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diff --git a/Mechanical_Metallurgy_by_George_E._Dieter/Chapter_3.ipynb b/Mechanical_Metallurgy_by_George_E._Dieter/Chapter_3.ipynb
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-{

- "cells": [

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "# Chapter 3: Elements of the Theory of Plasticity"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "### Example 3.1, True Stress and True Strain, Page No. 76"

-   ]

-  },

-  {

-   "cell_type": "code",

-   "execution_count": 4,

-   "metadata": {

-    "collapsed": false

-   },

-   "outputs": [

-    {

-     "name": "stdout",

-     "output_type": "stream",

-     "text": [

-      "\n",

-      "Engineering Stress at maximum load = 99852.1 psi\n",

-      "True Fracture Stress = 112785 psi\n",

-      "True Strain at fracture = 0.344939\n",

-      "Engineering strain at fracture = 0.411903\n"

-     ]

-    }

-   ],

-   "source": [

-    "from math import pi\n",

-    "from math import log\n",

-    "from math import exp\n",

-    "\n",

-    "#variable declaration\n",

-    "D_i=0.505;\n",

-    "L=2;\n",

-    "P_max=20000;\n",

-    "P_f=16000;\n",

-    "D_f=0.425;\n",

-    "\n",

-    "#calculation\n",

-    "E_St= P_max*4/(pi*D_i**2);\n",

-    "T_fr_St= P_f*4/(pi*D_f**2);\n",

-    "e_f=log(D_i**2/D_f**2);\n",

-    "e=exp(e_f)-1;\n",

-    "\n",

-    "#result\n",

-    "print('\\nEngineering Stress at maximum load = %g psi\\nTrue Fracture Stress = %g psi\\nTrue Strain at fracture = %g\\nEngineering strain at fracture = %g')%(E_St,T_fr_St,e_f,e);\n"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "### Example 3.2, Yielding Criteria for Ductile Metals, Page No. 78"

-   ]

-  },

-  {

-   "cell_type": "code",

-   "execution_count": 2,

-   "metadata": {

-    "collapsed": false

-   },

-   "outputs": [

-    {

-     "name": "stdout",

-     "output_type": "stream",

-     "text": [

-      "\n",

-      "Since the calculated value of sigma0 = 224.054 MPa, which is less than the yield strength of the aluminium alloy\n",

-      "Thus safety factor is = 2.23161\n"

-     ]

-    }

-   ],

-   "source": [

-    "\n",

-    "from math import sqrt\n",

-    "\n",

-    "#variable declaration\n",

-    "sigma00=500;\n",

-    "sigma_z=-50;\n",

-    "sigma_y=100;\n",

-    "sigma_x=200;\n",

-    "T_xy=30;\n",

-    "T_yz=0;\n",

-    "T_xz=0;\n",

-    "\n",

-    "#calculation\n",

-    "sigma0=sqrt((sigma_x-sigma_y)**2+(sigma_y-sigma_z)**2+(sigma_z-sigma_x)**2+6*(T_xy**2+T_yz**2+T_xz**2))/sqrt(2);\n",

-    "s=sigma00/sigma0;\n",

-    "\n",

-    "#result\n",

-    "print('\\nSince the calculated value of sigma0 = %g MPa, which is less than the yield strength of the aluminium alloy\\nThus safety factor is = %g')%(sigma0,s);\n"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "### Example 3.3, Tresca Criterion, Page No. 81"

-   ]

-  },

-  {

-   "cell_type": "code",

-   "execution_count": 6,

-   "metadata": {

-    "collapsed": false

-   },

-   "outputs": [

-    {

-     "name": "stdout",

-     "output_type": "stream",

-     "text": [

-      "\n",

-      "Since the calculated value of sigma0 = 250 MPa, which is less than the yield strength of the aluminium alloy\n",

-      "Thus safety factor is = 2\n"

-     ]

-    }

-   ],

-   "source": [

-    "\n",

-    "\n",

-    "#variable declaration\n",

-    "sigma00=500;\n",

-    "sigma_z=-50;\n",

-    "sigma_y=100;\n",

-    "sigma_x=200;\n",

-    "T_xy=30;\n",

-    "T_yz=0;\n",

-    "T_xz=0;\n",

-    "\n",

-    "#calculation\n",

-    "sigma0=sigma_x-sigma_z;\n",

-    "s=sigma00/sigma0;\n",

-    "\n",

-    "#result\n",

-    "print('\\nSince the calculated value of sigma0 = %g MPa, which is less than the yield strength of the aluminium alloy\\nThus safety factor is = %g')%(sigma0,s);\n"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {

-    "collapsed": true

-   },

-   "source": [

-    "### Example 3.4, Levy-Mises Equation, Page No. 91"

-   ]

-  },

-  {

-   "cell_type": "code",

-   "execution_count": 4,

-   "metadata": {

-    "collapsed": false

-   },

-   "outputs": [

-    {

-     "name": "stdout",

-     "output_type": "stream",

-     "text": [

-      "\n",

-      "Plastic Strain = 0.199532\n"

-     ]

-    }

-   ],

-   "source": [

-    "from math import sqrt\n",

-    "\n",

-    "#variable declaration\n",

-    "r_t=20;\n",

-    "p=1000;\n",

-    "\n",

-    "#calculation\n",

-    "sigma1=p*r_t;\n",

-    "sigma1=sigma1/1000;                     #conversion to ksi\n",

-    "sigma=sqrt(3)*sigma1/2;\n",

-    "e=(sigma/25)**(1/0.25);\n",

-    "e1=sqrt(3)*e/2;\n",

-    "\n",

-    "#result\n",

-    "print('\\nPlastic Strain = %g')%(e1);\n"

-   ]

-  }

- ],

- "metadata": {

-  "kernelspec": {

-   "display_name": "Python 2",

-   "language": "python",

-   "name": "python2"

-  },

-  "language_info": {

-   "codemirror_mode": {

-    "name": "ipython",

-    "version": 2

-   },

-   "file_extension": ".py",

-   "mimetype": "text/x-python",

-   "name": "python",

-   "nbconvert_exporter": "python",

-   "pygments_lexer": "ipython2",

-   "version": "2.7.9"

-  }

- },

- "nbformat": 4,

- "nbformat_minor": 0

-}