COMPUTATIONAL MATERIALS ENGINEERING Episode 5 pot

... basic cellular automata. 110 COMPUTATIONAL MATERIALS ENGINEERING Particle Dimple Boundary Grain B Grain A r ρ y o θ γ BP γ AP (a) 55 50 45 40 35 30 25 10 15 20 25 30 40 35 X Z Hellman and Hillert ... [2] Static Monte Carlo θ θ = 45 (b) Boundary Detaches 1 .5 0 .5 -0 .5 -1 .5 1 -1 -2 0 Force/πγY -0 .5 0 .5 1 .5 2 .51 20-1 s/r (c) Theory kT′ = 1 kT′ = 2 kT′ = 3 FIGURE...

Ngày tải lên: 13/08/2014, 08:21

... kT s =0. 75, the isotropic case, (b) R A = R B =1 .5, kT s =0. 75, (c) R A >R B ,R A =1,R B =0.67, kT s =0. 75, (d) R A = R B =0 .5, kT s =0, (e) R A >R B ,R A =1 .5, R B =1, kT s =0. 75, (f) R A = ... function, and kT s =0. 75. 74 COMPUTATIONAL MATERIALS ENGINEERING FIGURE 3-21 Potts model simulation carried out on a square lattice, using Glauber dynamics and kT s =0. 75. The s...

Ngày tải lên: 13/08/2014, 08:21

... vector. As a 286 COMPUTATIONAL MATERIALS ENGINEERING and for the stress field, σ 13 = − b 3 2π  C 44 C 55 − C 2 45  1/2  C 45 x 1 − C 55 x 2 C 44 x 2 1 − 2 C 45 x 1 x 2 + C 55 x 2 2  σ 23 = ... C 55 x 2 C 44 x 2 1 − 2 C 45 x 1 x 2 + C 55 x 2 2  σ 23 = − b 3 2π  C 44 C 55 − C 2 45  1/2  C 44 x 1 − C 45 x 2 C 44 x 2 1 − 2 C 45 x 1 x 2 + C 55 x 2 2  (8.1...

Ngày tải lên: 13/08/2014, 08:21

... grid 200 CA simulations 250 ´ 250 grid 200 CA simulations 250 ´ 250 grid 100 CA simulations 250 ´ 250 grid 10 CA simulations 250 ´ 250 grid 1 CA simulation FIGURE 4- 15 Application of ... neighborhood and state transformation function. 120 COMPUTATIONAL MATERIALS ENGINEERING 0 250 50 0 750 1000 1 1000 CA Increment Number of Grains 0 5 10 15 20 Normal...

Ngày tải lên: 13/08/2014, 08:21

... species. Fick published his result in 1 855 [Fic 55] and accordingly, for the one-dimensional case with the spatial coordinate r,wehave J = −D ∂c ∂r (5. 15) Equation (5. 15) is known as Fick’s first law. ... (10 3 K -1 ) T (C) -32 -28 -24 -20 -16 -12 -8 -4 0 0 0 .5 1 .5 2.0 3.0 3 .51 .0 2 .5 Al Mo W Ni Fe Cu 1000 300 200 10 050 03000 Log( ) X eq Va FIGURE 5- 2 Equilibrium vacancy concen...

Ngày tải lên: 13/08/2014, 08:21

... semi-infinite boundary, that is, c(0,t)=c 0 (5. 35) x (Length) 0 0 .5 1.0 1 .5 2.0 -3 -2 -1 01 3 2 0.0 25 0. 05 0.1 0. 25 1 c(x)/M (Length −1 ) Dt = 0 FIGURE 5- 7 Solutions to Fick’s second law for a point ... of equations (5. 51) and (5. 54) shows that the thermodynamic factor φ in a binary system and in terms of mole fraction variables X i is φ A = X A RT  ∂µ A ∂X A − ∂µ A ∂X B  (...

Ngày tải lên: 13/08/2014, 08:21

... 0.3 0 .5 0.7 0.9 1.1 1.3 1 .5 1.7 1.9 0.0 0 .5 1.0 1 .5 2.0 2 .5 Normalized Precipitate Radius Normalized Number Density 3.0 C 0.1 0.3 0 .5 0.7 0.9 1.1 1.3 1 .5 1.7 1.9 0.0 0 .5 1.0 1 .5 2.0 2 .5 Normalized ... =  ρ 2 0 +4K 2 Dt (6 .57 ) where K can unfortunately only be given in implicit form as 2K 2 ·  1 − √ πKe K 2 erfc(K)  = S (6 .58 ) With the additional substitution Φ=2K 2...

Ngày tải lên: 13/08/2014, 08:21