clc clear close all %% LOADING CONDITION %% t = 30; %% MATERIAL PARAMETERS %% A = 3*10^-10; sigma_cr = 47*10^6; R = 8.314; i = 0; j = 0; k = 0; for stress = 0.2*sigma_cr:10^4:sigma_cr; i = i+1; for Temp = 300:0.5:600; j = j+1; % power-law exponent n n = 3.1943019-0.002283*Temp; % fit activition energy using bilinear interpolation if Temp<=548 Q = 123*10^3; end if Temp>548 && Temp<=558 if stress<=0.45*sigma_cr Q = 123*10^3; end if stress>0.45*sigma_cr && stress<=0.6*sigma_cr a = 123-(stress/sigma_cr-0.45)/0.15*3; Q = (123-(Temp-548)/10*(123-a))*10^3; end if stress>0.6*sigma_cr a = 120-(stress/sigma_cr-0.6)/0.1*4; Q = (123-(Temp-548)/10*(123-a))*10^3; end end if Temp>558 if stress<=0.3*sigma_cr Q = 123*10^3; end if stress>0.3*sigma_cr && stress<=0.45*sigma_cr a = 123-(stress/sigma_cr-0.3)/0.15*4; Q = (123-(Temp-558)/15*(123-a))*10^3; end if stress>0.45*sigma_cr && stress<=0.6*sigma_cr a = 119-(stress/sigma_cr-0.45)/0.15*5; b = 123-(stress/sigma_cr-0.45)/0.15*3; Q = (b-(Temp-558)/15*(b-a))*10^3; end if stress>0.6*sigma_cr a = 114-(stress/sigma_cr-0.6)/0.1*8; b = 120-(stress/sigma_cr-0.6)/0.1*4; Q = (b-(Temp-558)/15*(b-a))*10^3; end end x(i,j) = Temp; y(i,j) = stress; eps_ss = A*stress^n*exp(-Q/(R*Temp)); Q1(i,j) = Q; if Temp<=523 slope = 0.00687.*523.^2-7.2317.*523+1877.184; end if Temp>523 slope = 0.00687.*Temp.^2-7.2317.*Temp+1877.184; end % elastic modulus E_ave = -1.2148*10^7.*Temp+8.5038*10^9; E = slope.*(stress-0.51*sigma_cr)+E_ave; eps_elastic = stress/E; % transient constant if Temp<=548 C = 10^(6.6184)*(stress/10^6)^(-2.1575); end if Temp>548 T1 = 548; a = -3.8947+(573-Temp)/(573-T1)*1.7372; b = 8.3528-(573-Temp)/(573-T1)*1.7344; C = 10^(b)*(stress/10^6)^(a); end % transient strain eps_t = ((1.022*10^-9*exp(0.0227*Temp))*exp((0.00689*exp(0.00487*Temp))*(stress/10^6))); % plastic strain calcualte by power-law model eps_plastic = eps_t*(1-exp(-C*eps_ss*t))+eps_ss*t; % total creep strain (polymer matrix) eps(i,j) = eps_elastic+eps_plastic; eps_matrix = eps_elastic+eps_plastic; % total creep strain (carbon fiber) E_fiber = 15.4*10^9; eps_fiber = stress/E_fiber; % total creep strain (composite) eps_composite(i,j) = 0.4*eps_matrix+0.6*eps_fiber; % total plastic strain (composite) trial = 0.4*eps_plastic; if trial>0.00199 && trial<0.002 k = k+1; x1(k) = Temp; design(k) = stress/1.25; end end j = 0; end %% TRANSIENT MAP AND DESIGN SPACE %% temp = [400 600]; ultimate = [37.6 37.6]; %ultimate tensile strength of composite figure v = [10^-3 2*10^-3 4*10^-3 6*10^-3 8*10^-3 10^-2 2*10^-2 4*10^-2 6*10^-2 8*10^-2 10^-1]; c = contour(x,y/10^6,eps,v); clabel(c) hold on plot(x1,design/10^6,'k','LineWidth',2) hold on plot(temp,ultimate,'--k','LineWidth',2) xlabel('Temperature (K)') ylabel('Stress (MPa)') axis([400 580 10 40]) text(430,38.5,'ultimate tensile strength in transverse fiber direction') title('T650-35/PMR-15 in transverse fiber direction, for a time of 30 seconds') %% DESIGN STRESS %% figure plot((x1-273.15)*9/5+32,design/10^6,'LineWidth',2) xlabel('Temperature (F)') ylabel('Design Stress \sigma_D (MPa)')