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+{
+ "metadata": {
+  "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Chapter 12 : Fracture"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.1, Page No 302"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "#initialisation of variables\n",
+      "c = 2.0 \t# crack of half length in micro meter\n",
+      "Y = 70.0 \t# young\u2019s modulus in GN m^-2\n",
+      "Gamma = 1.0\t # specific surface energy \n",
+      "\n",
+      "#Calculations\n",
+      "sigma_f = math.sqrt(2*Gamma*Y*1e9/(math.pi*c*1e-6))/1e6\n",
+      "r = Y*1e3/sigma_f\n",
+      "\n",
+      "#Results\n",
+      "print(\" Fracture strength of %d MN m^-2 is 1/%d th of young\u2019s modulus. \"%(math.ceil(sigma_f),math.ceil(r/100.0)*100.0))\n",
+      "print(\" Thus Griffiths criterion bridges the gap between the  observed and ideal strengths of brittle material\")\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        " Fracture strength of 150 MN m^-2 is 1/500 th of young\u2019s modulus. \n",
+        " Thus Griffiths criterion bridges the gap between the  observed and ideal strengths of brittle material\n"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.2, Page No 304"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "#initialisation of variables\n",
+      "Gamma = 1.5\t\t# specific surface energy in J/m^2\n",
+      "Y = 200.0\t \t# Young\u2019s modulus in GN/m^2\n",
+      "c = 2.0\t\t    # half length of crack\n",
+      "\n",
+      "#Calculations\n",
+      "sigma_f = math.sqrt(2*Gamma*Y*1e9/(math.pi*c*1e-6))\n",
+      "\n",
+      "#Results\n",
+      "print(\" Brittle fracture strength at low temperatures is %d MNm^-2 \" %(sigma_f/1e6))# answer in book is 310MNm^-2\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        " Brittle fracture strength at low temperatures is 309 MNm^-2 \n"
+       ]
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 12.3, Page No 306"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "#initialisation of variables\n",
+      "Gamma = 2.0\t\t # specific surface energy in J/m**2\n",
+      "Y = 350.0\t\t # Young\u2019s modulus in GN/m**2\n",
+      "c = 2.0\t\t\t # half length of crack\n",
+      "de_dt1 = 1e-2 \t\t# strain rate\n",
+      "de_dt2 = 1e-5 \t# strain rate\n",
+      "\n",
+      "#Calculations\n",
+      "print(\" Part A:\")\n",
+      "sigma_f = math.sqrt(2*Gamma*Y*1e9/(math.pi*c*1e-6))\n",
+      "sigma_y = sigma_f/1e6\n",
+      "T = 173600/(sigma_y-20.6-61.3*math.log(de_dt1,10))\t# temperature calculation\n",
+      "\n",
+      "print(\" Transition temperature for strain rate %.0e s**-1 is %d K\" %(de_dt1,T))   # answer in book is 300 K\n",
+      "print(\" Part B:\")\n",
+      "\n",
+      "T = 173600/(sigma_y-20.6-61.3*math.log(de_dt2,10))\t# temperature calculation\n",
+      "\n",
+      "\n",
+      "#Results\n",
+      "print(\" Transition temperature for strain rate %.0e s**-1 is %d K\" %(de_dt2,T))   # answer in book is 230 K\n",
+      "# Solution in book for two parts is divided into three parts\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        " Part A:\n",
+        " Transition temperature for strain rate 1e-02 s**-1 is 302 K\n",
+        " Part B:\n",
+        " Transition temperature for strain rate 1e-05 s**-1 is 229 K\n"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
+\ No newline at end of file