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diff --git a/Materials_Science_and_Engineering/Chapter11.ipynb b/Materials_Science_and_Engineering/Chapter11.ipynb new file mode 100755 index 00000000..c7f0e650 --- /dev/null +++ b/Materials_Science_and_Engineering/Chapter11.ipynb @@ -0,0 +1,209 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 11 : Plastic Deformation and Creep in Crystalline Materials"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.2, Page No 272"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "b = 2.0 \t\t# burger vector in angstrom\n",
+ "v = 20*b**3 \t# activation volume \n",
+ "tau_pn = 1000.0 # P-N stress of crystal in MNm**-2\n",
+ "k = 1.38e-23 \t# physical constant\n",
+ "t1 = 0 \t\t\t# temperature in K\n",
+ "t2 = 100.0\t\t# temperature in K \n",
+ "t3 = 300.0\t\t# temperature in K\n",
+ "t4 = 500.0\t\t# temperature in K\n",
+ "T = t1\t\n",
+ "\n",
+ "#Calculations\n",
+ "tau_app = tau_pn - 40.0*k*T/(v*1e-30)\n",
+ "print(\"The stress required to move the dislocation at temperature %dK is %d MNm**-2\" %(T,tau_app))\n",
+ "print(\"Part B:\")\n",
+ "T = t2\n",
+ "tau_app = tau_pn - 40*k*T/(v*1e-30*1e6)\n",
+ "print(\"The stress required to move the dislocation at temperature %dK is %d MNm**-2\" %(T,tau_app))\n",
+ "print(\"Part C:\")\n",
+ "T = t3\n",
+ "tau_app = tau_pn - 40*k*T/(v*1e-30*1e6)\n",
+ "if tau_app<0 :\n",
+ " print(\" Stress to be applied is zero\")\n",
+ " print(\"The stress required to move the dislocation at temperature %dK entirely overcome by thermal fluctuations\" %T)\n",
+ "\n",
+ "print(\"Part D:\")\n",
+ "T = t4\n",
+ "tau_app = tau_pn - 40*k*T/(v*1e-30*1e6)\n",
+ "\n",
+ "#Results\n",
+ "if tau_app<0 :\n",
+ " print(\"Stress to be applied is zero\")\n",
+ " print(\"The stress required to move the dislocation at temperature %dK entirely overcome by thermal fluctuations\" %T)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The stress required to move the dislocation at temperature 0K is 1000 MNm**-2\n",
+ "Part B:\n",
+ "The stress required to move the dislocation at temperature 100K is 655 MNm**-2\n",
+ "Part C:\n",
+ " Stress to be applied is zero\n",
+ "The stress required to move the dislocation at temperature 300K entirely overcome by thermal fluctuations\n",
+ "Part D:\n",
+ "Stress to be applied is zero\n",
+ "The stress required to move the dislocation at temperature 500K entirely overcome by thermal fluctuations\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.3, Page No 278"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "mu = 44.0 # shear modulus of copper in GN m^-2\n",
+ "b = 2.55 # burgers vector in angstrom\n",
+ "tau = 35.0 # shear stress in MN m^-2\n",
+ "\n",
+ "#Calculations\n",
+ "l = mu*1e9*b*1e-10/(tau*1e6)\n",
+ "rho = 1/l**2\n",
+ "\n",
+ "#Results\n",
+ "print(\"Dislocation density in copper is %.1e m^-2\" %rho)\n",
+ "# Answer in book is 1e12 m^-2\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Dislocation density in copper is 9.7e+12 m^-2\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.4, Page No 280"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "sigma1 = 120.0 # initial yield strength of material in MNm**-2\n",
+ "sigma2 = 220.0 # Final yield strength of material in MN m**-2\n",
+ "d1 = 0.04 # initial diameter in mm\n",
+ "d2 = 0.01 # final diameter in mm\n",
+ "n = 9.0 # astm number\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"Example 11.4\")\n",
+ "k = (sigma2-sigma1)*1e6/(1/math.sqrt(d2*1e-3)-1/math.sqrt(d1*1e-3))\n",
+ "sigma_i = sigma1*1e6 -k/math.sqrt((d1*1e-3))\n",
+ "d = 1/math.sqrt(2**(n-1)*1e4/645)\n",
+ "sigma_y = sigma_i+k*(d*1e-3)**(-0.5)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Yield stress for a grain size of ASTM 9 is %d MN m**-2\" %math.ceil(sigma_y/1e6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Example 11.4\n",
+ "Yield stress for a grain size of ASTM 9 is 179 MN m**-2\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.5 Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "n1 = 1e6 # initial number of particles\n",
+ "n2 = 1e3 # final number of particle\n",
+ "\n",
+ "#Calculations\n",
+ "k = (n1/n2)**(1.0/3)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Yield strength would have decreased to %d percent of its initial value.\" %(100.0/k))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Yield strength would have decreased to 10 of its initial value.\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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