In addition, longer staying time dislocation width over v also allows more interacting time and enhanced viscous drag and hence less obvious under-damped motion or even over-damped motion see Ta screw in Fig.
Another extremity is that, when dislocation velocity v approaches to the transverse sound speed c t , the energy radiation increases dramatically, as shown by Gao et al. Although inertia still exists, dislocation motion is expected to be dominated by damping again, even at low temperature and without electron drag. It is also worth noting that, as seen in the spatial distribution of the potential energy in Fig.
The significant contraction was also considered to be one of the reasons that a subsonic dislocation can hardly go transonic in real systems, since transonic dislocations have much wider cores 56 , Dislocation motion is driven by shear stress, not normal stress, and can release only shear strain. Here we show an example of negative mechanical response in normal loading, namely tensile stress in compression.
A periodic inclined sample is created by a novel trimming method. A small inclination angle of 1 degree is adopted, and both the dislocation line direction and sample lateral direction are set periodic. After absorption, the stress increases linearly again. When the stress becomes positive again, the energy gain also increases again.
Simulations using the MEAM potential 34 , 35 also show similar results. The stress profiles are also examined in normal loading. The stress profiles at different stress levels are found to be quite homogeneous. Since the stress state is uniaxial, the resolved shear stress is also negative and the dislocation indeed holds positive velocities at these negative stresses.
This observation is not a coincidence. For a given sample, the maximum distance a dislocation can travel is geometrically determined. Thus in Eq. In structural elements, negative-stiffness does exist buckled column and pre-stressed springs and is always connected to instabilities Elastic composites containing negative-stiffness phase can even be stable In solids, phase change can lead to negative-stiffness 59 too.
Similarly, plasticity and fracture in solids can also be considered as instabilities, and negative-stiffness e. It is concluded that, via atomistic simulations, under-damped inertial motion of dislocation does exist in the absence of phonon drag and electron drag, and the nature of dislocation motion is both inertial and dissipative.
The inertia originates from the kinetic energy imparted from strain energy and stored in the core during motion. The simulations are performed at low temperature, in order to mimic the super-conducting state. This condition allows for uncovering of explicit under-damped oscillatory motion of dislocations at both low and high velocities. The only dissipative process present here is the phonon radiation from dislocation core.
Besides, effects of electrons are also present in states other than supper-conducting state, making the inertia effects even less significant in most real circumstances. Nevertheless, the demonstrated inertia phenomenon and its underlying physics revealed here are still of great generality and significance. When dislocation moves at high velocities, such as in high rate deformation and shocks 4 , 13 , 49 , inertial effects, whether explicitly visible or not, have to be taken into consideration.
Treating dislocations as quasi-static might introduce unphysical artifacts in these conditions The kinetic energy associated with dislocation motion might make dislocation activities, such as cross-slip, dislocation-obstacle interactions and so on, energetically more active.
New physical understanding of the relevant phenomena work-hardening, dynamic recovery, fatigue and so on and even novel phenomena might arise. It is recently reported that 61 , a dislocation moving at a high velocity towards a free surface, got bounced back surprisingly, instead of being absorbed. In the perspective of dislocation inertia, this phenomenon is inevitable: the surface can absorb the configuration potential energy, but can only rebound not absorb the high particle velocities of the incident dislocation, which in turn re-creates a dislocation carrying the same amount of kinetic energy traveling in the opposite direction.
Under some circumstances, motion of high-velocity dislocations was reported to transition to rough and twinning modes and produce debris and twin embryo The kinetic energy carried by the dislocation might also play an important role in these processes. Finally, as inspired by the discovery of the negative mechanical response demonstrated in Fig. Orowan, E. Physik 89 , — Article Google Scholar. Taylor, G. The mechanism of plastic deformation of crystals.
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Dynamic transitions from smooth to rough to twinning in dislocation motion. Nature Mater. Download references. You can also search for this author in PubMed Google Scholar. Correspondence to Yizhe Tang. Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Reprints and Permissions. Uncovering the inertia of dislocation motion and negative mechanical response in crystals. Sci Rep 8, Download citation. Received : 06 July Accepted : 08 December Published : 09 January Anyone you share the following link with will be able to read this content:.
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Skip to main content Thank you for visiting nature. Download PDF. Subjects Atomistic models Mechanical properties. Figure 1. Full size image. Results Mechanics of dislocation motion Crystals, when subject to external loading, deform elastically first until the stress reaches a critical level, the Peierls stress, and then dislocations start to move.
Figure 2. Full size table. Figure 3. Figure 4. Figure 5. Figure 6. Figure 7. Figure 8. Figure 9. Figure Discussion and Conclusions It is concluded that, via atomistic simulations, under-damped inertial motion of dislocation does exist in the absence of phonon drag and electron drag, and the nature of dislocation motion is both inertial and dissipative.
The repulsively oriented forest screws, rather than obstructing the motion of an incoming screw dislocation, glide collectively at no additional applied stress. The present work shows that the interaction zone is limited to a very small region of the interacting dislocations. These results deeply change the concept of internal stresses, at least in bcc metals or materials where the kink-pair mechanism govern dislocation motion. In 2-D models it is generally assumed that moving dislocations are subjected to a uniform stress along their line, and that this stress oscillates in the direction of motion.
This strongly increases the average dislocation velocity in comparison with classical models, not only for the driven dislocations studied in this article, but also for all dislocations.
We also obtain the surprising result that the dislocation velocity tends to increase with increasing internal stress, i. Depending on the loading state, the number of active repulsive dislocation pairs varies and is highest for the [] orientation, explaining the observed extended work hardening behaviour of tungsten. This strain-softening effect compensates for other classical strain-hardening ones and may also accounts for a lower global strain-hardening of bcc metals.
These effects must be taken into account in macroscopic models like CP. The relevance for the coupled motion increases with dislocation density, as the density of possible pairs increases too. For very high dislocation densities, the internal stresses fluctuate over short distances, thus triggering possibly the coupled motion. Therefore this may also lead to the enhanced ductility observed for heavily cold rolled tungsten 38 , 39 , 40 , The DDD model used to simulate the screw dislocation motion is described in Srivastava et al.
The mobility of the screw dislocation is governed by an Arrhenius law and accounts for the influence of the entire stress tensor on the activation energy of screw dislocations 30 as against a pure shear stress based formulation in literature 43 , 44 , The model effectively takes into account changes in the dislocation core structure due to the applied stress by including non-Schmid terms in the activation enthalpy.
In the DDD model the effective kink-pair nucleation rate for the screw dislocation section is calculated on all three possible glide planes for a screw dislocation. In principle, a screw dislocation may glide on different glide planes and therefore split into distinct sectors depending on the local stress state. This is not the case for the current setups. For all non-screw orientations phonon drag limited glide is assumed as for fcc metals.
The dislocations are labelled as I and II depending on their respective role. Dislocation I is mobile due to the externally applied loading and drives dislocation II, once a critical minimal distance is reached. Both dislocations have screw orientation. In order to be repulsively oriented, the line direction of dislocation I is chosen parallel to its Burgers vector, while for dislocation II the line direction is antiparallel to its Burgers vector.
During further simulation the externally applied load is kept constant. The Schmid factors on dislocation I respectively II are 0.
The minimum activation enthalpy of kink-pair nucleation of dislocation II occurs at the position of nearest approach where the total interaction is strongest. The velocity of dislocation II is dominated by the kink pairs nucleated in the interaction zone which then spread out along the dislocation line. As mentioned in the main part, the overall direction of the Peach—Koehler force would drive both the dislocation in a similar direction. Therefore once, kink pairs are nucleated, the stress level on the dislocation line outside the interaction zone drives these pairs along the dislocation line.
This used velocity law implicitly assumes also that kink collision is unlikely 18 , 30 , For dislocation II this is obviously true, as the zone of interaction, where the kink-pair nucleation rate is drastically increased, is extremely small and both kinks will glide easily to the opposite sides of this zone. Outside this zone of interaction nearest approach , kink-pair nucleation is very unlikely and therefore this assumption justified.
For dislocation I the length dependency of the mobility law is supported by observations on Fe at room temperature Coupled motion occurs only if both dislocations remain in their initial habit plane, therefore the question of cross slip has to be addressed: cross slip occurs only if the activation energy of glide for screw dislocation is minimum on a plane other than the habit plane.
Supplementary Fig. Supplementary Figure 3b shows that the corresponding activation enthalpy for the driven dislocation II in the interaction zone is reduced significantly below the activation enthalpy of the driving dislocation I because it needs to nucleate all its kinks in the short interaction zone. Rectangular microsamples were cut in a single crystal of high-purity tungsten described in Then, they were glued on a copper grid fixed on the holder.
The Burgers vectors were determined by the classical extinction rules using several diffraction conditions, and the slip planes were deduced from the directions and separation distances of the slip traces left by the moving dislocations at the two surfaces.
The local direction of the tensile axis can slightly deviate from the imposed one by several degrees in the foil plane. However, it can be determined with a pretty good accuracy in samples with rounded holes and containing no cracks, on the basis of finite element calculations. Local Schmid factors can then be determined with an accuracy of a few percent. The local shear-stress intensity can be deduced from the critical widths of expanding screw dipoles, using elasticity models.
After determining the dipole plane on the basis of the slip trace direction at its emergence point noted tr. The observations confirm that the coupling is a mechanism present in crystal structures, where screw dislocation have to overcome a barrier by the kink-pair mechanism in order to glide.
The datasets generated during or analyzed during the current study are available from the corresponding author on reasonable request. Access to the code will be provided at the host institution of the corresponding author upon reasonable request. The occurrence of the coupling mechanism does not depend on code details.
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Correspondence to D. Peer review information Nature Communications thanks Brady Butler and the other anonymous reviewer s for their contribution to the peer review of this work.
Peer reviewer reports are available. Reprints and Permissions. Repulsion leads to coupled dislocation motion and extended work hardening in bcc metals. Nat Commun 11, Download citation. Received : 07 February Accepted : 14 September Published : 09 October Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative.
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. Advanced search. Skip to main content Thank you for visiting nature. Download PDF. Subjects Materials science Mechanical properties Metals and alloys Theory and computation.
Abstract Work hardening in bcc single crystals at low homologous temperature shows a strong orientation-dependent hardening for high symmetry loading, which is not captured by classical dislocation density based models.
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