3):1099-1115, 2012,
    https://doi.org/10.1016/j.actamat.2011.10.047
  - N. Jia et al.,
    Acta Materialia 60:3415-3434, 2012,
    https://doi.org/10.1016/j.actamat.2012.03.005

gamma_0_sb: 0.0001
tau_sb: 180.0e6 # tau_hat_sb
Q_sb: 4.0e-19 # Q_0
p_sb: 1.15
q_sb: 1.0
isotropic_free-surface#
type: isotropic

references:
  - T. Maiti and P. Eisenlohr,
    Scripta Materialia 145:37-40, 2018,
    https://doi.org/10.1016/j.scriptamat.2017.09.047

output: [xi]

dot_gamma_0: 0.001
n: 20.
xi_0: 0.3e+6
xi_inf: 0.6e+6
a: 2.
h_0: 1.e+6
M: 1.
h: 1.
dilatation: True
nonlocal_Al#
type: nonlocal

references:
  - C. Kords,
    On the role of dislocation transport in the constitutive description of crystal plasticity,
    RWTH Aachen 2013,
    http://publications.rwth-aachen.de/record/229993/files/4862.pdf

output: [rho_u_ed_pos, rho_b_ed_pos, rho_u_ed_neg, rho_b_ed_neg, rho_u_sc_pos, rho_b_sc_pos, rho_u_sc_neg, rho_b_sc_neg, rho_d_ed, rho_d_sc]

N_sl: [12]

b_sl: [2.86e-10]
V_at: 0.017e-27 # Omega
d_ed: [1.6e-9]
d_sc: [10.e-9]
i_sl: [60]      # k_2 (lambda_0 in Tab. 7.1)
f_ed_mult: 0.1  # k_1

rho_u_ed_neg_0: [1.25e9] # 6e10 / (12*4)
rho_u_ed_pos_0: [1.25e9] # 6e10 / (12*4)
rho_u_sc_neg_0: [1.25e9] # 6e10 / (12*4)
rho_u_sc_pos_0: [1.25e9] # 6e10 / (12*4)
rho_d_ed_0: [0]
rho_d_sc_0: [0]

D_0: 7.e-29
Q_cl: 0.0 # no temperature dependency
Q_sol: 2.00272e-19 # 1.25 eV
c_sol: 1.5e-6       # correct unit?
f_sol: 2.0          # d_obst in multiples of b
tau_Peierls_ed: [.1e6]
tau_Peierls_sc: [.1e6]
w: 10              # w_k in multiple of b

p_sl: 1
q_sl: 1

nu_a: 50.e+9
B: 1.e-2
f_ed: 1.0  # k_3

h_sl-sl: [0, 0, 0.625, 0.07, 0.137, 0.137, 0.122] # Table 3.4

chi_GB: 0.0      # full blocking at GB
chi_surface: 1.0 # no blocking at surface

f_F: 0.0         # no line tension correction
sigma_rho_u: 0   # no random distribution


short_range_stress_correction: false
rho_significant: 1.e6
nonlocal_Ni#
type: nonlocal

references:
  - C. Kords,
    On the role of dislocation transport in the constitutive description of crystal plasticity,
    RWTH Aachen 2013,
    http://publications.rwth-aachen.de/record/229993/files/4862.pdf

output: [rho_u_ed_pos, rho_b_ed_pos, rho_u_ed_neg, rho_b_ed_neg, rho_u_sc_pos, rho_b_sc_pos, rho_u_sc_neg, rho_b_sc_neg, rho_d_ed, rho_d_sc]

N_sl: [12]

b_sl: [2.48e-10]
V_at: 0.012e-27 # Omega
d_ed: [2.6e-9]
d_sc: [12.e-9]
i_sl: [45]      # k_2
f_ed_mult: 0.1  # k_1

rho_u_ed_neg_0: [6.e+10] # 2.88e12 / (12*4)
rho_u_ed_pos_0: [6.e+10] # 2.88e12 / (12*4)
rho_u_sc_neg_0: [6.e+10] # 2.88e12 / (12*4)
rho_u_sc_pos_0: [6.e+10] # 2.88e12 / (12*4)
rho_d_ed_0: [0]
rho_d_sc_0: [0]

D_0: 3.e-53
Q_cl: 0.0 # no temperature dependency
Q_sol: 1.79444e-19 # 1.12 eV
c_sol: 5.e-7       # correct unit?
f_sol: 1.          # d_obst
tau_Peierls_ed: [.1e6]
tau_Peierls_sc: [.1e6]
w: 10              # w_k

p_sl: 1
q_sl: 1

nu_a: 50.e+9
B: 1.e-3
f_ed: 0.01  # k_3

h_sl-sl: [0, 0, 0.625, 0.07, 0.137, 0.137, 0.122] # Table 3.4

chi_GB: 0.0      # full blocking at GB
chi_surface: 1.0 # no blocking at surface

f_F: 0.0         # no line tension correction
sigma_rho_u: 0   # no random distribution


short_range_stress_correction: false
rho_significant: 1.e6
phenopowerlaw_Al#
type: phenopowerlaw

references:
  - W.F. Hosford et al.,
    Acta Metallurgica 8(3):187-199, 1960,
    https://doi.org/10.1016/0001-6160(60)90127-9,
    fitted from Fig. 5
  - U.F. Kocks,
    Metallurgical and Materials Transactions B 1:1121–1143, 1970,
    https://doi.org/10.1007/BF02900224

output: [xi_sl, gamma_sl]

N_sl: [12]

n_sl: 20
a_sl: 3.1
h_0_sl-sl: 1.7e+8
xi_0_sl: [5.0e+6]
xi_inf_sl: [37.5e+6]
h_sl-sl: [1, 1, 1.4, 1.4, 1.4, 1.4, 1.4]
dot_gamma_0_sl: 7.5e-5
phenopowerlaw_Au#
type: phenopowerlaw

references:
  - D. Ma et al.,
    Acta Materialia 103:796-808, 2016,
    https://doi.org/10.1016/j.actamat.2015.11.016
  - I. Kovács and G.Vörös,
    International Journal of Plasticity 12:35-43, 1996,
    https://doi.org/10.1016/S0749-6419(95)00043-7
  - U.F. Kocks,
    Metallurgical and Materials Transactions B 1:1121–1143, 1970,
    https://doi.org/10.1007/BF02900224

output: [xi_sl, gamma_sl]

N_sl: [12]

n_sl: 83.3
a_sl: 1.0
h_0_sl-sl: 75.0e+6
xi_0_sl: [26.25e+6]
xi_inf_sl: [53.0e+6]
h_sl-sl: [1, 1, 1.4, 1.4, 1.4, 1.4, 1.4]
dot_gamma_0_sl: 0.001
phenopowerlaw_Cu#
type: phenopowerlaw

references:
  - T Takeuchi,
    Transactions of the Japan Institute of Metals 16(10):629-640, 1975,
    https://doi.org/10.2320/matertrans1960.16.629,
    fitted from Fig. 3b
  - U.F. Kocks,
    Metallurgical and Materials Transactions B 1:1121–1143, 1970,
    https://doi.org/10.1007/BF02900224

output: [xi_sl, gamma_sl]

N_sl: [12]

n_sl: 20
a_sl: 1.0
h_0_sl-sl: 2.4e+8
xi_0_sl: [1.5e+6]
xi_inf_sl: [112.5e+6]
h_sl-sl: [1, 1, 1.4, 1.4, 1.4, 1.4, 1.4]
dot_gamma_0_sl: 3.e-3
phenopowerlaw_DP-steel-ferrite#
type: phenopowerlaw

references:
  - C.C. Tasan et al.,
    Acta Materialia 81:386-400, 2014,
    https://doi.org/10.1016/j.actamat.2014.07.071
  - U.F. Kocks,
    Metallurgical and Materials Transactions B 1:1121–1143, 1970,
    https://doi.org/10.1007/BF02900224

output: [xi_sl, gamma_sl]

N_sl: [12, 12]

n_sl: 20
a_sl: 2.25
h_0_sl-sl: 1.0e+9
xi_0_sl: [95.e+6, 96.e+6]
xi_inf_sl: [222.e+6, 412.e+6]
h_sl-sl: [1, 1.4, 1, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4]
dot_gamma_0_sl: 0.001
phenopowerlaw_Mg#
type: phenopowerlaw

references:
  - F. Wang et al.,
    Acta Materialia 80:77-93, 2014,
    https://doi.org/10.1016/j.actamat.2014.07.048

output: [xi_sl, xi_tw]

N_sl: [3, 3, 6, 0, 6]  # basal, prism, 1. pyr<a>, -, 2. pyr<c+a>
N_tw: [6, 0, 6]        # tension, -, compression

xi_0_sl:   [10.e+6,  55.e+6,  60.e+6, 0.,  60.e+6]
xi_inf_sl: [40.e+6, 135.e+6, 150.e+6, 0., 150.e+6]
xi_0_tw:   [40.e+6, 0., 60.e+6]

a_sl: 2.25
dot_gamma_0_sl: 0.001
dot_gamma_0_tw: 0.001
n_sl: 20
n_tw: 20
f_sat_sl-tw: 10.0

h_0_sl-sl: 500.0e+6
h_0_tw-tw:  50.0e+6
h_0_tw-sl: 150.0e+6
h_sl-sl: [+1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0, -1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0, -1.0, -1.0, -1.0, -1.0,  1.0,  1.0,  1.0,  1.0,
          -1.0, -1.0, -1.0, -1.0,  1.0,  1.0,  1.0,  1.0,  1.0]  # unused entries are indicated by -1.0
h_tw-tw: [+1.0,  1.0, -1.0, -1.0, -1.0, -1.0,  1.0, -1.0,  1.0,  1.0,
          -1.0,  1.0]  # unused entries are indicated by -1.0
h_tw-sl:  [1.0, -1.0,  1.0, -1.0,  1.0, -1.0,  1.0, -1.0,  1.0, -1.0,
           1.0, -1.0, -1.0, -1.0, -1.0, -1.0, +1.0, -1.0,  1.0, -1.0]  # unused entries are indicated by -1.0
h_sl-tw:  [1.0, -1.0,  1.0, -1.0,  1.0, -1.0,  1.0, -1.0,  1.0, -1.0,
           1.0, -1.0, -1.0, -1.0, -1.0, -1.0, +1.0, -1.0,  1.0]  # unused entries are indicated by -1.0
phenopowerlaw_Pt-5%Cu#
type: phenopowerlaw

references:
  - K.M. Jackson and C. Lang,
    Platinum Metals Review 50:15-19, 2006,
    https://doi.org/10.1595/147106705X93359,
    fitted from Fig. 5 (Pt-5% Cu recrystallised)
  - U.F. Kocks,
    Metallurgical and Materials Transactions B 1:1121–1143, 1970,
    https://doi.org/10.1007/BF02900224

N_sl: [12]

n_sl: 1.6
a_sl: 0.8
h_0_sl-sl: 300.0e+6
xi_0_sl: [150.0e+6]
xi_inf_sl: [500.0e+6]
h_sl-sl: [1, 1, 1.4, 1.4, 1.4, 1.4, 1.4]
dot_gamma_0_sl: 0.0001
phenopowerlaw_Sn-beta#
type: phenopowerlaw

references:
  - A. Chakraborty and P. Eisenlohr,
    Journal of Applied Physics 124:025302, 2018,
    https://doi.org/10.1063/1.5029933

output: [xi_sl, gamma_sl]

N_sl: [2, 2, 2, 4, 2, 4, 2, 2, 4, 0, 0, 8]

n_sl: 6.0
a_sl: 2.0
h_0_sl-sl: 20.0e+6
xi_0_sl:   [8.5e+6,  4.3e+6, 10.4e+6, 4.5e+6,  5.6e+6,  5.1e+6,  7.4e+6, 15.0e+6, 6.6e+6, 0.0, 0.0, 12.0e+6]
xi_inf_sl: [11.0e+6, 9.0e+6, 11.0e+6, 9.0e+6, 10.0e+6, 10.0e+6, 10.0e+6, 10.0e+6, 9.0e+6, 0.0, 0.0, 13.0e+6]
h_sl-sl: [+1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0, # 50
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, # 100
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
          -1.0, -1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0, -1.0, -1.0,  1.0,  1.0, -1.0, -1.0,  1.0,  1.0,  1.0, # 150
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0]  # unused entries are indicated by -1.0
dot_gamma_0_sl: 2.6e-8
phenopowerlaw_Ti#
type: phenopowerlaw

references:
  - C. Zambaldi et al.,
    Journal of Materials Research 27(1):356-367, 2021,
    https://doi.org/10.1557/jmr.2011.334
  - L. Wang et al.,
    Acta Materialia 132:598-610, 2017,
    https://doi.org/10.1016/j.actamat.2017.05.015

output: [gamma_sl]

N_sl: [3, 3, 0, 12]   # basal, prism, -, 1. pyr<c+a>

n_sl: 20
a_sl: 2.0
dot_gamma_0_sl: 0.001
h_0_sl-sl: 200.e+6

##C. Zambaldi et al.:
xi_0_sl:   [349.e+6, 150.e+6, 0.0, 1107.e+6]
xi_inf_sl: [568.e+6, 150.e+7, 0.0, 3420.e+6]
##L. Wang et al. :
##xi_0_sl:   [127.e+6, 96.e+6, 0.0, 240.e+6]

h_sl-sl: [+1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0, -1.0, -1.0,
          -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,
          +1.0,  1.0,  1.0,  1.0,  1.0,  1.0] # unused entries are indicated by -1.0

thermal#

AISI304#

references:
  - B.F. Blackwell et al.
    Proceedings of 34th National Heat Transfer Conference 2000
    https://www.osti.gov/servlets/purl/760791
  - R.H. Bogaard et al.
    Thermochimica Acta 218:373-393, 1993
    https://doi.org/10.1016/0040-6031(93)80437-F

C_p: 470.0
K_11: 14.34

Al#

references:
  - J.G. Hust and A.B. Lankford,
    Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
    US Department of Commerce, Boulder, Colorado, 1984,
    fit to Tab. 3.4.1 (RRR=1000, T_min=200K, T_max=900K)
  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

output: [T]

K_11: 2.380e+2
K_11,T: 2.068e-3
K_11,T^2: -7.765e-5

T_ref: 293.15

C_p: 910.0

Au#

references:
  - https://de.wikipedia.org/wiki/Gold

C_p: 128.0
K_11: 320.0

Cu#

references:
  - J.G. Hust and A.B. Lankford,
    Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
    US Department of Commerce, Boulder, Colorado, 1984,
    fit to Tab. 2.4.1 (RRR=1000, T_min=200K, T_max=1000K)
  - https://www.mit.edu/~6.777/matprops/copper.htm

output: [T]

K_11: 4.039e+2
K_11,T: -8.119e-2
K_11,T^2: 1.454e-5

T_ref: 293.15

C_p: 385.0

Fe#

references:
  - J.G. Hust and A.B. Lankford,
    Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
    US Department of Commerce, Boulder, Colorado, 1984,
    fit to Tab. 4.4.1 (RRR=300, T_min=200K, T_max=1000K)
  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

output: [T]

K_11: 8.055e+1
K_11,T: -1.051e-1
K_11,T^2: 5.464e-5

T_ref: 293.15

C_p: 450.0

Ni#

references:
  - Y.S. Touloukian et al.,
    TPRC Data Series Volume 1. Thermal conductivity - metallic elements and alloys,
    IFI/Plenum, 1970,
    fit to Tab. 35R (T_min=150K, T_max=500K)
  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

output: [T]

K_11: 9.132e+1
K_11,T: -1.525e-1
K_11,T^2: 3.053e-4

T_ref: 293.15

C_p: 440.0

Sn-beta#

references:
  - Y.S. Touloukian et al.,
    TPRC Data Series Volume 1. Thermal conductivity - metallic elements and alloys,
    IFI/Plenum, 1970,
    fit to Tab. 61R (T_min=100K, T_max=400K)
  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

output: [T]

K_11: 7.414e+1
K_11,T: -6.465e-2
K_11,T^2: 2.066e-4

K_33: 5.147e+1
K_33,T: -4.506e-2
K_33,T^2: 1.435e-4

T_ref: 293.15

C_p: 210.0

W#

references:
  - J.G. Hust and A.B. Lankford,
    Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
    US Department of Commerce, Boulder, Colorado, 1984,
    fit to Tab. 5.4.1 (RRR=300, T_min=200K, T_max=1000K)
  - https://www.mit.edu/~6.777/matprops/tungsten.htm

output: [T]

K_11: 1.758e+2
K_11,T: -1.605e-1
K_11,T^2: 1.160e-4

T_ref: 293.15

C_p: 132.51

adiabatic#

C_p: 1
K_11: 0
K_33: 0

fast-convection#

C_p: 1
K_11: 1.e+30
K_33: 1.e+30

steel-0.5C#

references:
  - https://www.engineeringtoolbox.com/thermal-conductivity-metals-d_858.html
  - https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

C_p: 490.0
K_11: 54.0

source#

dissipation_generic#
type: dissipation

kappa: .9
externalheat_ramp-and-hold#
type: externalheat

f_T: [1, 1, 0, 0]
t_n: [0, 500, 500.001, 1000]