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{
"metadata": {
"name": "CH7"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7: Dislocation and Strengthening Mechanisms"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 7.1 Page no 183"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Resolved Shear Stress Computations\n",
"\n",
"#Direction for given plane\n",
"u1=1\n",
"v1=1\n",
"w1=0\n",
"u2=0\n",
"v2=1\n",
"w2=0\n",
"#For lamda\n",
"u3=-1\n",
"v3=1\n",
"w3=1\n",
"\n",
"#Calculation\n",
"import math\n",
"phi=math.acos((u1*u2+v1*v2+w1*w2)/(math.sqrt((u1**2+v1**2+w1**2)*(u2**2+v2**2+w2**2))))\n",
"lam=math.acos((u3*u2+v3*v2+w3*w2)/(math.sqrt((u3**2+v3**2+w3**2)*(u2**2+v2**2+w2**2))))\n",
"sigma=52 #in MPa, Tensile stress\n",
"tr=sigma*math.cos(phi)*math.cos(lam)\n",
"trc=30 #in MPa Critical resolved shear stress\n",
"sy=trc/(math.cos(phi)*math.cos(lam))\n",
"\n",
"#Result\n",
"print\"(a)The resolved shear stress is \",round(tr,2),\"MPa\"\n",
"print\"(b)Yield strength is\",round(sy,1),\"MPa\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The resolved shear stress is 21.23 MPa\n",
"(b)Yield strength is 73.5 MPa\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 7.2 Page no 194"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Tensile Strength and Ductility Determinations for Cold-Worked Copper\n",
"\n",
"#Given\n",
"df=12.2 #Final dia in mm\n",
"di=15.2 #Initial dia in mm\n",
"\n",
"#Calculation\n",
"CW = ((di**2-df**2)/di**2)*100\n",
"ts=340 #in Mpa tensile strength, from fig 7.19 (b)\n",
"duc=7 #in % Ductility from fig 7.19 (c)\n",
"\n",
"#result\n",
"print\"Percent Cold Work is \",round(CW,1),\"%\"\n",
"print\"Tensile strength is\",ts,\"MPa\"\n",
"print\"Ductility is \",duc,\"%\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Percent Cold Work is 35.6 %\n",
"Tensile strength is 340 MPa\n",
"Ductility is 7 %\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Design Example 7.3 Page no 199"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Description of Diameter Reduction Procedure\n",
"\n",
"#Given\n",
"di=6.4 #Initial dia in mm\n",
"df=5.1 #Final dia in mm\n",
"\n",
"#Calculation\n",
"#Cold Work Computation\n",
"CW = ((di**2-df**2)/di**2)*100\n",
"#From Figures 7.19a and 7.19c, \n",
"#A yield strength of 410 MPa \n",
"#And a ductility of 8% EL are attained from this deformation\n",
"dmid = math.sqrt(df**2/(1-0.215))\n",
"\n",
"#Result\n",
"print\"Cold work is \",round(CW,1),\"%\"\n",
"print\"But required ductility and yield strength is not matched at this cold work\"\n",
"print\"Hence required Cold work is 21.5 %\"\n",
"print\"Hence original diameter for second drawing is \",round(dmid,1),\"mm\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Cold work is 36.5 %\n",
"But required ductility and yield strength is not matched at this cold work\n",
"Hence required Cold work is 21.5 %\n",
"Hence original diameter for second drawing is 5.8 mm\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
|
