lesson_2_raw.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "#@title\n",
        "#HIDDEN\n",
        "from IPython.display import display, clear_output\n",
        "import numpy as np\n",
        "import numpy.ma as ma\n",
        "import matplotlib as mpl\n",
        "import matplotlib.pyplot as plt\n",
        "from ipywidgets import interactive, widgets\n",
        "from mpl_toolkits.axisartist import SubplotZero\n",
        "from IPython.display import YouTubeVideo\n",
        "from matplotlib.patches import Ellipse, Rectangle, Arc\n",
        "from matplotlib.ticker import FormatStrFormatter\n",
        "from matplotlib import patches\n",
        "from scipy import stats\n",
        "mpl.rc('font', **{'family': 'serif', 'serif':['Computer Modern'], 'size': 14})\n",
        "mpl.rc('text', usetex=True)\n",
        "\n",
        "%config InlineBackend.figure_formats = ['svg']\n",
        "%matplotlib inline"
      ],
      "outputs": [],
      "execution_count": 7,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-04-03T01:42:02.050516Z",
          "start_time": "2021-04-03T01:42:02.015335Z"
        },
        "hide_input": true
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "def arrowed_spines(fig, ax, w_scl=40, l_scl=40, xlim=None, ylim=None):\n",
        "    '''\n",
        "    Solution provided in \n",
        "    https://stackoverflow.com/questions/33737736/matplotlib-axis-arrow-tip\n",
        "    '''\n",
        "    if xlim==None:\n",
        "        xmin, xmax = ax.get_xlim()\n",
        "    else:\n",
        "        xmin, xmax = xlim\n",
        "    if ylim==None:\n",
        "        ymin, ymax = ax.get_ylim()\n",
        "    else:\n",
        "        ymin, ymax = ylim\n",
        "    # removing the default axis on all sides:\n",
        "    for side in ['bottom','right','top','left']:\n",
        "        ax.spines[side].set_visible(False)\n",
        "\n",
        "    # removing the axis ticks\n",
        "    ax.set_xticks([]) # labels \n",
        "    ax.set_yticks([])\n",
        "    ax.xaxis.set_ticks_position('none') # tick markers\n",
        "    ax.yaxis.set_ticks_position('none')\n",
        "\n",
        "    # get width and height of axes object to compute \n",
        "    # matching arrowhead length and width\n",
        "    dps = fig.dpi_scale_trans.inverted()\n",
        "    bbox = ax.get_window_extent().transformed(dps)\n",
        "    width, height = bbox.width, bbox.height\n",
        "\n",
        "    # manual arrowhead width and length\n",
        "    hw = 1./w_scl*(ymax-ymin) \n",
        "    hl = 1./l_scl*(xmax-xmin)\n",
        "    lw = 1. # axis line width\n",
        "    ohg = 0 # arrow overhang\n",
        "\n",
        "    # compute matching arrowhead length and width\n",
        "    yhw = hw/(ymax-ymin)*(xmax-xmin)* height/width \n",
        "    yhl = hl/(xmax-xmin)*(ymax-ymin)* width/height\n",
        "\n",
        "    # draw x and y axis\n",
        "    ax.arrow(xmin, 0, xmax-xmin, 0., fc='k', ec='k', lw = lw, \n",
        "             head_width=hw, head_length=hl, overhang = ohg, \n",
        "             length_includes_head= True, clip_on = False) \n",
        "\n",
        "    ax.arrow(0, ymin, 0., ymax-ymin, fc='k', ec='k', lw = lw, \n",
        "             head_width=yhw, head_length=yhl, overhang = ohg, \n",
        "             length_includes_head= True, clip_on = False)\n",
        "    \n",
        "def add_interval(ax, xdata, ydata, caps=\"  \"):\n",
        "    line = ax.add_line(mpl.lines.Line2D(xdata, ydata, zorder=12, c='k'))\n",
        "    anno_args = {\n",
        "        'ha': 'center',\n",
        "        'va': 'center',\n",
        "        'size': 16,\n",
        "        'color': line.get_color()\n",
        "    }\n",
        "    a0 = ax.annotate(caps[0], xy=(xdata[0], ydata[0]), zorder=12, **anno_args)\n",
        "    a1 = ax.annotate(caps[1], xy=(xdata[1], ydata[1]), zorder=12, **anno_args)\n",
        "    return (line,(a0,a1))\n",
        "\n",
        "def plot_arrow(ax, theta):\n",
        "    x_0 = 0\n",
        "    y_0 = 0\n",
        "    if theta >= 0:\n",
        "        y_1 = 0.1\n",
        "    else:\n",
        "        y_1 = -0.1\n",
        "    if theta !=0:\n",
        "        x_1 = y_1/np.tan(theta)\n",
        "    else:\n",
        "        x_1 = y_1/np.tan(1e-8)\n",
        "    x_h_1 = x_1/np.linalg.norm([x_1, y_1])\n",
        "    y_h_1 = y_1/np.linalg.norm([x_1, y_1])\n",
        "    ax.quiver(x_0, y_0, x_h_1*0.75, y_h_1*0.75, units='xy', scale=1, color='gray', label='Direction of Propagation')\n",
        "    ax.add_patch(Arc([x_0, y_0], 0.5, y_h_1/2, theta1=0, theta2=np.degrees(np.arctan(y_h_1/x_h_1)), color='gray', lw=2))\n",
        "    props = dict(boxstyle='round', facecolor='white', alpha=0.75)\n",
        "    ax.text(x_h_1*0.25+0.1, y_h_1*0.25+0.01, r'$\\theta$', c='k', bbox=props)\n",
        "\n",
        "    ax.set_aspect('equal')\n",
        "    ax.set_xlim(-1.2, 1.2)\n",
        "    ax.set_ylim(-1.2, 1.2)\n",
        "    \n",
        "def create_multipleChoice_widget(description, options, correct_answer):\n",
        "    if correct_answer not in options:\n",
        "        options.append(correct_answer)\n",
        "    \n",
        "    correct_answer_index = options.index(correct_answer)\n",
        "    \n",
        "    radio_options = [(words, i) for i, words in enumerate(options)]\n",
        "    alternativ = widgets.RadioButtons(\n",
        "        options = radio_options,\n",
        "        description = '',\n",
        "        disabled = False\n",
        "    )\n",
        "    \n",
        "    description_out = widgets.HTMLMath(description)\n",
        "        \n",
        "    feedback_out = widgets.Output()\n",
        "\n",
        "    def check_selection(b):\n",
        "        a = int(alternativ.value)\n",
        "        if a==correct_answer_index:\n",
        "            s = '\\x1b[6;30;42m' + \" Congratulations! You're right! \" + '\\x1b[0m' +\"\\n\" #green color\n",
        "        else:\n",
        "            s = '\\x1b[5;30;41m' + \" Wrong Anwser! Try again!\" + '\\x1b[0m' +\"\\n\" #red color\n",
        "        with feedback_out:\n",
        "            clear_output()\n",
        "            print(s)\n",
        "        return\n",
        "    \n",
        "    check = widgets.Button(description=\"Submit!\")\n",
        "    check.on_click(check_selection)\n",
        "    \n",
        "    \n",
        "    return widgets.VBox([description_out, alternativ, check, feedback_out])\n",
        "\n",
        "\n",
        "def sbs(texts):\n",
        "    btn_next = widgets.Button(description='Next')\n",
        "    btn_back = widgets.Button(description='Back')\n",
        "    btn_back.disabled = True\n",
        "    texts_disps = []\n",
        "    total_texts = len(texts)\n",
        "    for text in texts:\n",
        "        texts_disps.append(widgets.HTMLMath(text))\n",
        "    for text_disp in texts_disps:\n",
        "        text_disp.layout = widgets.Layout(display='none')\n",
        "\n",
        "    global i_vis \n",
        "    i_vis = 0\n",
        "\n",
        "    def update_vis(i_vis):\n",
        "        if i_vis == total_texts:\n",
        "            btn_next.disabled = True\n",
        "        else:\n",
        "            btn_next.disabled = False\n",
        "        if i_vis != 0:\n",
        "            btn_back.disabled = False\n",
        "        else:\n",
        "            btn_back.disabled = True\n",
        "\n",
        "        for text_disp in texts_disps:\n",
        "            text_disp.layout = widgets.Layout(display='none')\n",
        "        for i in range(i_vis):\n",
        "            try:\n",
        "                texts_disps[i].layout.display = 'block'\n",
        "            except:\n",
        "                pass\n",
        "    \n",
        "    def clicked_btn_next(btn_object):\n",
        "        global i_vis\n",
        "        i_vis += 1\n",
        "        update_vis(i_vis)\n",
        "        \n",
        "    def clicked_btn_back(btn_object):\n",
        "        global i_vis\n",
        "        i_vis -= 1\n",
        "        update_vis(i_vis)\n",
        "    \n",
        "    btn_next.on_click(clicked_btn_next)\n",
        "    btn_back.on_click(clicked_btn_back)\n",
        "    bts = widgets.HBox([btn_back, btn_next])\n",
        "    out = widgets.VBox(texts_disps + [bts], layout=widgets.Layout(width='100%', display='column-flex'))\n",
        "    return out"
      ],
      "outputs": [],
      "execution_count": 2,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-04-03T01:40:52.301681Z",
          "start_time": "2021-04-03T01:40:52.247030Z"
        },
        "hide_input": true
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Quick Review"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "In [Lesson 1](https://murilohmoreira.github.io/host_widgets/lesson_1.html) we found that the tip of the defect acts as a stress raiser because of the concentration of force lines around it, and as shown below, the geometry of the defect influences how much this effect occurs:"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "\n",
        "def circle(C, R):\n",
        "    t=np.linspace(0,2*np.pi, 200)\n",
        "    return C+R*np.exp(1j*t)\n",
        "def Juc(z, lam):#Joukowski transformation\n",
        "    return z+(lam**2)/z\n",
        "\n",
        "def deg2radians(deg):\n",
        "    return deg*np.pi/180\n",
        "\n",
        "def compute_lines(rho):\n",
        "    '''\n",
        "    Based on the Joukowski transformation of the potential flow past a cylinder.\n",
        "    For reference:\n",
        "    https://people.eng.unimelb.edu.au/asho/PotentialFlow/notes.pdf\n",
        "    https://github.com/luca6331/joukowskiAirfoilVisualization/blob/master/Report.pdf\n",
        "    https://nbviewer.jupyter.org/github/empet/Math/blob/master/Joukowski-airfoil.ipynb\n",
        "    \n",
        "    '''\n",
        "\n",
        "    V_inf = 1\n",
        "    R = 1\n",
        "    lam = (R**2 + R*rho/2 - R*(8*R*rho + rho**2)**0.5/2)**0.5\n",
        "    alpha=deg2radians(0) # angle of attack\n",
        "    beta=deg2radians(0)  # -beta is the argument of the complex no (Joukovski parameter - circle center)\n",
        "    center_c= 0 # Center of the circle\n",
        "    x=np.arange(-3.5, 3.5, 0.1)\n",
        "    y=np.arange(-5, 5, 0.1)\n",
        "    x,y=np.meshgrid(x,y)\n",
        "    z=x+1j*y\n",
        "    z=ma.masked_where(np.absolute(z-center_c)<=R, z)\n",
        "    Z=z-center_c\n",
        "    Z = -1j*Z\n",
        "    Gamma=-4*np.pi*V_inf*R*np.sin(beta+alpha)\n",
        "    U=np.zeros(Z.shape, dtype=np.complex)\n",
        "    with np.errstate(all='ignore'):#avoid warning when evaluates np.log(0+1jy).\n",
        "                                         #In this case the arg is arctan(y/0)+cst\n",
        "            for m in range(Z.shape[0]):\n",
        "                for n in range(Z.shape[1]):\n",
        "                    #U[m,n]=Gamma*np.log(Z[m,n]/R)/(2*np.pi)# \n",
        "                     U[m,n]=Gamma*np.log((Z[m,n]*np.exp(-1j*alpha))/R)/(2*np.pi)\n",
        "    c_flow= V_inf*Z*np.exp(-1j*alpha) + (V_inf*np.exp(1j*alpha)*R**2)/Z - 1j*U #the complex flow\n",
        "    J=Juc(z, lam)\n",
        "    Circle=circle(0, R)\n",
        "    Airfoil=Juc(Circle, lam)# airfoil \n",
        "    return J, c_flow.imag, Airfoil, rho"
      ],
      "outputs": [],
      "execution_count": 3,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-04-03T01:40:56.464919Z",
          "start_time": "2021-04-03T01:40:56.449524Z"
        },
        "hide_input": true
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "\n",
        "np.seterr(all='ignore')\n",
        "def f(rho, defect, show_lines):\n",
        "    fig, ax = plt.subplots(figsize=(6, 6))\n",
        "    r = Rectangle([-3.5, -4.75], 6.95, 9.5, facecolor='none', edgecolor='k', zorder=10)\n",
        "    if not defect:\n",
        "        if not show_lines:\n",
        "            ax.add_patch(r)\n",
        "\n",
        "            \n",
        "        if show_lines:\n",
        "            xcoords = np.linspace(-3.5, 3.5, 50)\n",
        "            ax.add_patch(r)\n",
        "            for xc in xcoords:\n",
        "                perf = plt.axvline(x=xc, c='blue', lw=1)\n",
        "                perf.set_clip_path(r)\n",
        "    if defect: \n",
        "        if not show_lines:\n",
        "            R = 1\n",
        "            lam = (R**2 + R*rho/2 - R*(8*R*rho + rho**2)**0.5/2)**0.5\n",
        "            c = 1\n",
        "            b = c*rho**0.5\n",
        "            Circle=circle(0, R)\n",
        "            Airfoil=Juc(Circle, lam)\n",
        "            ax.plot(Airfoil.real, Airfoil.imag, c='k')\n",
        "            ax.add_patch(r)\n",
        "\n",
        "        if show_lines:\n",
        "            J, stream_func, Airfoil, rho = compute_lines(rho)\n",
        "            cp=ax.contour(J.real, J.imag, stream_func,levels=100, colors='blue', linewidths=1,\n",
        "                            linestyles='solid')# this means that the flow is evaluated at Juc(z) since c_flow(Z)=C_flow(csi(Z))\n",
        "            ax.add_patch(r)\n",
        "\n",
        "            for col in cp.collections:\n",
        "                col.set_clip_path(r)\n",
        "            ax.plot(Airfoil.real, Airfoil.imag, c='k')\n",
        "            ax.set_xlim(-5.5, 5.5)\n",
        "            ax.set_ylim(-5.5, 5.5)\n",
        "        \n",
        "    plt.annotate('', xy = (0, 4.725), \\\n",
        "        xytext = (0, 5.5), fontsize = 20, \\\n",
        "        color = '#303030', arrowprops=dict(edgecolor='black', arrowstyle = '<-'))\n",
        "    plt.text(0.25, 5.25, r'$\\sigma_{app}$', fontsize=14)\n",
        "        \n",
        "    plt.annotate('', xy = (0, -4.725), \\\n",
        "        xytext = (0, -5.5), fontsize = 20, \\\n",
        "        color = '#303030', arrowprops=dict(edgecolor='black', arrowstyle = '<-'))\n",
        "    plt.text(0.25, -5.5, r'$\\sigma_{app}$', fontsize=14)\n",
        "\n",
        "    ax.axis('off')\n",
        "    ax.set_xlim(-5.5, 5.5)\n",
        "    ax.set_ylim(-5.5, 5.5)\n",
        "    ax.set_aspect('equal')\n",
        "    plt.show()\n",
        "\n",
        "interactive_plot = interactive(f, show_lines=widgets.ToggleButton(True, description='Plot Force Lines'),\n",
        "                               rho=widgets.FloatSlider(value=5,\n",
        "                                                       min=0.01,\n",
        "                                                       max=1,\n",
        "                                                       step=0.01,\n",
        "                                                       description=r'$\\rho$',\n",
        "                                                       readout_format='.2f'),\n",
        "                                defect=widgets.ToggleButton(False, description='Add defect'))\n",
        "output = interactive_plot.children[-1]\n",
        "output.layout.height = '460px'\n",
        "interactive_plot.layout = widgets.Layout(display='flex',\n",
        "                               flex_flow='column-reverse',\n",
        "                               align_items='center',\n",
        "                               align_content='center',\n",
        "                               justify_content='center',\n",
        "                               width='100%')\n",
        "interactive_plot\n"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "9df8b22bf4c04da09ba9a4066856abf0",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": "interactive(children=(FloatSlider(value=1.0, description='$\\\\rho$', max=1.0, min=0.01, step=0.01), ToggleButto…"
          },
          "metadata": {}
        }
      ],
      "execution_count": 4,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-04-03T01:41:04.030549Z",
          "start_time": "2021-04-03T01:40:59.011806Z"
        },
        "hide_input": true,
        "scrolled": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For an elliptical deffect we found that we could calculate by how much the stress was increased:"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2020-09-25T12:15:56.987390Z",
          "start_time": "2020-09-25T12:15:56.970438Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "fig, ax = plt.subplots(figsize=(10, 4))\n",
        "\n",
        "\n",
        "r2 = Rectangle([0.3, 0], 0.25, 1, ec='k', lw=1.5, fc='skyblue')\n",
        "# plt.text(0.3+0.045, 0.85, '$S_2$', fontsize=14, zorder=9)\n",
        "ax.add_patch(r2)\n",
        "# plt.plot([0+0.3, 0.2+0.3], [0.3, 0.3], c='k', lw=1.5, zorder=9)\n",
        "e1 = Ellipse([0.425, 0.5], 0.1, 0.05, zorder=9, fc='w', ec='k')\n",
        "# plt.arrow(0.4, 0.4, 0.075, 0, head_width=0.075, head_length=0.0,\n",
        "#           ec='k', lw=1.5, fc='k', zorder=9, stylr='')\n",
        "\n",
        "plt.annotate(s='', xy=(0.345+0.025,0.45), xytext=(0.455+0.025,0.45),\n",
        "             arrowprops=dict(arrowstyle='|-|, widthA=0.4,widthB=0.4', linewidth=1.5))\n",
        "\n",
        "plt.text(0.325+0.115/2+0.025, 0.35, '2c', fontsize=14)\n",
        "\n",
        "\n",
        "plt.annotate(s='', xy=(0.49, 0.475), xytext=(0.49,0.525),\n",
        "             arrowprops=dict(arrowstyle='|-|, widthA=0.4,widthB=0.4', linewidth=1.5))\n",
        "\n",
        "plt.text(0.505, 0.475, '2b', fontsize=14)\n",
        "\n",
        "ax.add_patch(e1)\n",
        "for i in np.linspace(0.3, 0.55, 6):\n",
        "    plt.arrow(i+0.001, -0.01, 0, -0.11, head_width=0.025, head_length=0.04,\n",
        "          ec='k', lw=1.5, fc='k', zorder=9)\n",
        "    plt.arrow(i+0.001, 1, 0, 0.11, head_width=0.025, head_length=0.04,\n",
        "          ec='k', lw=1.5, fc='k', zorder=9)\n",
        "\n",
        "ax.arrow(0.3+0.05+0.025, 0.5, 0, 0.225, head_width=0.025, head_length=0.04,\n",
        "          lw=1.5, fc='k', zorder=11)\n",
        "plt.text(0.125+0.16+0.025, 0.8, r'$\\sigma_{y} = \\sigma_{ap} \\left(1 + 2 \\sqrt{ \\displaystyle \\frac{c}{\\rho}} \\right)$', fontsize=13)\n",
        "# plt.text(0.095+0.3, 0.34, '$A_1$', fontsize=14, zorder=9)\n",
        "# ax.arrow(0.1+0.3, -0.01, 0, -0.14, head_width=0.025, head_length=0.04,\n",
        "#           lw=1.5, fc='k')\n",
        "# plt.text(0.125+0.3, -0.15, '$F_2$', fontsize=14)\n",
        "plt.text(0.085+0.3, 1.225, '$\\sigma_{ap}$', fontsize=14)\n",
        "plt.text(0.085+0.3, -0.25, '$\\sigma_{ap}$', fontsize=14)\n",
        "\n",
        "plt.text(0.6, 0.825, r'$K_t = \\displaystyle \\frac{\\sigma_{y}}{\\sigma_{app}} = \\left(1 + 2 \\sqrt{ \\displaystyle \\frac{c}{\\rho}} \\right)$', fontsize=14)\n",
        "\n",
        "# plt.plot([0.3, 0.325], [0.5, 0.5], c='w', lw=2, zorder=4)\n",
        "# plt.plot([0.475, 0.51], [0.5, 0.5], c='w', lw=2, zorder=4)\n",
        "\n",
        "ax.set_xlim(-0.1, 1)\n",
        "ax.set_ylim(-0.2, 1.2)\n",
        "\n",
        "ax.axis('off')\n",
        "plt.show()"
      ],
      "outputs": [
        {
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        "Now we may consider that we increase $\\sigma_{ap}$ until the material fails. In this case, what do you think $\\sigma_y$ would be?\n",
        "\n",
        "We may consider that on the defect tip, we reached the theoretical failure stress that we modeled earlier deriving from the Lennard-Jones potential, that is, mathematically we find that:\n",
        "\n",
        "\\begin{equation}\\label{eq:sig_theo_Kt}\n",
        "\\begin{array}{ll}\n",
        "\\sigma_y & = \\sigma_{ap}  \\ K_t \\\\\n",
        "\\ \\downarrow & \\ \\ \\ \\ \\downarrow \\\\\n",
        "\\sigma_{th} & = \\sigma_{f} \\  K_t\n",
        "\\end{array}\n",
        "\\end{equation}\n"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2020-09-25T12:10:33.572689Z",
          "start_time": "2020-09-25T12:10:33.554738Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now, **the gap between $\\sigma_{th}$ and $\\sigma_{f}$** shows to us **how much one can improve the material's strength by reducing the defects introduced during its processing steps**.\n",
        "\n",
        "**Or:**\n",
        "\n",
        "How a specific material **can \"resist\" to the decrease of strength** due to the **defects introduced during the processing steps**."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "We now may wonder if there is a criterion for failure based on the **characteristics of the material** and **of the defects** and if there is, **what is its analytical form**!"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Irwin Failure Criterion"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "We recall from [Lesson 1](./lesson_1) that the theoretical strength of a material, $\\sigma_{th}$ can be described as:\n",
        "\n",
        "\\begin{equation}\\label{eq:sigma_th}\n",
        "\\sigma_{th} = \\sqrt{\\frac{E \\gamma_0}{a_0}}\n",
        "\\end{equation}\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "From experimental results one can find the following relationships:\n",
        "\n",
        "\\begin{equation}\\label{eq:sth_ineq}\n",
        "\\frac{E}{5} \\gt \\sigma_{th} \\gt \\frac{E}{10}\n",
        "\\end{equation}\n",
        "\n",
        "\n",
        "\\begin{equation}\\label{eq:sexp_ineq}\n",
        "\\frac{E}{100} \\gt \\sigma_{th} \\gt \\frac{E}{1000}\n",
        "\\end{equation}\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "This difference is explained by the stress intensity factor:\n",
        "\n",
        "\\begin{equation}\\label{eq:sf}\n",
        "\\begin{array}{ll}\n",
        "\\sigma_y & = \\sigma_{ap}  \\ K_t \\\\\n",
        "\\ \\downarrow & \\ \\ \\ \\ \\downarrow \\\\\n",
        "\\sigma_{th} & = \\sigma_{f} \\  K_t\n",
        "\\end{array}\n",
        "\\end{equation}\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Which for an elliptical small defect we found it could be described as:\n",
        "\n",
        "\\begin{equation}\\label{eq:sif_def}\n",
        "K_t \\approx 2 \\sqrt{\\frac{c}{\\rho}}\n",
        "\\end{equation}\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Substituting the definition of the stress intensity factor, Equation \\ref{eq:sif_def}, into the theoretical strength, Equation \\ref{eq:sigma_th} we can find:\n",
        "\n",
        "\\begin{equation}\\label{eq:pre_irw}\n",
        "\\sqrt{\\frac{E \\gamma_0}{a_0}} = \\sigma_f  \\left( 2 \\sqrt{\\frac{c}{\\rho}}\\right)\n",
        "\\end{equation}\n",
        "\n",
        "\n",
        "Solving for the failure stress, $\\sigma_f$, we find the Irwin Failure Criteria:\n",
        "\\begin{equation}\\label{eq:irwin}\n",
        "\\sigma_f = \\left( \\frac{E \\gamma_0}{a_0} \\frac{\\rho}{4 c} \\right)^{\\frac{1}{2}}\n",
        "\\ \\ {\\text{Irwin Failure Criteria}}\n",
        "\\end{equation}\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "The first term on the parenthesis is related to properties that belongs to the material. The second term accounts for the geometry and size of the defect. \n",
        "\n",
        "Now, before proceeding, let's review our insight about the ductility of materials."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Ductility of Materials"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "We have a natural feeling for deciding which material is ductile and which one is fragile, for example:\n",
        "<center>\n",
        "<style type=\"text/css\">\n",
        ".tg  {border-collapse:collapse;border-spacing:0;}\n",
        ".tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;\n",
        "  overflow:hidden;padding:10px 5px;word-break:normal;}\n",
        ".tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;\n",
        "  font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;}\n",
        ".tg .tg-0lax{text-align:left;vertical-align:top}\n",
        "</style>\n",
        "<table class=\"tg\">\n",
        "<thead>\n",
        "  <tr>\n",
        "    <th class=\"tg-0lax\">Fragile</th>\n",
        "    <th class=\"tg-0lax\">Ductile</th>\n",
        "  </tr>\n",
        "</thead>\n",
        "<tbody>\n",
        "  <tr>\n",
        "    <td class=\"tg-0lax\">Ice</td>\n",
        "    <td class=\"tg-0lax\">Steel</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td class=\"tg-0lax\">Glass</td>\n",
        "    <td class=\"tg-0lax\">Lead</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td class=\"tg-0lax\">Chalk</td>\n",
        "    <td class=\"tg-0lax\">Copper</td>\n",
        "  </tr>\n",
        "</tbody>\n",
        "</table>\n",
        "</center>    \n",
        "\n",
        "This however, occurs at room temperature and standard conditions. There are multiple conditions that may change the behavior of these materials, such as:\n",
        "- Temperature effect (i.e. glass $T_g$, Ductile-to-Brittle Transition Temperature)\n",
        "- Load application rate (piche, polymers)\n",
        "- Environment conditions (luminosity, humidity, hydrogen)"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "<span id=\"call-ref_db_trans\" class=\"img_container center\" style=\"display: inline_block; vertical-align: top; text-align: center;\" > <img alt=\"test\" src=\"https://yenaengineering.nl/wp-content/uploads/2020/11/fm-3-dbtt-2.png\" style=\"display:block; margin-left: auto; margin-right: auto; text-align: left;\" title=\"caption\" align=\"center\" width=\"500\" height=\"600\" /> <div class=\"img_caption\" style=\"border-style: solid; border-width: 2px; border-radius: 5px; border-color:lightgrey; padding: 2px 5px; text-align: left; width=980px\"><b>Figure 1:</b> Ductile-Brittle transition temperature for mild steel <a href=\"#cit-ref_db_trans\">[1]</a>.</div> </span>\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now one question can be made: Is there any relationship between the strength of a material and its ductility?"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "# The Fracture Toughness - $K_{IC}$"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's consider how the tensile stress normal to the crack opening direction behaves in front of the crack. For doing this, we consider the Mode I of fracture, which is the *opening of the crack by tensile stress*."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "<span id=\"call-ref_mode\" class=\"img_container center\" style=\"display: inline_block; vertical-align: top; text-align: center;\" > <img alt=\"test\" src=\"https://www.researchgate.net/profile/Benoit_Derode/publication/258004229/figure/download/fig11/AS:669534277083151@1536640819817/Les-trois-modes-de-rupture-dune-fracture-Mode-I-ouverture-normale-aux-epontes-Mode.png\" style=\"display:block; margin-left: auto; margin-right: auto; text-align: left;\" title=\"caption\" align=\"center\" width=\"500\" height=\"600\" /> <div class=\"img_caption\" style=\"border-style: solid; border-width: 2px; border-radius: 5px; border-color:lightgrey; padding: 2px 5px; text-align: left; width=980px\"><b>Figure 2:</b> The three different modes of fracture: Mode I - tensile opening, Mode II - In plane shear, Mode III - Antiplane shear <a href=\"#cit-ref_mode\">[2]</a>.</div> </span>\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "We might expect that as we move further away from the crack tip, the concentration of the force lines decrease and as a consequence the stress decays towards the applied stress.\n",
        "\n",
        "Considering only the vicinity of the defect it is possible to find an analytical equation that describes how the stress decays. This may be visualized in the blue sample under tensile stress below. The decay of the local stress in the front of a defect is described too."
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "\n",
        "r = np.linspace(1e-3, 1, 1000)\n",
        "c = 1\n",
        "sigma_app = 10\n",
        "fig = plt.figure(figsize=(5, 6))\n",
        "plt.plot(r, sigma_app * (np.pi * c)**0.5 / (2*np.pi*r)**0.5, lw=2, c='Navy')\n",
        "plt.ylim(-50, 250)\n",
        "plt.xlim(-0.305, 0.825)\n",
        "\n",
        "e = Ellipse([-0.3, 0], 0.6, 40,  facecolor='w', edgecolor='k', zorder=10)\n",
        "plt.gca().add_patch(e)\n",
        "arrowed_spines(fig, plt.gca(), ylim=[-8, 250])\n",
        "add_interval(plt.gca(), [-0.3, -0.0001], [-35, -35], \"II\")\n",
        "plt.text(-0.15, -45, 'c', c='k', fontsize=20)\n",
        "plt.text(-0.08, 235, '$\\sigma_y$', c='k', fontsize=20)\n",
        "plt.text(0.775, -25, '$r$', c='k', fontsize=20)\n",
        "plt.arrow(0.45, -50, 0, -30., fc='k', ec='k', lw = 1, \n",
        "             head_width=0.01, head_length=5,\n",
        "             length_includes_head= True, clip_on = False)\n",
        "plt.text(0.46, -75, '$\\sigma_{ap}$', c='k', fontsize=20)\n",
        "\n",
        "plt.arrow(0.45, 250, 0, 30., fc='k', ec='k', lw = 1, \n",
        "             head_width=0.01, head_length=5,\n",
        "             length_includes_head= True, clip_on = False)\n",
        "plt.text(0.46, 265, '$\\sigma_{ap}$', c='k', fontsize=20)\n",
        "plt.text(0.225, 140, r'$\\sigma_y = \\frac{\\sigma_{ap}\\sqrt{\\pi c}}{\\sqrt{2 \\pi r}}$', c='k', fontsize=28)\n",
        "\n",
        "e = Ellipse([0.59, 160], 0.265, 32.5, lw=2,  facecolor='none', edgecolor='orangered', zorder=10)\n",
        "plt.gca().add_patch(e)\n",
        "plt.gca().set_facecolor('skyblue')\n",
        "plt.text(0.6, 185, r'$K_{{\\textrm I}}$', c='orangered', fontsize=24)\n",
        "plt.show()"
      ],
      "outputs": [
        {
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            "text/plain": "<Figure size 360x432 with 1 Axes>"
          },
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        }
      ],
      "execution_count": 194,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-22T11:25:43.187551Z",
          "start_time": "2021-03-22T11:25:43.072910Z"
        },
        "hide_input": true
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    },
    {
      "cell_type": "markdown",
      "source": [
        "One can see that the local stress, $\\sigma_y$, is inversely proportional to the distance from the crack tip, $r$. We can check that such equation is only valid on the vicinity of the defect when we analyze the behavior of it on both limits (if we consider $r \\rightarrow 0$, then $\\sigma_y \\rightarrow \\infty$, which is not real, and conversely, $r \\rightarrow \\infty$, then $\\sigma_y \\rightarrow 0$, which is also not true).\n",
        "\n",
        "Another interesting aspect is that we also find that there is a constant on the numerator which comprises the applied stress and the size of the defect. This is the **stress intensity factor**, which in mode I is represented by $K_I$."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "If we increase the applied stress, $\\sigma_{app}$, until the material breaks, we can define the critical stress intensity factor, $K_{Ic}$:\n",
        "\n",
        "\\begin{equation}\\label{eq:kic}\n",
        "\\begin{array}{ll}\n",
        "K_{{\\textrm I}} & = \\sigma_{ap}  \\ \\sqrt{\\pi c} \\\\\n",
        "\\ \\downarrow & \\ \\ \\ \\ \\downarrow \\\\\n",
        "K_{{\\textrm Ic}} & = \\sigma_{f} \\  \\sqrt{\\pi c}\n",
        "\\end{array}\n",
        "\\end{equation}\n",
        "\n",
        "The **critical stress intensity factor** is also known as the **fracture toughness** and has units of $\\textrm{MPa} . \\textrm{m}^{\\frac{1}{2}}$"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now considering this new quantity, analyze the following pairs of values of failure stress, $\\sigma_{f}$, and defect size, $c$:"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "# nbi:right\n",
        "K_Ic_1 = 4\n",
        "K_Ic_2 = 10\n",
        "fig = plt.figure(figsize=(4, 3))\n",
        "sigma_f = lambda K_Ic, c: K_Ic/(np.pi*c)**0.5\n",
        "cs = np.linspace(1e-1, 1, 100)\n",
        "plt.plot(cs, sigma_f(K_Ic_1, cs), '-o', markevery=6,  c='navy', zorder=5)\n",
        "plt.plot(cs, sigma_f(K_Ic_2, cs), '-o', markevery=6,  c='orangered', zorder=5)\n",
        "\n",
        "plt.scatter([0.805], [sigma_f(K_Ic_2, 0.805)], marker='o', c='k', s=100, zorder=10)\n",
        "plt.scatter([0.2075], [sigma_f(K_Ic_2, 0.2075)], marker='o', c='k', s=100, zorder=10)\n",
        "plt.scatter([0.805], [sigma_f(K_Ic_1, 0.805)], marker='o', c='k', s=100, zorder=10)\n",
        "plt.scatter([0.2075], [sigma_f(K_Ic_1, 0.2075)], marker='o', c='k', s=100, zorder=10)\n",
        "\n",
        "plt.text(0.805*1.015, sigma_f(K_Ic_1, 0.805)*1.2, r'I', fontsize=20, c='k')\n",
        "plt.text(0.2075*1.1, sigma_f(K_Ic_1, 0.2075)*1.15, r'II', fontsize=20, c='k')\n",
        "plt.text(0.805, sigma_f(K_Ic_2, 0.805)*1.15, r'III', fontsize=20, c='k')\n",
        "plt.text(0.2075*1.1, sigma_f(K_Ic_2, 0.2075)*1.05, r'IV', fontsize=20, c='k')\n",
        "\n",
        "arrowed_spines(fig, plt.gca(), ylim=[-1, 20], xlim=[-0.05, 1])\n",
        "\n",
        "plt.text(1, -1, 'c', fontsize=20)\n",
        "plt.text(-0.115, 20, r'$\\sigma_f$', fontsize=20)\n",
        "# plt.axhline(8, ls='--', c='navy')\n",
        "# plt.text(0.01, 8.5, r'$\\sigma_{ys, 1}$', fontsize=20, c='navy')\n",
        "\n",
        "# plt.axhline(13, ls='--', c='orangered')\n",
        "# plt.text(0.01, 13.5, r'$\\sigma_{ys, 2}$', fontsize=20, c='orangered')\n",
        "\n",
        "plt.show()"
      ],
      "outputs": [
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            "text/plain": "<Figure size 288x216 with 1 Axes>"
          },
          "metadata": {}
        }
      ],
      "execution_count": 117,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-19T19:33:11.817993Z",
          "start_time": "2021-03-19T19:33:11.722763Z"
        },
        "cell_style": "split",
        "hide_input": true
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "# nbi:right\n",
        "\n",
        "question = '''\n",
        "          <div style=\"align_content: center; font-size: 12px; font-weight: bold; width: 140%!important;\">\n",
        "          Which affirmation is right?\n",
        "          \n",
        "          <p>a)   $K_{IC, IV} > K_{IC, III} > K_{IC, II} > K_{IC, I}$</p>\n",
        "          \n",
        "          <p>b)  $K_{IC, I} > K_{IC, II} > K_{IC, III} > K_{IC, IV}$</p>\n",
        "          \n",
        "          <p>c) $K_{IC, IV} = K_{IC, III} > K_{IC, II} = K_{IC, I}$</p>\n",
        "          \n",
        "          <p>d) $K_{IC, II} = K_{IC, IV} > K_{IC, III} = K_{IC, I}$</p>\n",
        "          </div>\n",
        "          '''\n",
        "Q1 = create_multipleChoice_widget(question,['a','b','c', 'd'], 'c')\n",
        "Q1.layout = widgets.Layout(display='flex',\n",
        "                               flex_flow='column',\n",
        "                               align_items='center',\n",
        "                               align_content='center',\n",
        "                               justify_content='center',\n",
        "                               width='100%')\n",
        "display(Q1)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "f82b9c4a53fb4eecbad0e075e360aad2",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": "VBox(children=(HTMLMath(value='\\n          <div style=\"align_content: center; font-size: 12px; font-weight: bo…"
          },
          "metadata": {}
        }
      ],
      "execution_count": 165,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-25T11:26:29.473018Z",
          "start_time": "2021-03-25T11:26:29.429866Z"
        },
        "cell_style": "split",
        "hide_input": true,
        "run_control": {
          "marked": false
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Did you get it right in the first try? No worries, let's explain it!"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "What we have is in fact two different materials:"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "K_Ic_1 = 4\n",
        "K_Ic_2 = 10\n",
        "fig = plt.figure(figsize=(10, 6))\n",
        "sigma_f = lambda K_Ic, c: K_Ic/(np.pi*c)**0.5\n",
        "cs = np.linspace(1e-1, 1, 100)\n",
        "plt.plot(cs, sigma_f(K_Ic_1, cs), '-o', markevery=6,  c='navy', zorder=5)\n",
        "plt.text(0.8, 1.25, r'Material 1', fontsize=16, c='navy')\n",
        "plt.plot(cs, sigma_f(K_Ic_2, cs), '-o', markevery=6,  c='orangered', zorder=5)\n",
        "plt.text(0.8, 4.75, r'Material 2', fontsize=16, c='orangered')\n",
        "\n",
        "arrowed_spines(fig, plt.gca(), ylim=[-1, 20], xlim=[-0.05, 1])\n",
        "plt.annotate(r'$\\uparrow$ K$_{IC}$', xy=(0.3, 6), xytext=(0.6, 15),\n",
        "             arrowprops=dict(arrowstyle='<-', linewidth=1), fontsize=16)\n",
        "\n",
        "plt.plot([0.275, 0.275], [0, sigma_f(K_Ic_2, 0.275)], c='k', ls='--', lw=1)\n",
        "plt.plot([0, 0.275], [sigma_f(K_Ic_1, 0.275), sigma_f(K_Ic_1, 0.275)], c='k', ls='--', lw=1)\n",
        "plt.plot([0, 0.275], [sigma_f(K_Ic_2, 0.275), sigma_f(K_Ic_2, 0.275)], c='k', ls='--', lw=1)\n",
        "plt.text(-0.07, sigma_f(K_Ic_1, 0.275), r'$\\sigma_{f, 1}$', fontsize=20, c='navy')\n",
        "plt.text(-0.07, sigma_f(K_Ic_2, 0.275), r'$\\sigma_{f, 2}$', fontsize=20, c='orangered')\n",
        "\n",
        "plt.text(0.275*0.9, -1.3, r'$c_0$', fontsize=20, c='k')\n",
        "plt.text(0.7, 18, r'$\\sigma_{f, 2}$', fontsize=20, c='orangered')\n",
        "plt.text(0.765, 18, r'$>$', fontsize=20, c='k')\n",
        "plt.text(0.8, 18, r'$\\sigma_{f, 1}$', fontsize=20, c='navy')\n",
        "plt.text(0.865, 18, r'for fixed $c_0$', fontsize=20, c='k')\n",
        "\n",
        "\n",
        "\n",
        "plt.text(1, -1, 'c', fontsize=20)\n",
        "plt.text(-0.075, 20, r'$\\sigma_f$', fontsize=20)\n",
        "plt.axhline(8, ls='--', c='navy')\n",
        "plt.text(0.01, 7.3, r'$\\sigma_{ys, 1}$', fontsize=20, c='navy')\n",
        "\n",
        "plt.axhline(9.5, ls='--', c='orangered')\n",
        "plt.text(0.01, 8.8, r'$\\sigma_{ys, 2}$', fontsize=20, c='orangered')\n",
        "\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": "<Figure size 720x432 with 1 Axes>"
          },
          "metadata": {}
        }
      ],
      "execution_count": 287,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-23T11:25:19.409938Z",
          "start_time": "2021-03-23T11:25:19.213861Z"
        },
        "hide_input": true,
        "scrolled": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Consider that we take two perfect samples (single crystals, no defects) of these materials and introduce a single defect of size $c_0$. \n",
        "\n",
        "If we test these samples applying increasingly higher tensile stress, we see that: \n",
        "> 1. The failure stress of the **<span style=\"color:orangered\">Material 2 </span>** is higher than the one of **<span style=\"color:navy\">Material 1</span>**.\n",
        "> 1. If these materials have the yield strengths described by the horizontal dashed lines, then, **<span style=\"color:orangered\">Material 2 </span>** have displayed plastic deformation before failure, while **<span style=\"color:navy\">Material 1</span>** broke before showing any plasticity\n",
        "\n",
        "In other words, **<span style=\"color:navy\">Material 1</span>**  is an overall example of a *ceramic* while **<span style=\"color:orangered\">Material 2 </span>** is the example of a *metal* (both at room temperatures).\n",
        "\n",
        "Another insight that we can derive from this plot:\n",
        "> We can have a metal behaving as a ceramics without changing environmental conditions such as temperature. All is needed is that its defect is big enough to reduce the failure stress to levels below the yield strength! **The lack of understanding of this concept was responsible to multiple failures where people did not expect brittle fractures in metal structures.**\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Overall Behavior of Materials"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can see the overall behavior of the classes of materials regarding their strength, $\\sigma_f$, and their fracture toughness, $K_{IC}$:"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "<span id=\"call-ref_ashby\" class=\"img_container center\" style=\"display: inline_block; vertical-align: top; text-align: center;\" > <img alt=\"test\" src=\"https://upload.wikimedia.org/wikipedia/commons/a/a4/Fracture_toughness_vs._Strength.jpg\" style=\"display:block; margin-left: auto; margin-right: auto; text-align: left;\" title=\"caption\" align=\"center\" width=\"500\" height=\"600\" /> <div class=\"img_caption\" style=\"border-style: solid; border-width: 2px; border-radius: 5px; border-color:lightgrey; padding: 2px 5px; text-align: left; width=980px\"><b>Figure 3:</b> Ashby plot of the fracture toughness, $K_{IC}$, and the strength, $\\sigma_f$ <a href=\"#cit-ref_ashby\">[3]</a>.</div> </span>\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "This behavior can be explained by the relationship of these properties:"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\\begin{array}{l}\n",
        "\\sigma_f \\ \\ \\text{(Strength)} \\longrightarrow \\text { bond energy } +  \\text { defects } \\\\\n",
        "\\mathrm{K}_{\\mathrm{Ic}} \\ \\ \\text{(Fracture Toughness)} \\longrightarrow \\text { bond energy } + \\text{plastic deformation} \n",
        "\\end{array}\n"
      ],
      "metadata": {
        "hide_input": true
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "One should keep in mind that toughness and fracture toughness are fundamentally different properties!\n",
        "Consider the graph below, which represents the stress-strain curve for a general material that shows plastic deformation:"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "fig, ax = plt.subplots(figsize=(10, 5))\n",
        "def force(displacement):\n",
        "    E = 1\n",
        "    var = -2.5\n",
        "    force_vals_elastic = E *  displacement[displacement < 0.2] \n",
        "    force_vals_non_elastic = E *  displacement[(displacement >= 0.2)*(displacement < 0.5)] +\\\n",
        "                             E *  (displacement[(displacement >= 0.2)*(displacement < 0.5)]**2)[0] -\\\n",
        "                             E *  displacement[(displacement >= 0.2)*(displacement < 0.5)]**2\n",
        "    x = displacement[(displacement >= 0.5)]\n",
        "    force_vals_break = force_vals_non_elastic[-1] * np.exp(var*(x-1.25)) / (1 + np.exp(var*(x-1.25)))*x**-0.2\n",
        "    force_vals = np.concatenate([force_vals_elastic, force_vals_non_elastic, force_vals_break])\n",
        "    return force_vals\n",
        "plt.plot(x1, 200*force(x1), c='blue', lw=3)\n",
        "x2 = np.linspace(0.2, 0.5001, 1000)\n",
        "plt.plot(x2, 200*force(x2), c='coral', lw=3)\n",
        "x = np.linspace(0, 0.50, 1000)\n",
        "plt.fill_between(x, 200*force(x), color='lightskyblue', alpha=0.75)\n",
        "plt.scatter(0.5, 58, marker='x', s=75, c='k', zorder=4)\n",
        "\n",
        "plt.xlim(-0.1, 1)\n",
        "plt.ylim(-10, 75)\n",
        "plt.arrow(0, 0, 0, 70., fc='k', ec='k', lw = 1, \n",
        "             head_width=0.0125, head_length=4,\n",
        "             length_includes_head= True, clip_on = False)\n",
        "plt.text(-0.115, 67, r'$\\sigma [N/m²]$', c='k', fontsize=16)\n",
        "plt.arrow(0, 0, 0.75, 0., fc='k', ec='k', lw = 1, \n",
        "             head_width=2, head_length=0.025,\n",
        "             length_includes_head=True, clip_on=False)\n",
        "plt.text(0.665, -8, r'$\\epsilon [m/m]$', c='k', fontsize=16)\n",
        "r1 = Rectangle([0, -2], 0.2, -6, ec='k', lw=1, fc='blue')\n",
        "ax.add_patch(r1)\n",
        "r2 = Rectangle([0.2, -2], 0.3, -6, ec='k', lw=1, fc='coral')\n",
        "ax.add_patch(r2)\n",
        "plt.text(0.0075, -6, r'Elastic Deformation', c='w', fontsize=12)\n",
        "plt.text(0.225, -6, r'Non-Elastic Deformation', c='k', fontsize=12)\n",
        "plt.text(0.175, 25, r'Toughness, $U_T$ [J/m$^3$]', fontweight='bold', c='k', fontsize=14, bbox=dict(facecolor='w'))\n",
        "plt.axvline(0.2, ymax=0.85, c='k', ls='--', lw=1, zorder=3, alpha=0.5)\n",
        "plt.axvline(0.5, ymax=0.85, c='k', ls='--', lw=1, zorder=3, alpha=0.5)\n",
        "plt.axhline(58, c='k', ls='--', lw=1, zorder=3, xmin=0.09, xmax=0.54)\n",
        "plt.text(-0.19, 58, r'$\\sigma_f = \\frac{\\sigma_{th}}{K_t} = \\frac{K_{IC}}{\\sqrt{\\pi c}}$', c='k', fontsize=16)\n",
        "plt.annotate(r'Fracture Toughness [MPa m$^{\\frac{1}{2}}$]',\n",
        "             xy=(-0.01, 61),\n",
        "             xytext=(0.015, 65),\n",
        "             textcoords='data',\n",
        "             fontsize=14, \n",
        "             arrowprops=dict(arrowstyle= '<-',\n",
        "                             color='k',\n",
        "                             lw=1.5,\n",
        "                             ls='-')\n",
        "           )\n",
        "\n",
        "plt.annotate('Stress \\nConcentration \\nFactor [-]',\n",
        "             xy=(-0.1, 55),\n",
        "             xytext=(-0.1, 35),\n",
        "             textcoords='data',\n",
        "             fontsize=14, \n",
        "             horizontalalignment='center',\n",
        "             arrowprops=dict(arrowstyle= '<-',\n",
        "                             color='k',\n",
        "                             lw=1.5,\n",
        "                             ls='-'))\n",
        "plt.gca().axis('off')\n",
        "plt.show()"
      ],
      "outputs": [
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            "text/plain": "<Figure size 720x360 with 1 Axes>"
          },
          "metadata": {
            "needs_background": "light"
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        }
      ],
      "execution_count": 164,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-25T11:14:33.598241Z",
          "start_time": "2021-03-25T11:14:33.431599Z"
        },
        "hide_input": true
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "> **Do not get confused!**\n",
        ">\n",
        "> *Strength*, *Toughness*, *Stress Concentration Factor* and *Fracture Toughness* are all different quantities and even though are closely related, they have distinct units and physical meaning:\n",
        "> - The strength, $\\sigma_f$, of a specific material is the stress at failure of a sample under a specific test. It is not intrinsic to the material as it depends on the presence and geometrical features of the defects;\n",
        "> - $\\sigma_f$ is related to the stress concentration factor, $K_t$, by the fact that the presence of defects in the sample increases the stress felt at the crack tip. When we reach the failure stress, the value \"felt\" at the crack tip is the theoretical stress, $\\sigma_{th}$;\n",
        "> - The susceptibility of a material to this stress concentration effect for a given defect of size $c$ is intrinsic to the material and it is known as the Fracture Toughness (also known as Critical Stress Intensity Factor), $K_{IC}$. This quantity represents the resistance to the start of crack propagation;\n",
        "> - Finally, the Toughness, $U_T$, is the ability of a material to absorb energy and plastically deform without fracturing, it has units of Joules by cubic meter."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Application of the Concepts"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's now apply this new set of tools to different scenarios and understand multiple situations that we encounter in our day-today lives!"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Crack Deflection"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's consider two different ordinary materials, the mortar and concrete. One may even wrongly consider them the same material, but they have very distinct characteristics and even applications!\n",
        "\n",
        "Consider first the microstructure of them:\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "<span id=\"call-ref_micro\" class=\"img_container center\" style=\"display: inline_block; vertical-align: top; text-align: center;\" > <img alt=\"test\" src=\"./Mortar_and_concrete.png\" style=\"display:block; margin-left: auto; margin-right: auto; text-align: left;\" title=\"caption\" align=\"center\" width=\"300\" /> <div class=\"img_caption\" style=\"border-style: solid; border-width: 2px; border-radius: 5px; border-color:lightgrey; padding: 2px 5px; text-align: left; width=980px\"><b>Figure 4:</b> Examples of Concrete and Mortar. Adapted from <a href=\"#cit-ref_micro\">[4]</a>.</div> </span>\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "It is clear that the concrete has a distinct phase, the aggregates. Otherwise, the composition of mortar and concretes are equal. They have very important contributions to the properties of such materials. Let's check the applications of these materials and see if we have any clue!\n",
        "\n",
        ">**Mortar**:\n",
        ">\n",
        "> Used as a binding agent between other construction materials\n",
        "\n",
        ">**Concrete**:\n",
        ">\n",
        "> Used as a construction material\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Some questions that you might have right now:\n",
        "\n",
        "- Why do people don't make structures of mortar alone?\n",
        "- Why do they need to add aggregates if they are bigger potential defects?\n",
        "- Wouldn't the aggregates decrease their strength?\n",
        "\n",
        "Let's check the experimental results:"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "<span id=\"call-ref_cs\" class=\"img_container center\" style=\"display: inline_block; vertical-align: top; text-align: center;\" > <img alt=\"test\" src=\"https://www.researchgate.net/profile/Hakim-Abdelgader-2/publication/272564768/figure/tbl1/AS:614271020961807@1523465032906/Cylinder-compressive-strength-of-concrete-and-mortar-at-28-days_W640.jpg\" style=\"display:block; margin-left: auto; margin-right: auto; text-align: left;\" title=\"caption\" align=\"center\" width=\"300\" /> <div class=\"img_caption\" style=\"border-style: solid; border-width: 2px; border-radius: 5px; border-color:lightgrey; padding: 2px 5px; text-align: left; width=980px\"><b>Figure 5:</b> Compressive strength of Concrete and Mortar. From <a href=\"#cit-ref_cs\">[5]</a>.</div> </span>\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Indeed the compressive strength of the mortar is roughly the double of the one of the concrete. Let's try to use the concepts that we learned to understand why no one uses mortar as a building material even though it has a higher strength!"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "We know that the stress at the tip of the defect is increased due to the concentration of the force lines. \n",
        "\n",
        "However, when we consider a direction that is not perpendicular to the application of the forces we can intuitively expect that the stress \"felt\" at that direction is lower. \n",
        "\n",
        "This is exactly what happens:"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "\n",
        "r = np.linspace(1e-3, 1, 1000)\n",
        "c = 1\n",
        "sigma_app = 10\n",
        "fig = plt.figure()\n",
        "plt.plot(r, sigma_app * (np.pi * c)**0.5 / (2*np.pi*r)**0.5, lw=2, c='Navy')\n",
        "plt.ylim(-50, 250)\n",
        "plt.xlim(-0.3, 0.8)\n",
        "\n",
        "e = Ellipse([-0.3, 0], 0.6, 40,  facecolor='w', edgecolor='k', zorder=10)\n",
        "plt.gca().add_patch(e)\n",
        "arrowed_spines(fig, plt.gca(), ylim=[-8, 250])\n",
        "add_interval(plt.gca(), [-0.3, -0.0001], [-35, -35], \"II\")\n",
        "plt.text(-0.15, -50, 'c', c='k', fontsize=20)\n",
        "plt.text(-0.08, 240, '$\\sigma_y$', c='k', fontsize=20)\n",
        "plt.text(0.775, -25, '$r$', c='k', fontsize=20)\n",
        "plt.arrow(0.45, -50, 0, -30., fc='k', ec='k', lw = 1, \n",
        "             head_width=0.01, head_length=5,\n",
        "             length_includes_head= True, clip_on = False)\n",
        "plt.text(0.46, -75, '$\\sigma_{ap}$', c='k', fontsize=20)\n",
        "\n",
        "plt.arrow(0.45, 250, 0, 30., fc='k', ec='k', lw = 1, \n",
        "             head_width=0.01, head_length=5,\n",
        "             length_includes_head= True, clip_on = False)\n",
        "plt.text(0.46, 265, '$\\sigma_{ap}$', c='k', fontsize=20)\n",
        "plt.text(0.225, 140, r'$\\sigma_y = \\displaystyle \\frac{K_{\\textrm I}}{\\sqrt{2 \\pi r}} = \\frac{\\sigma_{ap}\\sqrt{\\pi c}}{\\sqrt{2 \\pi r}}$', c='k', fontsize=16)\n",
        "plt.text(0.225, 70, r'$\\sigma_y = \\displaystyle \\frac{K_{\\textrm I}}{\\sqrt{2 \\pi r}} \\ f(\\cos{(\\theta))}$', c='k', fontsize=16)\n",
        "ax2 = plt.gca().twinx()\n",
        "y_0 = 0.17\n",
        "x_1 = 0.1\n",
        "y_1 = 0.2\n",
        "ax2.arrow(0.0, y_0, x_1, y_1, fc='k', ec='k', lw = 1, \n",
        "          head_width=0.02, head_length=0.02)\n",
        "arc = ax2.add_patch(Arc([0, y_0], x_1, y_1, theta1=0, theta2=np.degrees(np.arctan(y_1/x_1)), color='k'))\n",
        "plt.text(0.0525, 0.18, r'$\\theta$', c='k', fontsize=20)\n",
        "\n",
        "ax2.set_ylim(0, 1)\n",
        "ax2.axis('off')\n",
        "plt.show()"
      ],
      "outputs": [
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            "text/plain": "<Figure size 432x288 with 2 Axes>"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "execution_count": 138,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-19T19:41:38.854704Z",
          "start_time": "2021-03-19T19:41:37.323051Z"
        },
        "hide_input": true
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<div id=\"call-ref_book\"</div>\n",
        "The closed form of f is more complex as it is derived from a polar coordinates analysis of the problem. For more information check the work of Professor Brian Lawn <a href=\"#cit-ref_book\">[6]</a>. \n",
        "\n",
        "What we need to understand is that if by some reason the crack needs to deviate from its original path, there is a decrease on the stress at the tip of the crack, which is proportional to the cosine of the angle of this deviation with respect to the original direction.\n",
        "\n",
        "The next graph presents this decrease:\n",
        "\n",
        " "
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# HIDDEN\n",
        "%config InlineBackend.figure_formats = ['png']\n",
        "def f_theta(theta):\n",
        "    return np.cos(theta / 2)**3\n",
        "\n",
        "# fig, axs = plt.subplots(1, 2, subplot_kw=dict(polar=True))\n",
        "fig = plt.figure(figsize=(8, 3), dpi=300)\n",
        "ax1 = plt.subplot(121)\n",
        "ax2 = plt.subplot(122, projection='polar')\n",
        "\n",
        "thetas = np.linspace(-(np.pi/2), (np.pi/2), 100)\n",
        "ax1.plot(np.rad2deg(thetas), f_theta(thetas), '-o', markevery=7, c='navy', lw=2)\n",
        "ax1.set_ylim(0, 1.2)\n",
        "ax1.set_xlabel(r'$\\theta$')\n",
        "ax1.set_ylabel(r'$f(\\theta)$')\n",
        "ax1.set_xticks(np.linspace(-90, 90, 7))\n",
        "ax1.grid()\n",
        "\n",
        "ax2.plot(thetas, f_theta(thetas), '-o', markevery=7, c='navy', lw=2)\n",
        "ax2.set_ylim(0, 1.2)\n",
        "# plt.ylim(-np.pi/2, np.pi/2)\n",
        "ax2.set_xlim(-np.pi/2, np.pi/2)\n",
        "ax2.set_xticks(np.linspace(-np.pi/2, np.pi/2, 7))\n",
        "ax2.text(-np.pi/1.35, 1., r'$f(\\theta)$')\n",
        "# axs[1].projection('polar')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
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            "text/plain": "<Figure size 2400x900 with 2 Axes>"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "execution_count": 167,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-26T13:37:31.389828Z",
          "start_time": "2021-03-26T13:37:30.633884Z"
        },
        "hide_input": true,
        "scrolled": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "You can visualize the effect of the crack deflection on the example below. Change the values of the angle theta below and see how the stress at the tip of the defect changes:"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "def see_theta(theta_deg):\n",
        "    %config InlineBackend.figure_formats = ['png']\n",
        "\n",
        "    theta = np.deg2rad(theta_deg)\n",
        "    c = 1\n",
        "    sigma_app = 30\n",
        "    fig = plt.figure(figsize=(8, 3), dpi=300)\n",
        "    ax1 = plt.subplot(121)\n",
        "    ax2 = plt.subplot(122, projection='polar')\n",
        "    r = np.linspace(1e-3, 1, 1000)\n",
        "    ax1.plot(r, sigma_app * (np.pi * c)**0.5 / (2*np.pi*r)**0.5 * f_theta(theta), lw=2, c='Navy')\n",
        "    ax1.plot(r, sigma_app * (np.pi * c)**0.5 / (2*np.pi*r)**0.5 * f_theta(0), lw=1, ls='--', c='Navy', label=r'$\\sigma_y$ with $\\theta=0$')\n",
        "    ax1.scatter(-10, -10, c='grey',marker=r'$\\rightarrow$',s=120, label='Direction of Fracture' )\n",
        "    ax1.set_ylim(-150, 150)\n",
        "    e = Ellipse([-0.45, 0], 0.9, 40,  facecolor='w', edgecolor='k', zorder=10)\n",
        "    ax1.add_patch(e)\n",
        "    r = Rectangle([-0.9, -25], 0.45, 45,  facecolor='w', edgecolor='w', zorder=11)\n",
        "    ax1.add_patch(r)\n",
        "    arrowed_spines(fig, ax1, ylim=[-8, 250], xlim=[-0.2, 1])\n",
        "    ax1.annotate(s='', xy=(-0.3, -35), xytext=(-0.0001,-35),\n",
        "             arrowprops=dict(arrowstyle='|-|, widthA=0.4,widthB=0.4', linewidth=1))\n",
        "    \n",
        "    ax1.text(-0.175, -55, 'c', c='k', fontsize=14)\n",
        "    ax1.text(-0.175, 240, '$\\sigma_y$', c='k', fontsize=14)\n",
        "    ax1.text(0.975, -25, '$r$', c='k', fontsize=14)\n",
        "    ax1.set_xlim(-0.3, 0.8)\n",
        "    ax1.axis('off')\n",
        "    ax1.legend(fontsize=8)\n",
        "    ax3 = ax1.twinx()\n",
        "    ax3.axis('off')\n",
        "    plot_arrow(ax3, theta)\n",
        "    ax1.arrow(0.45, -50, 0, -30., fc='k', ec='k', lw = 1, \n",
        "          head_width=0.05, head_length=5,\n",
        "          length_includes_head= True, clip_on = False)\n",
        "    ax1.text(0.485, -75, '$\\sigma_{ap}$', c='k', fontsize=12)\n",
        "\n",
        "    ax1.arrow(0.45, 220, 0, 30., fc='k', ec='k', lw = 1, \n",
        "              head_width=0.05, head_length=5,\n",
        "              length_includes_head= True, clip_on = False)\n",
        "    ax1.text(0.485, 230, '$\\sigma_{ap}$', c='k', fontsize=12)\n",
        "    \n",
        "    ax2.plot([theta, theta], [0, 1.2])\n",
        "    ax2.plot(thetas, f_theta(thetas), '-', markevery=7, c='navy', lw=2)\n",
        "    ax2.plot(theta, f_theta(theta),'-o', c='orangered', zorder=3)\n",
        "    ax2.plot([theta]*5, [0, 0.2, 0.4, 0.8, 1.2], '-', c='k')\n",
        "    ax2.set_ylim(0.2, 1.2)\n",
        "    ax2.set_xlim(-np.pi/2, np.pi/2)\n",
        "    ax2.set_xticks(np.linspace(-np.pi/2, np.pi/2, 7))\n",
        "    ax2.text(-np.pi/1.35, 1., r'$f(\\theta)$')\n",
        "interactive_plot = interactive(see_theta, theta_deg=widgets.FloatSlider(value=0,\n",
        "                                                       min=-90,\n",
        "                                                       max=90,\n",
        "                                                       step=5,\n",
        "                                                       description=r'$\\theta \\ [°]$',\n",
        "                                                       readout_format='.2f'))\n",
        "output = interactive_plot.children[-1]\n",
        "output.layout.height = '550px'\n",
        "interactive_plot.layout = widgets.Layout(display='flex',\n",
        "                               flex_flow='column',\n",
        "                               align_items='center',\n",
        "                               align_content='center',\n",
        "                               justify_content='center',\n",
        "                               width='100%')\n",
        "interactive_plot"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "44b8b06de04c48c691b0b6949e4eeafd",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": "interactive(children=(FloatSlider(value=0.0, description='$\\\\theta \\\\ [°]$', max=90.0, min=-90.0, step=5.0), O…"
          },
          "metadata": {}
        }
      ],
      "execution_count": 206,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-26T15:10:01.422923Z",
          "start_time": "2021-03-26T15:10:00.873849Z"
        },
        "hide_input": true
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "This have plenty of effects and explains one of the most common toughening mechanism, the *crack deflection*."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "One can easily understand its effectiveness when comparing the resulting fracture surface (represented as a line below):"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "\n",
        "n = 30\n",
        "x_1 = np.linspace(0.1, 0.5, n)\n",
        "x_2 = np.linspace(1.5, 1.9, n)\n",
        "y = np.ones(n) * 0.9 \n",
        "np.random.seed(23)\n",
        "noise = np.random.normal(0, 1, n)\n",
        "noise[:3] = 0\n",
        "noise[-3:] = 0\n",
        "plt.plot(x_1, y+noise*0.0025, c='orangered')\n",
        "plt.plot(x_2, y+noise*0.025, c='orangered')\n",
        "\n",
        "r1 = Rectangle([0.1, 0.65], 0.4, 0.5, ec='k', lw=1.5, fc='skyblue')\n",
        "plt.gca().add_patch(r1)\n",
        "r2 = Rectangle([1.5, 0.65], 0.4, 0.5, ec='k', lw=1.5, fc='skyblue')\n",
        "plt.gca().add_patch(r2)\n",
        "\n",
        "plt.ylim(0.5, 1.35)\n",
        "plt.xlim(0, 2)\n",
        "\n",
        "plt.arrow(0.3, 1.15, 0, 0.04, head_width=0.025, head_length=0.02,\n",
        "      ec='k', lw=1.5, fc='k', zorder=9)\n",
        "plt.arrow(1.7, 1.15, 0, 0.04, head_width=0.025, head_length=0.02,\n",
        "      ec='k', lw=1.5, fc='k', zorder=9)\n",
        "plt.arrow(0.3, 0.65, 0, -0.04, head_width=0.025, head_length=0.02,\n",
        "      ec='k', lw=1.5, fc='k', zorder=9)\n",
        "plt.arrow(1.7, 0.65, 0, -0.04, head_width=0.025, head_length=0.02,\n",
        "      ec='k', lw=1.5, fc='k', zorder=9)\n",
        "\n",
        "plt.text(0.15, 1.3, r'Case 1:', fontsize=18)\n",
        "plt.text(1.55, 1.3, r'Case 2:', fontsize=18)\n",
        "plt.text(0.3, 0.55, r'$\\sigma_{ap}$', fontsize=18)\n",
        "plt.text(0.3, 1.225, r'$\\sigma_{ap}$', fontsize=18)\n",
        "plt.text(1.7, 0.55, r'$\\sigma_{ap}$', fontsize=18)\n",
        "plt.text(1.7, 1.225, r'$\\sigma_{ap}$', fontsize=18)\n",
        "\n",
        "\n",
        "plt.gca().axis('off')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": "<Figure size 432x288 with 1 Axes>"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "execution_count": 337,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-26T17:52:54.851748Z",
          "start_time": "2021-03-26T17:52:54.740114Z"
        },
        "hide_input": true
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The resulted surface area of Case 1 is clear smaller than the one created in Case 2. This suggests that the energy necessary to create such surfaces is indeed higher."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Thus, we can understand that the crack deflection done by the aggregates will increase the resulting work of fracture, $\\gamma_{wof}$, and this explains why we need to add aggregates to the mortar in order to construct structural elements that should prevent by all means catastrophic failure!"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Comparison of Surface and Bulk Defects"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now consider the definition of the fracture toughness, Equation \\ref{eq:kic} and solve for $\\sigma_f$:\n",
        "\n",
        "\\begin{equation}\\label{eq:sig_f}\n",
        "\\sigma_f = \\dfrac{K_{IC}}{\\sqrt{\\pi c}}\n",
        "\\end{equation}\n",
        "\n",
        "We see that the greater the size of the defect, the lower the failure stress. Conversely, when we increase the fracture toughness, the material is less susceptible to the defect size."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now one question that may arise is if there is any difference if the defect is on the surface or on the bulk of the material. Consider these two cases below:"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "%config InlineBackend.figure_formats = ['svg']\n",
        "\n",
        "fig, axs = plt.subplots(1, 2, figsize=(10, 4))\n",
        "\n",
        "\n",
        "r2 = Rectangle([0.3, 0], 0.3, 1, ec='k', lw=2.5, fc='skyblue')\n",
        "axs[0].add_patch(r2)\n",
        "e1 = Ellipse([0.45, 0.5], 0.1, 0.05, zorder=9, fc='w', ec='k')\n",
        "axs[0].add_patch(e1)\n",
        "\n",
        "axs[0].arrow(0.1+0.3+0.05, 1, 0, 0.14, head_width=0.025, head_length=0.04,\n",
        "          lw=2.5, fc='k')\n",
        "axs[0].text(0.125+0.3+0.05, 1.15, '$\\sigma_{ap}$', fontsize=18)\n",
        "axs[0].arrow(0.1+0.3+0.05, 0, 0, -0.14, head_width=0.025, head_length=0.04,\n",
        "          lw=2.5, fc='k')\n",
        "axs[0].text(0.125+0.3+0.05, -0.25, '$\\sigma_{ap}$', fontsize=18)\n",
        "\n",
        "r2 = Rectangle([0.3, 0], 0.3, 1, ec='k', lw=2.5, fc='skyblue')\n",
        "axs[1].add_patch(r2)\n",
        "e1 = Ellipse([0.3, 0.5], 0.2, 0.05, zorder=9, fc='w', ec='k', lw=2.5)\n",
        "axs[1].add_patch(e1)\n",
        "r3 = Rectangle([0.19, 0], 0.1, 1, ec='w', lw=2.5, fc='w', zorder=10)\n",
        "axs[1].add_patch(r3)\n",
        "\n",
        "\n",
        "axs[1].arrow(0.1+0.3+0.05, 1, 0, 0.14, head_width=0.025, head_length=0.04,\n",
        "          lw=2.5, fc='k')\n",
        "axs[1].text(0.125+0.3+0.05, 1.15, '$\\sigma_{ap}$', fontsize=18)\n",
        "axs[1].arrow(0.1+0.3+0.05, 0, 0, -0.14, head_width=0.025, head_length=0.04,\n",
        "          lw=2.5, fc='k')\n",
        "axs[1].text(0.125+0.3+0.05, -0.25, '$\\sigma_{ap}$', fontsize=18)\n",
        "\n",
        "axs[0].annotate(s='', xy=(0.39,0.45), xytext=(0.51,0.45),\n",
        "             arrowprops=dict(arrowstyle='|-|, widthA=0.4,widthB=0.4', linewidth=2))\n",
        "axs[0].text(0.425, 0.35, r'$\\ell$', fontsize=18, zorder=10)\n",
        "\n",
        "axs[1].annotate(s='', xy=(0.29,0.45), xytext=(0.41,0.45),\n",
        "             arrowprops=dict(arrowstyle='|-|, widthA=0.4,widthB=0.4', linewidth=2))\n",
        "axs[1].text(0.325, 0.35, r'$\\ell$', fontsize=18, zorder=10)\n",
        "\n",
        "axs[0].text(0.325, 0.9, 'b', fontsize=18, zorder=10)\n",
        "axs[1].text(0.325, 0.9, 's', fontsize=18, zorder=10)\n",
        "\n",
        "\n",
        "\n",
        "for ax in axs:\n",
        "    ax.axis('off')\n",
        "    ax.set_xlim(-0.1, 1)\n",
        "    ax.set_ylim(-0.2, 1.2)\n",
        "\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
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            "text/plain": "<Figure size 720x288 with 2 Axes>"
          },
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        }
      ],
      "execution_count": 10,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-04-03T01:42:32.963304Z",
          "start_time": "2021-04-03T01:42:32.743958Z"
        },
        "hide_input": true,
        "scrolled": true
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    {
      "cell_type": "markdown",
      "source": [
        "Both samples are made of the same material, thus $K_{IC}$ is the same.\n",
        "\n",
        "\\begin{equation*}\n",
        "\\sigma_f = \\dfrac{K_{IC}}{\\sqrt{\\pi c}}\n",
        "\\end{equation*}\n",
        "\n",
        "\\begin{equation*}\n",
        "\\sigma_{f, b} \\ \\sqrt{\\pi \\dfrac{\\ell}{2}} = \\sigma_{f, s} \\ \\sqrt{\\pi \\ell}\n",
        "\\end{equation*}\n",
        "\n",
        "\\begin{equation*}\n",
        "\\sigma_{f, b}^2 \\ \\pi \\dfrac{\\ell}{2} = \\sigma_{f, s}^2 \\ \\pi \\ell\n",
        "\\end{equation*}\n",
        "\n",
        "\\begin{equation*}\n",
        "\\dfrac{\\sigma_{f, b}^2}{\\sigma_{f, s}^2} = 2\n",
        "\\end{equation*}\n",
        "\n",
        "\\begin{equation*}\n",
        "\\dfrac{\\sigma_{f, b}}{\\sigma_{f, s}} = \\sqrt{2}\n",
        "\\end{equation*}\n",
        "\n",
        "\\begin{equation*}\n",
        "\\sigma_{f, s} = 0.7 \\sigma_{f, b}\n",
        "\\end{equation*}"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "This result is of fundamental importance as it shows that for defects of same sizes, the defects on the surface are more critical as the mechanical strength of the sample with the defect on the surface is lower than the one with the defect in the bulk."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "> This justifies a lot of situations, for example:\n",
        "> - The use of surface treatments to increase the strength of glass components (such as using \n",
        "hydrofluoric acid to dissolve imperfections on the surface of soda lime glasses, or using chemical substitution of cations to create compressive strength on the surface of the glass, such as the Gorilla Glass family)\n",
        "> - Using machining to remove defects on the surface of advanced ceramics (for example \n",
        "prosthesis, where machining is used both for defining precisely the dimensions and to reduce the surface defects )"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Ball Milling"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Another example where we can see the usefulness of the concepts learned in this lesson is the mechanisms behind ball milling!\n",
        "\n",
        "The particles are broken by the impact between the balls and the material that is being milled. In simplified terms:\n",
        "\n",
        "1. The rotation carries the balls up high and provides them with gravitational potential energy;\n",
        "2. When the centrifugal acceleration equals the gravity one, the ball starts to fall, transforming the potential energy in kinetic energy;\n",
        "3. During the impact of the balls with the material that is being milled, the kinetic energy is converted once again into stored elastic energy, deforming the material and stressing it until it fails;\n",
        "4. In parallel, the relative movement of the balls provide milling through friction."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "\n",
        "\n",
        "<span id=\"call-ref_bml\" class=\"img_container center\" style=\"display: inline_block; vertical-align: top; text-align: center;\" > <img alt=\"test\" src=\"https://www.911metallurgist.com/blog/wp-content/uploads/2016/02/ball-mill-animation.gif\" style=\"display:block; margin-left: auto; margin-right: auto; text-align: left;\" title=\"caption\" align=\"center\" width=\"350\" /> <div class=\"img_caption\" style=\"border-style: solid; border-width: 2px; border-radius: 5px; border-color:lightgrey; padding: 2px 5px; text-align: left; width=980px\"><b>Figure 6:</b> Animation of ball milling. <a href=\"#cit-ref_bml\">[7]</a>.</div> </span>\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "One good question is:\n",
        "\n",
        "> **If we let the ball milling running for hours, or even days, will the size of the particulates decrease indefinitely?**\n",
        "\n",
        "Obviously, this is not the case!\n",
        "\n",
        "> What truly happens is:\n",
        "> The balls will provide a constant compressive stress to the particulates, $\\sigma_{impact}$, which will be able to break the particulates that have a critical defect, $c$,such that:\n",
        ">\\begin{equation*}\n",
        " \\sigma_{impact} \\ge \\sigma_f(c) = \\dfrac{K_{IC}}{\\sqrt{\\pi c}}\n",
        " \\end{equation*}\n",
        ">\n",
        "> Once the particulates diameter $D$ becomes smaller than $c$, for sure the new critical defect, $c'$, will be smaller than it originally was ($c'<c$) and the \"impact\" griding mechanism is halted. Onwards the only process that continues is the milling due to the friction, since the provided stress is smaller than the fracture stress for this new defect, $\\sigma_f(c')$, that is:\n",
        ">\\begin{equation*}\n",
        " \\sigma_{impact} < \\sigma_f(c') = \\dfrac{K_{IC}}{\\sqrt{\\pi c'}}\n",
        " \\end{equation*}\n",
        ">\n"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Designing Philosophy"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Throughout the examples of this last section, what should become clear is that we constantly made use of the fracture toughness to understand real world scenarios. \n",
        "\n",
        "However, this powerful tool also allows us to project innovations using what we call as the Design Philosophy:"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "fig, axs = plt.subplots()\n",
        "plt.text(0.1, 0.9, 'Design Philosophy:', fontsize=20)\n",
        "\n",
        "plt.text(0.3, 0.5, '$K_{IC} = Y \\ \\sigma \\ \\sqrt{\\pi c}$', fontsize=20)\n",
        "plt.annotate('Materials Selection', xy=(0.35, 0.485), xytext=(0., 0.15),\n",
        "             arrowprops=dict(arrowstyle='<-', linewidth=1), fontsize=18)\n",
        "\n",
        "plt.annotate('Crack\\'s Geometrical Factor', xy=(0.525, 0.6), xytext=(0.5, 0.715),\n",
        "             arrowprops=dict(arrowstyle='->', linewidth=1), fontsize=18)\n",
        "\n",
        "plt.annotate('Project\\'s Stress', xy=(0.565, 0.5), xytext=(0.5, 0.15),\n",
        "             arrowprops=dict(arrowstyle='<-', linewidth=1), fontsize=18)\n",
        "\n",
        "plt.annotate('Material and Process', xy=(0.7, 0.5), xytext=(0.85, 0.25),\n",
        "             arrowprops=dict(arrowstyle='<-', linewidth=1), fontsize=18)\n",
        "\n",
        "\n",
        "plt.gca().axis('off')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
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            "text/plain": "<Figure size 432x288 with 1 Axes>"
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        }
      ],
      "execution_count": 264,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-04-05T12:47:58.254731Z",
          "start_time": "2021-04-05T12:47:55.384478Z"
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    {
      "cell_type": "markdown",
      "source": [
        "As previously noted the fracture toughness, $K_{IC}$, is an intrinsic property of the material, thus it is directly correlated to the material selection. This might be limited by costs, availability and other additional necessary properties, such as low density (i.e. for transport), high operation temperature, or chemical attack resistance. The factor $Y$ comprises the geometrical factor of the crack, which will be related to the stress state, and the features of the crack. The stress, $\\sigma$, is often fixed by the project and will be a constraint that must be followed. Safety factors are imposed here to guarantee that the design is safe. Finally, the critical size of the defect, $c$, is a direct consequence of the process needed to produce the material and its decrease is often limited by feasibility, cost and duration of advanced process."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "As an example of applying this design philosophy, we will consider the leak before burst systems for pressurized pipes."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Example: Leak Before Burst Systems"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "In a pressurized pipe the internal pressure ($P$) will yield a tensile stress, $\\sigma$, as can be seen in the figure below:"
      ],
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-28T18:10:18.367383Z",
          "start_time": "2021-03-28T18:10:18.361431Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "from matplotlib.patches import ConnectionPatch\n",
        "\n",
        "D_ext = 0.5 # External Diameter\n",
        "w_t = 0.5/8 # Wall thickness\n",
        "\n",
        "fig, axs = plt.subplots(1, 2, figsize=(12, 6.85))\n",
        "\n",
        "e1 = Ellipse([0.5, 0.5], D_ext, D_ext, zorder=9, fc='lightskyblue', ec='k')\n",
        "axs[0].add_patch(e1)\n",
        "e2 = Ellipse([0.5, 0.5], D_ext-w_t, D_ext-w_t, zorder=9, fc='w', ec='k')\n",
        "axs[0].add_patch(e2)\n",
        "axs[0].axis('equal')\n",
        "\n",
        "angles = np.linspace(0, 2*np.pi, 10)\n",
        "for ang in angles:\n",
        "    axs[0].arrow(0.5 + D_ext/3.2*np.sin(ang), 0.5 + D_ext/3.2*np.cos(ang),\n",
        "              0.05*np.sin(ang), 0.05*np.cos(ang), fc='k',\n",
        "              head_width=0.0125, head_length=0.0125, zorder=10)\n",
        "    axs[0].text(0.5 + D_ext/3.75*np.sin(ang), 0.4925 + D_ext/3.75*np.cos(ang),\n",
        "                'P', horizontalalignment='center', zorder=11, fontsize=16)\n",
        "r1 = Rectangle([0.50025, 0.245], 0.09975, 0.0625, zorder=12,\n",
        "               fc=\"None\", ls='--', ec='k', lw=2)\n",
        "axs[0].add_patch(r1)\n",
        "axs[0].text(0.275, 0.275, 'Pipe', c='k', zorder=11, fontsize=16)\n",
        "axs[0].set_xlim(0.15, 0.85)\n",
        "axs[0].set_ylim(0.15, 0.85)\n",
        "\n",
        "\n",
        "r1 = Rectangle([0.50025, 0.245], 0.09975, 0.0625, zorder=12,\n",
        "               fc=\"None\", ls='--', ec='k', lw=2)\n",
        "axs[1].add_patch(r1)\n",
        "e1 = Ellipse([0.5, 0.5], D_ext, D_ext, zorder=9, fc='lightskyblue', ec='k')\n",
        "axs[1].add_patch(e1)\n",
        "e2 = Ellipse([0.5, 0.5], D_ext-w_t, D_ext-w_t, zorder=9, fc='w', ec='k')\n",
        "axs[1].add_patch(e2)\n",
        "style = \"Simple, tail_width=0.5, head_width=4, head_length=8\"\n",
        "kw = dict(arrowstyle='<->, head_width=4, head_length=8', color=\"k\", lw=2)\n",
        "a3 = patches.FancyArrowPatch((0.5, 0.265), (0.6, 0.29),\n",
        "                             connectionstyle=\"arc3,rad=0.125\", zorder=10, **kw)\n",
        "axs[1].add_patch(a3)\n",
        "axs[1].set_xlim(0.5, 0.6)\n",
        "axs[1].set_ylim(0.225, 0.325)\n",
        "axs[1].text(0.5035, 0.2675, r'$\\sigma$', c='k', zorder=11, fontsize=20)\n",
        "axs[1].text(0.5925, 0.29, r'$\\sigma$', c='k', zorder=11, fontsize=20)\n",
        "\n",
        "kw = dict(linestyle=\"--\", color=\"k\", lw=2)\n",
        "cp1 = ConnectionPatch((0.68, 0.23), (0, 0.825), \"axes fraction\", \"axes fraction\",\n",
        "                      axesA=axs[0], axesB=axs[1], **kw)\n",
        "cp2 = ConnectionPatch((0.68, 0.135), (0, 0.2), \"axes fraction\", \"axes fraction\",\n",
        "                      axesA=axs[0], axesB=axs[1], **kw)\n",
        "cps = [cp1, cp2]\n",
        "for cp in cps:\n",
        "    axs[1].add_artist(cp)\n",
        "\n",
        "\n",
        "plt.axis('off')\n",
        "for ax in axs.flatten():\n",
        "     ax.axis('off')\n",
        "#     ax.set_xticks([], [])\n",
        "#     ax.set_yticks([], [])\n",
        "\n",
        "plt.show()"
      ],
      "outputs": [
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            "text/plain": "<Figure size 864x493.2 with 2 Axes>"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "execution_count": 263,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-04-05T12:47:38.230742Z",
          "start_time": "2021-04-05T12:47:37.997907Z"
        },
        "hide_input": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For a specific case where the radius of the pipe (r) is considerably greater than the its thickness ($t$), this is stress, $\\sigma$, can be found as:\n",
        "\n",
        "\\begin{equation}\n",
        "\\sigma = \\frac{P \\ r}{t}\n",
        "\\end{equation}"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "In a pipe, we could have a defect inside the wall or on its surface. As we saw earlier, surface defects are more critical than defects in the bulk of the material and consequently, as a safety measure, we will focus on a possible surface defect as shown below:"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "from matplotlib.patches import Polygon\n",
        "fig, axs = plt.subplots(1, 1, figsize=(8, 8*0.6))\n",
        "\n",
        "e1 = Ellipse([0.5, 0.5], D_ext, D_ext, zorder=10, fc='lightskyblue', ec='k')\n",
        "axs.add_patch(e1)\n",
        "e2 = Ellipse([0.5, 0.5], D_ext-w_t, D_ext-w_t, zorder=12, fc='w', ec='k')\n",
        "axs.add_patch(e2)\n",
        "e3 = Ellipse([0.5, 0.5], (D_ext-w_t)*0.999, (D_ext-w_t)*0.999, zorder=14, fc='w', ec='w')\n",
        "axs.add_patch(e3)\n",
        "style = \"Simple, tail_width=0.5, head_width=4, head_length=8\"\n",
        "kw = dict(arrowstyle='<->, head_width=4, head_length=8', color=\"k\", lw=2)\n",
        "a3 = patches.FancyArrowPatch((0.5, 0.265), (0.6, 0.29),\n",
        "                             connectionstyle=\"arc3,rad=0.125\", zorder=11, **kw)\n",
        "axs.add_patch(a3)\n",
        "axs.add_patch(Polygon([[0.55,0.2825],[0.545,0.29],[0.5525,0.29]],\n",
        "                     closed=True,fill=True, fc='w', ec='k', zorder=12)) \n",
        "e4 = Ellipse([0.55, 0.285], 0.01, 0.01, zorder=14, fc='None', ec='k', ls='--')\n",
        "axs.add_patch(e4)\n",
        "plt.text(0.55, 0.2915, r'Defect', c='k', zorder=15, fontsize=20)\n",
        "plt.text(0.5515, 0.2835, r'c', c='k', zorder=15, fontsize=20)\n",
        "\n",
        "\n",
        "plt.arrow(0.55-2*0.0005, 0.2825+2*0.004,\n",
        "              +0.00045, -0.0035, fc='k', width=0.00025,\n",
        "              head_width=0.00225, head_length=0.001, zorder=16)\n",
        "plt.arrow(0.55+0.00055, 0.2825-0.0045,\n",
        "              -0.00045, +0.0035, fc='k', width=0.00025,\n",
        "              head_width=0.00225, head_length=0.001, zorder=16)\n",
        "plt.xlim(0.5, 0.6)\n",
        "plt.ylim(0.245, 0.305)\n",
        "plt.text(0.5035, 0.2675, r'$\\sigma$', c='k', zorder=11, fontsize=20)\n",
        "plt.text(0.5925, 0.29, r'$\\sigma$', c='k', zorder=11, fontsize=20)\n",
        "\n",
        "plt.axis('off')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
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            "text/plain": "<Figure size 576x345.6 with 1 Axes>"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "execution_count": 267,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-04-06T11:25:24.766831Z",
          "start_time": "2021-04-06T11:25:24.670361Z"
        },
        "hide_input": false
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    },
    {
      "cell_type": "markdown",
      "source": [
        "This small crack can be originated during the processing of the pipe, during its installation, or be the result of a slow crack propagation due to fatigue or corrosion, for example. If the defect is internal, it is even harder to identify such defects.\n",
        "\n",
        "Thus, the crack or defect might slowly achieve a critical size leading to unexpected catastrophic failure.\n",
        "\n",
        "How can we use the design philosophy to create a system that \"fails safe\"?\n",
        "\n",
        "Let's consider the following widget. We have our blue pipe with a specific thickness $t$. For a given material and internal pressure we can calculate the critical size of defect. On the right side, we plot the pairs failure stress-defect size and see the effect of using different values of thickness."
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "#HIDDEN\n",
        "def see_pipe(w_t):\n",
        "    D_ext = 0.5 # External Diameter\n",
        "    fig, axs = plt.subplots(1, 2, figsize=(12, 6))\n",
        "    e1 = Ellipse([0.5, 0.5], D_ext/2, D_ext/2, zorder=9, fc='lightskyblue', ls='--', ec='k')\n",
        "    axs[0].add_patch(e1)\n",
        "    e2 = Ellipse([0.5, 0.5], D_ext/2-2*w_t, D_ext/2-2*w_t, zorder=9, fc='w', ec='k')\n",
        "    axs[0].add_patch(e2)\n",
        "    e3 = Ellipse([0.5, 0.5], D_ext/2-0.5/8, D_ext/2-0.5/8, zorder=9, ls='--', fc='none', ec='k')\n",
        "    axs[0].add_patch(e3)\n",
        "    e4 = Ellipse([0.5, 0.5], D_ext/2, D_ext/2, zorder=9, fc='gold', alpha=0.5, ec='k')\n",
        "#     axs.add_patch(e4)\n",
        "    axs[0].axis('equal')\n",
        "    axs[0].arrow(D_ext, 0.5+0.125-0.0625/2,\n",
        "              0, +0.0625/2*0.925, fc='k', width=0.00025,\n",
        "              head_width=0.0025, head_length=0.002, zorder=16)\n",
        "    axs[0].arrow(D_ext, 0.5+0.125,\n",
        "              0, -0.0625/2*0.925, fc='k', width=0.00025,\n",
        "              head_width=0.0025, head_length=0.002, zorder=16)\n",
        "    axs[0].text(D_ext+0.005, 0.5+0.125-0.0625/4-0.005, r'$c^*$', zorder=16, fontsize=18)\n",
        "    axs[0].axis('off')\n",
        "    K_Ic_2 = 10\n",
        "    sigma_f = lambda K_Ic, c: K_Ic/(np.pi*c)**0.5\n",
        "    cs = np.linspace(0.5/32, 0.5/7, 100)\n",
        "    axs[1].plot(cs, sigma_f(K_Ic_2, cs), '-o', markevery=6,  c='orangered', zorder=5)\n",
        "    axs[1].scatter([w_t], [sigma_f(K_Ic_2, w_t)], marker='x', color='k', zorder=20)\n",
        "#     axs[1].text(0.8, 4.75, r'Material 2', fontsize=16, c='orangered')\n",
        "    axs[1].axvline(w_t, c='blue', lw=2, ymax=0.85, zorder=17)\n",
        "    axs[1].axis('off')\n",
        "    axs[1].set(xlim=(0, 0.075), ylim=(20, 50))\n",
        "    axs[1].arrow(0, 20.75, 0.0735, 0, head_width=0.5, head_length=0.0015, fc='k')\n",
        "    axs[1].arrow(0.001, 20.5, 0, 26, width=0.00001, head_width=0.00125, head_length=0.75, fc='k')\n",
        "    axs[1].text(0.0575, 24, r'$\\sigma_f = \\frac{K_{IC}}{\\sqrt{\\pi c}}$', fontsize=18)\n",
        "    axs[1].axhline(K_Ic_2/(np.pi*0.5/16)**0.5, c='k', ls='--')\n",
        "    axs[1].text(-0.005, K_Ic_2/(np.pi*0.5/16)**0.5, r'$\\sigma_y$', fontsize=18)\n",
        "    r1 = Rectangle([0.001, 20.75], 0.0735, K_Ic_2/(np.pi*0.5/16)**0.5-20-0.75,\n",
        "                   zorder=9, alpha=0.25, fc='red', ls='--', ec='k')\n",
        "    axs[1].add_patch(r1)\n",
        "    axs[1].text(0.0025, 22, r'Failure Before Yield', fontsize=14)\n",
        "    r2 = Rectangle([0.001, K_Ic_2/(np.pi*0.5/16)**0.5], 0.0735, 15,\n",
        "                   zorder=9, alpha=0.25, fc='green', ls='--', ec='k')\n",
        "    axs[1].add_patch(r2)\n",
        "    axs[1].text(0.0475, 45, r'Failure After Yield', fontsize=14)\n",
        "    axs[1].text(w_t, 18.5, r'$t$', fontsize=14)\n",
        "    axs[1].text(0.5/16, 19.5, r'$c^*$', fontsize=14)\n",
        "    plt.plot([0.5/16, 0.5/16], [20.5, 21], c='k', zorder=17)\n",
        "    axs[1].text(-0.005, 47, r'$\\sigma_f$', fontsize=18)\n",
        "    axs[1].text(0.07, 19.5, r'$c$', fontsize=18)\n",
        "    plt.show()\n",
        "interactive_plot = interactive(see_pipe, w_t=widgets.FloatSlider(value=0.5/16,\n",
        "                                                       min=0.5/32,\n",
        "                                                       max=0.5/8,\n",
        "                                                       step=0.5/64,\n",
        "                                                       description='$t$',\n",
        "                                                       readout_format='.4e'))\n",
        "output = interactive_plot.children[-1]\n",
        "output.layout.height = '550px'\n",
        "interactive_plot.layout = widgets.Layout(display='flex',\n",
        "                               flex_flow='column',\n",
        "                               align_items='center',\n",
        "                               align_content='center',\n",
        "                               justify_content='center',\n",
        "                               width='100%')\n",
        "interactive_plot"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "17c2f941154d43298fc693c89ec8a036",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": "interactive(children=(FloatSlider(value=0.03125, description='$t$', max=0.0625, min=0.015625, readout_format='…"
          },
          "metadata": {}
        }
      ],
      "execution_count": 273,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-04-07T01:36:51.308558Z",
          "start_time": "2021-04-07T01:36:51.125051Z"
        },
        "hide_input": true
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "If we use values of thickness higher than $c^*$ we can have the catastrophic failure scenario. If, however, we decrease the thickness to values lower than the critical defect size, we can find that the failure will occur after yielding, in a not catastrophic way, being able to easily identify and repair before daunting consequences."
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "# References"
      ],
      "metadata": {
        "run_control": {
          "marked": true
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "[1] <a href=\"https://yenaengineering.nl/ductile-brittle-transition-temperature-and-impact-energy-tests/\" target=\"_blank\" rel=\"noopener noreferrer\">Yena Engineering, Ductile-Brittle Transition Temperature and Impact Energy Tests.</a> <a id=\"cit-ref_db_trans\" href=\"#call-ref_db_trans\">[↩]</a>\n",
        "\n",
        "[2] <a href=\"https://www.researchgate.net/publication/258004229_In-situ_experimental_study_of_the_seismic_signatures_of_the_role_of_fluids_in_the_rupture_of_fault_zones_Application_to_large_rockslides_failure_studies/figures?lo=1&utm_source=bing&utm_medium=organic\" target=\"_blank\" rel=\"noopener noreferrer\">Deroide B., In-situ experimental study of the seismic signatures of the role of fluids in the rupture of fault zones: Application to large rockslides failure studies.</a> <a id=\"cit-ref_modes\" href=\"#call-ref_mode\">[↩]</a>\n",
        "\n",
        "[3] <a href=\"https://commons.wikimedia.org/wiki/File:Fracture_toughness_vs._Strength.jpg\" target=\"_blank\" rel=\"noopener noreferrer\">Wikimedia Commons, the free media repository, Fracture toughness vs. Strength.</a> <a id=\"cit-ref_ashby\" href=\"#call-ref_ashby\">[↩]</a>\n",
        "\n",
        "[4] <a href=\"https://www.mdpi.com/2624-5558/1/2/14\" target=\"_blank\" rel=\"noopener noreferrer\">Taheri et al., Corrosion Inhibitory Effects of Mullite in Concrete Exposed to Sulfuric Acid Attack.</a> <a id=\"cit-ref_micro\" href=\"#call-ref_micro\">[↩]</a>\n",
        "\n",
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        "\n",
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        "\n",
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