Dislocations multiply by generating curvature density alongside dislocation density, which increases the line length on the glissile system and creates new, closed dislocation loops.
Here's a more detailed explanation:
Dislocation multiplication is a critical process in materials science as it explains how materials deform plastically far more than theoretically predicted based on the initial dislocation density. Several mechanisms contribute to this multiplication, but they all essentially involve the creation of new dislocation line length.
Here's a breakdown of the key mechanisms:
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Frank-Read Source: This is perhaps the most well-known mechanism. Imagine a dislocation line pinned at two points (A and B). As stress is applied, the segment between A and B bows out. With increasing stress, the bowed-out segment eventually forms a loop that pinches off, creating a new dislocation loop that can then move through the material, while the original dislocation segment reforms between the pinning points ready to repeat the process. This acts as a continuous source of dislocations.
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Cross-Slip: Screw dislocations can cross-slip onto different slip planes. This process can create jogs and kinks in the dislocation line. These jogs and kinks can then act as obstacles to further dislocation motion, leading to stress concentrations. Under sufficient stress, these stress concentrations can initiate new dislocations.
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Double Cross-Slip: A screw dislocation can undergo cross-slip, followed by another cross-slip back onto a plane parallel to the original slip plane. If the distance between the two slip planes is substantial, the segment connecting the two cross-slipped segments will form a dislocation dipole. The stresses associated with the dipole can be large enough to generate more dislocations in its vicinity.
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Dislocation Interactions: When dislocations encounter obstacles or other dislocations, they can become pinned or entangled. The stress concentrations near these pinned points can lead to the nucleation of new dislocations. Reactions between dislocations with different Burgers vectors can also create new dislocations.
In essence, dislocation multiplication is not simply about increasing the number of dislocations, but also about increasing the line length of dislocations within the material. The increased line length results in an increase in the dislocation density, which facilitates further plastic deformation. The creation of new closed dislocation loops is a key feature of this process. These loops expand under stress, contributing to the overall strain in the material.
