tailieunhanh - Kinetics of Materials - R. Balluff_ S. Allen_ W. Carter (Wiley_ 2005) Episode 10

Tham khảo tài liệu 'kinetics of materials - r. balluff_ s. allen_ w. carter (wiley_ 2005) episode 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 390 CHAPTER 16 MORPHOLOGICAL EVOLUTION DIFFUSIONAL CREEP AND SINTERING Figure Force-balance diagram for a body with capillary forces and applied load Fapp. The plane cuts the body normal to the applied force. There are two contributions from the body itself. One is the projection of the surface capillary force per unit length 7s onto the normal direction and integrated over the bounding curve. The second is the normal stress ơnn integrated over the cross-sectional area in the case of fluids bounded by a surface of uniform curvature K . ơnn 7sK3 4 . The constant A is determined from the force balance in Eq. pR-b CỊ Fapp 2 r crnn r rdr 277Rb s cos Ỡ Using Young s force-balance equation Eq. . u Ĩ A 7s 2 cos 0 sin I -T-c 2 y 2 s J at the grain boundary surface intersection and the elongation rate Eq. becomes dL _ Qaỏ DbA _ 8ÍÌAỖ DB dt kT TtRịkT app 1 bamboo s I Í r bamboo 7 7 Fb I 21 1 I I Rbfa I y 27s When the grain boundaries are not spaced too closely the quantity Tbamboo is generally negative because Rbn 1 is less than 2ựl - 7s 27s 2 and 7s 27s RS 1 6 for metals. T the capillary shrinkage force arises from a balance between reductions of surface and grain-boundary area. If Fapp is adjusted so that the elongation rate goes to zero Fapp Tbamboo and this provides an experimental method to determine 7s 7s and thus 7s if V is measured. This is known as the Udin-Schaler-Wulff zero-creep method 6 . Scaling arguments can be used to estimate elongation behavior. Because K and 1 Rb will scale with TĩLỊVg and the grain volume Vg is constant Eq. implies that . dL r2 ex L dt d app 7 MORPHOLOGICAL EVOLUTION FOR SIMPLE GEOMETRIES 391 where Tbamboo iĩ sRb is replaced by a term that depends on L alone. Elongation proceeds according to5 1 1 A F ị L t ữ L t J appt r _L - J L. . I msv1 2t Ạl L t y L t 0 J 7 9 Evolution of a Bundle of Parallel Wires via Grain-Boundary Diffusion For the boundary of width 2w in Fig.