COMPUTATIONAL MATERIALS ENGINEERING Episode 13 potx

... traversing a closed circuit about the dislocation line 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 − ... computed by integration, equation (8 .136 ), and S T ij algebraically by equations (8.140)–(8.143) because it has a more complicated 296 COMPUTATIONAL MATERIALS ENGINE...

Ngày tải lên: 13/08/2014, 08:21

... are stable (due to the ratios of R A and R B ) grain growth can stop due to the 70 COMPUTATIONAL MATERIALS ENGINEERING the plots; this is due to the size of the domain initially increasing, corresponding ... no obvious faceting, nor is it shown in the migration of boundaries in general. 62 COMPUTATIONAL MATERIALS ENGINEERING FIGURE 3-19 The effect of anisotropic boundary energy on...

Ngày tải lên: 13/08/2014, 08:21

... kinetically prevented to evolve into a minimum free-energy 4 COMPUTATIONAL MATERIALS ENGINEERING do not evolve in the way living materials do. The use of the word evolution probably originated from ... Data Computational materials engineering: an introduction to microstructure evolution/editors Koenraad G. F. Janssens [et al.]. p. cm. Includes bibliographical references and index...

Ngày tải lên: 13/08/2014, 08:21

... alloy. 20 COMPUTATIONAL MATERIALS ENGINEERING 2.2.1 Entropy of Mixing In Section 2.1.4, the entropy S was formally introduced in the framework of reversible thermodynamics [equation (2 .13) ] and ... (ln X A − ln(1 − X A )) ∂ 2 ∆G ∂X A 2 = −Z ·ω + RT ·  1 X A + 1 1 − X A  (2.60) 24 COMPUTATIONAL MATERIALS ENGINEERING heat Q 1 =∆S · T a is transferred into the cooler heat reservo...

Ngày tải lên: 13/08/2014, 08:21

... Comprehensive Guide. Pergamon Materials Series, Pergamon, Oxford, 1998. [Wag52] C. Wagner. Thermodynamics of Alloys. Addison-Wesley Press, Reading, MA, 1952. 46 COMPUTATIONAL MATERIALS ENGINEERING corresponding ... 2.22; 6.00000E+03 N ! PARAMETER TC(BCC_A2,CR:C;0) 2.98150E+02 -311.5; 6.00000E+03 N ! 38 COMPUTATIONAL MATERIALS ENGINEERING FUNCTION 3-1: Basic Glauber Dynamics Usin...

Ngày tải lên: 13/08/2014, 08:21

... starting configuration for an isotropic grain growth simulation using the Potts model. 90 COMPUTATIONAL MATERIALS ENGINEERING Grain B D/2 DD/2 Grain A Grain C Grain B q 1 q 1 q 1 q 2 q 2 g 1 g 1 g 2 f 12 FIGURE ... cannot be resolved. That is, at some point, the last step is removed, the boundary 94 COMPUTATIONAL MATERIALS ENGINEERING = 500 ; Map1; Step = 3 ; Grid501 × 98 FIGURE 3...

Ngày tải lên: 13/08/2014, 08:21

... tabulated function. 114 COMPUTATIONAL MATERIALS ENGINEERING 4.4 +2D CA Modeling of Grain Growth One could argue that precise modeling of grain boundary surfaces, that is, making sure the computational ... neighborhood for one cell using the definition as given in the text is indicated. 130 COMPUTATIONAL MATERIALS ENGINEERING FIGURE 4-11 Figure 4-10 continued. Corrected (Probabil...

Ngày tải lên: 13/08/2014, 08:21

... small but finite time-step, which in the limiting case of an infinitesimally small 136 COMPUTATIONAL MATERIALS ENGINEERING C _ C 0 _ C 0 + C 1 Dt 1 2 1 0.8 0.6 0.4 0.4 0.2 0.2 0.4 0.6 0.8 ... V i with a concen- tration of solute atoms c i or a number of solute atoms n i . 138 COMPUTATIONAL MATERIALS ENGINEERING time step is the same as computing them concurrently. Both models...

Ngày tải lên: 13/08/2014, 08:21

... lattice frame of reference, a convenient measure when operating on the atomic scale. 170 COMPUTATIONAL MATERIALS ENGINEERING The solution to equation (5.24) with the constraint (5.32) is closely related ... movement of the markers is related to the difference in the diffusion coefficients. 168 COMPUTATIONAL MATERIALS ENGINEERING Equation (5.48) shows that the macroscopic diffusion coeffi...

Ngày tải lên: 13/08/2014, 08:21

... shape of the normalized size distribution is time invariant. In the representative 208 COMPUTATIONAL MATERIALS ENGINEERING The total energy change due to formation of this cluster is then ∆G =∆G bulk +∆G surf = 4 3 πρ 3 ∆G 0 bulk +4πρ 2 γ ... following sections, three approaches will be presented that solve the problem with 200 COMPUTATIONAL MATERIALS ENGINEERING Log(Cluster Size)...

Ngày tải lên: 13/08/2014, 08:21