Critical Resolved Shear Stress For Slip Research Articles

Critical resolved shear stress for twinning and twinning-induced plasticity in single crystals of the CoCrFeNiMo0.2 high-entropy alloy

The effect of alloying with Mo atoms 4 at.% on the twinning deformation, critical resolved shear stresses (CRSS) for slip τcrsl and twinning τcrtw and plasticity was studied in [1‾11]-, [1‾44]- and [001]- oriented crystals of the Co24Cr24Fe24Ni24Mo4 (at.%) high-entropy alloy (HEA) under tension at 296 and 77 K. The stacking fault energy of the Co24Cr24Fe24Ni24Mo4 HEA, measured in the present paper on the triple dislocation nodes, is equal to 0.027 J/m2. It is shown that initial yield behavior along studied orientations is governed by dislocation slip and the CRSS for slip are independent of crystal orientation. Under tensile strain, twinning develops in the [1‾11]- and [1‾44]- oriented crystals only at 77 K and is not detected in the [001]-oriented crystals. Two types of twins are found in the [1‾11]- and [1‾44]-oriented crystals (thin nanotwins and macrotwins). Nanotwins develop after a low slip deformation of 5–10% and are observed only by transmission electron microscopy. Macrotwins are detected after a significant slip deformation of 20 and 60% and are determined metallographically and X-ray by the precession of the crystal axis, respectively, in the [1‾11]- and [1‾44]-oriented crystals. In the [1‾11]- oriented crystals, there is no precession of the crystal axis due to the development of slip simultaneously in several systems. It is shown that CRSS for nano- and macrotwins are dependent on the crystal orientation. In the [1‾44]-oriented crystals, τcrtw = 212 MPa for nanotwinning and τcrtw = 400 MPa for macrotwinning. In the [1‾11]-oriented crystals, τcrtw = 250 MPa for nanotwinning and τcrtw = 335 MPa for macrotwinning. For the transition to deformation by macrotwinning, it is necessary that the effective stacking fault energy γef is approaching to zero and the condition τcrtw <τcrsl is satisfied. Deformation by macrotwinning suppresses slip multiplicity and shifts the formation of the neck formation according to the Considère condition to higher stress levels. This increases plasticity from 72% at 296 K to 108% at 77 K in [1‾44]-oriented crystals and from 48% at 296 K to 57% at 77 K in [1‾11]-oriented crystals.

Plastic deformation of single crystals of CrB2, TiB2 and ZrB2 with the hexagonal AlB2 structure

The plastic deformation behavior of single crystals of three transition-metal diborides with the AlB2 structure, CrB2, TiB2 and ZrB2 has been investigated as a function of crystal orientation in the temperature range from room temperature to 1500 °C. Plastic flow is observed above 800 °C by the operation of slip on {11¯00}<112¯3> in CrB2, while in ZrB2, the onset temperature for slip on {11¯00}<112¯3> is 700 °C and that for slip on (0001)<112¯0> is 800 °C. In contrast, any appreciable plastic flow is not observed in TiB2 at 1500 °C and below. The critical resolved shear stress (CRSS) for slip on {11¯00}<112¯3> in CrB2 monotonously decreases with increasing temperature up to 1500 °C. On the other hand, the CRSS for slip on {11¯00}<112¯3> in ZrB2 decreases with increasing temperature up to 1000 °C and then increases anomalously with increasing temperature. Similarly, the CRSS for slip on (0001)<112¯0> in ZrB2 decreases with increasing temperature up to 1200 °C and then increases anomalously with increasing temperature, followed again by the decrease above 1400 °C. Generalized stacking fault (GSF) energy calculations well explain slip direction on the relevant slip plane, dislocation dissociation scheme and relative ease of slip among the three transition-metal diborides. The existence of planar growth faults on prism planes in CrB2 and TiB2 significantly affects the plastic deformation behavior so that the high onset temperature for plastic flow for these two diborides cannot be predicted solely by GSF energy calculations.

Critical resolved shear stress for slip and twin nucleation in single crystalline FeNiCoCrMn high entropy alloy

High entropy alloys is an emerging class of materials with superior mechanical properties down to cryogenic temperatures. At 77K, and unlike traditional metallic alloys, an increase in strength, strain hardening rate, and ductility has been reported. This enhancement in properties has been attributed to the activation of twinning as an additional deformation mechanism at low deformation temperatures. The tendency for the formation of twinning and the hardening response dependence on crystal orientation has not been fully explored. This study is dedicated to explore the deformation evolution across several crystal orientations for the equiatomic FeNiCoCrMn high entropy alloy at room temperature (RT) and 77K. The works aims to establish the critical resolved shear stresses (CRSS) for slip and twinning and study the orientation and temperature dependence in these magnitudes. The experimental results have revealed a strong temperature dependence in the CRSS for slip, increasing from 56MPa at RT to 153MPa at 77K, with negligible orientation dependence. At 77K, not all crystal orientations developed twinning even at high levels of deformation. The lack of twinning has been attributed to differences in the hardening response resulting in low stress levels below the twinning CRSS of 153MPa, as established in this work. No twinning was observed in any of the crystal orientations deformed at room temperature, regardless of the level of hardening and the achieved stresses. Overall, the results discussed in this work enhances our understanding of the local deformation response in single crystalline FeNiCoCrMn high entropy alloy, particularly the nucleation of slip, nucleation of twinning, and the effect of crystal orientation and loading temperature on these deformation mechanisms.

Classification of the critical resolved shear stress in the hexagonal-close-packed materials by atomic simulation: Application to α-zirconium and α-titanium

We have studied the hierarchy of the activation of dislocation glide in zirconium and titanium alloys and presented experimental results in zirconium alloys. We have compared the experimental results with simulations obtained by two different approaches. The first is by using the stacking fault energy maps (γ surfaces) obtained by molecular dynamics (MD) and by ab initio approaches. A good agreement was observed between the two approaches and with recent published work. The second is to compare the experimental critical resolved shear stresses (CRSS) with those determined by MD simulations based on embedded atom method (EAM) potentials. The CRSS for slip in the -direction for the basal, prismatic (type 1) and pyramidal (type 2) planes for edge dislocations are obtained. Finally, we discuss the hierarchy of the glide systems with the energy criterion of the γ surfaces and with the CRSS values and we compare with both experimental and modeling data.

Twinning in nanocrystalline metals

Twinning is a commonly observed deformation mode in lowsymmetry crystals such as hexagonal-close packed metals, but not in high-symmetry metals that possess many possible slip systems with lower critical resolved shear stress (CRSS) than the twinning stress. However, if the CRSS for slip can be increased to a level greater than the twinning stress, then twinning may be favored as a deformation mechanism even in cubic materials. Nanostructured metals present such a scenario. Following the observation of deformation twinning in nano-crystalline metals, even in high stacking fault energy metals such as aluminum, recently there has been signifi cant interest in studying twinning as a deformation mode in nanocrystalline face-centered cubic (fcc) metals. Another important breakthrough is the fabrication of fcc metals with nanotwinned structures using methods such as electro-deposition or sputter deposition. Nanoscale growth twins have also been observed in nanowires. Nanotwinned fcc metals made via sputtering can have twin boundary spacing as small as 2–4 nm and preferential alignment of {111} twin boundaries normal to the growth direction. These as-grown nanotwinned structures exhibit unusual properties as compared to nanocrystalline metals. Typically, in the equiaxed grain nanocrystalline metals with high-angle grain boundaries the increased strength is accompanied by a loss in ductility, thermal stability, and electrical conductivity. Twinning in Nanocrystalline Metals

Coefficient of thermal expansion anisotropy and texture effects in ultra-thin titanium sheet

Several measurements have been made for the coefficient of thermal expansion (COTE) of titanium in both single crystal and polycrystalline samples. The most commonly observed preferred crystallographic orientation of cold-rolled Ti has been presented by Clark and others to be a 209 to 40{degree} tilt of the c-axis in both transverse directions. This rolling texture is common among HCP metals with a c/a ratio lower than the ideal, and it results from the two most common slip systems active in Ti at room temperature. These were first reported by Anderson, Jillson, and Dunbar, who found that the critical resolved shear stress (CRSS) for slip in the {l_angle}11{bar 2}0{r_angle} direction on the (0002) basal plane is 110 MPa, and the CRSS for slip in the {l_angle}11{bar 2}0{r_angle} direction on the {l_brace}10{bar 1}0{r_brace} first order prism planes is 50 MPa. Thus the Ti unit cell is oriented for easiest slip when it lies in a position near the CRSS maximum for the first order prism plane slip system, while still permitting cross slip on the basal plane.

An analysis of constrained deformation by slip and twinning in hexagonal close packed metals and alloys

A procedure for predicting the isostrain behavior of hcp metals and alloys which deform by basal, prism, and pyramidal slip as well as twinning is developed. This procedure assumes that deformation will occur on four slip systems and one or more twinning system(s). Stress states are derived for the simultaneous operation of all combinations of four slip systems for allc/a ratios as well as all values of the three critical-resolved shear stresses for slip. A numerical procedure for obtaining the remaining kinemati-cally required deformation by twinning is outlined for the case of impure titanium.