% % notch fatigue factor efficiency % % Peterson: q =(Kf-1)/(Kt-1) = 1/(1+rhostar/rho) % % clear figure rhonorm=logspace(-2,3,20); q = 1./(1+ 1./rhonorm); semilogx(rhonorm,q,'-b'); xlabel(' \rho / \rho^{P}'); ylabel(' q \equiv ( K_f - 1 ) / ( K_t - 1 )'); title('Normalized notch fatigue factor, K_f'); hold on text(3.,.5,'\rho : notch root radius'); text(3.,.4,'\rho^{P} : Peterson material "blocksize" '); text(3.,.3,'\rho^{P} \cong \rho_0 (\sigma_0/UTS)^{1.8} (wrought steels)'); text(5.,.2,'\rho_0 = .001 in = 25.4 \mu m;'); text(5.,.1,'\sigma_0 = 300 ksi = 2070 MPa'); text(.02,.9,'K_f : notch fatigue factor'); text(.02,.8,'K_t : theoretical (elastic)'); text(.04,.75,'stress concentration factor'); hold off % % draw figure of K_f and K_t vs rhonorm figure Kt=3 Kf = 1 + q.*(Kt-1); semilogx(rhonorm,Kf,'-b'); [m,n]=size(q) kfmax=ones(m,n)*Kt; kfmin=ones(m,n); axis([.01,1000.,0,Kt+1]); xlabel('\rho / \rho^{P} = ( \rho /\rho_0 ) * ( UTS / \sigma_0 )^{1.8}'); ylabel('K_f'); hold on semilogx(rhonorm,kfmax,'-.r'); semilogx(rhonorm,kfmin,'-.r'); text(.02,3.2,'\bf{Example}: K_t = 3; \rho=0.05 in; UTS = 100 ksi'); UTS = 100; % 100 ksi notchrho=0.05 ;% IN INCHES Rpeterson= .001* (300/UTS)^(1.8);% in inches xspot=notchrho/Rpeterson yspot=1+(Kt-1)*(1/(1+1/xspot)) plot(xspot,yspot,'*r'); stringer=sprintf('K_f =%g',yspot); stringer2=sprintf('%g inches is Peterson blocksize',Rpeterson); text(.1,2.5,stringer); text(.1,2.8,'\rho^{P} = .00722 in.'); text(3.,2.3,'\rho : notch root radius'); text(3.,2.0,'\rho^{P} : Peterson material "blocksize" '); text(3.,1.7,'\rho^{P} \cong \rho_0 (\sigma_0/UTS)^{1.8} (wrought steels)'); text(5.,0.8,'\rho_0 = .001 in = 25.4 \mu m;'); text(5.,0.5,'\sigma_0 = 300 ksi = 2070 MPa'); hold off figure rbya=linspace(1,7,100); sconc_circ=1 + 1.5*rbya.^(-4)+ 0.5*rbya.^(-2); plot(rbya,sconc_circ); axis([1,7,0,4]); xlabel(' r / a '); ylabel(' \sigma_{yy}(x=a+r, 0) / \sigma^{\infty}'); text(2,3.5,'Stress concentration near circular hole'); text(1.2,3,'\bf{Maximum stress concentration: K_t = 3}') text(2.5,2,'\sigma_{yy}(x=a+r, y=0) = \sigma^{\infty} [ 1 + 1.5 (a/r)^4 + 0.5 (a/r)^2]');