Heat_Capacity_from_pycalphad.ipynb

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    "# Specific Heat Capacity from pycalphad\n",
    "\n",
    "In this notebook, the interaction between PyRolL and pycalphad is demonstrated. \n",
    "In this example, the calphad method is used to calculate the specific heat capacity of the low-carbon steel C15 (1.0401) using free `tdb` databases provided by [MatCalc Engineering GmbH](https://www.matcalc.at/index.php/databases/open-databases). The measured chemical composition (wt%) of a example can be seen in the following table: \n",
    "\n",
    "| Steel grade  | C    | Si   | Mn   | Cr   | Ni   | Cu   | P     | S      | Fe    |\n",
    "|--------------|------|------|------|------|------|------|-------|--------|-------|\n",
    "| C15 (1.0401) | 0.16 | 0.16 | 0.69 | 0.12 | 0.09 | 0.17 | 0.002 | 0.0065 | 98.43 |\n",
    "\n",
    "Further, thermodynamical database files (`tdb`) for other alloying systems can be found [here](https://avdwgroup.engin.brown.edu/). The specific-heat-capacity is mostly important when considering cooling processes which often follow a hot rolling process. As always, we first import the necessary python modules."
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    "import numpy as np\n",
    "import pyroll.core as pr\n",
    "import matplotlib.pyplot as plt\n",
    "import pycalphad.variables as v\n",
    "import scipy.interpolate as interpolate\n",
    "\n",
    "\n",
    "from pycalphad import Database\n",
    "from scipy.integrate import quad\n",
    "from pycalphad import equilibrium\n",
    "from pyroll.freiberg_flow_stress import FreibergFlowStressCoefficients"
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   "source": [
    "Loading of the thermodynamic database from file. A warning here regarding a type definition character is to be expected and no error."
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      "/home/christoph/.local/share/virtualenvs/pyroll-examples-YS1GospC/lib/python3.10/site-packages/pycalphad/io/tdb.py:929: UserWarning: The type definition character `%` was defined in the following phases: ['LIQUID', 'FCC_A1', 'BCC_A2', 'H_BCC', 'BCC_DISL', 'HCP_A3', 'ALPHA_MN', 'BETA_MN', 'BETA_RHOMBO_B', 'DIAMOND_A4', 'GRAPHITE', 'BCC_B2', 'CHI_A12', 'CO3MO', 'CO3V', 'COV3', 'CR3MN5', 'G_PHASE', 'LAVES_PHASE', 'MNNI', 'MNNI2', 'MNNI_T3', 'MU_PHASE', 'MU_PHASE_I', 'ETA', 'NITI2', 'PI_PHASE', 'R_PHASE', 'SIGMA', 'FE17Y2', 'NI5Y', 'PDFE_L12', 'PDMN_AF', 'PDMN_P', 'PDMN_B2', 'PD2MN', 'PD3MN', 'PD5MN3', 'PD6FE5MN2', 'CEMENTITE', 'CR2VC2', 'K_CARB', 'KSI_CARBIDE', 'M3C2', 'M6C', 'M7C3', 'M12C', 'M23C6', 'MOC_ETA', 'V3C2', 'WC', 'EPS_CARB', 'ETA_CARB', 'FE24C10', 'KSI_FE5C2', 'ALN', 'ALN_EQU', 'BN_HP4', 'CR3NI2SIN', 'FE4N', 'MN6N4', 'MN6N5', 'MNSIN2', 'SI3N4', 'ZET', 'CRB', 'CR2B', 'CR5B3', 'FEB', 'FENBB', 'FE3NB3B4', 'M2B', 'MNB2', 'MNB4', 'O_MN2B', 'MN3B4', 'MOB', 'MOB2', 'MO2M1B2', 'NBB', 'NB3B2', 'M5B6', 'TIB', 'TIB2', 'TI3B4', 'A_CHALC', 'ANILITE', 'B_CHALC', 'COVELLITE', 'CU2S', 'DIGENITE', 'DISULF', 'DJURLEITE', 'FC_MONO', 'FC_ORTHO', 'FES_P', 'MNS_Q', 'PYRR', 'TIS', 'TI4C2S2', 'CORUND', 'HALITE', 'HF1O2_M', 'HF1O2_T', 'HF1O2_C', 'LA2O3_A', 'LA2O3_H', 'LA2O3_C', 'SIO2', 'SPINEL', 'TIO2', 'TI2O3', 'TRID', 'Y2O3_C', 'Y2O3_H', 'YALO3', 'Y4AL2O9', 'Y2TIO5', 'Y2TI2O7', 'O1_GAS', 'M2P', 'M3P'], but no corresponding TYPE_DEFINITION line was found in the TDB.\n",
      "  warnings.warn(f\"The type definition character `{typechar}` was defined in the following phases: \"\n"
     ]
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   "source": [
    "database = Database('mc_fe_v2.059.pycalphad.tdb')"
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    "## Conversion of weight-fractions to molar-fractions\n",
    "The industrial standard, how to provide the chemical composition of an alloy is to use weight-fractions. In the scientific realm, however, molar-fractions are more common. Therefore, we need a function which converts weight-fractions to molar fractions. This can be handled by the `get_mole_fractions` function of `pycalphad`. Further, one needs to calculate the total molar mass of the alloy. Therefore, a dict with the respective molar masses of each atom is defined."
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    "molar_masses_grams_per_mol = {\n",
    "    'H': 1.008, 'HE': 4.0026, 'LI': 6.94, 'BE': 9.0122, 'B': 10.81,\n",
    "    'C': 12.011, 'N': 14.007, 'O': 15.999, 'F': 18.998, 'NE': 20.180,\n",
    "    'NA': 22.990, 'MG': 24.305, 'AL': 26.982, 'SI': 28.085, 'P': 30.974,\n",
    "    'S': 32.06, 'CL': 35.45, 'AR': 39.948, 'K': 39.098, 'CA': 40.078,\n",
    "    'SC': 44.956, 'TI': 47.867, 'V': 50.942, 'CR': 51.996, 'MN': 54.938,\n",
    "    'FE': 55.845, 'CO': 58.933, 'NI': 58.693, 'CU': 63.546, 'ZN': 65.38,\n",
    "    'GA': 69.723, 'GE': 72.63, 'AS': 74.922, 'SE': 78.971, 'BR': 79.904,\n",
    "    'KR': 83.798, 'RB': 85.468, 'SR': 87.62, 'Y': 88.906, 'ZR': 91.224,\n",
    "    'NB': 92.906, 'MO': 95.95, 'TC': 98.0, 'RU': 101.07, 'RH': 102.91,\n",
    "    'PD': 106.42, 'AG': 107.87, 'CD': 112.41, 'IN': 114.82, 'SN': 118.71,\n",
    "    'SB': 121.76, 'TE': 127.6, 'I': 126.9, 'XE': 131.29, 'CS': 132.91,\n",
    "    'BA': 137.33, 'LA': 138.91, 'CE': 140.12, 'PR': 140.91, 'ND': 144.24,\n",
    "    'PM': 145.0, 'SM': 150.36, 'EU': 151.96, 'GD': 157.25, 'TB': 158.93,\n",
    "    'DY': 162.5, 'HO': 164.93, 'ER': 167.26, 'TM': 168.93, 'YB': 173.05,\n",
    "    'LU': 174.97, 'HF': 178.49, 'TA': 180.95, 'W': 183.84, 'RE': 186.21,\n",
    "    'OS': 190.23, 'IR': 192.22, 'PT': 195.08, 'AU': 196.97, 'HG': 200.59,\n",
    "    'TL': 204.38, 'PB': 207.2, 'BI': 208.98, 'PO': 209.0, 'AT': 210.0,\n",
    "    'RN': 222.0, 'FR': 223.0, 'RA': 226.0, 'AC': 227.0, 'TH': 232.04,\n",
    "    'PA': 231.04, 'U': 238.03, 'NP': 237.0, 'PU': 244.0, 'AM': 243.0,\n",
    "    'CM': 247.0, 'BK': 247.0, 'CF': 251.0, 'ES': 252.0, 'FM': 257.0,\n",
    "    'MD': 258.0, 'NO': 259.0, 'LR': 266.0\n",
    "}\n"
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   "source": [
    "## Definition of incoming profile\n",
    "Now let's define a profile and use it to calculate the molar fractions as well as the molar mass."
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    "profile = pr.Profile.round(\n",
    "    diameter=50e-3,\n",
    "    temperature=1200 + 273.15,\n",
    "    material=[\"steel\", \"C15\"],\n",
    "    density=7.5e3,\n",
    "    strain=0,\n",
    "    chemical_composition={\n",
    "        \"C\": 0.16 / 100,\n",
    "        \"SI\": 0.16 / 100,\n",
    "        \"MN\": 0.69 / 100,\n",
    "        \"CR\": 0.12 / 100,\n",
    "        \"NI\": 0.09 / 100,\n",
    "        \"CU\": 0.17 / 100,\n",
    "        \"P\": 0.002 / 100,\n",
    "        \"S\": 0.0065/ 100,\n",
    "        \"FE\": 98.43 / 100\n",
    "    },\n",
    "    freiberg_flow_stress_coefficients=FreibergFlowStressCoefficients(\n",
    "        a=2098.29 * 1e6,\n",
    "        m1=-0.00272,\n",
    "        m2=0.22312,\n",
    "        m4=0.00003,\n",
    "        m5=0.00028,\n",
    "        m7=-0.58508,\n",
    "        m8=0.000137,\n",
    "        baseStrain=0.1,\n",
    "        baseStrainRate=0.1\n",
    "    )\n",
    ")"
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    "mass_fractions = {\n",
    "    v.W('C'): profile.chemical_composition['C'],\n",
    "    v.W('CU'): profile.chemical_composition['CU'],\n",
    "    v.W('SI'): profile.chemical_composition['SI'],\n",
    "    v.W('MN'): profile.chemical_composition['MN'],\n",
    "    v.W('CR'): profile.chemical_composition['CR'],\n",
    "    v.W('NI'): profile.chemical_composition['NI'],\n",
    "    v.W('P'): profile.chemical_composition['P'],\n",
    "    v.W('S'): profile.chemical_composition['S'],\n",
    "}\n",
    "\n",
    "mole_fractions = v.get_mole_fractions(mass_fractions=mass_fractions, dependent_species=v.Species('FE'), pure_element_mass_dict=database)\n",
    "mole_mass = sum(profile.chemical_composition[element] * molar_masses_grams_per_mol[element] for element in profile.chemical_composition.keys())"
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    "## Stepped Equilibrium \n",
    "Now we have to calculate a stepped equilibrium using the `pycalphad` package. This equilibrium gives us information about the phase compositions of the alloy at various temperatures between a start and a stop temperature. Further information we have to provide to run the calculations is the atmospheric pressure as well as the number of moles we want to consider. Also, we need information about the expected phases. This information can be gained from literature or a phase diagram. In this case we expect the liquid phase (LIQUID), cementite (CEMENTITE), austenite (FCC_A1) as well as ferrite (BCC_A2) regarding the temperature. At last the composition (chemical elements) of the alloy."
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    "start_temperature_kelvin = 20 + 273.15\n",
    "end_temperature_kelvin = 1400 + 273.15\n",
    "number_of_moles = 1\n",
    "atmospheric_pressure = 101325\n",
    "\n",
    "conditions = {\n",
    "    v.X('C'): mole_fractions[v.MoleFraction(v.Species('C'))],\n",
    "    v.X('CU'): mole_fractions[v.MoleFraction(v.Species('CU'))],\n",
    "    v.X('SI'): mole_fractions[v.MoleFraction(v.Species('SI'))],\n",
    "    v.X('MN'): mole_fractions[v.MoleFraction(v.Species('MN'))],\n",
    "    v.X('CR'): mole_fractions[v.MoleFraction(v.Species('CR'))],\n",
    "    v.X('NI'): mole_fractions[v.MoleFraction(v.Species('NI'))],\n",
    "    v.X('P'): mole_fractions[v.MoleFraction(v.Species('P'))],\n",
    "    v.X('S'): mole_fractions[v.MoleFraction(v.Species('S'))],\n",
    "    v.N: number_of_moles,\n",
    "    v.P: atmospheric_pressure,\n",
    "    v.T: (start_temperature_kelvin, end_temperature_kelvin, 10)  # temperature (start, stop, step)\n",
    "}\n",
    "phases = ['LIQUID', 'FCC_A1', 'BCC_A2', 'CEMENTITE']\n",
    "composition = ['FE', 'C', 'CU', 'SI', 'MN', 'CR', 'NI', 'P', 'S', 'VA']\n",
    "eq = equilibrium(database, composition, phases, conditions, output=['heat_capacity'])\n",
    "specific_heat_capacity = (np.squeeze(eq['heat_capacity'].values) / mole_mass) * 1000\n",
    "temperature = eq['T'].values"
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    "## Extracting the specific-heat-capacity \n",
    "Now let's inspect the result.\n",
    "More methods about how to check if the results are valid, can be taken from the pycalphad documentation which can be found [here](https://pycalphad.org/docs/latest/examples/EquilibriumWithOrdering.html)."
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig: plt.Figure = plt.figure(figsize=(15,5))\n",
    "ax: plt.Axes = fig.add_subplot()\n",
    "\n",
    "ax.set_title('C15: Heat capacity over Temperature')\n",
    "ax.set_xlabel(r\"$T$ in $\\mathrm{K}$\")\n",
    "ax.set_ylabel(r\"$c_{p}$ in $\\mathrm{\\frac{J}{kg K}}$\")\n",
    "ax.grid(True)\n",
    "ax.set_aspect(\"equal\")\n",
    "ax.plot(temperature, specific_heat_capacity, label=r'$c_{p}$ pycalpad')\n",
    "ax.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-06T11:28:45.955475297Z",
     "start_time": "2024-03-06T11:28:45.619105346Z"
    }
   },
   "id": "79c9a9bc0b853a2a",
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Comparison to Data from Spittel et al.\n",
    "Normally when you set up a PyRolL simulation, we use mean specific heat capacity values. \n",
    "A reference for values, is the book \"Numerical data and functional relationships in science and technology. Part 1: Metal forming data Ferrous alloys\" from Spittel et al.. We will now calculate the mean specific heat capacity values for C15 and compare them with the published values."
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "c731f3bb393c3e70"
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/christoph/.local/share/virtualenvs/pyroll-examples-YS1GospC/lib/python3.10/site-packages/numpy/core/fromnumeric.py:3504: RuntimeWarning: Mean of empty slice.\n",
      "  return _methods._mean(a, axis=axis, dtype=dtype,\n",
      "/home/christoph/.local/share/virtualenvs/pyroll-examples-YS1GospC/lib/python3.10/site-packages/numpy/core/_methods.py:129: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  ret = ret.dtype.type(ret / rcount)\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 1500x500 with 1 Axes>",
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_specific_heat_capacity_spittel = np.array(\n",
    "    [472.11, 484.14, 497.07, 516.92, 541.07, 567.8, 596.65, 627.42, 691.57, 681.08, 686.60, 684.14, 681.68])\n",
    "temperatures_spittel = np.array([20, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200]) + 273.15\n",
    "\n",
    "temperature_ranges = np.arange(100, 1600, 100)\n",
    "np.insert(temperature_ranges, 0, 20)\n",
    "\n",
    "mean_specific_heat_values = []\n",
    "\n",
    "for start_temp in temperature_ranges:\n",
    "    end_temp = start_temp + 100\n",
    "    indices = np.where((temperature >= start_temp) & (temperature < end_temp))\n",
    "    mean_specific_heat = np.mean(specific_heat_capacity[indices])\n",
    "    mean_specific_heat_values.append(mean_specific_heat)\n",
    "\n",
    "mean_specific_heat_values = np.array(mean_specific_heat_values)\n",
    "\n",
    "fig: plt.Figure = plt.figure(figsize=(15,5))\n",
    "ax: plt.Axes = fig.add_subplot()\n",
    "\n",
    "ax.set_title('C15: Heat capacity over Temperature')\n",
    "ax.set_xlabel(r\"$T$ in $\\mathrm{K}$\")\n",
    "ax.set_ylabel(r\"$c_{p}$ in $\\mathrm{\\frac{J}{kg K}}$\")\n",
    "ax.grid(True)\n",
    "ax.set_aspect(\"equal\")\n",
    "ax.plot(temperature_ranges, mean_specific_heat_values, label=r'$c_{p,m}$ pycalpad')\n",
    "ax.scatter(temperature_ranges, mean_specific_heat_values, c='C0')\n",
    "ax.plot(temperatures_spittel, mean_specific_heat_capacity_spittel, label=r'$c_{p,m}$ Spittel et al.')\n",
    "ax.scatter(temperatures_spittel, mean_specific_heat_capacity_spittel, c='C1')\n",
    "ax.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-06T11:28:46.125576400Z",
     "start_time": "2024-03-06T11:28:45.960388693Z"
    }
   },
   "id": "a74068cbe728bd23",
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Difference between the data\n",
    "One can clearly see the advantage of the gained specific heat capacity values. As Spittel et al. published mean specific heat capacity values witch where calculated using a model of Livschitz, `pycalphad` calculates the actual specific heat capacity values. The double peak at around 1000 K arises due to the curie temperature being passed and later the phase change from austenite to ferrite taking place. So one can finally state that when just taking into account the hot forming process, usage of mean specific heat transfer values yields a limited error. When analysing \"warm\" rolling processes or cooling processes, usage of the specific heat capacity is more accurate than a mean value.\n",
    "\n",
    "## Usage in PyRolL\n",
    "To use the specific heat capacity, we will interpolate the function and provide it as a hook for the profile."
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "4335185550839220"
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "data": {
      "text/plain": "Profile(\n    chemical_composition={'C': 0.0016,\n     'SI': 0.0016,\n     'MN': 0.0069,\n     'CR': 0.0012,\n     'NI': 0.0009,\n     'CU': 0.0017000000000000001,\n     'P': 2e-05,\n     'S': 6.5e-05,\n     'FE': 0.9843000000000001},\n    classifiers={'generic_elongation', 'oval', 'swedish_oval'},\n    cross_section=Polygon(\n        area=0.0014976631456151905,\n        height=0.027999999999999997,\n        perimeter=0.1545024092875257,\n        width=0.06,\n        ),\n    density=7500.0,\n    freiberg_flow_stress_coefficients=FreibergFlowStressCoefficients(a=2098290000.0, m1=-0.00272, m2=0.22312, m3=0, m4=3e-05, m5=0.00028, m6=0, m7=-0.58508, m8=0.000137, m9=0, baseStrain=0.1, baseStrainRate=0.1),\n    length=0.0,\n    material=['steel', 'C15'],\n    strain=0,\n    t=6.0571064266249754,\n    temperature=1473.15,\n    )",
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     },
     "execution_count": 9,
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   ],
   "source": [
    "specific_heat_capacity_function = interpolate.interp1d(temperature, specific_heat_capacity)\n",
    "\n",
    "@pr.Profile.specific_heat_capacity\n",
    "def heat_capacity_interpolated(self: pr.Profile):\n",
    "    return specific_heat_capacity_function(self.temperature)\n",
    "\n",
    "sequence = pr.PassSequence([\n",
    "    pr.RollPass(\n",
    "        label=\"K 02/001 - 1\",\n",
    "        roll=pr.Roll(\n",
    "            groove=pr.SwedishOvalGroove(\n",
    "                r1=6e-3,\n",
    "                r2=26e-3,\n",
    "                ground_width=38e-3,\n",
    "                usable_width=60e-3,\n",
    "                depth=7.25e-3\n",
    "            ),\n",
    "            nominal_radius=321e-3 / 2,\n",
    "            rotational_frequency=0.99,\n",
    "\n",
    "        ),\n",
    "        gap=13.5e-3,\n",
    "        coulomb_friction_coefficient=0.4,\n",
    "        back_tension=0,\n",
    "        front_tension=0\n",
    "    ),\n",
    "    pr.Transport(\n",
    "        label=\"I->II\",\n",
    "        duration=6,\n",
    "    )\n",
    "])\n",
    "\n",
    "sequence.solve(profile)"
   ],
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   "id": "7f48a357c1ef6039",
   "execution_count": 9
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   "id": "16388cb4100573e1",
   "execution_count": 9
  }
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