As we know the lowest theoretical limit for dislocation density is zero i.e. perfect crystal. Similarly, if we have a very very large dislocation density, the material is no longer in a crystalline state. Therefore there must exist a higher limit for dislocation density.
Dear Haydar,
We refer Dieter book extensively, but I have not found anywhere about this limit. Can you please mention a specific chapter or page number?
Regards
Sainath
Hi Sainath,
dislocation density has its own limits which depends on many factors. Few of this factors can be only calculated, so we probably can´t expect the exact value. Try to study this article, I think it could be helpful for you:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1018.2797&rep=rep1&type=pdf
Dear Haydar
Dislocation density in materials depends on such factors as technology of reception, temperature and machining. Precisely to define density difficultly (studying on TЕМ is required).
The density of dislocations changes over a wide range and depends on a material condition. After annealing the density of dislocations makes 105 … 107 м-2, in crystals with strongly deformed crystal lattice the density of dislocations reaches 1015 … 10 16 m-2.
In agreement with most of the above comments the max dislocation density depends on material, composition, temperature etc. In theory it is limited by the increasing rate of dislocation annihilation as the dislocation spacing is reduced to small distances at high densities. It is therefore controlled by the ease of dislocation cross slip which, in turn, depends on stacking fault energy, temperature and solute content: low SFEs and low deformation temperatures can enable high dislocation densities to be attained. To give some typical order of magnitudes, low SFE metals (e.g.austenitic stainless steels) strongly deformed at low temperatures can develop dislocation densities of around 10 exp 17 to18 m-2 but Al alloys deformed at high temperatures are limited to densities of about 10 exp14 m-2 .
Thank you all for your enlightening answers. For the same question, I found the following paper by Cotterill very interesting. You can have a look. Article Does dislocation density have a natural limit?
Dear Haydar,
Dislocation density also depend on the strain rate. For example, it can reach 10^16 m^-2 for very high strain rate in molecular dynamics, of the order of 10^8-10^9 s-1. Experimentally and for the same material, it not exceed the 10^12-10^13 m^-2 with strain rate 10^3 s-1.
Dear Selim,
This large difference in dislocation density is mainly because in experiments (TEM) reveal only ex-situ (post-mortem) density whereas MD simulations provides in-situ (during straining) density. Several mechanisms of density relaxation (recovery) comes into play after straining, and thus the ex-situ density (experiments) is much lower than the in-situ density (obtained in MD).
Dear G. Sainath,
Most posts refer to experimental data for the crystalline materials. For this case, I really like the answer of prof. J.H. Driver (Professor, I send you greetings from Krakow).
However, if I understand your question well, it rather concerns the problem for what dislocation density the material loses the long range order and cannot be treated as the crystal. I am afraid that it is difficult to find a sharp general border between the crystalline state and the amphous one. It should depend on the model of the amorphous material structure. Some models can be found in the literature (eq. X. Yue, et al. Mat. Res. 20, 2017, http://dx.doi.org/10.1590/1980-5373-mr-2016-0318).
It may be helpful to refer to description of the material microstructure/structure. For the crystalline body, the disclinations (related mainly to some grain boundaries) can be neglected, and the microstructure description using dislocations is sufficient; for the amorphous one the disclination based description is necessary. So, range of the critical dislocation density can be related to change in the way necessarily for the description.
By the way, for the structures of metallic glasses it was proposed approach which is based on a continuous three‐dimensional network of disclinations containing the dislocation subnetwork (R.C. Morris, J. Appl. Phys., 50, 1979, 3250).
Yours
Mirek
- Badges
- Science topic
- Similar topics
- Chemistry, Organic
- Organic