{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mechanical Properties from Stress-Strain Curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# imports\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import linregress\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[0m\u001b[01;35mABS_HIPS_plot_with_error_bars.png\u001b[0m\r\n",
      "Al60601_raw_data.xls\r\n",
      "bar_plot_with_error_bars.ipynb\r\n",
      "calculate-yield-strength-programmatically.ipynb\r\n",
      "\u001b[01;34mimages\u001b[0m/\r\n",
      "mechanical-properties-from-stress-strain-curves.ipynb\r\n",
      "mechanical-properties-intro.md\r\n",
      "plotting-stress-strain-curves.ipynb\r\n",
      "Steel1018_raw_data.xls\r\n",
      "\u001b[01;35mstress-strain_curve.png\u001b[0m\r\n",
      "stress_strain_curve_with_inset_elastic_region.ipynb\r\n",
      "\u001b[01;35mstress_strain_curve_with_inset.png\u001b[0m\r\n"
     ]
    }
   ],
   "source": [
    "%ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING *** OLE2 inconsistency: SSCS size is 0 but SSAT size is non-zero\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TESTNUM</th>\n",
       "      <th>POINTNUM</th>\n",
       "      <th>TIME</th>\n",
       "      <th>POSIT</th>\n",
       "      <th>FORCE</th>\n",
       "      <th>EXT</th>\n",
       "      <th>CH5</th>\n",
       "      <th>CH6</th>\n",
       "      <th>CH7</th>\n",
       "      <th>CH8</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>542</td>\n",
       "      <td>1</td>\n",
       "      <td>8.470</td>\n",
       "      <td>0.02256</td>\n",
       "      <td>201.146011</td>\n",
       "      <td>-0.001444</td>\n",
       "      <td>0.007552</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>542</td>\n",
       "      <td>2</td>\n",
       "      <td>8.632</td>\n",
       "      <td>0.02330</td>\n",
       "      <td>206.599442</td>\n",
       "      <td>0.000302</td>\n",
       "      <td>0.007552</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>542</td>\n",
       "      <td>3</td>\n",
       "      <td>10.027</td>\n",
       "      <td>0.02846</td>\n",
       "      <td>287.512573</td>\n",
       "      <td>0.003044</td>\n",
       "      <td>0.018898</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>542</td>\n",
       "      <td>4</td>\n",
       "      <td>11.031</td>\n",
       "      <td>0.03232</td>\n",
       "      <td>365.380981</td>\n",
       "      <td>0.009881</td>\n",
       "      <td>0.022061</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>542</td>\n",
       "      <td>5</td>\n",
       "      <td>11.928</td>\n",
       "      <td>0.03616</td>\n",
       "      <td>447.813965</td>\n",
       "      <td>0.014085</td>\n",
       "      <td>0.033652</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   TESTNUM  POINTNUM    TIME    POSIT       FORCE       EXT       CH5  CH6  \\\n",
       "0      542         1   8.470  0.02256  201.146011 -0.001444  0.007552  NaN   \n",
       "1      542         2   8.632  0.02330  206.599442  0.000302  0.007552  NaN   \n",
       "2      542         3  10.027  0.02846  287.512573  0.003044  0.018898  NaN   \n",
       "3      542         4  11.031  0.03232  365.380981  0.009881  0.022061  NaN   \n",
       "4      542         5  11.928  0.03616  447.813965  0.014085  0.033652  NaN   \n",
       "\n",
       "   CH7  CH8  \n",
       "0  NaN  NaN  \n",
       "1  NaN  NaN  \n",
       "2  NaN  NaN  \n",
       "3  NaN  NaN  \n",
       "4  NaN  NaN  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_al = pd.read_excel('Al60601_raw_data.xls')\n",
    "df_al.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING *** OLE2 inconsistency: SSCS size is 0 but SSAT size is non-zero\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TESTNUM</th>\n",
       "      <th>POINTNUM</th>\n",
       "      <th>TIME</th>\n",
       "      <th>POSIT</th>\n",
       "      <th>FORCE</th>\n",
       "      <th>EXT</th>\n",
       "      <th>CH5</th>\n",
       "      <th>CH6</th>\n",
       "      <th>CH7</th>\n",
       "      <th>CH8</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>523</td>\n",
       "      <td>1</td>\n",
       "      <td>6.189</td>\n",
       "      <td>0.07302</td>\n",
       "      <td>202.924728</td>\n",
       "      <td>0.000402</td>\n",
       "      <td>-0.028272</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>523</td>\n",
       "      <td>2</td>\n",
       "      <td>6.549</td>\n",
       "      <td>0.07396</td>\n",
       "      <td>205.714890</td>\n",
       "      <td>-0.000238</td>\n",
       "      <td>-0.034549</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>523</td>\n",
       "      <td>3</td>\n",
       "      <td>7.148</td>\n",
       "      <td>0.07624</td>\n",
       "      <td>217.763336</td>\n",
       "      <td>-0.000713</td>\n",
       "      <td>-0.030140</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>523</td>\n",
       "      <td>4</td>\n",
       "      <td>9.146</td>\n",
       "      <td>0.08438</td>\n",
       "      <td>316.306122</td>\n",
       "      <td>0.002377</td>\n",
       "      <td>-0.025968</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>523</td>\n",
       "      <td>5</td>\n",
       "      <td>10.041</td>\n",
       "      <td>0.08822</td>\n",
       "      <td>417.003357</td>\n",
       "      <td>0.003089</td>\n",
       "      <td>-0.024100</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   TESTNUM  POINTNUM    TIME    POSIT       FORCE       EXT       CH5  CH6  \\\n",
       "0      523         1   6.189  0.07302  202.924728  0.000402 -0.028272  NaN   \n",
       "1      523         2   6.549  0.07396  205.714890 -0.000238 -0.034549  NaN   \n",
       "2      523         3   7.148  0.07624  217.763336 -0.000713 -0.030140  NaN   \n",
       "3      523         4   9.146  0.08438  316.306122  0.002377 -0.025968  NaN   \n",
       "4      523         5  10.041  0.08822  417.003357  0.003089 -0.024100  NaN   \n",
       "\n",
       "   CH7  CH8  \n",
       "0  NaN  NaN  \n",
       "1  NaN  NaN  \n",
       "2  NaN  NaN  \n",
       "3  NaN  NaN  \n",
       "4  NaN  NaN  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_steel = pd.read_excel('Steel1018_raw_data.xls')\n",
    "df_steel.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = 0.506\n",
    "r = d/2\n",
    "A = np.pi*r**2\n",
    "\n",
    "stress_al = (df_al['FORCE']/A)*0.001\n",
    "strain_al = df_al['CH5']*0.01\n",
    "\n",
    "stress_steel = (df_steel['FORCE']/A)*0.001\n",
    "strain_steel = df_steel['CH5']*0.01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the full stress strain curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots()\n",
    "ax.plot(strain_al, stress_al)\n",
    "ax.plot(strain_steel, stress_steel)\n",
    "ax.set_xlabel('Strain (in/in)')\n",
    "ax.set_ylabel('Stress (ksi)')\n",
    "ax.set_title('Stress-Strain Curve of Al6061 and Steel1018 in Tension')\n",
    "ax.legend(['Al6061','Steel1018'])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate tensile strength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The tensile strength of Al6061 is: 47.3 ksi\n",
      "The tensile strength of Steel1018 is: 95.5 ksi\n"
     ]
    }
   ],
   "source": [
    "# Calculate the tensile strength\n",
    "ts_al = np.max(stress_al)\n",
    "ts_steel = np.max(stress_steel)\n",
    "print(f'The tensile strength of Al6061 is: {round(ts_al,1)} ksi')\n",
    "print(f'The tensile strength of Steel1018 is: {round(ts_steel,1)} ksi')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Caclulate elastic modulus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gxRfQ4WpLGMaUImvXrmX9+vV5n5csWULjxo2pXLkyaWlpAHTr1o1ffvkl706lI0eOsG7dOlq2bElKSkpe0sjKymLlypV+l33ZZZcxduxYVJW5c+dSpUqVU1ZNVatWjYMHD7Ju3ToApk2b5nmHj8FMGlHA2cA7qtoJOMJJVVHqdLFbYN2Nqo5U1SRVTSoTA5k07QXx1WH9NKc6av4oyD4G597rdWTGmHwOHz7MsGHDaNOmDe3bt2fVqlU8+eSTjBgxggEDBtCnTx9q1arFRx99xDXXXEP79u3p3r07a9asISYmhokTJ/LII4/QoUMHOnbsyJw5c35Xxuuvv05iYiLJycm0b9+eW2+9FXAGdGrWrBnNmzfntttu4+23387b5rzzzuOqq65i+vTpJCYm8v333xMVFcWoUaO44oor6NChAx9//DEvvvhiyI5VQYLWNbqI1AXmqmoT9/N5OEmjOdBbVXeKSD1gpqq2PNW+Sn3X6FlHYdFYmPWC065xz0J4vy80Oheu+bfX0RlTaljX6MFT5rtGV9VdwDYRyU0IfYFVwBRgmDtvGDA5WDEEnS/HeRbjtQ7w7cNQqxUMmwIbpsPR/dDjPq8jNMaYgAp2Zfs9wKciEgNsAm7CSVQTROQWYCswJMgxBM/mWfDdo9C4B1z5ATTpCZt/ghnPQsOu0Kir1xEaY0xABTVpqOoSoKBLo77BLDdkcrKc9wufhgadYfGn8H/3QuV68If3vI3NmFJKVfOGQjWBEcoRWO22ntOx4QfnPb668z7nDfBlw8Ft8N75UKftia/arSH29098GlNexMXFsXfvXmrUqGGJI0BUlb179xIXFxeS8ixplNSWX5wH97reAdWbOvNum+484bp7hdNp4e5VsPQzyEw7vl3VxlChOkgEIM67RDjPdeTNkwLmFbZevmWctN0J8yh8vd/tX05RZnHWyx8HBcwrLF45RZknz8PP9U6Ot6g4/Ij3hM/+xpsbR/mUe0dRmbiNvgyJi4sjMTExJGVZ0iipHYud98gY5xZbEYip6DwJ3qjb8fVU4cBvThLZ4yaSY2mAgvrclzsNzrsvJ988PXGdvHlawLwi1iuwzPzb+bGeCRB/kq2/Sa6A9UL2g6R4P1yiJYKmAf1BUhp+CODHd3fffdmQk+m+styXO+3LN33ycl/+dTOdh4lzp/P2WcB2QWBJo6S63Qmp62DO684ttwOeL/ghPhGo1th5tRoY+jgDrcDkcqrkpf6th564TYmSXGH7L0a8cIoy/Y23oP1TeJkFxXvK717c9fJ/r6J+aLjr+XyFr1fcHxp+/xv4eYzKm4go58dpZLTzHhF9fDoy/3QMRMVBbIL7OQqYH/BwLGmUVEQkXPoaxCU4bRl7Vjl3UFWu63VkwZX3KzDC60hMeVXihOnvDwF/ruCLSHKFJfiIyAJO/O4JPm862l3uTp9OdebQ33e1frosaZwOEbjwGahUB6b+Bd49D27+Dmqc4XVkxoSvE9qFIj0NpTyypFESqrBrGaz7HtZ+CzsWOfOj4pyuQ4wxJkxZ0iiuHYvhs+vg0HZAIDEJLvgrnDnAua22HN8ZY4wJf5Y0ik3g8G7nAb5bp0OVwrs1NsaYcGOtmcVVvyNc9gak7YR573odjTHGhJQljZJoer5zz3WENcIZY8oXSxol8fPLTmN45+FeR2KMMSFlSaO45o+GBaOdh/uqNfE6GmOMCSlLGsWRlQHfPgLRFeDsYV5HY4wxIWdJozii4+CSl52nNd/tCdOfguzg9O9ijDGlkSWN4uo8DG6Z6jzi//PLsGmG1xEZY0zIWNIornVT4aNLnB4k+/wFzgiP8aSMMcYf9nBfcf3nzxBf1RkLvE5br6MxxpiQsiuN4lIg8RxLGMaYcsmSRnEl1IOdS9yujo0xpnyxpFFcHa91xs7Y9l+vIzHGmJCzpFFc7a5wbrld+43XkRhjTMgFtSFcRLYAaUAOkK2qSSJSHRgPNAG2AENUdX8w4wgsgYT6sPknrwMxxpiQC8WVRh9V7aiqSe7nR4HpqtoCmO5+Lhs2/wTvdIcDv0HLMBjv2xhjismL6qnBwBh3egxwuQcxFN+cN2DMpU7V1M3fwfkPex2RMcaEXLCThgJTRWShiIxw59VR1Z3u9C6gTkEbisgIEVkgIgtSUlKCHGYR5r7jjAHe5nK4YzY06uZtPMYY45FgP9zXU1W3i0htYJqIrMm/UFVVRAq8d1VVRwIjAZKSkry7v3X3KvjuUYiuCF1uheh4z0IxxhivBfVKQ1W3u+97gK+Ac4DdIlIPwH3fE8wYTlvNFtDjPoiMgjGDYOT5sGQc+HxeR2aMMSEXtKQhIhVFpHLuNHAhsAKYAuT2Kz4MmBysGAIiMhr6PwUPrIZLXnG6R590B8x92+vIjDEm5IJ5pVEHmC0iS4H/At+o6nfA80B/EVkP9HM/l34xFaHLLXDXPGjWG2a/AscOex2VMcaEVNDaNFR1E9ChgPl7gbLbNeyuZXB4D6TvhdR10OBsryMyxpiQsSfC/aUKs/4Joy5wEsbV/7aEYYwpd6xrdH9Nf8qpkmp3JQx8ESpU9zoiY4wJOUsaRVGFn150Ekbn4TDoXyDidVTGGOMJSxqn4vPB94/BvHeh/dXO3VOWMIwx5ZgljcJkZzq31q74ArrdBRc+AxHWBGSMKd/sLFiYDT84CSO+mtttiA26ZIwxljQK0+JCGPACxCbAhBvgjbNhwYc2Yp8xplyzpFGYyCjodgfcuxiGjHXmfX0/HEvzNCxjjPGSJY2iRERCq0Hgy4FmfSAuweuIjDHGM5Y0/LFsAhzc5nQjYowx5ZglDX/M/AfU6wgtL/E6EmOM8ZQljaKoOj3bVqhht9waY8o9OwsWRQS63g4bp8OuFV5HY4wxnrKk4Y/cjgnXfedtHMYY4zFLGkU5vAcm3QVVG0PSzV5HY4wxnrJuRE5FFb7+k9MV+m3TrWdbY0y551fSEJEk4DygPnAUZ9jWaaq6P4ixeW/FF7Dma2e417pneR2NMcZ47pRJQ0RuAu4BNgMLgbVAHNATeEREVgB/VdXfgh1oyB3eA/95CBokQfe7vY7GGBPGfD4l26fk+JQcdd/dl++kzzmq+Nz37Jzjy33uZ2c55ASpy6OirjQqAD1U9WhBC0WkI9ACCL+kMfWvkHkYBr/lPBVujPFMjk/JzPaRme3jWE7O8Wn3PTPHd+K8Ez7nkJXjI9uneSfnvJO0Kjk57jzVgtdxX79fx4fPB9k+X97JPPckXuh+3PJyTlqnLDll0lDVt4pYviSg0ZQmke6hiYz2Ng5jPJCV4yM9M4eMrByOZuaQnpnD0Sznc+700cxsjmbmcDTL50xn5c53Tto5Pp/zy9c9MWaf9DnHp2Tl+E44Keefl52bKNzPgRYVIUTme53wWYTISPc9QoiKiCDCXSf3PXdZTFRU3vaFrZO/jILXiSAqUogQITICIiMiiBSIdNc7eT8RcnwfBS1zpiHphYAftiKrpx5W1X+KyBsU0De4qt4b+JBKiQv+BqumwMzn4Ir3vY7GmDw5PuVoVg7pmdlkZPrypk84qWeedIJ3T/5HM/NNZ500nW95SX79xkdHEh8TSXx0JDFREXknyahI96TontRioyOokO+zs87Jn52TYXRkBLHREcREOvvMfcVG5pvOnX/yvJO2yUsK4pxsTckUVT212n1fEOxASp3KdaB2G6dtw5gAUFWOZOZwID2TA+lZHDyaxYH0LA4czf/ZmT5a2Mk/M4fMHF+xy46NiiA+JpIK0ZHEuSf2CjGRVIqNolalWCrEOCf8OHd+fHTudBTxMRFuQohy3qMjnXn5PsdFRyA2qmW5UFT11P+572Ny54lIBFBJVQ/5U4CIROIkne2qOkhEmgKfATVwGtdvUNXMEsYfPCu+hN0rodn5XkdiSrnMbB+7D2Ww61AGuw66L3d696EM9qdn5iWIU/2Cj4uOoGp8DFXio6kY65ywq1WIyTvZ/+6knm9+/Cne46IjibRf1iZA/L3l9t/AHUAOMB9IEJHXVPVFPza/D+eKJbdP8ReAV1X1MxF5F7gFeKfYkQdLZjpMuQdWTIQGneHCp72OyHjsUEYWv+1NZ9u+dLbtT+e3fensPHA8Mew98vvfPPHRkdStEkedhFha1U2gSoVoqsZHU7VCtJMY8j7HULVCNFXio4mLthsuTOnn78N9bVT1kIhcB3wLPIpzlXDKpCEiicAlwLPAA+Jcv14AXOuuMgZ4ktKUNOa96ySMPn+Bnn863iBuwlpWjo/1uw+zYsdBNqce4bd9TpL4bV86B9KzTli3Snw09avGU69KHO0Tq1I3IY56VeKoUyWOuglx1K0SR0JclFXXmLDk7xkxWkSigcuBN1U1y8//EP8CHgYqu59rAAdUNdv9nAw08DvaYMs+BovGQuMecP5DXkdjgkRVWb79IMuSD7Jyx0FWbD/E2l1peW0F0ZFCYrUKNKxegfaJVWhUvQKNqlfIm1cl3u6oM+WXv0njPWALsBT4SUQaAwdPtYGIDAL2qOpCEeld3MBEZAQwAqBRo0bF3bz4crLg85tg/2a46Nngl2c8sftQBg9+vpSf16cCzlVDuwYJ3NSjCW0bVKFd/QQa16hobQDGFMLvpKGqr+d+EJHfcK46TqUHcJmIDMR5ijwBeA2oKiJR7tVGIrC9oI1VdSQwEiApKSn4T79M/Sus/QbOvhFaDgx6cSa0dh3M4PMF23h/9mYys338bVAbLmxbhwZV460ayZhi8DdpfCkig/NVK9UFvgY6F7aBqj4GPAbgXmk8qKrXicjnwJU4d1ANAyaXLPQAq9USYqs41VPbF0GXW6H9EIip6HVk5jTMXp/KmF+38OOaPeT4lPNa1OTvl7WlWa1KXodmTJnkb9KYBHwuIlcCDYEpwIMlLPMR4DMReQZYDIwu4X4CK+kmJ0ks/Qy+fxy+vh/WfAPXT/Q6MlNCY3/dwt8mr6RmpRhuO68Z15zTkMY17EeAMafDr6ShqqNEJAYneTQBblfVOf4WoqozgZnu9CbgnGLGGRrrp8HctyH7KNTrAL1KmheNF45m5vDrplRmrk1h1roUtu5Np1/rOrx1XSdio+x2VmMCoahuRB7I/xFoBCwBuolIN1V9JYixhdaRVPh8OKBO1dTAl5yhXk2pp6q8NHUto3522ivioiM494ya3HpeM4YmNSQmysYaMyZQirrSqHzS5y8LmV/2VawJQ8bC1L/A/Pdh/1a4YhTEV/M6MnMKm1OP8MaP6/ly0XYu7VCfIUmJdGlS3R6UMyZIiupG5O+hCqRUaHMZnHmR84DftL/B4k/hXBtLozT6eX0K783axOwNqURGCHf2PoOHL2ppd0IZE2RFVU+NAl5T1RUFLKsIDAWOqeqnQYov9Hw5kNAAImNg5xKvozEF2HHgKMM++C91EuL4c/8zGdqlIbUT4rwOy5hyoajqqbeAv4nIWThDvKbgPHPRAue5iw+Asp8wfD7YOhuWjodVkyEzDao0tOc1SqnJS3bgU5hwe3caVq/gdTjGlCtFVU8tAYaISCUgCaiHM0b4alVdG/zwQmTSnbDsM4ipDG0HQ4droNG5EGENqKVNemY2363cRYvalSxhGOMBf2+5PYx7y2xYOvNCWPml0+jd5Tao39HriEwBlicf5L7xi9mceoSnB7fzOhxjyiX7KQ3Q6lI4awgc/M25e8qUKhlZOTz37WoGvzWbI8ey+fTWrlzfrbHXYRlTLlm/39sXwZe3wd4N0LwfDAjCoLqmxLYfOMqIsQtYueMQV3dpyGMDW1svs8Z4qNhJo7gj95V6675zEkaT8+Ca8TZ+Rimydlca170/l4wsH+/fmES/NnW8DsmYcs+v6ikR+beIJLi32a4AVolIeAw40ethOPNi2PIzTL7L62iMa2PKYa4fPY8IESbdda4lDGNKCX/bNNq4VxaX44zc1xS4IVhBhcSxw7DwIxjdD9Z9C1FxUL2Z11EZnAf3/vDWL/h8yr9v60rz2uHXAYExZdXpjNwX/DEugunrP8HyCVClEVz8T6eHW+syxFMH07N4ceoaPp33Gy3rVGbUjUl2W60xpczpjNxXtts0utwCm2ZCeirEVbGE4bGZa/fw5wlL2Z+eyfBzm/DghS2pGGvtS8aUNqJasguGfKPvBV1SUpIuWLAg8DtO2wXjr4fk+dDv79Dz/sCXYYr00S+b+fvXq2hZpzIvD+lA2/pVvA7JmLAgIgtVNSmQ+/S3Ifw+tyFcRGS0iCwCLghkICGXlQGLP4bdKyEyFipZQ6sXVJWP526lTb0EvvqfHpYwjCnl/L3+v1lVXxORi4BqOI3gHwNTgxZZsH11O6yaBK0vhf5PQ/WmXkdUbqSkHWPOxlRmr0/llw2p7DiYQa8zaxEfY92ZG1Pa+Zs0cvubHgh8rKorpaz3Qb1ntdMh4dBPvI6kXJmwYBsPT1wGQJX4aHo0r8H/nFGTi9rW9TgyY4w//E0aC0VkKs6tto+JSGXAF7ywQiC+Gmz+CVZOgraXex1NuXDkWDbfrdhFfHQkE27vTpv6CURGlO3fHsaUN/4+p3EL8CjQRVXTgRjgpqBFFQpXjnbGzfh8GPzyutfRhL1P523l/Bdn8OOaPQxJSuSsxCqWMIwpg/y90lCgDTAIeAqoiDOuRtmTtgtWfAHLJkDqWkDg6D6vowprE+Zv4/GvVtC1aXXeu6EVnRvb7c3GlFX+Jo23caqjLsBJGmnAF0CXIMUVHL/NhQ8HguZAvQ5w4bPQ7gpIqOd1ZGFn35FMvlm2g0lLdrBw6356NK/B2Ju72tWFMWWcv0mjq6qeLSKLAVR1v4jEnGoDEYkDfgJi3XImquoTItIU+AyoASwEblDVzBJ/g+JIaADR8VCrJdzygw2yFARZOT5embaOUT9tItuntKxTmYcHtOT6bo0tYRgTBvxNGlkiEolTTYWI1KLohvBjwAWqetjtgmS2iHwLPAC8qqqfici7OO0l75Qs/GKq2hAGPAdT7oHFY6Hz8JAUW14k70/nvs+WsHDrfq44O5Fbz2tK63oJXodljAkgf39qvw58BdQWkWeB2cA/TrWBOg67H6Pdl+JUcU1054/B6c8qdDrdALFVYNfykBYbzrJzfIz6aRMXvvoTa3el8fo1nXh5SAdLGMaEoSKvNNzxMzYDDwN9cZ7ZuFxVV/uxbSROFVRz4C1gI3AgX/cjyUCDkoVeQiKgPtixBI7shYo1Qlp8OLpt7AJmrE3hgla1+ftlba2TQWPCWJFXGqrqA95S1TWq+paqvulPwnC3zVHVjkAicA7Qyt/ARGSEiCwQkQUpKSn+buafgf90rjTe62VXHKdp2750ZqxNYUSvZoweZr3SGhPu/K2emi4iV5T0KXBVPQDMALoDVUUk9wonEdheyDYjVTVJVZNq1apVkmIL1/Fa6PUgHEqGZeMDu+9yQlX5bsUuLntzNhVjIrmqcyJlvZMAY0zR/G0Ivx2nATtbRDJwqqhUVQuttHYby7NU9YCIxAP9gRdwkseVOHdQDQMmn0b8xafqDL406wVo2A3OfzSkxZd12Tk+vlm+k3dmbmTNrjRa1a3M29edTbNalbwOzRgTAn4lDVUtydBp9YAxbrtGBDBBVb8WkVXAZyLyDLAYGF2CfZfMoZ3OnVMbpkGz3jDkY4i1k11xPPuf1Xz4yxZa1K7ES1d14LIO9YmJsluXjSkv/EoaIjJdVfsWNS8/VV0GdCpg/iac9o3Q++SPsG+zM1Jfl9vsOY0SSN5/lJqVYvn+/l5E2HMXxpQ7p0wa7gN6FYCaIlKN473dJhDqu54CoVId586prrd7HUmZo6q8NWMD01btZvi5TSxhGFNOFXWlcTtwP1Af59bZ3DPFIeDN4IUVBDuXOXdKRZXNLrO8dDA9iwcmLGH6mj0M7lifvw5q43VIxhiPnDJpqOprwGsico+qvhGimAJv/1YYMwhiKsONoW13DweTlmxn+po9/Knfmdzbt7ndJWVMOXbKSn0R6SIidXMThojcKCKTReR1EakemhADYNl4yDgEw6ZAzeZeR1OmqCqHjznPYtaoFGMJw5hyrqiW4PeATAAR6QU8D4wFDgIjgxtaAG2bBzWaQ40zvI6kTEnPzObucYt58fu1nHtGDQa0s9H1jCnvimrTiFTV3MEmhgIjVfUL4AsRWRLUyAKpfifY+COk74MKZecCyUv7j2Ry/eh5rN55iIcHtOSOXmdY47cxpuikISJRbl9RfYERxdi29Kh/tnPX1P7NljT8kJ3j4+5xi1i/5zCjh3WhT6vaXodkjCkliqqeGgfMEpHJwFHgZwARaY5TRVU2RLpDfxz4zds4yoA1uw5x/eh5/LJhL89c3s4ShjHmBEXdPfWsiEzHebp7qqqquygCuCfYwQVM43Ohdhv4+k/OVUe1xl5HVOosSz7Ah79sYfKS7STER/OPP5zFkKSGXodljClliqxiUtW5BcxbF5xwgiSmAgx+C0b1gfVT4ZzbvI6o1Nh7+Bh3fLKQ+Vv2UzEmkpt6NOWeC5pTtcIpB2Y0xpRTZadd4nSkrINf33Km6/+uZ5NybX96FvO37Kdvq9q8enVHEuKivQ7JGFOKhXfS2DgDfn0TNvwAkbFwzu1O9ZTJU6tSLDUrxbBtf7olDGNMkcIzaajCrH/CzH84/U31eRw63wSVAjwuRxn3y4ZU/jppBQePZvHEpW29DscYUwaEZ9KY84aTMDpcA5e+BlGxXkdUqqgqD01cxsSFyTSqXoGxN3el+xk27K0xpmjhmTTSdjnvbf9oCaMAk5ZsZ+LCZG47ryl/vrAlcdGRXodkjCkjwnNAib5/hTrt4KvbnYGXTJ5pq3bz+Fcr6NCwKo9d3NoShjGmWMIzaUTHQ4er4eg+2LfJ62g85/MpM9bu4aYP/8ttYxfQonYlRt7Q2boFMcYUW3hWTwEs+BASz3Ee7CvHMrN9XPbmbNbsSqNW5Vju79eCO84/w64wjDElEp5JIysDDiZDq0ugnHflHSGw/cBRzmtRk9HDuth43saY0xJ+SePQThh/PeQcg0bdvI7GU3sOZfDqD+s4ciybrByfJQxjzGkLv6Qx6Q7YvgCa9XGqp8qpJdsOcMtH8zmUkcWwc5twzwUtvA7JGBMGwi9p9HoIfDmwaQa80hraXAZJt0CTHl5HFhK7D2Xw3qxNfDJvK3USYhl/ezea167sdVjGmDAhxzuuLb2SkpJ0wYIFxdsoZR1M/h9Inu98vnEKNDs/8MGVElk5Pl74dg1j524lx6dc3rEBj17cilqV7TkVY8orEVmoqkmB3GfQrjREpCHO0LB1AMUZ9e81d2zx8UATYAswRFX3B7TwlHXw5W2wcwlUqOn0ahvG7RtZOT7u+2wx/1m+iyFJidzdpwWNalTwOixjTBgKZvVUNvBnVV0kIpWBhSIyDRgOTFfV50XkUeBR4JGAlerzwaQ7nQGXBv3LeV4jOj5guy9t5m3ay98mr2Tt7jT+cklrbj2vmdchGWPCWNCShqruBHa602kishpoAAwGerurjQFmEqikkZMNP7/sNIRf/i50vCYguy2NVJW//98qPpqzhQZV4xl5Q2cubFvX67CMMWEuJA3hItIE6ATMA+q4CQVgF071VUHbjMAdk7xRo0ZFF7LxR/jufyFlNbS8xLnCCGNfLd7OR3O2cF3XRvzlkjbEx9jDesaY4At60hCRSsAXwP2qekjyPWynqioiBbbEq+pIYCQ4DeGnLOTAb/DxH5yxwK8aA20Gh/VDfd+v3MXDE5dxTtPq/P2ytkRF2vMXxpjQCOrZRkSicRLGp6r6pTt7t4jUc5fXA/acdkFVGkLSzZCTCRumhXXCyPEpfxq/hNb1Enh/WJIlDGNMSAXtjCPOJcVoYLWqvpJv0RRgmDs9DJgcgMLggr9CTGVIXX/auyvNVmw/SFaOj7b1E2ykPWNMyAWzeqoHcAOwXESWuPP+F3gemCAitwBbgSEBKe3HpyErHQa+FJDdlTY/rNrNO7M2snDrfirFRnFO0+peh2SMKYeCeffUbKCweqK+AS8wNgE0BzIPB3zXXjt8LJtbxy4gsVo8T1zahis7J1LZrjKMMR4InwrxXg9B1Ubw6VWw5N/OOOFhYv6WfQDc2fsMburR1BKGMcYz4ZM0YivBTd9BvY7Ow31f3ALHyv5Vx8dzt3LrmAU0r12J/m0KvDvZGGNCJnySBkCVBjBsitMovvIr+HAAHNrhdVQlNmdjKn+bvILeZ9Zi0l09qF05zuuQjDHlXHglDYCISOj1IFw7AfZthlF9nec4ypA9hzJ4cspKhn8wn6Y1K/LGtZ2oFBt+HRIbY8qe8D0T+XIgugIc2eMMzFTVj6fKS4Fpq3Zzz7hFZOUoV3VO5P5+Z1IhJnz/mYwxZUt4no3mvQffPgy128D1E6FeB68j8ouq8sq0dTSoGs8Hw7vQuEZFr0MyxpgThF/1FEDVxhAZCxkHITvT62j89v7Pm1m98xC39zrDEoYxplQKz6TRcgDcMhUiopzG8A0/eB1RkX7duJfnv1vDgLZ1uSop0etwjDGmQOGZNADqd4TbZ0Gt1jDxZti70euICrT9wFHemL6eOz9dSJMaFXjxqvZIGPedZYwp28I3aQDEV4Oe9zvVVPPe9TqaE2zYk8b178+j5ws/8vK0dbSqW5lRNybZg3vGmFItPBvCc22dA5PvhhotoMf9XkeTx+dT/vz5MrbuPcK9F7Tgys6JNKxuw7MaY0q/8E4am2ZB9lFo0R8S6nsdDQC7Dmbw0MSlLN12gBevbM9VSQ29DskYY/wW3kmj10NwKBnmvg1RcdDvCU/DOZqZw6VvzuZwRjbPXN6OKztbg7cxpmwJ76QRGeVUTQGk7/U2FmDWuhRS0o7x4U1d6NOyttfhGGNMsYV3Q/ivb8MPT0C7K+CSl72Ohl83phITGUHP5jW9DsUYY0okfK801v8AUx+H1pfCH0c5fVJ5JC0ji6e/XsWEBcn0a12baBui1RhTRoVv0vjvSFCf0+Othwnj1417efDzpew8eJS7+pzBfX3P9CwWY4w5XeH7k7f/UxBbxXmwz5fjSQjvztrINaPmEhMVwed3nMtDF7UiJip8D7kxJvyF75XGkRRn+NfsY07SCPHVxpSlO3j+2zUMal+Pf17Z3nqqNcaEhfD82ZtxEP49FKokwvCvISom5CFs2J0GwO29zrCEYYwJG+GZNHYth6wj0Od/oXJdT0K4pqszfsevm1I9Kd8YY4IhPJOGRAACE2+BL0fA9oUhD2HJbwcAaFazUsjLNsaYYAla0hCRD0Rkj4isyDevuohME5H17nu1oBRe9ywY9CpEx8Oy8TDqApj7TlCKOpmqMmXpDv73q+W0qF2J3i1rhaRcY4wJhWBWtn8EvAmMzTfvUWC6qj4vIo+6nx8JSGk7lsDCDyF5AexZ5dxuC1DzTEjsAk3OC0gxRXn0i+WMX7CNDolVeHlIR6LsmQxjTBgJWtJQ1Z9EpMlJswcDvd3pMcBMApU0lo2HhR8502cNgfZDocHZUKF6QHbvr29X7KRf6zq8d0NnIiNsXAxjTHgJ9c/gOqq6053eBdQpbEURGSEiC0RkQUpKStF77v80DHgBYirDqsmQcSDkCQOgcY2KLNl2gK17j4S8bGOMCTbP6k5UVQE9xfKRqpqkqkm1avnRLhAZBZ2HQ+NzIeeYZx0UPjygJamHj/Hg50s9Kd8YY4Ip1Eljt4jUA3Df9wRsz9mZ8MkVsP57uOgf0PX2gO3aXz+s2s094xZTMSaSEb2ahbx8Y4wJtlAnjSnAMHd6GDA5YHv+bQ5sne30Ztv9roDt1h8+n/LsN6u4dewCGlSN5+t7z2NAu3ohjcEYY0IhaA3hIjIOp9G7pogkA08AzwMTROQWYCswJGAFJi9w3pv1Cdgu/bU7LYNRP29m4Fl1eXVoR2KjvOsg0RhjgiloVxqqeo2q1lPVaFVNVNXRqrpXVfuqagtV7aeq+wJW4BkXQHRF+PRK2L81YLstSnpmNlNX7gagUfWKljCMMWEtfB4iaHA2XDMO9m2CWS+EpMgJC7bR/bkfeWLKStonVmHgWd50WWKMMaESPj3pZR+D9VOd6Y7XhaTI/1u6g+jICD6/oztJjashYs9lGGPCW9lNGj6f8+T3phmwaSZsnQNZ6c5DfU16BL34A+mZbD9wlOoVo+nSJPTPgxhjjBfKXtLw5cA3D8Cab5wxM8DpKqTT9dCsN7S4MKjF7z18jM8XJvPxr1tJSTvGezd0Dmp5xhhTmpTBpJENv811EkZsAlz1ITTvF/Ri1+9O480ZG/h2+S4yc3yc06Q6Lw/pQLdmNYJetjHGlBZlL2lExcLtPztXG4s/hin3wZ9WQBDbE1LSjnHt+/PIyMrh2q6NuK5rI1rUqRy08owxprQqe0nj2GH46UVY8m+oWBsG/jNoCWNL6hE+nbeVCQuSycjKYfLdPWhVNyEoZRljTFlQdpKGzwdLx8H0p+DwLqcN48JnID5wQ3Iczcxh8bb9zN+8n183pTJ30z6iIoSL2tZlRK9mljCMMeVe2Ugah7bDW+fA3vXQIAmGfgINuwRk15tSDvPV4u3M3pDKiu0HycpRRKBlncrc17cF13ZtRJ2EuICUZYwxZV3ZSBpHUiGhC5z/CLS7AiJO75nEjKwcvlq8nYkLk1m4dT8RAp0aVeOWns04p2k1OjeqTpUK0QEK3hhjwkfZSBp1z4JhU057Nzk+5avF23l56lp2HsygRe1KPHZxK/7QqQG17WrCGGOKVDaShpx+byez1qXw3H9Ws2ZXGu0Tq/DykA50b1bDnuI2xphiKBtJ4zQ9+PlSJi5MpmH1eF6/phODzqpHhA3FaowxxRb2SWPOxlQmLkxm+LlNeGxgK+uF1hhjTkPYJo3Dx7J5e8YG3vtpE/WrxPHgRS0tYRhjzGkKu6SxJy2DD3/Zwidzt5KWkc1VnRN5/JLWVIoNu69qjDEhF1Zn0rSMLC574xf2pGVwcbt63NarGR0bVvU6LGOMCRthkTT2Hclk2qpdjJ+/jd1pGXx+e3eSrLtyY4wJuDKdNBb/tp+Xp67j1017yfEpjapX4KnB7SxhGGNMkJTJpOHzKfM27+P2jxcQHxPJHec34+J29WhbP8GeuzDGmCAqM0lDVVm4dT/fLN/Jdyt2sfNgBrUrxzLxjnNpWL2C1+EZY0y5UGaSxncrdnHnp4sA6N+mDg8PaEnf1nVIiLM+oowxJlQ8SRoiMgB4DYgE3lfV54vapknNitxzQXNu6NbY+okyxhiPhDxpiEgk8BbQH0gG5ovIFFVddartWtdLoHU9G8/CGGO8dPo9ARbfOcAGVd2kqpnAZ8BgD+IwxhhTTF5UTzUAtuX7nAx0PXklERkBjHA/HhORFSGIrSyoCaR6HUQpYcfiODsWx9mxOK5loHdYahvCVXUkMBJARBaoapLHIZUKdiyOs2NxnB2L4+xYHCciCwK9Ty+qp7YDDfN9TnTnGWOMKeW8SBrzgRYi0lREYoCrgdMfls8YY0zQhbx6SlWzReRu4HucW24/UNWVRWw2MviRlRl2LI6zY3GcHYvj7FgcF/BjIaoa6H0aY4wJU15UTxljjCmjLGkYY4zxW8iThogMEJG1IrJBRB4tYHmsiIx3l88TkSb5lj3mzl8rIhf5u8/SKtDHQkQaisgMEVklIitF5L4Qfp3TEoy/C3dZpIgsFpGvQ/A1AiJI/0eqishEEVkjIqtFpHuIvs5pCdKx+JP7/2OFiIwTkTLRL1FJj4WI1HDPC4dF5M2TtuksIsvdbV4Xf7oJV9WQvXAavjcCzYAYYCnQ5qR1/gd4152+GhjvTrdx148Fmrr7ifRnn6XxFaRjUQ84212nMrCuvB6LfNs9APwb+Nrr7+nlsQDGALe60zFAVa+/qxfHAufh4s1AvLveBGC41981yMeiItATuAN486Rt/gt0AwT4Fri4qFhCfaXhTxcig3H+wAEmAn3d7DcY+ExVj6nqZmCDu7+y2i1JwI+Fqu5U1UUAqpoGrMb5T1LaBePvAhFJBC4B3g/BdwiUgB8LEakC9AJGA6hqpqoeCP5XOW1B+bvAuWs0XkSigArAjiB/j0Ao8bFQ1SOqOhvIyL+yiNQDElR1rjoZZCxweVGBhDppFNSFyMkntbx1VDUbOAjUOMW2/uyzNArGscjjXpp2AuYFMuggCdax+BfwMOALeMTBE4xj0RRIAT50q+reF5GKwQk/oAJ+LFR1O/AS8BuwEzioqlODEn1gnc6xONU+k4vY5+9YQ3gYEpFKwBfA/ap6yOt4vCAig4A9qrrQ61hKgSjgbOAdVe0EHAHKTNtfIIlINZxf5E2B+kBFEbne26jKllAnDX+6EMlbx718rALsPcW2ZbVbkmAcC0QkGidhfKqqXwYl8sALxrHoAVwmIltwLuUvEJFPghF8gAXjWCQDyaqae9U5ESeJlHbBOBb9gM2qmqKqWcCXwLlBiT6wTudYnGqfiUXs8/dC3JgTBWzCyfK5jTltT1rnLk5szJngTrflxIatTTiNQ0XuszS+gnQsBKde8l9efz+vj8VJ2/am7DSEB+VYAD8DLd3pJ4EXvf6uXhwLnB61V+K0ZQhOG8A9Xn/XYB6LfMuHU3RD+MAiY/Hgyw/EuatnI/C4O+8p4DJ3Og74HKfh6r9As3zbPu5ut5Z8rfwF7bMsvAJ9LHDukFBgGbDEfRX5R1AaXsH4u8i3vDdlJGkE61gAHYEF7t/GJKCa19/Tw2Pxd2ANsAL4GIj1+nuG4FhsAfYBh3GuPNu485Pc47AReBO3l5BTvawbEWOMMX6zhnBjjDF+s6RhjDHGb5Y0jDHG+M2ShjHGGL9Z0jDGGOM3SxomLIjI427PpctEZImIdHXn3y8iFUqwv6dEpF8xt+kkIqPd6csK6om0kO2+FZFEt3uPNkWse7eI3FycuIwJJLvl1pR5bjffrwC9VfWYiNQEYlR1h/tEeJKqphawXaSq5gQwjs+BZ1R1aTG2iQdmqeo5Ra7srF8B+EWd7kCMCTm70jDhoB6QqqrHAFQ11U0Y9+L0LzRDRGYAuGMKvCwiS4HuIvI3EZnvjq0wMnc8ARH5SESudKe3iMjfRWSRO/ZAq5MDEJHKQPvchCEiw3PHLnD39bqIzBGRTbn7dfUGZrrrzRSRpHxxPisiS0VkrojUcb9bOrBFRPxKMsYEmiUNEw6mAg1FZJ2IvC0i5wOo6us43V73UdU+7roVgXmq2kGd7qLfVNUuqtoOiAcGFVJGqqqeDbwDPFjA8twnawtTD+eJ/UHA8/nmXwx8V8D6FYG5qtoB+Am4Ld+yBcB5pyjLmKCxpGHKPFU9DHQGRuB0AT5eRIYXsnoOToeOufq4o5wtBy7A6bOoILmdPy4EmhSwvJ5bdmEmqapPVVcBdfLN7wHMLmD9TCB3tMGTy9yDcwVlTMhFeR2AMYHgtk3MBGa6CWAY8FEBq2bktmO4w3y+jdPmsU1EnsTpv6cgx9z3HAr+f3P0FNvm3x6czuEQkWbANnUG1TlZlh5vcDy5zDi3PGNCzq40TJknIi1FpEW+WR2Bre50Gs7QtwXJPcmnumOQXFnIev5YDTQv5jaFVU0V5UxOXRVmTNBY0jDhoBIwRkRWicgynPGhn3SXjQS+y20Iz0+dIU9H4ZyAvwfmlzQAVV0DVHEbxP01gJIljR7AtBJsZ8xps1tujQkQEfkTkKaqRY5JLiKxOLfOJhWzjE7AA6p6QwnDNOa02JWGMYHzDie2XRRKVY8VN2G4agJ/LcF2xgSEXWkYY4zxm11pGGOM8ZslDWOMMX6zpGGMMcZvljSMMcb4zZKGMcYYv/0/Lp2nRz8GWtoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots()\n",
    "ax.plot(strain_al, stress_al)\n",
    "ax.plot(strain_steel, stress_steel)\n",
    "\n",
    "ax.set_title('Inset of elastic region')\n",
    "ax.set_xlabel('Strain (in/in)')\n",
    "ax.set_ylabel('Stress (ksi)')\n",
    "ax.legend(['Al6061','Steel1018'])\n",
    "\n",
    "ax.set_xlim([0,0.01])\n",
    "ax.set_ylim([0,70])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The elastic modulus of Al6061 is 9909.4 ksi\n"
     ]
    }
   ],
   "source": [
    "# Find the elastic modulus of Al6061\n",
    "# use stress and strain values from stress=0 to stress=35 ksi\n",
    "linear_stress_al_mask = stress_al < 35\n",
    "linear_stress_al = stress_al[linear_stress_al_mask]\n",
    "linear_strain_al = strain_al[linear_stress_al_mask]\n",
    "\n",
    "linear_regression_output = linregress(linear_strain_al, linear_stress_al)\n",
    "E_al = linear_regression_output[0]\n",
    "\n",
    "print(f'The elastic modulus of Al6061 is {round(E_al,1)} ksi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The elastic modulus of Steel1018 is 40125.4 ksi\n"
     ]
    }
   ],
   "source": [
    "# Find the elastic modulus of Steel1018\n",
    "# use stress and strain values from stress=0 to stress=55 ksi\n",
    "linear_stress_steel_mask = stress_steel < 55\n",
    "linear_stress_steel = stress_steel[linear_stress_steel_mask]\n",
    "linear_strain_steel = strain_steel[linear_stress_steel_mask]\n",
    "\n",
    "linear_regression_output_steel = linregress(linear_strain_steel, linear_stress_steel)\n",
    "E_steel = linear_regression_output_steel[0]\n",
    "\n",
    "print(f'The elastic modulus of Steel1018 is {round(E_steel,1)} ksi')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate ductility"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ductility of a metal is calculated from a stress strain curve by drawing a line down from the fracture point on the curve, parallel to the linear elastic region. Where that line crosses the strain axis is the ductility.\n",
    "\n",
    "Point-Slope Formula for a line:\n",
    "\n",
    "$$ y - y_1 = m(x-x_1) $$\n",
    "\n",
    "Where $m=$ slope in the linear elastic region (elastic modulus), $x_1=$ last strain point on the stress strain curve, $y_1 =$ last stress point on the stress strain curve.\n",
    "\n",
    "Solve the equation above for $x$, when $y=0$ in terms of $x_1$, $x_2$ and $m$.\n",
    "\n",
    "$$ x = \\frac{-y_1}{m}+x_1 $$\n",
    "\n",
    "Substitue in ductility, elastic modulus $E$, and the last stress and strain points.\n",
    "\n",
    "$$ \\%EL = \\frac{-stress_{last}}{E}+strain_{last} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The ductility of Al6061 is 20.4%\n"
     ]
    }
   ],
   "source": [
    "# Find the ductility for Al6061\n",
    "stress_al_array = np.array(stress_al)\n",
    "stress_al_last = stress_al_array[-1]\n",
    "strain_al_array = np.array(strain_al)\n",
    "strain_al_last = strain_al_array[-1]\n",
    "EL_al = -stress_al_last/E_al + strain_al_last\n",
    "print(f'The ductility of Al6061 is {round(EL_al*100,1)}%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The ductility of Steel1018 is 25.0%\n"
     ]
    }
   ],
   "source": [
    "# Find the ductility of Steel1018\n",
    "stress_steel_array = np.array(stress_steel)\n",
    "stress_steel_last = stress_steel_array[-1]\n",
    "strain_steel_array = np.array(strain_steel)\n",
    "strain_steel_last = strain_steel_array[-1]\n",
    "EL_steel = -stress_steel_last/E_steel + strain_steel_last\n",
    "print(f'The ductility of Steel1018 is {round(EL_steel*100,1)}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cacluate Yield Strength"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The yield strength of a metal is calculated from a stress strain curve by drawing a line parallel to the elastic modulus that goes through the point strain=0.002. Where that line crosses the stress strain curve, that amount of stress is the yield strength\n",
    "\n",
    "Point-Slope Formula for a line:\n",
    "\n",
    "$$ y - y_1 = m(x-x_1) $$\n",
    "\n",
    "Where $m=$ slope in the linear elastic region (elastic modulus, E), $x_1=0.002$, and $y_1 = 0$\n",
    "\n",
    "Rewrite the equation, where $y=stress_{offset}$ and the elastic modulus and value of $x_1$ and $y_1$ are included.\n",
    "\n",
    "$$ stress_{offset} = E(strain-0.002) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# calculate the yield strength of Al6061\n",
    "stress_offset_al = E_al*(strain_al_array-0.002)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(strain_al,stress_al,strain_al,stress_offset_al)\n",
    "ax.set_ylim([0,70])\n",
    "ax.set_xlim([0,0.01])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The yield strength of Al6061 is 41.4 ksi\n"
     ]
    }
   ],
   "source": [
    "YS_al = 41.3653 # by zooming into the plot that contains the stress strain curve of Al6061 and the offset stress\n",
    "print(f'The yield strength of Al6061 is {round(YS_al,1)} ksi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate the yield strength of Steel1018\n",
    "stress_offset_steel = E_steel*(strain_steel_array-0.002)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(strain_steel,stress_steel,strain_steel,stress_offset_steel)\n",
    "ax.set_ylim([0,70])\n",
    "ax.set_xlim([0,0.01])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the yield strength of steel1018 is 57.4 ksi\n"
     ]
    }
   ],
   "source": [
    "YS_steel = 57.4495 # by zooming into a plot showing the stress strain curve of steel1018 and the offset stress\n",
    "print(f'the yield strength of steel1018 is {round(YS_steel,1)} ksi')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}