Single crystal yield criterion for chromium based on atomistic studies of isolated 1/2[111] screw dislocations


The processes responsible for the plasticity of close-packed metals and deformation of body-centered cubic (BCC) and their dilute alloys are generally different. Over the past decades, numerous studies, both theoretically and experimentally, have been conducted to elucidate the origin of the differences. In particular, the fact that a ½ (100) screw dislocations are generally non-polar and exhibit at least three-fold rotational symmetry has been attracting the attention of researchers in many fields. A systematic approach for developing interatomic potentials for BCC metals, especially chromium, remains one of the most outstanding problems in crystallography. Attempts to solve this problem have run into difficulty because the magnetic ground state of chromium is characterized by longitudinal spin density waves with wavevectors parallel to spins and (100) direction. Moreover, little is known about the plastic deformation of chromium despite its practical implications.

Previous studies showed that the chromium samples deform at different temperatures and exhibit slips, twinning, and cleavage along different planes. Nanoindentation methods have been recently proposed to study the incipient plasticity of Cr and its underlying mechanisms at low and high temperatures. This has led to the advancement of the bond-order potential for chromium to correctly cover the covalent and metallic characters of bonds as well as the effects of electrons on the bonds. However, a clear understanding of the underlying mechanism governing the plastic deformation of a single chromium crystal at low temperatures remains elusive.

To address this challenge, Professor Roman Gröger from the Czech Academy of Sciences, together with Professor Vaclav Vitek from the University of Pennsylvania, investigated the mobility of the isolated ½(111) screw dislocations under stress at 0 K. The study aimed at bridging the existing gap in the theoretical understanding of plasticity in Cr single crystals by developing a single crystal yield criterion for Cr. Their research work is currently published in the International Journal of Plasticity.

In their approach, the recently developed Bond Order Potential for Cr was used to study the single crystal yield criterion for chromium based on atomistic simulations. The mobility of the isolated screw dislocation was investigated under pure shear stress parallel to the slip direction, under uniaxial load applied in tension and compression, and under a combination of shear stresses parallel and perpendicular to the slip direction. Also, the dependence of the critical resolved shear stress (CRSS) on the orientation of the maximum resolved shear stress plane (MRSSP) was explored. Based on the atomistic simulation results, the authors developed a single crystal yield criterion for chromium, taking into account the non-Schmid contributions and Peierls stress.

The results showed that the dependence of CRSS on the orientation of MRSSP exhibited significant twinning- antitwinning asymmetry. For most MRSSP orientations, the dislocation moved by a single slip on the low-stressed plane due to pure stress parallel to the slip direction, whereas MRSSP close to one of the two (112) planes resulted in the change in the slip plane. The observed differences were mainly attributed to the pronounced and different core transformations in Cr under applied shear stresses. The resulting yield criterion was capable of reproducing the twinning-antitwinning asymmetry of the CRSS with orientations of the MRSSP. Furthermore, it was used to predict the most operative slip systems in both tension and compression, including the shape of the yield surface and regular Tresca’s hexagon produced by the Schmid law.

In summary, the study reported the successful development of a single crystal yield criterion for chromium based on the atomistic studies of the isolated ½(111) screw dislocations. The resulting criterion can quantify the character and magnitude of the compression-tension asymmetry of the uniaxial load in all directions. The Gröger-Vitek study gives more insights into chromium’s structural properties that may contribute to the development of high-performance chromium-based materials.


Gröger, R., & Vitek, V. (2020). Single crystal yield criterion for chromium based on atomistic studies of isolated 1/2[111] screw dislocationsInternational Journal of Plasticity, 132, 102733.

Go To International Journal of Plasticity

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