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   "source": [
    "# Chapter 11: Fracture Mechanics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 11.1, Fracture Toughness, Page No. 354"
   ]
  },
  {
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   "execution_count": 1,
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     "text": [
      "Since Fracture Toughness of the material is = 172.852 MPa\n",
      " and the applied stress is 172 MPa thus the flaw will propagate as a brittle fracture\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from math import sqrt\n",
    "from math import pi\n",
    "from math import cos\n",
    "\n",
    "#variable declaration\n",
    "a=5;\n",
    "a=a*10**-3;             #conversion to m\n",
    "t=1.27;          #in cm\n",
    "t=t*10**-2;        #conversion to m\n",
    "def sec(x):\n",
    "    return 1/cos(x);\n",
    "\n",
    "#calculation\n",
    "K_Ic=24;\n",
    "sigma=K_Ic/(sqrt(pi*a)*sqrt(sec(pi*a/(2*t))));\n",
    "\n",
    "#result\n",
    "print('Since Fracture Toughness of the material is = %g MPa\\n and the applied stress is 172 MPa thus the flaw will propagate as a brittle fracture')%(sigma);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 11.2, Fracture Toughness, Page No. 354"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Critical Crack depth = 15.4981 mm\n",
      "which is greater than the thickness of the vessel wall, 12mm\n"
     ]
    }
   ],
   "source": [
    "from math import pi\n",
    "\n",
    "#variable declaration\n",
    "K_Ic=57;\n",
    "sigma0=900;\n",
    "sigma=360;\n",
    "Q=2.35;\n",
    "\n",
    "#calculation\n",
    "a_c=K_Ic**2*Q/(1.21*pi*sigma**2);\n",
    "a_c=a_c*1000;                         #conversion to mm\n",
    "\n",
    "#result\n",
    "print('\\nCritical Crack depth = %g mm\\nwhich is greater than the thickness of the vessel wall, 12mm')%(a_c);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 11.3, Plasticity, Page No. 361"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Plastic zone size = 0.113177 mm\n",
      "Stress Intensity Factor = 42.8659 MPa m^(1/2)\n",
      "\n",
      "\n",
      "Note: Calculation Errors in book\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "from math import pi\n",
    "\n",
    "#variable declaration\n",
    "a=10;\n",
    "a=a*10**-3;                 #conversion to m\n",
    "sigma=400;\n",
    "sigma0=1500;\n",
    "\n",
    "#calculation\n",
    "rp=sigma**2*a/(2*pi*sigma0**2);\n",
    "rp=rp*1000;                      #conversion to mm\n",
    "K=sigma*sqrt(pi*a);\n",
    "K_eff=sigma*sqrt(pi*a)*sqrt(a+pi*rp);\n",
    "\n",
    "#result\n",
    "print('\\nPlastic zone size = %g mm\\nStress Intensity Factor = %g MPa m^(1/2)\\n\\n\\nNote: Calculation Errors in book')%(rp,K_eff);"
   ]
  }
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