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{
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"name": "",
"signature": "sha256:ccc34ac1a23df3ea87c02161eb6957101119525a84db5440299d3d3e0c490bb9"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 11 :\n",
"Deformation of Materials"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.1 Page No : 369"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\t\t\n",
"import math \n",
"\n",
"# Variables\n",
"h_1 = 1;\n",
"k_1 = 1;\n",
"l_1 = 1;\n",
"#Miller indices of slip plane\n",
"h_2 = 1;\n",
"k_2 = -1;\n",
"l_2 = 1;\n",
"#Miller indices of stress plane\n",
"h_3 = 1;\n",
"k_3 = 1;\n",
"l_3 = 0;\n",
"\n",
"# Calculation\n",
"#Miller indices of slip direction\n",
"A = (h_1*h_2+k_1*k_2+l_1*l_2)/(((h_1**2+k_1**2+l_1**2)**(1./2))*((h_2**2+k_2**2+l_2**2)**(1./2)));\t\t\t#Value of math.cos(x) where x = angle between slip plane and stress plane\n",
"B = (h_1*h_3+k_1*k_3+l_1*l_3)/(((h_1**2+k_1**2+l_1**2)**(1./2))*((h_3**2+k_3**2+l_3**2)**(1./2)));\t\t\t#Value of math.cos(y) where y = angle between slip direction and stress direction\n",
"C = (1-A**2)**(1./2);\t\t\t#Value of math.sin(x)\n",
"stress = 3.5;\t\t\t#Applied Stress in Mpa\n",
"T_cr = stress*A*B*C;\t\t\t#Critical resolved shear stress(in MPa)\n",
"\n",
"# Results\n",
"print 'Critical resolved shear stress in = %.3f MPa'%T_cr\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Critical resolved shear stress in = 0.898 MPa\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.3 Page No : 370"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\t\t\n",
"import math \n",
"\n",
"# Variables\n",
"D = 0.022;\t\t\t#Grain diameter(in mm)\n",
"d = D*10**(-3);\t\t\t#Grain diameter(in m)\n",
"K = 0.63;\t\t\t#Constant(in MNm**(-3/2))\n",
"\n",
"# Calculation\n",
"sigma_i = 80;\t\t\t#in MNm**-2\n",
"sigma_y = sigma_i+K*d**(-1./2);\t\t\t#Yield stress for a polycrystalline alloy\n",
"\n",
"# Results\n",
"print 'Yield stress for a polycrystalline alloy in = %.2f MN/m**2'%sigma_y\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Yield stress for a polycrystalline alloy in = 214.32 MN/m**2\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.4 Page No : 370"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\t\t\n",
"import math \n",
"\n",
"# Variables\n",
"sigma_y1 = 120;\t\t\t#primary yield strength of polycrystalline material(in MN*m**-2)\n",
"sigma_y2 = 220;\t\t\t#increased yield strength of polycrystalline material(in MN*m**-2)\n",
"d_1 = 0.04*10**(-3);\t\t\t#primary grain diameter(in meter)\n",
"d_2 = 0.01*10**(-3);\t\t\t#grain diameter after decreasing(in meter)\n",
"\n",
"# Calculation\n",
"#sigma_y1 = sigma_i+K*(d_1)**(-1/2)\n",
"#sigma_y2 = sigma_i+K*(d_2)**(-1/2)\n",
"#putting the values and solving the equation\n",
"K = (220-120)/((d_2**(-1./2))-((d_1**(-1./2))));\t\t\t#consmath.tant(in MN*m(-3/2))\n",
"sigma_i = sigma_y1-K*(d_1)**(-1./2);\t\t\t#in MN*m**-2\n",
"d = 1./((10**4)*(256./645))**(1./2);\t\t\t#grain diameter for grain size ASTM 9(in mm)\n",
"D = d*10**(-3);\t\t\t #grain diameter for grain size ASTM 9(in meter)\n",
"sigma_y = sigma_i+K*(D)**(-1./2);\t\t\t#Yield stress for a polycrystalline alloy for grain size ASTM 9(in MN*m**-2)\n",
"\n",
"# Results\n",
"print 'Yield stress for a polycrystalline alloy for grain size ASTM 9 in = %.0f MN*m**-2'%round(sigma_y)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Yield stress for a polycrystalline alloy for grain size ASTM 9 in = 179 MN*m**-2\n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}
|
