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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 6: Strengthening Mechanisms"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 6.1, Grain Size Measurement, Page No. 193"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Yield Stress = 254.464 MPa\n"
]
}
],
"source": [
"from math import sqrt\n",
"\n",
"#variable declaration\n",
"sigma_i=150;\n",
"k=0.7;\n",
"n=6;\n",
"\n",
"#calculation\n",
"N_x=2**(n-1);\n",
"N=N_x/(0.01)**2; #in grains/in^2\n",
"N=N*10**6/25.4**2; # in grains/m^2\n",
"D=sqrt(1/N);\n",
"sigma0=sigma_i+k/sqrt(D);\n",
"\n",
"#result\n",
"print ('\\nYield Stress = %g MPa')%(sigma0);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 6.2, Strengthing Mechanism, Page No. 219"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Particle Spacing = 2.3e-08 m\n",
"Particle Size = 7.35948e-10 m\n"
]
}
],
"source": [
"#variable declaration\n",
"sigma0=600;\n",
"G=27.6;\n",
"G=G*10**9 #conversion to Pa\n",
"b=2.5*10**-8;\n",
"b=b*10**-2; #conversion to m\n",
"T0=sigma0/2;\n",
"T0=T0*10**6; #conversion to Pa\n",
"\n",
"#calculation\n",
"lambda1=G*b/T0;\n",
"Cu_max=54;\n",
"Cu_eq=4;\n",
"Cu_min=0.5;\n",
"rho_al=2.7;\n",
"rho_theta=4.43;\n",
"wt_a=(Cu_max-Cu_eq)/(Cu_max-Cu_min);\n",
"wt_theta=(Cu_eq-Cu_min)/(Cu_max-Cu_min);\n",
"V_a=wt_a/rho_al;\n",
"V_theta=wt_theta/rho_theta;\n",
"f=V_theta/(V_a+V_theta);\n",
"r=(3*f*lambda1)/(4*(1-f));\n",
"\n",
"#result\n",
"print('\\nParticle Spacing = %g m\\nParticle Size = %g m')%(lambda1,r);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 6.3, Fiber Strengthing, Page No. 222"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Ec for 10 vol% = 92 GPa\n",
"\n",
"\n",
"Ec for 60 vol% = 252 GPa\n",
"\n"
]
}
],
"source": [
"#variable declaration\n",
"Ef=380;\n",
"Em=60;\n",
"\n",
"#calculation\n",
"#Case 1\n",
"f_f1=0.1;\n",
"Ec1=Ef*f_f1+(1-f_f1)*Em;\n",
"\n",
"#Case 2\n",
"f_f2=0.6;\n",
"Ec2=Ef*f_f2+(1-f_f2)*Em;\n",
"\n",
"#result\n",
"print('\\nEc for 10 vol%% = %g GPa\\n')%(Ec1);\n",
"print('\\nEc for 60 vol%% = %g GPa\\n')%(Ec2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 6.4, Load Transfer, Page No. 225"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"sigma_cu = 2.55 GPa for L=100um\n",
"\n",
"sigma_cu = 0.596875 GPa for L=2mm\n"
]
}
],
"source": [
"#variable declaration\n",
"sigma_fu=5;\n",
"sigma_fu=sigma_fu*10**9; #Conversion to Pa\n",
"sigma_m=100;\n",
"sigma_m=sigma_m*10**6; #Conversion to Pa\n",
"T0=80;\n",
"T0=T0*10**6; #Conversion to Pa\n",
"f_f=0.5;\n",
"d=100;\n",
"d=d*10**-6;\n",
"B=0.5;\n",
"L1=10;\n",
"L1=L1*10**2; #conversion to m\n",
"Lc=sigma_fu*d/(2*T0);\n",
"sigma_cu1=sigma_fu*f_f*(1-Lc/(2*L1))+sigma_m*(1-f_f);\n",
"sigma_cu1=sigma_cu1*10**-9;\n",
"print('\\nsigma_cu = %g GPa for L=100um\\n')%(sigma_cu1);\n",
"\n",
"L2=2;\n",
"L2=L2*10**-3; #conversion to m\n",
"sigma_cu2=sigma_fu*f_f*(1-Lc/(2*L2))+sigma_m*(1-f_f);\n",
"sigma_cu2=sigma_cu2*10**-9;\n",
"print('sigma_cu = %g GPa for L=2mm')%(sigma_cu2);"
]
}
],
"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
}
|
