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Discussion of fracture paper #41 - Are dislocations good or bad guys? It depends!
Shifting from macroscopic to microscopic plasticity helps us understand mechanisms that can help us develop high-strength metallic materials. Things that prevent dislocation dynamics or generation, such as other dislocations and grain boundaries in polycrystalline materials, lead to higher strength.
The interesting and well-written paper
"Dislocation penetration in basal-to-prismatic slip transfer in Mg: A fracture mechanics criterion" by Ryosuke Matsumoto in Engineering Fracture Mechanics, vol. 306, 2024, https://doi.org/10.1016/j.engfracmech.2024.110250,
analyses the penetration behaviour of pileup dislocations using molecular dynamics. The author guides us through different stages of dislocations that attack grain boundaries.
The reviewer especially likes the analogy connection to mode II cracks and Takeo Yokobori's analysis from the 1950's. A good reference for basic mathematics is found in Some basic problems in the theory of elasticity by N Muskhelishvili in Russian from 1933 and English from 1954. The solution for a dislocation becomes a tiny cut where one end has a positive square root singular stress tensile stress and at the other end a negative ditto and a displacement discontinuity, i.e. the image of a single atomic layer inserted in an edge crack. Square root singularities do not decay as fast as the 1/r singularity but the negative singularity at one end of the cut and a positive singularity at the other end cancels the square root part and leaves a dominating 1/r singularity, as we recognise as the dislocation far field. The arrangement was used by many of us because it provided a length scale that advised us of the distance related to the short-range interaction between dislocations.
It would be interesting to hear from anyone who would like to discuss or provide comments or thoughts, regarding the subject, the method, or anything related. Perhaps the author can cast some light on future actions regarding the subject. If anyone wishes to comment and does not have an iMechanica account, please register to be able to file a comment. Many applications are rejected for reasons that are not revealed and nor understood by me. If it happens to you, please email me at per.stahle@solid.lth.se and I will post your comments in your name. The paper is available with open access.
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Per Ståhle
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Comments
Thank you for highlighting my
Thank you for highlighting my recent paper in the official blog of ESIS and iMechanica. I also acknowledge the introduction of the stress field around an edge dislocation from the theory of elasticity.
In the paper, I treated a series of dislocation penetration at a grain boundary by MD simulation and fracture mechanics by replacing a dislocation pile-up as a mode II crack. The treatment is based on energy criteria, i.e. the energy release rate is larger than the materials resistance related to the formation energy of a step in GB at the penetration.
The theory agreed with the MD results quite well. On the other hand, some researchers treated the dislocation penetration through the dislocation bow-out mechanism from GBs, and shear stress and the distance between both ends of bow-out dislocation were used for the condition.
I have interests in the applicability of the energy criterion to other GBs and more general cases. Also, how energy and stress criteria should be treated in dislocation penetration at GBs.
Ryosuke Matsumoto