notes for 382 exam - H5 If not told assume that the unit...

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H5 If not told assume that the unit volume is 1m^3 Dislocation density: 4*Vo/b^2=4*(ΔV/ (ρo/ρ-1)) Energy per unit length dislocation: U/Lb= (Gb^2)/2 ΔG αβ =ΔH αβ -T 1 ΔS αβ = ΔH αβ (1-T/Te) where S αβ = ΔH αβ /T e Q=-k*T*ln(6*h*v/(dΔH αβ *(1-T/Te))) h=Planck’s k=Boltzmann’s Time to recrystallize t r = A*exp(Q/(R*T)) ln(t r )=(Q/R)(1/T)+ln(A) y=m*x+b use t and T to find Q and A. First find A where A=a^q t r = A*exp(Q/(R*T r )) T r = annealing temperature ΔG αβ = -V* ΔG αβ +A* γ αβ ΔG αβ =ΔH αβ (1-T/Te) =4*π*(-1/3*ΔG αβ *r+ γ αβ )*r^2 ΔG αβ* dr | r=r0 = 4*π*(- ΔG αβ *r0+2 γ αβ )*r=0 r0=critical radius r0=2 αβ / ΔG αβ =2 γ αβ / ΔH αβ (1-T/Te) surface energy=4*π*r^2 γ αβ volume energy=-4/3*π*r^3*ΔG αβ total energy=-4/3*π*r^3*ΔG αβ+ 4*π*r^2 γ αβ number of molecules =4*π*6.022e23*ρ*r0^3/(3(X A (wt elementA )+Y B *( wt elementB ))) H7 W=work done loading= P*u, P=load, u=deflection (databook) U=stored strain energy=W/2 Energy release rate: G = (1/b)*d/da(W-U)=1/b*d/da(W/2)=1/b*d/db(P*u/2) l=a C=δ/P ΔC/Δa=(C 2 -C 1 )/(a 2 -a 1 )=(δ 2 1 )/(P 0 (a 2 -a 1 )) W-U=W/2=Pδ/2=P 2 C/2 Г= G=  (1/t)*d/da(W-U)=(1/t)*d/da(W/2)= P fracture 2 /(2t) (ΔC/Δa)=P fracture 2 /(2t)(δ 2 1 )/(P 0 (a 2 -a 1 )) K IC =sqrt(E*Г/(1-υ 2 )) Maximum force to supply on a beam before fracture. M=M(Length/2)=F/2(length/2)
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This note was uploaded on 10/20/2009 for the course EECS EECS314 taught by Professor Ganago during the Spring '09 term at University of Michigan.

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notes for 382 exam - H5 If not told assume that the unit...

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