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diff --git a/Materials_Science_by_Dr._M._Arumugam/Chapter12_1.ipynb b/Materials_Science_by_Dr._M._Arumugam/Chapter12_1.ipynb new file mode 100755 index 00000000..c8688bf4 --- /dev/null +++ b/Materials_Science_by_Dr._M._Arumugam/Chapter12_1.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
+}
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