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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 11: Fracture Mechanics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 11.1, Fracture Toughness, Page No. 354"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Since Fracture Toughness of the material is = 172.852 MPa\n",
" and the applied stress is 172 MPa thus the flaw will propagate as a brittle fracture\n"
]
}
],
"source": [
"\n",
"from math import sqrt\n",
"from math import pi\n",
"from math import cos\n",
"\n",
"#variable declaration\n",
"a=5;\n",
"a=a*10**-3; #conversion to m\n",
"t=1.27; #in cm\n",
"t=t*10**-2; #conversion to m\n",
"def sec(x):\n",
" return 1/cos(x);\n",
"\n",
"#calculation\n",
"K_Ic=24;\n",
"sigma=K_Ic/(sqrt(pi*a)*sqrt(sec(pi*a/(2*t))));\n",
"\n",
"#result\n",
"print('Since Fracture Toughness of the material is = %g MPa\\n and the applied stress is 172 MPa thus the flaw will propagate as a brittle fracture')%(sigma);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 11.2, Fracture Toughness, Page No. 354"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Critical Crack depth = 15.4981 mm\n",
"which is greater than the thickness of the vessel wall, 12mm\n"
]
}
],
"source": [
"from math import pi\n",
"\n",
"#variable declaration\n",
"K_Ic=57;\n",
"sigma0=900;\n",
"sigma=360;\n",
"Q=2.35;\n",
"\n",
"#calculation\n",
"a_c=K_Ic**2*Q/(1.21*pi*sigma**2);\n",
"a_c=a_c*1000; #conversion to mm\n",
"\n",
"#result\n",
"print('\\nCritical Crack depth = %g mm\\nwhich is greater than the thickness of the vessel wall, 12mm')%(a_c);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 11.3, Plasticity, Page No. 361"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Plastic zone size = 0.113177 mm\n",
"Stress Intensity Factor = 42.8659 MPa m^(1/2)\n",
"\n",
"\n",
"Note: Calculation Errors in book\n"
]
}
],
"source": [
"from math import sqrt\n",
"from math import pi\n",
"\n",
"#variable declaration\n",
"a=10;\n",
"a=a*10**-3; #conversion to m\n",
"sigma=400;\n",
"sigma0=1500;\n",
"\n",
"#calculation\n",
"rp=sigma**2*a/(2*pi*sigma0**2);\n",
"rp=rp*1000; #conversion to mm\n",
"K=sigma*sqrt(pi*a);\n",
"K_eff=sigma*sqrt(pi*a)*sqrt(a+pi*rp);\n",
"\n",
"#result\n",
"print('\\nPlastic zone size = %g mm\\nStress Intensity Factor = %g MPa m^(1/2)\\n\\n\\nNote: Calculation Errors in book')%(rp,K_eff);"
]
}
],
"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
}
|
