Understanding Precipitate Shape Factors in Material Science
Explore the complex factors influencing precipitate shape in material science, including definitions, growth mechanisms, and effects on Gibbs energy dissipation. Learn about shape parameters, interface modifications, and evolution equations affecting precipitate growth.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Precipitate shape factors (MatCalc 5.61.0027) P. Warczok
Outline Introduction, definition Precipitate growth Precipitation strengthening
Introduction Usual assumption: spherical precipitates i k i k 4 = + + + 3 2 4 G N c Precipitate/matrix interface contribution 3 , 0 , 0 , , i i k k k i k i k k Matrix contribution Precipitate contribution k kc, k - Mechanical contribution of k G - Gibbs energy of the system i 0 k - element N, 0 k - i content in k - Number of i moles in the matrix i i - matrix - Chemical potential of I in k - Chemical potential of i in the matrix k, i i , 0 - precipitate class - Interfacial energy of k - Radius of k Svoboda et. al., Mater. Sci. Eng. A., 385 (2004) 166-174
Definition Shape parameter Spherical cylindrical Cylinder aspect ratio Discs (oblate) = / h H D Needles h H D - Shape parameter (prolate) - Cylinder height - Cylinder diameter Kozeschnik et. al., Mater. Sci. Eng. A., 441 (2006) 68-72
Effects Shape modification interface area changed i k i k 4 = + + + 3 2 4 G N c S 3 , 0 , 0 , , i i k k k i k i k k k For h = 1 Sk= 1.1447 ! 3 / 2 = 3816 . 0 + 3 / 1 h 7631 . 0 Sk h Kozeschnik et. al., Mater. Sci. Eng. A., 441 (2006) 68-72
Effects Influence on Gibbs energy dissipation contributions Q 2 2 4 Interface k = k k Q K 3 / 1 = 5824 . 0 + 3 / 2 h 2912 . 0 Kk h 1 k IF k M migration 5 2 4 RT c k Precipitate , = k k i Q I / 2 = 6453 . 0 + 3 / 4 h 3 4239 . 0 Ik h 2 k 45 c D diffusion , , k i k i ( ( ) ) 2 D + 3 4 / 3 RT c c c Matrix k , , 0 , = k k k c i i k k i Q O Ok= 3 / 2 h 0692 . 1 3 k diffusion i , 0 , 0 i i Kozeschnik et. al., Mater. Sci. Eng. A., 441 (2006) 68-72
Precipitate growth Evolution equations affected i k i k 4 = + + + 3 2 4 G N c S 3 , 0 , 0 , , i i k k k i k i k k k 1 G Q = i q 2 2 4 2 q k = k k Q K i 1 k IF k M 5 2 4 RT c = + + Q Q Q Q k , = k k i Q I 1 2 3 2 k 45 c D , , k i k i ( ( ) ) , q c 2 D + 3 4 / 3 RT c c c k , , 0 , = k k k c i i k k i , i k k i Q O 3 k i , 0 , 0 i i
Precipitate growth Shape factors do not influence the precipitate nucleation stage in MatCalc !!!
Precipitate growth Growth rates (Anisotropy effects neglected!) Minimal diffusion distances for disc growth Kozeschnik et. al., Mater. Sci. Eng. A., 441 (2006) 68-72
Precipitation strengthening Surface-surface precipitate distance - Shear stress ( ) r Orowan - Shear stress for Orowan mechanism 1 ~ Lp f - Shear stress for shearable precipitates shear ( ) L r - Distance between the precipitates Orowan 1 ~ L ln R p p eq - Precipitate radius ( )m eq r R eq r - Outer cut-off radius eq shear L1 ~ p - Equivalent radius Sonderegger B., Kozeschnik E., Scripta Mater., 66 (2012) 52-55
Precipitation strengthening Surface-surface precipitate distance ( ) r f Lp ~ 1 L = KL p sph / 1 4 + 2 2 h = / 1 6 K h 3 - Shear stress L - Distance between the precipitates p L - Distance between the spherical precipitates Sonderegger B., Kozeschnik E., Scripta Mater., 66 (2012) 52-55 sph
Precipitation strengthening Equivalent radius - Shearable precipitate ( ) eq r eq r - Equivalent radius for edge disl. L1 ~ f , edge p sph r - Sphere radius for edge disl. , edge = + r edge P edge r screw P screw r eq r eq - Equivalent radius for screw disl. , screw sph r 2 3 3 6 h - Sphere radius for screw disl. , = + screw 2 r r , , eq edge sph edge + + 2 2 3 2 1 5 h h edge P - Fraction of edge disl. 2 3 1 h 2 h screw P = + - Fraction of screw disl. 2 r r , , eq screw sph screw + 2 3 1 h Ahmadi M.R. et al., Mater. Sci. Eng. A, 590 (2014) 262-266
Precipitation strengthening Equivalent radius - Shearable precipitate ( ) eq r L1 ~ f p = + r edge P edge r screw P screw r eq 2 3 3 6 h = + 2 r r , , eq edge sph edge + + 2 2 3 2 1 5 h h 2 3 1 h 2 h = + 2 r r , , eq screw sph screw + 2 3 1 h Ahmadi M.R. et al., Mater. Sci. Eng. A, 590 (2014) 262-266
Precipitation strengthening Outer cut-off radius Orowan mechanism ( eq p R f L1 ~ ) R - Equivalent radius for edge disl. , eq edge R - Sphere radius for edge disl. , sph edge = + R edge P R screw P screw R eq edge R - Equivalent radius for screw disl. , eq screw 2 3 2 3 3 h 3 h R - Sphere radius for screw disl. = + + R R , sph screw , , eq edge sph edge + + 2 2 2 3 2 2 h h edge P - Fraction of edge disl. 2 3 2 1 h 1 h 9 h = + + screw P R R - Fraction of screw disl. , , eq screw sph screw + 2 2 3 2 h Ahmadi M.R. et al., Mater. Sci. Eng. A, 590 (2014) 262-266
Precipitation strengthening Outer cut-off radius Orowan mechanism ( eq p R f L1 ~ ) = + R edge P R screw P screw R eq edge 2 3 2 3 3 h 3 h = + + R R , , eq edge sph edge + + 2 2 2 3 2 2 h h 2 3 2 1 h 1 h 9 h = + + R R , , eq screw sph screw + 2 2 3 2 h Ahmadi M.R. et al., Mater. Sci. Eng. A, 590 (2014) 262-266
Precipitation strengthening Dislocation characterization = + r edge P edge r screw P screw r eq = + R edge P R screw P screw R eq edge
