Abstract
Understanding long range internal stresses (LRIS) may be crucial for elucidating the basis of the Bauschinger effect, plastic deformation in fatigued metals, and plastic deformation in general. Few studies have evaluated LRIS using convergent beam electron diffraction (CBED) in cyclically deformed single crystals oriented in single slip and there are no such studies carried out on cyclically deformed single crystals in multiple slip. In our earlier and recent study, we assessed the LRIS in a cyclically deformed copper single crystal in multiple slip via measuring the maximum dislocation dipole heights. Nearly equal maximum dipole heights in the high dislocation density walls and low dislocation density channels suggested a uniform stress state across the labyrinth microstructure. Here, we evaluate the LRIS by determining the lattice parameter in the channels and walls of the labyrinth dislocation structure using CBED. Findings of this work show that lattice parameters obtained were almost equal near the walls and within the channels. Thus, a homogenous stress state within the heterogeneous dislocation microstructure is again suggested. Although the changes in the lattice parameter in the channels are minimal (less than 10−4 nm), CBED chi-squared analysis suggests that the difference between the lattice parameter values of the cyclically deformed and unstrained copper are slightly higher in the proximity of the walls in comparison with the channel interior. These values are less than 6.5% of the applied stress. It can be concluded that the dominant characteristics of the Bauschinger effect may need to include the Orowan-Sleeswyk mechanism type of explanation since both the maximum dipole height measurements and the lattice parameter assessment through CBED analysis suggest a homogenous stress state. This work complements our earlier work that determined LRIS based on dipole heights by assessing LRIS through a different methodology, carried out on a cyclically deformed copper single crystal oriented for multiple slip.
Highlights
The concept of long range internal stresses (LRIS) in metals refers to the deviation of local stress from the applied stress that occurs over relatively long length scales such as that of the spacing of dislocation heterogeneities (e.g. labyrinth microstructure [1], persistent slip bands (PSB) walls, cell walls, subgrain boundaries, etc).LRIS may have been initially discussed in connection with the Bauschinger effect [2]
We evaluated the lattice parameters using convergent beam electron diffraction (CBED) in the channels and close to the walls of the labyrinth microstructure of a cyclically deformed copper single crystal oriented in multiple slip which complements the dipole study of our earlier work [1]
The of zone axis has been shown to be highly sensitive to changes in strain of face centered The zone axis has been shown to be highly sensitive to changes in strain of face centered cubic cubic (FCC) crystals [31]
Summary
The concept of LRIS in metals refers to the deviation of local stress from the applied stress that occurs over relatively long length scales such as that of the spacing of dislocation heterogeneities (e.g. labyrinth microstructure [1], persistent slip bands (PSB) walls, cell walls, subgrain boundaries, etc).LRIS may have been initially discussed in connection with the Bauschinger effect [2]. Crystals 2020, 10, 1071 yielding occurs at a much lower (absolute value) stress than if the material continued monotonic deformation. This effect is referred to as the Bauschinger effect and is contrary to what is expected based on isotropic hardening. When a metal is cyclically deformed, the lost strength due to the Bauschinger effect occurs with each reversal of the applied stress. This results in low hardening rates and saturation stresses compared to the (monotonic) fracture stress [3]. The two prominent theories are Mughrabi’s composite model [5], which proposed relatively high values of LRIS, and the Orowan-type mechanism [6], which involves no internal stresses
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