From 4a1f703f1c1808d390ebf80e80659fe161f69fab Mon Sep 17 00:00:00 2001 From: Thomas Stephen Lee Date: Fri, 28 Aug 2015 16:53:23 +0530 Subject: add books --- .../Chapter12.ipynb | 454 +++++++++++++++++++++ 1 file changed, 454 insertions(+) create mode 100755 Materials_Science_by_Dr._M._Arumugam/Chapter12.ipynb (limited to 'Materials_Science_by_Dr._M._Arumugam/Chapter12.ipynb') diff --git a/Materials_Science_by_Dr._M._Arumugam/Chapter12.ipynb b/Materials_Science_by_Dr._M._Arumugam/Chapter12.ipynb new file mode 100755 index 00000000..c8688bf4 --- /dev/null +++ b/Materials_Science_by_Dr._M._Arumugam/Chapter12.ipynb @@ -0,0 +1,454 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#12: Mechanical Behaviour of Materials" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 12.1, Page number 12.115" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "yield strength is 86.026 kg/mm**2\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "sigma0=8.55;\n", + "K=2.45; \n", + "sigma=10**-3; #steel size(mm)\n", + "\n", + "#Calculation\n", + "sigma=sigma0+(K/math.sqrt(sigma)); #yield strength\n", + "\n", + "#Result\n", + "print \"yield strength is\",round(sigma,3),\"kg/mm**2\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 12.2, Page number 12.115" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "fracture strength is 0.211 GPa\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "E=70*10**9; #young's modulus(Pa)\n", + "gama=1; #surface energy(joule/m**2)\n", + "C=1*10**-6; #depth(m)\n", + "\n", + "#Calculation\n", + "sigma_f=math.sqrt(2*E*gama/(math.pi*C)); #fracture strength(GPa)\n", + "\n", + "#Result\n", + "print \"fracture strength is\",round(sigma_f/10**9,3),\"GPa\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 12.3, Page number 12.116" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ultimate tensile strength is 736.0 MPa\n", + "ductility % of elongation is 10.0 %\n", + "ductility % of reduction is 75.0 %\n", + "modulus of toughness is 49 *10**6 Pa\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "ml=57800; #load(N)\n", + "d=10*10**-3; #diameter(m)\n", + "D=5; #diameter after fracture(mm)\n", + "l=50; #guage length(mm)\n", + "L=55; #length after fracture(mm)\n", + "\n", + "#Calculation\n", + "ts=ml/(math.pi*(d/2)**2); #ultimate tensile strength(MPa)\n", + "de=(L-l)*100/l; #ductility % of elongation(%)\n", + "dr=((2*D)**2-D**2)*100/(2*D)**2; #ductility % of reduction(%)\n", + "t=(2/3)*ts*de/100; #modulus of toughness(Pa)\n", + "\n", + "#Result\n", + "print \"ultimate tensile strength is\",round(ts/10**6),\"MPa\"\n", + "print \"ductility % of elongation is\",de,\"%\"\n", + "print \"ductility % of reduction is\",dr,\"%\"\n", + "print \"modulus of toughness is\",int(t/10**6),\"*10**6 Pa\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 12.4, Page number 12.116" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "elastic strain in 1st case is 0.001\n", + "ratio of elastic and plastic strain in 2nd case is 2.5 %\n", + "ratio of elastic and plastic strain in 3rd case is 1.0 %\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "pl1=206850*10**3; #proportional limit(Pa)\n", + "pl2=310275*10**3; #proportional limit(Pa)\n", + "pl3=413700*10**3; #proportional limit(Pa)\n", + "s2=0.0615; #strain\n", + "s3=0.2020; #strain\n", + "Y=2.0685*10**11; #young's modulus(Pa)\n", + "\n", + "#Calculation\n", + "e1=pl1/Y; #elastic strain in 1st case\n", + "e2=pl2/Y; #elastic strain in 2nd case\n", + "p2=s2-e2; #plastic strain in 2nd case\n", + "r2=e2*100/p2; #ratio of elastic and plastic strain in 2nd case\n", + "e3=pl3/Y; #elastic strain in 2nd case \n", + "p3=s3-e3; #plastic strain in 2nd case \n", + "r3=e3*100/p3; #ratio of elastic and plastic strain in 3rd case\n", + "\n", + "#Result\n", + "print \"elastic strain in 1st case is\",e1\n", + "print \"ratio of elastic and plastic strain in 2nd case is\",r2,\"%\"\n", + "print \"ratio of elastic and plastic strain in 3rd case is\",r3,\"%\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 12.5, Page number 12.117" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "effective modulus is 738750.0 *10**3 Pa\n", + "cross sectional area is 1.0831 *10**-4 m**2\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "s=12411*10**3; #stress(Pa)\n", + "t=0.0168; #tension\n", + "e=0.127; #elongation(cm)\n", + "l=15.24; #length(cm)\n", + "g=9.8;\n", + "L=68.04; #load(kg)\n", + "\n", + "#Calculation\n", + "E_eff=s/t; #effective modulus(Pa)\n", + "S=e/l; \n", + "W=E_eff*S;\n", + "A=L*g/W; #cross sectional area(m**2)\n", + "\n", + "#Result\n", + "print \"effective modulus is\",E_eff/10**3,\"*10**3 Pa\"\n", + "print \"cross sectional area is\",round(A*10**4,4),\"*10**-4 m**2\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 12.6, Page number 12.117" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "transition temperature is 229.0 K\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "E=35*10**10; #youngs modulus(Pa)\n", + "gama=2; #specific surface energy(J/m**2)\n", + "C=2*10**-6; #length(m)\n", + "x=17700; \n", + "y=2.1;\n", + "z=31.25;\n", + "\n", + "#Calculation\n", + "sigma_f=math.sqrt(2*E*gama/(math.pi*C)); #fracture stress(Pa)\n", + "T=x/((sigma_f/(9.8*10**6))-y+z); #transition temperature(K)\n", + "\n", + "#Result\n", + "print \"transition temperature is\",round(T),\"K\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 12.7, Page number 12.118" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "critical resolved shear stress is 0.898 MPa\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "h1=1;\n", + "h2=1;\n", + "k1=1;\n", + "k2=1;\n", + "l1=1;\n", + "l2=1;\n", + "l3=0;\n", + "s=3.5*10**6; #stress(Pa)\n", + "\n", + "#Calculation\n", + "x=math.sqrt(h1**2+k1**2+l1**2);\n", + "y=math.sqrt(h2**2+k2**2+l2**2);\n", + "z=math.sqrt(h2**2+k2**2+l3**2);\n", + "cos_phi=((h1*h2)-(k1*k2)+(l1*l2))/(x*y);\n", + "sin_phi=math.sqrt(1-(cos_phi)**2);\n", + "cos_theta=((h1*h2)+(k1*k2)+(l1*l3))/(x*z);\n", + "ss=s*cos_theta*cos_phi*sin_phi; #critical resolved shear stress(Pa)\n", + "\n", + "#Result\n", + "print \"critical resolved shear stress is\",round(ss/10**6,3),\"MPa\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 12.8, Page number 12.119" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "activation energy is 192.393 kJ/mol\n", + "answer varies due to rounding off errors\n", + "diffusion coefficient is 0.394 *10**-4 m**2/s\n", + "diffusivity at 300 C is 11.37 *10**-23 m**2/s\n", + "diffusivity at 700 C is 1.846 *10**-15 m**2/s\n", + "answer given in the book is wrong\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "dz1=4*10**-18; #diffusivity(m**2/s)\n", + "dz2=5*10**-13; #diffusivity(m**2/s)\n", + "T1=773; #temperature(K)\n", + "T2=1273; #temperature(K)\n", + "T3=573; #temperature(K)\n", + "T4=973; #temperature(K)\n", + "\n", + "#Calculation\n", + "x1=round(math.log(dz1),2);\n", + "y1=round(math.log(dz2),3);\n", + "x2=round(-1/(8.314*T1),7);\n", + "y2=round(-1/(8.314*T2),7);\n", + "x=round((x1-y1),3);\n", + "y=round((x2-y2),6);\n", + "Q=x/y; #activation energy(J/mol)\n", + "z=round(y1-(y2*Q),4);\n", + "D0=math.exp(z); #diffusion coefficient(m**2/Vs)\n", + "D1=D0*math.exp(-Q/(8.314*T3)); #diffusivity at 300 C(m**2/s)\n", + "D2=D0*math.exp(-Q/(8.314*T4)); #diffusivity at 700 C(m**2/s)\n", + "\n", + "#Result\n", + "print \"activation energy is\",round(Q/10**3,3),\"kJ/mol\"\n", + "print \"answer varies due to rounding off errors\"\n", + "print \"diffusion coefficient is\",round(D0*10**4,3),\"*10**-4 m**2/s\"\n", + "print \"diffusivity at 300 C is\",round(D1*10**23,2),\"*10**-23 m**2/s\"\n", + "print \"diffusivity at 700 C is\",round(D2*10**15,3),\"*10**-15 m**2/s\"\n", + "print \"answer given in the book is wrong\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 12.9, Page number 12.119" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "diffusion is 4.9 *10**-15 m**2/s\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "D0=0.73*10**-4; #diffusion coefficient(m**2/s)\n", + "Q=170*10**3; #activation energy(J/mol)\n", + "R=8.314; \n", + "T=873; #temperature(K)\n", + "\n", + "#Calculation\n", + "D=D0*math.exp(-Q/(R*T)); #diffusion(m**2/s)\n", + "\n", + "#Result\n", + "print \"diffusion is\",round(D*10**15,1),\"*10**-15 m**2/s\"" + ] + } + ], + "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 +} -- cgit