When a dislocation faces precipitations, two probabilities might take place:
1)dislocation cut through precipitation particles or,
2)dislocation leave a loop around precipitation particles.
We know that both of these mechanisms rises the strength and hardness of the alloy, but which of these have more influence?
Dear Nima Tabatabaei,
please see the attached figure (for a constant volume fraction) where maximum strength is obtained at rcritical , i.e., the transition from dislocation cutting to Orowan bowing.
a) Dislocation cutting through the particles or by Orowan bowing mechanism depends on the particle size regime (constancy of volume fraction: finer particles means smaller inter-particle spacing in a given volume and coarser particles growing at the expense of smaller ones means larger inter-particle spacing in the same volume). This means it depends whether the particle is deformable or non-deformable.
b) If the size (or radius r) of the particle is small, then cutting will dominate. At larger particle size (as r increases), Orowan bowing (or looping) will dominate.
c) (i) Basically, small particles are coherent and deformable, and dislocations cut through them. In this case, strength is weakly dependent on particle size.
(ii) For non deformable particles, dislocations bypass (Orowan bowing) over particles and strength is strongly dependent on particle size. Particle bypass (Orowan bowing) results in high density of dislocation loops, dipoles thus leading to higher work hardening rate and also strength is strongly dependent on particle size.
To summarise, cutting (under-aged) is dominated at smaller particle size regime (smaller radius r) and bowing (over-aged condition) at larger particle size regime ( r). Orowan bowing mechanism leads to higher work hardening rate and strength is dependent on r. For cutting, strength varies weakly with particle size.
Please see (may be useful):-
1) Chapter 8, Page 265 and Fig. 8.7:- in Book "Modern Physical Metallurgy and Materials Engineering", by R.E. Smallman, R. J. Bishop, Butterworth & Heinemann, 2nd Edition, 1963. Pls. see the book link if you have access :-
http://www.sim.utcluj.ro/stm/download/Alba/ModernPhysicalMetallurgy.pdf
(2) Chapter 5 in Book:- "Mechanical Behavior of Materials", Second Edition By Thomas H. Courtney
(3) Chapter 4.12 in book "Dislocations and mechanical behaviour of materials, M.N. Shetty, 2013
(4) Please see the link if you have access: https://ocw.mit.edu/courses/materials-science-and-engineering/3-40j-physical-metallurgy-fall-2009/lecture-notes/MIT3_40JF09_lec18.pdf
(5) wikipedia: https://en.wikipedia.org/wiki/Precipitation_hardening
(6) attached figure.
(7) RG link:
https://www.researchgate.net/publication/229318833_Dislocation_dynamics_simulations_of_precipitation_hardening_in_Ni-based_superalloys_with_high_g%27_volume_fraction
Answer to your query:- both the mechanisms, particle cutting and Orowan bowing increases the strength compared to no-particle condition. But the subject is very complex as it depends on various mechanisms such as chemical, stacking fault, modulus, order, coherency hardening. Please see Table 1 in the overview by Z. Guo and W. Sha, Materials Transactions (The Japan Institute of Metals) , Vol.43, 2002, pp. 1273-1282:- pls. see the link if you have access:- https://www.jim.or.jp/journal/e/pdf3/43/06/1273.pdf
Best wishes
Article Dislocation dynamics simulations of precipitation hardening ...
Dear Nima,
It depends. Normally dislocations opt for doing the easiest, that is, the option that requires less energy; namely:
- If the particles are very large, they usually opt for cutting through the precipitate
- If the particles are very small, they usually opt for circumvent the precipitate
That is why generally the peak hardening is achieved neither for very fine nor very coarse precipitate distributions (very small particles with very high number density or very large particles with very low number density), but for intermediate precipitate distributions, for which it requires as much energy for a dislocation to cut through the precipitate as for circumvent the precipitate.
Hope this is useful,
Jose
Dear Nima Tabatabaei,
please see the attached figure (for a constant volume fraction) where maximum strength is obtained at rcritical , i.e., the transition from dislocation cutting to Orowan bowing.
a) Dislocation cutting through the particles or by Orowan bowing mechanism depends on the particle size regime (constancy of volume fraction: finer particles means smaller inter-particle spacing in a given volume and coarser particles growing at the expense of smaller ones means larger inter-particle spacing in the same volume). This means it depends whether the particle is deformable or non-deformable.
b) If the size (or radius r) of the particle is small, then cutting will dominate. At larger particle size (as r increases), Orowan bowing (or looping) will dominate.
c) (i) Basically, small particles are coherent and deformable, and dislocations cut through them. In this case, strength is weakly dependent on particle size.
(ii) For non deformable particles, dislocations bypass (Orowan bowing) over particles and strength is strongly dependent on particle size. Particle bypass (Orowan bowing) results in high density of dislocation loops, dipoles thus leading to higher work hardening rate and also strength is strongly dependent on particle size.
To summarise, cutting (under-aged) is dominated at smaller particle size regime (smaller radius r) and bowing (over-aged condition) at larger particle size regime ( r). Orowan bowing mechanism leads to higher work hardening rate and strength is dependent on r. For cutting, strength varies weakly with particle size.
Please see (may be useful):-
1) Chapter 8, Page 265 and Fig. 8.7:- in Book "Modern Physical Metallurgy and Materials Engineering", by R.E. Smallman, R. J. Bishop, Butterworth & Heinemann, 2nd Edition, 1963. Pls. see the book link if you have access :-
http://www.sim.utcluj.ro/stm/download/Alba/ModernPhysicalMetallurgy.pdf
(2) Chapter 5 in Book:- "Mechanical Behavior of Materials", Second Edition By Thomas H. Courtney
(3) Chapter 4.12 in book "Dislocations and mechanical behaviour of materials, M.N. Shetty, 2013
(4) Please see the link if you have access: https://ocw.mit.edu/courses/materials-science-and-engineering/3-40j-physical-metallurgy-fall-2009/lecture-notes/MIT3_40JF09_lec18.pdf
(5) wikipedia: https://en.wikipedia.org/wiki/Precipitation_hardening
(6) attached figure.
(7) RG link:
https://www.researchgate.net/publication/229318833_Dislocation_dynamics_simulations_of_precipitation_hardening_in_Ni-based_superalloys_with_high_g%27_volume_fraction
Answer to your query:- both the mechanisms, particle cutting and Orowan bowing increases the strength compared to no-particle condition. But the subject is very complex as it depends on various mechanisms such as chemical, stacking fault, modulus, order, coherency hardening. Please see Table 1 in the overview by Z. Guo and W. Sha, Materials Transactions (The Japan Institute of Metals) , Vol.43, 2002, pp. 1273-1282:- pls. see the link if you have access:- https://www.jim.or.jp/journal/e/pdf3/43/06/1273.pdf
Best wishes
Article Dislocation dynamics simulations of precipitation hardening ...
According to the literature, the solidification of the materials is due to more of the dislocation cut through precipitation particles.
Pease see also Overview No. 130 "Size effects in materials due to microstructural and dimensional constraints: a comparative review", E. Artz, Acta Materialia, Volume 46, Issue 16, 9 October 1998, Pages 5611–5626. Please see the link if you have access:-
http://www.sciencedirect.com/science/article/pii/S1359645498002316
Dear Joseph Ahn,
I clarify your doubt that dislocation cutting dominates at smaller particle size (r < rcritical) and at larger particle size (r > rcritical), Orowan bowing dominates. The stress for cutting is directly proportional to r, whereas for Orowan bowing, stress is proportional to (1/r). Please see the Figure that was attached in my detailed answer given before.
However, my suggestion is that please go through the references that were given during my earlier answer to this question.
Phaniraj
The following book reference may help: J.W. Martin, "Micromechanisms in particle-hardened alloys", Cambridge University Press, 1980.
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