A meta-analysis of the mechanical properties of ice-templated ceramics and metals

!A meta-analysis of the mechanical properties of ice-templated ceramics and metals.md

Writing academic papers in plain text with Markdown and Jupyter notebook

http://iopscience.iop.org/article/10.1088/1468-6996/16/4/043501/meta;jsessionid=92248EF2108F46848249B6885211DA71.c5.iopscience.cld.iop.org

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A_meta-analysis_of_the_mechanical_properties_of_ice-templated_ceramics_and_metals.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A meta-analysis of the mechanical properties of ice-templated ceramics and metals\n",
    "\n",
    "Welcome to the notebook accompanying this paper: \"A meta-analysis of the mechanical properties of ice-templated ceramics and metals\", published in *Science and Technology of Advanced Materials* (link coming as soon as the paper is available online).\n",
    "\n",
    "Follow through the notebook to generate the plots published in the paper. You need to have *Matplotlib*, *Numpy*, and *Pandas* installed. If you are not familiar with the IPython notebook format, start here: <http://ipython.org/index.html>\n",
    "\n",
    "Your files and directories should be organized as follow, in your working directory:\n",
    "\n",
    "* *code*: contains this IPython notebook\n",
    "* *figures*: where all figures will be saved\n",
    "* *data*: where the CSV files should be. There are two sets of data: \n",
    "    * The data compiled from the literature review on ice templating (*icetemplating.csv*). \n",
    "    * The data corresponding to the properties of cellular ceramics (*studart.csv*), and compiled in this paper: Studart, A. R., Gonzenbach, U. T., Tervoort, E., & Gauckler, L. J. (2006). Processing Routes to Macroporous Ceramics: A Review. Journal of the American Ceramic Society, 89(6), 1771–1789. doi:10.1111/j.1551-2916.2006.01044.x The paper can be found here <http://www.blackwell-synergy.com/doi/abs/10.1111/j.1551-2916.2006.01044.x> (paywall)\n",
    "\n",
    "    You can download these sets of data from Figshare here: <http://dx.doi.org/10.6084/m9.figshare.1412626>\n",
    "\n",
    "-May, 2015. Sylvain Deville, Sylvain Meille, Jordi Seuba\n",
    "\n",
    "Email to <sylvaindeville@gmail.com> or tweet to <http://twitter.com/DevilleSy> if you have any questions or comments, or just want to say hi!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import linspace\n",
    "from matplotlib import rc #for latex use on the plots\n",
    "from matplotlib.ticker import MultipleLocator, FormatStrFormatter # for labels formattings\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "perso_linewidth = 0.3\n",
    "# This will change your default rcParams\n",
    "def init_plotting():\n",
    "    plt.rcParams['figure.figsize'] = (3,3)\n",
    "    plt.rcParams['font.size'] = 8\n",
    "    plt.rcParams['font.family'] = 'serif'\n",
    "    plt.rcParams['axes.labelsize'] = plt.rcParams['font.size']\n",
    "    plt.rcParams['axes.titlesize'] = 1.5*plt.rcParams['font.size']\n",
    "    plt.rcParams['legend.fontsize'] = plt.rcParams['font.size']\n",
    "    plt.rcParams['xtick.labelsize'] = plt.rcParams['font.size']\n",
    "    plt.rcParams['ytick.labelsize'] = plt.rcParams['font.size']\n",
    "    plt.rcParams['savefig.dpi'] = 2*plt.rcParams['savefig.dpi']\n",
    "    plt.rcParams['axes.linewidth'] = perso_linewidth\n",
    "    plt.rcParams['savefig.dpi'] = '300'\n",
    "    plt.rcParams['axes.facecolor'] = 'white'\n",
    "    plt.rcParams['axes.edgecolor'] = '0'\n",
    "    plt.rcParams['axes.grid'] = False\n",
    "    plt.rcParams['grid.color']='white'\n",
    "    plt.rcParams['grid.linestyle'] = '-'\n",
    "    plt.rcParams['grid.linewidth'] = '0.1'\n",
    "    plt.rcParams['axes.axisbelow'] = True\n",
    "    plt.rcParams['lines.markersize']= 2.3 \n",
    "    plt.rcParams['lines.markeredgewidth']= '0.1'\n",
    "    plt.rcParams['lines.color']= 'r' \n",
    "    plt.rcParams['lines.marker']= 'o' \n",
    "    plt.rcParams['lines.linestyle']= '' \n",
    "    plt.rcParams['xtick.color']= '0'\n",
    "    plt.rcParams['ytick.color']= '0'\n",
    "    plt.rcParams['axes.color_cycle']= ['#3778bf', '#feb308', '#a8a495', '#7bb274', '#825f87']\n",
    "    plt.gca().spines['right'].set_color('none')\n",
    "    plt.gca().spines['right'].set_visible('False')\n",
    "    plt.gca().spines['top'].set_visible('False')\n",
    "    plt.gca().spines['top'].set_color('none')\n",
    "    plt.gca().xaxis.set_ticks_position('bottom')\n",
    "    plt.gca().yaxis.set_ticks_position('left')\n",
    "    plt.rcParams['ytick.minor.size']= 1.5\n",
    "    plt.rcParams['ytick.major.width']= perso_linewidth\n",
    "    plt.rcParams['ytick.minor.width']= perso_linewidth\n",
    "    plt.rcParams['xtick.major.width']= perso_linewidth\n",
    "    plt.rcParams['xtick.minor.width']= perso_linewidth\n",
    "\n",
    "init_plotting()\n",
    "\n",
    "plt.close() # this line to avoid an empty plot showing up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# function to list the bib key of papers used in the plots\n",
    "# The output is formatted to be used directly in Markdown. Pandoc can take care of the reference list from here.\n",
    "def list_authors(data):\n",
    "    authors = data.dropna()\n",
    "    authors = authors.drop_duplicates()\n",
    "    authors.tolist()\n",
    "    print str(len(authors)) + \" papers\"\n",
    "    print '@'+'; @'.join(authors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# common formatting for the plots, not passed as rcParams\n",
    "figuresize = 3\n",
    "titlefontsize = 8\n",
    "titleweight = 'bold'\n",
    "\n",
    "rc('font', **{'family':'serif', 'serif':['Palatino']})\n",
    "rc('text', usetex=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mechanical models used to predict the compressive strength\n",
    "\n",
    "## Closed cells\n",
    "$$\\sigma=\\sigma_{p}\\left(C_6\\left(\\phi\\frac{\\rho^*}{\\rho_s}\\right)+C_{6}^{''}\\left(1-\\phi\\right)\\frac{\\rho^*}{\\rho_s}\\right) \\text{  (eq. 1)}$$ \n",
    "with $C_6=0.65$ and $C_6^\"=1$, and where $\\phi$ is the solid fraction in the edges, $\\rho_s$ and $\\rho^*$ the apparent density of the dense and cellular material respectively, and $\\sigma_p$ the modulus of rupture of the solid cell wall material.\n",
    "\n",
    "## Open cell, brittle crushing model\n",
    "$$\\sigma=\\sigma_{p}C_4\\left(\\frac{\\rho^*}{\\rho_s}\\right)^{3/2}\\text{  (eq. 2)}$$ \n",
    "with $C_4=0.2$, and where $\\sigma_{p}$ is the modulus of rupture of the solid cell wall material, and $\\rho_s$ and $\\rho^*$ the apparent density of the dense and cellular material respectively.\n",
    "\n",
    "## Honeycomb, out of plane\n",
    "$$\\sigma=6 E_s \\left(\\frac{\\rho^*}{\\rho_s}\\right)^3 \\text{  (eq. 3)}$$\n",
    "where $E_s$ the Young's modulus of the corresponding dense material, and $\\rho_s$ and $\\rho^*$ the apparent density of the dense and cellular material respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Parameters of the Ashby model\n",
    "phi_edges = 0\n",
    "C2 = 0.2\n",
    "C6 = 0.65\n",
    "C6s = 1\n",
    "\n",
    "# data for the upper bound value of compressive strength vs porosity\n",
    "relative_density_table = linspace(0.0, 1.0, num=1000)\n",
    "relative_porosity = [(1-i)*100 for i in relative_density_table]\n",
    "\n",
    "# open cells model:\n",
    "brit_crush_str = [C2*i**(1.5) for i in relative_density_table]\n",
    "\n",
    "# closed cells models:\n",
    "closedcell_str = [C6*phi_edges*i +C6s*(1-phi_edges)*i for i in relative_density_table]\n",
    "\n",
    "# functions used to plot the prediction of the models on the plots\n",
    "def plot_upper_limit():\n",
    "        plt.plot(relative_porosity, brit_crush_str, linestyle=':', linewidth='0.5', marker='', dashes=[2, 2], color='0.5', zorder=1, dash_capstyle='round')\n",
    "        plt.plot(relative_porosity, closedcell_str, linestyle=':', linewidth='0.5', marker='', dashes=[2, 2], color='0.5', zorder=1, dash_capstyle='round')\n",
    "        \n",
    "def plot_upper_limit_log():\n",
    "        plt.plot(relative_density_table, brit_crush_str, linestyle=':', linewidth='0.5', marker='', dashes=[2, 2], color='0.5', zorder=1, dash_capstyle='round')\n",
    "        plt.plot(relative_density_table, closedcell_str, linestyle=':', linewidth='0.5', marker='', dashes=[2, 2], color='0.5', zorder=1, dash_capstyle='round')        \n",
    "\n",
    "strength_table = linspace(0.1, 1000.0, num=10000)\n",
    "        \n",
    "def plot_upper_limit_honeycomb():\n",
    "        plt.plot(strength_table, strength_table, linestyle='--', linewidth='0.5', marker='', dashes=[2, 2], color='0.5', zorder=1, dash_capstyle='round', markevery='2')    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = pd.io.parsers.read_csv('../data/icetemplating.csv', sep=';', decimal=',')\n",
    "foams = pd.io.parsers.read_csv('../data/studart.csv', sep=';', decimal=',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create a few subsets of data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "water = data[(data['Solvant'] == 'water') & (data['green body ?'] < 1)]\n",
    "camphene = data[(data['Solvant'] == 'camphene')]\n",
    "tba = data[(data['Solvant'] == 'TBA')]\n",
    "\n",
    "cellular = data[(data['failure mode'] == 'cellular')]\n",
    "brittle = data[(data['failure mode'] == 'brittle')]\n",
    "failureunknown = data[(data['failure mode'] == '?')]\n",
    "\n",
    "defects = data[(data['Defects'] == 'yes')]\n",
    "nodefects = data[(data['Defects'] == 'no')]\n",
    "notsureifdefects = data[(data['Defects'] == '?')]\n",
    "\n",
    "withparticlesize = data[(data['Granulo poudre'] > 0)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Porosity vs. solid loading, for the three most commonly used solvents\n",
    "Figure 3 of the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "328luZ7kZbP2AAAAHiRLAQAA7I0cBcB+GQAKAAAAAAAAAAAAMDCPHHUHAAAAAAAAAAAAANgbA0AB\n",
       "AAAAAAAAAAAABsYAUAAAAAAAAAAAAICBMQAUAAAAAAAAAAAAYGAMAAUAAAAAAAAAAAAYGANAAQAA\n",
       "AAAAAAAAAAbGAFAAAAAAAAAAAACAgTEAFAAAAAAAAAAAAGBgDAAFAAAAAAAAAAAAGBgDQAEAAAAA\n",
       "AAAAAAAGxgBQAAAAAAAAAAAAgIExABQAAAAAAAAAAABgYAwABQAAAAAAAAAAABgYA0ABAAAAAAAA\n",
       "AAAABsYAUAAAAAAAAAAAAICBMQAUAAAAAAAAAAAAYGAMAAUAAAAAAAAAAAAYGANAAQAAAAAAAAAA\n",
       "AAbGAFAAAAAAAAAAAACAgTEAFAAAAAAAAAAAAGBgDAAFAAAAAAAAAAAAGBgDQAEAAAAAAAAAAAAG\n",
       "xgBQAAAAAAAAAAAAgIExABQAAAAAAAAAAABgYAwABQAAAAAAAAAAABgYA0ABAAAAAAAAAAAABsYA\n",
       "UAAAAAAAAAAAAICBMQAUAAAAAAAAAAAAYGAMAAUAAAAAAAAAAAAYmP8fUeiAvPgzcgUAAAAASUVO\n",
       "RK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d2d19d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (3*figuresize, figuresize))\n",
    "\n",
    "ax = fig.add_subplot(1,3,1)\n",
    "plt.plot(water['Solid Loading'], water['Porosity'])\n",
    "ax.set_xlabel('Solid Loading (vol.\\%)')\n",
    "ax.set_ylabel('Porosity (\\%)')\n",
    "plt.title('Water', fontsize=titlefontsize, weight=titleweight)\n",
    "plt.xlim(0,65)\n",
    "plt.ylim(0,100)\n",
    "\n",
    "ax = fig.add_subplot(1,3,2)\n",
    "plt.plot(camphene['Solid Loading'], camphene['Porosity'])\n",
    "ax.set_xlabel('Solid Loading (vol.\\%)')\n",
    "plt.xlim(0,65)\n",
    "plt.ylim(0,100)\n",
    "ax.set_yticklabels([])\n",
    "plt.title('Camphene', fontsize=titlefontsize, weight=titleweight)\n",
    "\n",
    "ax = fig.add_subplot(1,3,3)\n",
    "plt.plot(tba['Solid Loading'], tba['Porosity'])\n",
    "ax.set_xlabel('Solid Loading (vol.\\%)')\n",
    "plt.xlim(0,65)\n",
    "plt.ylim(0,100)\n",
    "ax.set_yticklabels([])\n",
    "plt.title('TBA', fontsize=titlefontsize, weight=titleweight)\n",
    "\n",
    "plt.tight_layout()\n",
    "fig.savefig('../figures/figure3.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Range of pore size achieved for the three most commonly used solvents\n",
    "Figure 4 of the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10884d410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#extract the data with a pore value\n",
    "water_porewidth = water[(water['Pore width'] > 0)]\n",
    "camphene_porewidth = camphene[(camphene['Pore width'] > 0)]\n",
    "tba_porewidth = tba[(tba['Pore width'] > 0)]\n",
    "\n",
    "water_porewidth = water['Pore width'].tolist()\n",
    "camphene_porewidth = camphene['Pore width'].tolist()\n",
    "tba_porewidth = tba['Pore width'].tolist()\n",
    "\n",
    "# remove duplicate values\n",
    "water_porewidth = list(set(water_porewidth))\n",
    "camphene_porewidth = list(set(camphene_porewidth))\n",
    "tba_porewidth = list(set(tba_porewidth))\n",
    "\n",
    "# remove NaN and sort list\n",
    "water_porewidth = [x for x in water_porewidth if x>0]\n",
    "water_porewidth.sort()\n",
    "\n",
    "camphene_porewidth = [x for x in camphene_porewidth if x>0]\n",
    "camphene_porewidth.sort()\n",
    "\n",
    "tba_porewidth = [x for x in tba_porewidth if x>0]\n",
    "tba_porewidth.sort()\n",
    "\n",
    "# Figure \n",
    "fig = plt.figure(figsize=(figuresize, 0.75*figuresize))\n",
    "ax1 = fig.add_subplot(131)\n",
    "ax1.plot(water_porewidth)\n",
    "ax1.set_yscale('log')\n",
    "ax1.set_ylabel('Pore size (\\mu m)')\n",
    "rectangle = plt.Rectangle((-1, min(water_porewidth)), len(water_porewidth)+1, max(water_porewidth)-min(water_porewidth), color='0.9', zorder=0)\n",
    "plt.gca().add_patch(rectangle)\n",
    "plt.ylim(0,500)\n",
    "plt.xlim(-1,len(water_porewidth))\n",
    "plt.title('Water', fontsize=titlefontsize)\n",
    "plt.gca().xaxis.set_major_locator(plt.NullLocator())\n",
    "\n",
    "ax2 = fig.add_subplot(132, sharey=ax1)\n",
    "ax2.plot(camphene_porewidth)\n",
    "ax2.ticklabel_format(axis='both', visible=False)\n",
    "plt.setp(ax2.get_xticklabels(), visible=False)\n",
    "plt.setp(ax2.get_yticklabels(), visible=False)\n",
    "rectangle = plt.Rectangle((-1, min(camphene_porewidth)), len(camphene_porewidth)+1, max(camphene_porewidth)-min(camphene_porewidth), color='0.9', zorder=0)\n",
    "plt.gca().add_patch(rectangle)\n",
    "plt.ylim(0,500)\n",
    "plt.xlim(-1,len(camphene_porewidth))\n",
    "plt.title('Camphene', fontsize=titlefontsize)\n",
    "plt.gca().xaxis.set_major_locator(plt.NullLocator())\n",
    "\n",
    "ax3 = fig.add_subplot(133, sharey=ax1)\n",
    "ax3.plot(tba_porewidth)\n",
    "ax3.ticklabel_format(visible=False)\n",
    "plt.setp(ax3.get_xticklabels(), visible=False)\n",
    "plt.setp(ax3.get_yticklabels(), visible=False)\n",
    "rectangle = plt.Rectangle((-1, min(tba_porewidth)), len(tba_porewidth)+1, max(tba_porewidth)-min(tba_porewidth), color='0.9', zorder=0)\n",
    "plt.gca().add_patch(rectangle)\n",
    "plt.ylim(1,1000)\n",
    "plt.xlim(-1,len(tba_porewidth))\n",
    "plt.title('TBA', fontsize=titlefontsize)\n",
    "plt.tight_layout()\n",
    "fig.subplots_adjust(wspace=0)\n",
    "plt.gca().xaxis.set_major_locator(plt.NullLocator())\n",
    "\n",
    "fig.savefig('../figures/figure4.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pore size vs. total porosity content, all solvents\n",
    "Figure 5 of the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "AElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107e57c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "plt.plot(data['Porosity'], data['Pore width'])\n",
    "ax.set_ylabel('Pore size (\\mu m)')\n",
    "ax.set_xlabel('Porosity (\\%)')\n",
    "#ax.set_yscale('log')\n",
    "plt.ylim(-10, 520)\n",
    "plt.xlim(15, 100)\n",
    "plt.tight_layout()\n",
    "fig.savefig('../figures/figure5.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Overview of the compressive strength achieved\n",
    "Figure 6 of the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "AAAAAGWCBA8AAAAAygQJHgAAAACUCRI8AAAAACgTJHgAAAAAUCZI8AAAAACgTJDgAQAAAECZIMED\n",
       "AAAAgDJBggcAAAAAZYIEDwAAAADKBAkeAAAAAJQJEjwAAAAAKBMkeAAAAABQJkjwAAAAAKBMkOAB\n",
       "AAAAQJkgwQMAAACAMkGCBwAAAABlggQPAAAAAMoECR4AAAAAlAkSPAAAAAAoEyR4AAAAAFAmSPAA\n",
       "AAAAoEyQ4AEAAABAmfj/AfMiiX9ERc05AAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fbb1510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.optimize import curve_fit\n",
    "\n",
    "# function used to fit the regression. Strength is assumed to vary with the power law of the relative density\n",
    "def func (x, a, b, c):\n",
    "    return a*(1-x/100)**b+c\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "# fit the data with a regression analysis\n",
    "data_bis = data[(data['Porosity'] > 0) & (data['Normalized strength (compression)'] > 0)]\n",
    "fitParamsIT, fitCovIT = curve_fit(func, data_bis['Porosity'], data_bis['Normalized strength (compression)'])\n",
    "porosity_table = linspace(0, 100.0, num=10000)\n",
    "\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "plt.plot(data['Porosity'], data['Normalized strength (compression)'])\n",
    "plt.plot(foams['porosity'], foams['norm strength'])\n",
    "plt.plot(porosity_table, func(porosity_table, fitParamsIT[0], fitParamsIT[1], fitParamsIT[2]), marker='', linestyle=':', color='k', dashes=[0.3, 2], zorder=1, dash_capstyle='round')\n",
    "plot_upper_limit() # plot the open and close-cell model predictions\n",
    "ax.set_yscale('log')\n",
    "ax.set_xlabel('Porosity (\\%)')\n",
    "ax.set_ylabel('Compressive Strength (normalized)')\n",
    "xmin = 15\n",
    "xmax = 100\n",
    "ymin = 0.0001\n",
    "ymax = 2\n",
    "plt.ylim(ymin, ymax)\n",
    "plt.xlim(xmin, xmax)\n",
    "\n",
    "plt.tight_layout()\n",
    "fig.savefig('../figures/figure6.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exponent of the power law: 2.26321007527\n"
     ]
    }
   ],
   "source": [
    "# parameters of the fit\n",
    "print 'Exponent of the power law: '+str(fitParamsIT[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "125 papers\n",
      "@Shen2014a; @Yang2014; @Vijayan2014b; @Xing2014; @Lee2010b; @Flauder2014; @Souza2014a; @Kumar2014a; @Sadeghpour2014; @Hu2014a; @Tang2014a; @CHENG2014a; @Zeng2014a; @Xu2014; @Kim2014; @Kim2014b; @Dong2013; @Ai; @Farhangdoust2012a; @Naglieri2013; @MohammadHosseinGhzanfari2013; @Li2013a; @Sofie2004; @Liu2013a; @Xing2013; @Landi2013; @Zhang2013a; @Choi2012b; @Hunger2013; @Zamanian2012; @Flauder2012; @Zhang2012d; @Hunger2012; @Li2012f; @Hamamoto2012; @Farhangdoust2012; @Li2012d; @Xu2012a; @Hou2012; @Jung2013; @Hou2012a; @Du2012a; @Zhang2011a; @Zhang2012b; @Yook2012; @Choi2012; @Zhang2012a; @Liu; @Guo2010c; @Yao2011a; @Xia2012; @Li2011d; @Kim2011a; @Yue2011; @Han; @Mongkolkachit2010; @Guo2010b; @Guo2010; @Ye2010; @Liu2010; @Zhao2010; @Ye2010a; @Ye2010b; @Nakata2007; @Ding2007; @Landi2008; @Fife2009; @Jung2009; @Chino2008; @Fu2008a; @Fu2008; @Fu2007; @Chen2007a; @Deville2006; @Deng2007; @Cao2009; @Bettge; @Araki2005; @Araki2004a; @Araki2004; @Zuo2008; @Zhang2010; @Yoon2008a; @Yoon2007a; @Yoon2007b; @Yook2009; @Yook2009a; @Yang2010a; @Tang2010a; @Tallon2009; @Suetsugu2007; @Song2006; @Soon2009; @Rahaman2008; @Moon2003; @Mallick2009; @Macchetta2009; @Liu2010a; @Lee2007; @Lee2008; @Lee2007a; @Koh2007; @Ji2010; @Hong2010a; @Hong2009; @Han2010a; @Fukasawa2002; @Fukushima2008; @Fukushima2010; @Fukasawa2001a; @Fukasawa2001; @Fu2010; @Wildhack2006; @Deville2006b; @Flauder2014a; @Sepulveda2014; @Liu2015; @Fukasawa2002a; @Fukushima2014a; @Pekor2010; @Zuo2010; @Yoon2008; @Zeng2014b; @Ping2015; @Li2015b\n"
     ]
    }
   ],
   "source": [
    "# Extract the bibliographic references used for the plot\n",
    "authors = data['Mendeley key']\n",
    "list_authors(authors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Overview of the flexural strength achieved\n",
    "Figure 7 of the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1087efd90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "plt.plot(data['Porosity'], data['Normalized strength (flexion)'])\n",
    "ax.set_yscale('log')\n",
    "ax.set_xlabel('Porosity (\\%)')\n",
    "ax.set_ylabel('Flexural Strength (normalized)')\n",
    "plt.ylim(0.0001, 2)\n",
    "plt.xlim(20, 90)\n",
    "\n",
    "plt.tight_layout()\n",
    "fig.savefig('../figures/figure7.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16 papers\n",
      "@Shen2014a; @Yang2014; @Souza2014a; @Hu2014a; @Li2013a; @Hou2012a; @Zhang2012b; @Zhang2012a; @Yao2011a; @Xia2012; @Yue2011; @Ye2010; @Ye2010a; @Ye2010b; @Chen2007a; @Flauder2014a\n"
     ]
    }
   ],
   "source": [
    "# Extract the bib ref of the above plot\n",
    "dataplot = data[(data['Normalized strength (flexion)'] > 0)]\n",
    "authors = dataplot['Mendeley key']\n",
    "list_authors(authors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compressive strength vs. pore size\n",
    "Figure 8 of the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107a79150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "plt.plot(data['Pore width'], data['Normalized strength (compression)'])\n",
    "ax.set_xscale('log')\n",
    "ax.set_yscale('log')\n",
    "ax.set_xlabel('Pore size (\\mu m)')\n",
    "ax.set_ylabel('Compressive Strength (normalized)')\n",
    "plt.ylim(0.0001, 5)\n",
    "plt.xlim(2, 700)\n",
    "plt.tight_layout()\n",
    "\n",
    "# line with -1/2 slope\n",
    "poresize_table = linspace(60, 200.0, num=10000)\n",
    "plt.plot(poresize_table, 100*poresize_table**(-1/2), marker='', linestyle='-', color='black', linewidth='0.3')\n",
    "plt.plot([100, 120], [1, 1], 'k-', lw=0.3)\n",
    "plt.annotate('-1/2', (110, 1.2), fontsize='5')\n",
    "            \n",
    "fig.savefig('../figures/figure8.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "69 papers\n",
      "@Shen2014a; @Yang2014; @Vijayan2014b; @Lee2010b; @Flauder2014; @Souza2014a; @Kumar2014a; @Sadeghpour2014; @Hu2014a; @Tang2014a; @CHENG2014a; @Zeng2014a; @Xu2014; @Kim2014; @Kim2014b; @Dong2013; @Ai; @Farhangdoust2012a; @Naglieri2013; @MohammadHosseinGhzanfari2013; @Li2013a; @Liu2013a; @Landi2013; @Zhang2013a; @Choi2012b; @Hunger2013; @Flauder2012; @Zhang2012d; @Hunger2012; @Li2012f; @Hamamoto2012; @Farhangdoust2012; @Li2012d; @Hou2012; @Jung2013; @Hou2012a; @Du2012a; @Zhang2011a; @Choi2012; @Liu; @Li2011d; @Kim2011a; @Yue2011; @Liu2010; @Zhao2010; @Ding2007; @Landi2008; @Chino2008; @Fu2008a; @Fu2008; @Deville2006; @Cao2009; @Zuo2008; @Zhang2010; @Yoon2008a; @Yoon2007a; @Yoon2007b; @Yook2009; @Yook2009a; @Macchetta2009; @Liu2010a; @Hong2010a; @Hong2009; @Han2010a; @Fukushima2008; @Fukushima2010; @Fu2010; @Deville2006b; @Flauder2014a\n"
     ]
    }
   ],
   "source": [
    "# Extract the bib ref of the above plot\n",
    "dataplot = data[(data['Pore width'] > 0)]\n",
    "authors = dataplot['Mendeley key']\n",
    "list_authors(authors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compressive strength and failure modes\n",
    "Figure 9 of the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "AAAAgIYgwQMAAACAhvj/u6uEs1pJqjYAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10abba150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "plt.plot(cellular['Porosity'], cellular['Normalized strength (compression)'])\n",
    "plt.plot(brittle['Porosity'], brittle['Normalized strength (compression)'])\n",
    "\n",
    "ax.set_yscale('log')\n",
    "ax.set_xlabel('Porosity (\\%)')\n",
    "ax.set_ylabel('Compressive Strength (normalized)')\n",
    "plt.ylim(0.002, 1)\n",
    "plt.xlim(20, 100)\n",
    "\n",
    "plt.tight_layout()\n",
    "fig.savefig('../figures/figure9.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cellular:\n",
      "22 papers\n",
      "@Shen2014a; @Vijayan2014b; @Kumar2014a; @Kim2014; @Kim2014b; @Landi2013; @Hunger2012; @Hou2012; @Jung2013; @Yook2012; @Liu2010; @Ding2007; @Landi2008; @Chino2008; @Fu2008a; @Fu2008; @Deville2006; @Zuo2008; @Han2010a; @Fu2010; @Flauder2014a; @Ping2015\n",
      "brittle:\n",
      "3 papers\n",
      "@Hou2012; @Liu2010; @Ping2015\n"
     ]
    }
   ],
   "source": [
    "# Extract the bib ref of the above plot\n",
    "dataplot = cellular[(cellular['Normalized strength (compression)'] > 0)]\n",
    "authors = dataplot['Mendeley key']\n",
    "\n",
    "print \"cellular:\"\n",
    "list_authors(authors)\n",
    "\n",
    "dataplot = brittle[(brittle['Normalized strength (compression)'] > 0)]\n",
    "authors = dataplot['Mendeley key']\n",
    "\n",
    "print \"brittle:\"\n",
    "list_authors(authors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compressive strength in presence and absence of ice-lenses type structural defects\n",
    "Figure 11 of the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11048d510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "plt.plot(notsureifdefects['Porosity'], notsureifdefects['Normalized strength (compression)'], color='white')\n",
    "plt.plot(nodefects['Porosity'], nodefects['Normalized strength (compression)'])\n",
    "plt.plot(defects['Porosity'], defects['Normalized strength (compression)'])\n",
    "ax.set_yscale('log')\n",
    "ax.set_xlabel('Porosity (\\%)')\n",
    "ax.set_ylabel('Compressive Strength (normalized)')\n",
    "plt.ylim(0.001, 3)\n",
    "plt.xlim(20, 100)\n",
    "\n",
    "plt.tight_layout()\n",
    "\n",
    "fig.savefig('../figures/figure11.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Defects: \n",
      "5 papers\n",
      "@Zhang2013a; @Zhao2010; @Landi2008; @Fu2008; @Ping2015\n",
      "No defects: \n",
      "57 papers\n",
      "@Shen2014a; @Yang2014; @Vijayan2014b; @Xing2014; @Lee2010b; @Flauder2014; @Kumar2014a; @Tang2014a; @Zeng2014a; @Kim2014; @Kim2014b; @Ai; @Farhangdoust2012a; @MohammadHosseinGhzanfari2013; @Xing2013; @Landi2013; @Zhang2013a; @Choi2012b; @Hunger2013; @Zamanian2012; @Farhangdoust2012; @Hou2012; @Jung2013; @Du2012a; @Zhang2011a; @Yook2012; @Choi2012; @Liu; @Li2011d; @Kim2011a; @Liu2010; @Ding2007; @Landi2008; @Chino2008; @Deville2006; @Cao2009; @Zuo2008; @Zhang2010; @Yoon2008a; @Yoon2007a; @Yoon2007b; @Yook2009; @Yook2009a; @Yang2010a; @Suetsugu2007; @Soon2009; @Macchetta2009; @Ji2010; @Hong2010a; @Hong2009; @Han2010a; @Fukushima2008; @Fukushima2010; @Fu2010; @Deville2006b; @Flauder2014a; @Zeng2014b\n",
      "Not sure if defects: \n",
      "8 papers\n",
      "@CHENG2014a; @Xu2014; @Liu2013a; @Flauder2012; @Landi2008; @Fu2008a; @Fu2008; @Liu2010a\n"
     ]
    }
   ],
   "source": [
    "# Extract the bib ref of the above plot\n",
    "dataplot = defects[(defects['Normalized strength (compression)'] > 0)]\n",
    "authors = dataplot['Mendeley key']\n",
    "print \"Defects: \"\n",
    "list_authors(authors)\n",
    "\n",
    "dataplot = nodefects[(nodefects['Normalized strength (compression)'] > 0)]\n",
    "authors = dataplot['Mendeley key']\n",
    "print \"No defects: \"\n",
    "list_authors(authors)\n",
    "\n",
    "dataplot = notsureifdefects[(notsureifdefects['Normalized strength (compression)'] > 0)]\n",
    "authors = dataplot['Mendeley key']\n",
    "print \"Not sure if defects: \"\n",
    "list_authors(authors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Influence of the starting particle size over the compressive strength\n",
    "Figure 12 of the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "AABSggAPAAAAAFKCAA8AAAAAUoIADwAAAABSggAPAAAAAFKCAA8AAAAAUoIADwAAAABSggAPAAAA\n",
       "AFKCAA8AAAAAUoIADwAAAABSggAPAAAAAFKCAA8AAAAAUoIADwAAAABSggAPAAAAAFKCAA8AAAAA\n",
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       "ggAPAAAAAFLi/wfombUo6okTFwAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11048d590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "plt.plot(data['Granulo poudre'], data['Normalized strength (compression)'])\n",
    "ax.set_yscale('log')\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlabel('Particle size (\\mu m)')\n",
    "ax.set_ylabel('Strength (normalized)')\n",
    "plt.ylim(0.001, 10)\n",
    "plt.tight_layout()\n",
    "\n",
    "# line with -1/2 slope\n",
    "poresize_table = linspace(10, 50.0, num=10000)\n",
    "plt.plot(poresize_table, 20*poresize_table**(-1/2), marker='', linestyle='-', color='black', linewidth='0.3')\n",
    "plt.plot([20, 40], [1, 1], 'k-', lw=0.3)\n",
    "plt.annotate('-1/2', (20, 1.2), fontsize='5')\n",
    "\n",
    "fig.savefig('../figures/figure12.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "43 papers\n",
      "@Shen2014a; @Yang2014; @Vijayan2014b; @Flauder2014; @Tang2014a; @CHENG2014a; @Zeng2014a; @Xu2014; @MohammadHosseinGhzanfari2013; @Liu2013a; @Landi2013; @Zhang2013a; @Choi2012b; @Flauder2012; @Farhangdoust2012; @Hou2012; @Jung2013; @Du2012a; @Zhang2011a; @Yook2012; @Choi2012; @Liu; @Li2011d; @Kim2011a; @Liu2010; @Chino2008; @Fu2008a; @Fu2008; @Zuo2008; @Zhang2010; @Yoon2008a; @Yoon2007a; @Suetsugu2007; @Macchetta2009; @Liu2010a; @Hong2010a; @Hong2009; @Han2010a; @Fukushima2008; @Fukushima2010; @Fu2010; @Zeng2014b; @Li2015b\n"
     ]
    }
   ],
   "source": [
    "# Extract the bibliographic references used for the plot\n",
    "dataplot = data[(data['Granulo poudre'] > 0) & (data['Normalized strength (compression)']>0)]\n",
    "authors = dataplot['Mendeley key']\n",
    "list_authors(authors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Influence of the nature of the solvent over the compressive strength.\n",
    "Figure 13 of the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
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icetemplating.csv

studart.csv