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"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 15:Composite Materials"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.1 Page 552"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"v_f = 40.0 # volume percent of fibre in composite\n",
"E_f= 69.0 # Modulus of elasticity of fibre in GPa\n",
"v_m = 60.0 # volume percent of matrix in composite\n",
"E_m = 3.4# Modulus of elasticity of matrix in GPa\n",
"a = 250.0 # cross sectional area in mm^2\n",
"sigma = 50.0 # Tensile stress in MPa\n",
"Fm = 1.0 # let\n",
"Ff = 13.5*Fm \n",
"\n",
"#calculation\n",
"#Part A\n",
"E_cl = (v_f*E_f+v_m*E_m)/100.0\n",
"\n",
"#result\n",
"print\"\\n Modulus of elasticity of composite is %0.0f GPa\" %E_cl\n",
"\n",
"# Part B\"\n",
"Fc = a*sigma\n",
"Fm = Fc/(Fm+Ff) \n",
"Ff = Fc - Fm\n",
"\n",
"#result\n",
"print\" Force supported by m is %d\" %Fm, \"N Force supported by fibre is %d N\" %Ff\n",
"print \"Answer in book is as Fm = 860 N and Ff = 11640. It is due to approximation\"\n",
"\n",
"# Part C\n",
"a_m = v_m*a/100\n",
"a_f = v_f*a/100\n",
"sigma_m = Fm/a_m\n",
"sigma_f = Ff/a_f\n",
"epsilon_m = sigma_m/(E_m*1000)\n",
"epsilon_f = sigma_f/(E_f*1000)\n",
"\n",
"#result\n",
"print \"Strain for matrix phase is %0.2e\" %epsilon_m\n",
"print \" Strain for fibre phase is %.2e. Both are identical\" %epsilon_f"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Modulus of elasticity of composite is 30 GPa\n",
" Force supported by m is 862 N Force supported by fibre is 11637 N\n",
"Answer in book is as Fm = 860 N and Ff = 11640. It is due to approximation\n",
"Strain for matrix phase is 1.69e-03\n",
" Strain for fibre phase is 1.69e-03. Both are identical\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.2 Page 553"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"import math\n",
"E_gf=69 # Elasticity of glass fibre in GPa \n",
"mf_gf=0.4 #Volume percentage of glass fibre\n",
"E_pr=3.4 # Elasticity of polyester resin in GPa\n",
"mf_pr=0.6 #Vol percentage of polyester resin\n",
"\n",
"#calculation\n",
"E_ct=E_pr*E_gf/((E_pr*mf_gf)+(E_gf*mf_pr)) # Calculation of modulus of elasticity in GPa\n",
"\n",
"#result\n",
"print\"In transverse direction, modulus of elasticity is %.1f GPa.\" %E_ct"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"In transverse direction, modulus of elasticity is 5.5 GPa.\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Design Problem 15.1 Page 563"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from math import pi\n",
"F = 1000.0 # Force in N\n",
"L = 1.0 # length in m\n",
"del_y = 0.35 # extension in mm\n",
"d_o = 70 # Outer diameter in mm\n",
"d_i = 50 # Innrer diameter in mm\n",
"V_f_max = 0.6 # Maximum allowable fiber Volume in cm fraction \n",
"Vf_glass = 0.945 # V_f for glass\n",
"Vf_C_standard = 0.293# V_f for carbon standard modulus\n",
"Vf_c_intermediate = 0.237# V_f for carbon intermediate modulus\n",
"Vf_c_high = 0.168 # V_f for carbon high modulus\n",
"d_epoxy = 1.14 # density of epoxy resin in g/cm^3\n",
"d_C_sm = 1.8 # density of carbon fiber (Standard modulus) in g/cm^3\n",
"d_C_im = 1.8 # density of carbon fiber (intermediate modulus) in g/cm^3\n",
"d_C_hm = 1.8 # density of carbon fiber (high modulus) in g/cm^3\n",
"C_im_cost = 70.00 # cost of carbon fiber (intermediate modulus) in USD/kg \n",
"C_sm_cost = 35.00 # cost of carbon fiber (Standard modulus) in USD/kg \n",
"C_hm_cost = 175.00 # cost of carbon fiber (high modulus) in USD/kg \n",
"d_epoxy = 1.14 # density of epoxy resin in g/cm^3\n",
"epoxy_cost = 9.00 # cost of epoxy resin in USD/kg \n",
"\n",
"#calculation\n",
"I = pi/64* (1e-12*(d_o*1e-3)**4-(d_i*1e-3)**4)\n",
"E = 4*F*L**3/(3*pi*del_y*1e-3*((d_o*1e-3)**4-(d_i*1e-3)**4)) # Required modulus of elasticity\n",
"#parta\n",
"\n",
"if Vf_glass < V_f_max :\n",
" print \"Glass, when embedded in epoxy matrix, meet the stipulated criteria. \"\n",
" \n",
" \n",
"if Vf_C_standard < V_f_max :\n",
" print \" Carbon (standard modulus), when embedded in epoxy matrix, meet the stipulated criteria. \"\n",
" \n",
"\n",
"if Vf_c_intermediate < V_f_max :\n",
" print\" Carbon (intermediate modulus), when embedded in epoxy matrix, meet the stipulated criteria. \"\n",
" \n",
"\n",
"if Vf_c_high < V_f_max :\n",
" print\" Carbon (high modulus), when embedded in epoxy matrix, meet the stipulated criteria.\"\n",
" \n",
"#partb\n",
"Vc = pi*L*1e-6*(d_o**2 - d_i**2)/4\n",
"F_v_C_sm = Vc*Vf_C_standard*1e6 # Fiber Volume in cm^3 for carbon (Standard modulus)\n",
"F_m_C_sm = F_v_C_sm * d_C_sm/1000 # Fiber mass for carbon (Standard modulus) in kg\n",
"F_c_C_sm = F_m_C_sm * C_sm_cost # Fiber cost for carbon (Standard modulus) in USD\n",
"m_v_C_sm = Vc*(1-Vf_C_standard)*1e6 # Matrix Volume in cm^3 for carbon (Standard modulus)\n",
"m_m_C_sm = m_v_C_sm * d_epoxy/1000 # Matrix mass for carbon (Standard modulus) in kg\n",
"m_c_C_sm = m_m_C_sm * epoxy_cost # Matrix cost for carbon (Standard modulus) in USD\n",
"Total_c_C_sm = m_c_C_sm + F_c_C_sm # Total cost for carbon (Standard modulus) in USD\n",
"F_v_C_im = Vc*Vf_c_intermediate*1e6 # Fiber Volume in cm^3 for carbon (intermediate modulus)\n",
"F_m_C_im = F_v_C_im * d_C_im/1000 # Fiber mass for carbon (intermediate modulus) in kg\n",
"F_c_C_im = F_m_C_im * C_im_cost# Fiber cost for carbon (intermediate modulus) in USD\n",
"m_v_C_im = Vc*(1-Vf_c_intermediate)*1e6 # Matrix Volume in cm^3 for carbon (intermediate modulus)\n",
"m_m_C_im = m_v_C_im * d_epoxy/1000 # Matrix mass for carbon (intermediate modulus) in kg\n",
"m_c_C_im = m_m_C_im * epoxy_cost # Matrix cost for carbon (intermediate modulus) in USD\n",
"Total_c_C_im = m_c_C_im + F_c_C_im # Total cost for carbon (intermediate modulus) in USD\n",
"F_v_C_hm = Vc*Vf_c_high*1e6 # Fiber Volume in cm^3 for carbon (high modulus)\n",
"F_m_C_hm = F_v_C_hm * d_C_hm/1000 # Fiber mass for carbon (high modulus) in kg\n",
"F_c_C_hm = F_m_C_hm * C_hm_cost # Fiber cost for carbon (high modulus) in USD\n",
"m_v_C_hm = Vc*(1-Vf_c_high)*1e6 # Matrix Volume in cm^3 for carbon (high modulus)\n",
"m_m_C_hm = m_v_C_hm * d_epoxy/1000 # Matrix mass for carbon (high modulus) in kg\n",
"m_c_C_hm = m_m_C_hm * epoxy_cost # Matrix cost for carbon (high modulus) in USD\n",
"Total_c_C_hm = m_c_C_hm + F_c_C_hm # Total cost for carbon (high modulus) in USD\n",
"\n",
"#result\n",
"print\" Cost of Carbon (standard modulus) composite is:%.2f \" %Total_c_C_sm # whereas Value in table is 48.50 USD\n",
"print\" Cost of Carbon (intermediate modulus) composite is:%.2f \" %Total_c_C_im# whereas Value in table is 71.10 USD\n",
"print\" Cost of Carbon (high modulus) composite is:%.2f \" %Total_c_C_hm # whereas Value in table is 115.00 USD\n",
"print\" The material of choice (i.e. least expensive) is standard modulus carbon fiber composite; the relatively low cost per unit mass of this fiber offsets its relatively low modulus of elasticity and required high Volume fraction.\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Carbon (standard modulus), when embedded in epoxy matrix, meet the stipulated criteria. \n",
" Carbon (intermediate modulus), when embedded in epoxy matrix, meet the stipulated criteria. \n",
" Carbon (high modulus), when embedded in epoxy matrix, meet the stipulated criteria.\n",
" Cost of Carbon (standard modulus) composite is:48.47 \n",
" Cost of Carbon (intermediate modulus) composite is:71.04 \n",
" Cost of Carbon (high modulus) composite is:115.84 \n",
" The material of choice (i.e. least expensive) is standard modulus carbon fiber composite; the relatively low cost per unit mass of this fiber offsets its relatively low modulus of elasticity and required high Volume fraction.\n"
]
}
],
"prompt_number": 14
}
],
"metadata": {}
}
]
}