Cross-slip Research Articles

Achieving high strength and ductility in nitrogen-doped refractory high-entropy alloys

Refractory high-entropy alloys (HEAs) usually exhibit high strength but limited ductility. Here, we report high strength (∼1334 MPa) and large ductility (∼18.8%) in nitrogen-doped TiZrNbTa HEAs. The microstructural evolution and the corresponding mechanical properties of the as-cast/annealed nitrogen-doped HEAs were investigated. All as-cast (TiZrNbTa)100-xNx (x = 0, 0.3, 0.6) HEAs exhibit a single-phase body-centred cubic structure. Interstitial strengthening contributes to the enhanced strength. The improved ductility of the 0.6 at.% nitrogen-doped HEA originates from the promoted planar dislocation slip inside grains. Spinodal decomposition and grain boundary (Zr, N)-enriched precipitates emerge when the nitrogen content is 0.9 at.%, which results in significant embrittlement. Isothermal annealing of the 0.6 at.% nitrogen-doped HEA at 800 °C to 1200 °C was conducted to further improve the mechanical performance. The complicated precipitates and grain boundary impurity segregation in the alloys annealed at 800 °C and 1200 °C lead to deteriorated strength and ductility. However, in the alloy annealed at 1000 °C, a slight increase in both strength and ductility appears due to solid solution strengthening, in situ grain refinement and promoted dislocation cross slip, which is induced by the coherent boundaries. This work provides a promising conduit to approach high strength and ductility in HEAs.

Effects of helium bubbles on deformation of aluminum matrix

Helium bubble influence on the deformation of aluminum is investigated via simultaneous electron backscatter diffraction and digital image correlation (DIC) during in situ tensile and compressive tests . The majority of helium is generated through the transmutation reaction 10 B(n, α ) 7 Li under neutron irradiation , which is carried out at 40 ∘ C to ∼ 0.3 dpa. The mesoscale deformation behaviors of aluminum matrix with and without helium bubbles are compared, and the interactions between helium bubbles and slip bands are analyzed. Helium bubbles along with other types of irradiation-induced defects (like dislocation loops and black dots) harden significantly the aluminum matrix around second-phase AlB 2 particles. Slip bands cannot penetrate the areas with high-density irradiation-induced defects. They bypass such areas through cross slip, exhibiting slip band deflection. Transmission electron microscopy on irradiated materials after deformation reveals abundant helium bubbles, dislocations, dislocation loops and black dots around AlB 2 particles, due to complex interactions between irradiation-induced defects with dislocations. Helium bubbles together with other types of irradiation-induced defects have pinning effects on dislocations, and pressurized helium bubbles may also punch out dislocation loops. The multiscale analyses demonstrate the helium bubble-dominated hardening.

Microstructures and high-temperature oxidation behavior of laser cladded NiCoCrAlYSi coating on Inconel 625 Ni-based superalloy modified via high current pulsed Electron beam

NiCoCrAlYSi coatings were prepared on the surface of nickel-based high-temperature alloys (Inconel 625) by laser cladding (LC) technique, and then the surface was modified by high current pulsed electron beam (HCPEB). The microstructural results indicate that metallurgical defects on the original surface, including micropores and elemental segregations were eliminated, and a remelted layer consisting of high density of cross slips and nanostructures was obtained. High-temperature oxidation resistance at 900 °C, 1000 °C and 1100 °C of the original coatings was investigated. When oxidized at 900 °C for 100 h, the original coating followed the linear growth law, and the TGO was mainly consisted of Al 2 O 3 . When oxidized at 1000 °C and 1100 °C for 100 h, the original coating followed the parabola law, and the TGO existed in a double-layer structure. After HCPEB irradiation, a rather stable, continuous, and slow-growing α-Al 2 O 3 was formed on the surface after oxidation for 100 h at 1100 °C. The kinetic curves show that the growth rate of the TGO of the irradiated coatings was reduced by 43.9%, and the thickness was effectively decreased compared with the original sample. Thus, HCPEB technique is proved to be an effective method to improve the service life of laser cladding coatings. • Microstructures and oxidation behavior of NiCoCrAlYSi laser cladding coating was investigated. • Cladding coatings presented different oxidation rate and growth behavior at different temperatures. • HCPEB technique was used to further improve the microstructures and properties of cladding coating. • Restructured surface promoted the formation of a protective α-Al 2 O 3 layer at 1100 °C. • HCPEB technology is an effective way to improve the high-temperature service life of cladding coatings.

Elastic and plastic anisotropy in a refractory high entropy alloy utilizing combinatorial instrumented indentation and electron backscatter diffraction

A comprehensive study was carried out to predict the elastic and plastic anisotropy of the non-equiatomic Mo15Nb35Ta35V5W10 Refractory High Entropy alloy (RHEA) using a high throughput combinatorial approach employing instrumented micro-indentation with electron backscatter diffraction (EBSD). The Levenberg–Marquardt optimization algorithm was utilized to determine elastic stiffness constant (C11= 267, C12= 115 and C44= 52 GPa) for accessing elastic anisotropy. The anisotropy in plastic deformation of<001>,<011> and<111> orientated grains can be attributed to the activation of the different {112}<111> slip system along with cross slip and the conservative movement of jogs on the screw dislocation. The spatial distribution of misorientation on <001>, <011> and <111> orientated grains as well as slip plane trace analysis, indicates that symmetry in misorientation pattern results from the flow of material along <111> slip direction on the indented surface. The results of the present investigation clearly indicate that the anisotropy in the elastoplastic behavior of novel RHEA is distinct from its constituent elements and that simple rule of mixtures is not sufficient to determine elastic modulus and lattice friction stress of RHEAs. Thus, high throughput experimental techniques are necessary to establish the structure-property linkages in novel multicomponent multi-principal RHEA compositions.

Development of mean-field continuum dislocation kinematics with junction reactions using de Rham currents and graph theory

An accurate description of the evolution of dislocation networks is an essential part of discrete and continuum dislocation dynamics models. These networks evolve by motion of the dislocation lines and by forming junctions between these lines via cross slip, annihilation and junction reactions. In this work, we introduce these dislocation reactions into continuum dislocation models using the theory of de Rham currents. We introduce dislocations on each slip system as potentially open lines whose boundaries are associated with junction points and, therefore, still create a network of collectively closed lines that satisfy the classical relations α=curlβp and divα=0 for the dislocation density tensor α and the plastic distortion βp. To ensure this, we leverage Frank’s second rule at the junction nodes and the concept of virtual dislocation segments. We introduce the junction point density as a new state variable that represents the distribution of junction points within the crystal containing the dislocation network. Adding this information requires knowledge of the global structure of the dislocation network, which we obtain from its representation as a graph. We derive transport relations for the dislocation line density on each slip system in the crystal, which now includes a term that corresponds to the motion of junction points. We also derive the transport relations for junction points, which include source terms that reflect the topology changes of the dislocation network due to junction formation.

A Continuum Dislocation Dynamics Crystal Plasticity Approach to Irradiated Body-Centered Cubic α-Iron

Abstract Radiation-induced embrittlement of reactor pressure vessel (RPV) steels can potentially limit the operating life of nuclear power plants. Over extended exposure to radiation doses, these body-centered cubic (BCC) irons demonstrate irradiation damage. Here, we present a continuum dislocation density (CDD) crystal plasticity model to capture the interaction among dislocations and self-interstitial atom (SIA) loops in α-iron. We demonstrate the importance of modeling cross slip using a combined stochastic Monte Carlo approach and the role of slip system strength anisotropy in capturing stochastic cross slip interactions. Through these captured interactions, the CDD crystal plasticity model can capture both the stress response and the physical evolution of dislocations on different slip system planes. Single-crystal verification experiments are used to calibrate the CDD crystal plasticity model, and a set of simplified polycrystalline simulations demonstrates the model’s ability to capture the stress response from tensile experiments on α-iron.

Fatigue deformation behavior of revert Ni-based superalloys via electron beam technology at low and middle temperature

In this work, we investigated the low-cycle-fatigue (LCF) at room temperature (RT) and 750 °C of 100% revert commercial polycrystalline Ni-based superalloy (K417) blade re-melted by electron beam technology (EBT). The fatigue life of EBR-K417 reaches 2324, 6840, and 6925 cycles at 750 °C during the LCF, which is substantially improved compared with the as-prepared K417 (1050 cycles). Surface or subsurface defects became primary fatigue sources instead of inclusions inside alloy in purified revert K417, which is suggested to be the main reason for prolonging the fatigue life. In addition, the results and analysis show that the dislocation movement in K417 alloy at room temperature (RT) is mainly through strong-coupled-dislocation (SCD) shearing mechanism, and its contribution to yield stress is 203 MPa. Whereas the dislocation migration mechanism at 750 °C is mainly bypassing and cross slip, whose contribution to yield stress is 156 MPa. The theoretic critical resolved shearing stress (CRSS) for temperature at RT and 750 °C are calculated as 249 MPa and 198 MPa, which are very close numerically with the experimental CRSS values, 230.4 MPa and 204.6 MPa.

Investigation on the deformation mechanisms and size-dependent hardening effect of He bubbles in 84 dpa neutron irradiated Inconel X-750

Microstructural characterization and calculation of how several intrinsic features contribute to the mechanical properties of highly strained Inconel X-750 alloy specimens irradiated to 84 dpa at two distinct temperature ranges (300 °C–330 °C and 120 °C–280 °C) were performed. The individual contributions of different microstructural features to the critical resolved shear stress (CRSS) of the material, including the γ matrix, γ′ precipitates, irradiation induced defects, and helium bubbles, were calculated. The obstacle strength of He bubbles was found to be size-dependent and a critical size was determined. For bubbles < 2.4 nm, the obstacle strength is only approximately 0.03 while it can be as high as 0.55 for bubbles > 6.6 nm. In the high temperature range (300–330 °C) irradiated specimen, localised dislocation slip was found responsible for the failure of the specimen during micro-tensile testing, associated with significant helium bubble elongation. Elongation of helium bubbles on both the primary and adjacent secondary {1 1 1} planes was likely induced by the cross slip of screw dislocations. Nanotwins were also found adjacent to the shear failure surface in the high temperature specimen, but no elongated bubbles were found within the nano-twinned region. In the low temperature range (120–280 °C) irradiated highly strained specimen, a dislocation network structure was revealed.

Mechanism of microstructure and texture evolution during shear loading of AA6063 alloys

The cyclic shear test of 6063 aluminum alloys under T4 and T6 conditions was carried out at room temperature. The microstructure and texture evolution were investigated using electron backscattered diffraction (EBSD) at several instances during cyclic shear deformation. Hardly any change in grain size was observed during the cyclic shear test of T4 and T6 samples. The local residual strain distribution measured in the form of average kernel misorientations (KAM) values increases continuously with an increase in shear strain for both samples. The increase in KAM value was higher for the T6 sample compared to the T4 sample during forward (F) shearing. On reversing the loading path, the increase in KAM value was higher for forward + reverse (FR) and forward + reverse + forward (FRF) straining of the T4 sample compared to the T6 sample. The cube texture was found to be unstable during shear deformation. A significant rotation of texture was observed in both T4 and T6 samples. However, the extent of rotation was slightly greater for the T6 sample as compared to the T4 sample. It was observed that the latent hardening of (1-11)<101>was more than (111)<1-01>in the T4 sample. Similarly, the latent hardening of (1-1-1)<011>was more than the (111)<1-01>in the T6 sample. The origin of latent hardening was attributed to the formation of sessile jogs during dislocation-dislocation interactions on different planes of T4 samples and the difference in volume fraction of precipitates on different planes of T6 samples. The mechanical properties show that the 0.2% YS increases with subsequent reverse and forward shearing for the T4 sample. However, the 0.2% YS during subsequent reverse shearing is lower than the initial forward shearing for the T6 sample. This decrease in yield stress upon loading reversal is attributed to the presence of deformation-induced intragranular back stresses within the T6 material. It is observed that the rate of cross slip of dislocations depends on the athermal dislocation content, presence of dislocation debris in the unfavorable grains, and the difference in the latent hardening values of different slip systems for the T4 and T6 materials.

Microstructure and mechanical properties of high-Mn-ODS steels

The contribution of dislocation density to strength of Cr–Ni containing austenitic ODS steels is assumed to be limited by dynamic recovery during consolidation of mechanically alloyed powder [Seils et al. Materials Science and Engineering A 786 (2020) 139452]. In order to prevent the reduction in dislocation density by dislocation annihilation subsequent to thermally activated cross slip during recovery, Cr and Ni were replaced by 24 and 34 wt% of Mn in the present study. The comparably lower stacking fault energy leads to larger stacking fault widths and, hence, lower probability of cross slip. The Mn-ODS steels were successfully manufactured by mechanical alloying and subsequent field assisted sintering. X-ray diffraction analysis revealed increased dislocation densities for both Mn-ODS alloys compared to a previously reported Cr–Ni-ODS steel. Formation of additional ε-phase was observed in the lower Mn alloy. Compression and hardness tests confirmed an improved strength and hardness of the Mn-ODS steels. Less thermal stability was found compared to the Cr–Ni-ODS steels due to pronounced ripening of oxide particles as well as grain coarsening in both investigated alloys.

Effects of precipitate origin and precipitate-free zone development on the tensile creep behaviors of a hot-rolled Mg-13wt%Gd binary alloy

In heat-resistant Mg Gd based alloys, the relationship between the collective effects of precipitate origin and precipitate-free zone (PFZ) development on the creep resistance is still unclear. In this work, a hot-rolled Mg-13wt%Gd binary alloy was treated by solid solution (SS sample) and peak aging (AA sample). After peak aging, static precipitated β ′ phases were widely generated and PFZs were directly formed along both sides of the grain boundaries in AA sample. Tensile creep tests were performed at 523 K on both SS and AA samples. During creep testing, dynamic precipitated β ′ phases were gradually generated in SS sample while the β ′ phases persisted as large scales in AA sample. The dominant creep mechanisms of SS sample were twinning and cross-slip composed by < a > dislocations, since the late occurrence and low density of β ′ phases failed in hindering the movement < a > dislocations at the beginning of steady creep stage. On the contrary, the large-scale β ′ phases reduced the space for dislocation movement and succeeded in retarding cross-slip, leading to pyramidal < c + a > slip being the main creep mechanism of AA sample. Besides, PFZs were formed in SS sample (from zero to ~1.1 μm) while they became narrower in AA sample (from ~5 μm to ~1.7 μm). The large decreased ratio of PFZ width, the large scale of static precipitated β ′ phases and the resultant pyramidal < c + a > slip effectively enhanced the creep resistance of AA sample. Accordingly, AA sample behaved a higher creep resistance in comparison to SS sample at 523 K. It is hoped that the roles of precipitate origin and PFZ development in the creep properties can enrich the theories and methods in improving the service performance of Mg Gd series at medium to high temperatures. • Wide PFZs and large-scale static precipitates are obtained after peak aging. • For peak-aged alloy, PFZs are narrowed during creep and creep resistance rises. • For solid solute alloy, PFZs are widely developed and creep resistance falls. • Static precipitates can retard a -cross slip whereas dynamic precipitates fail. • As a -cross slip is delayed, pyramidal slip is activated to enhance creep resistance.

Bending stress relaxation of microscale single-crystal copper at room temperature: An in situ SEM study

The bending stress relaxation of microscale single-crystal copper was studied by in situ SEM bending experiments to elucidate the time-dependent plasticity involving the effect of the strain gradient and the sample size. Three specimens with varied heights of square cross sections were fabricated using a focused ion beam. Interestingly, an obvious bending plateau was observed in the load-displacement curves. The calculated flow stress on the cross section indicated an inverse relationship between the specimen size and strength. In addition, the proportion of decay stress is approximately 2.7% for the beam with a height of h = 1.82 μm and 13.9% for that of h = 0.94 μm in the bending plateau. Moreover, during the dwell period, a sudden stress drop occurred, which is ascribed to the strain burst or stress jerky during the deformation of single-crystal metals. Microbending is usually related to a significant increase in geometrically necessary dislocations (GNDs), which is supposed to improve the resistance for further deformation. However, the bending plateau implied perfect plastic flow and an evolving balance in the microstructures. On the other hand, thermal activation theory was employed to interpret the time-dependent plasticity. The apparent activation volume of the dwell periods in the bending plateau suggested that cross slip dominates the inelastic strain rate evolution. Finally, the inelastic strain rate for stress relaxation was derived from the curve of decay stress, and it was inversely proportional to the height of the microbeam, which is in complete contrast with the trend observed in the previous compression tests of micropillars. In current microscale bending specimens, the thinner beam containing fewer initial dislocation sources exhibits a larger creep ductility with the assistance of GNDs.

Reaction pathway analysis for the contraction of 4H-SiC partial-dislocations pair in the vicinity of surface

In order to reduce harmful dislocations in the 4H-SiC substrate, the improvement technique of basal plane dislocation-threading edge dislocation (BPD-TED) conversion ratio has been investigated. In this paper, we have investigated the effect of surface on the contraction of partial-dislocations pair using reaction pathway analysis and molecular dynamics to clarify the mechanism of the BPD-TED conversion. It is found that the contraction of the partial-dislocation parallel to the surface occurs if the distance from the surface is less than 0.25 nm. As for the partial-dislocations intersected to the surface, the dislocation segment which is located less than 0.25 nm below the surface is easily contracted. Depending on the direction of the Burgers vector, step slightly increase/decrease the energy barrier. Since the cross slip of the perfect screw dislocation easily occurs in the vicinity of the surface, the BPD-TED conversion is controlled by the contraction of partial-dislocations located less than 0.25 nm below the surface.

Orientation dependent hardening of {111} plate precipitate by parametric dislocation dynamics

The effects of the orientation, geometry of slip plane, existence of cross slip on the dislocation interaction with a {111} plate precipitate has been investigated by parametric dislocation dynamics based on Green's function method. The dislocation bypassing process is greatly influenced by the geometrical relation of the {111} precipitate and the dislocation Burgers vector, where the internal stress of the misfitting precipitate is found to be critical to the orientation dependent hardening behaviour of the {111} precipitation variants classified as Type-A (intersected by 0 deg.), Type-B (intersected by 60 deg.) and Type C variant (parallel to slip plane). The energy analysis reveals that the orientation dependent hardening in the simulated stress strain curves is attributed to the topological change in the dislocation microstructure influenced by the internal stress around {111} variants, where the cross slip enhances the increase of the dislocation self-energy. Hence, the simultaneous hardening mechanism by the misfit precipitates and dislocations is suggested.

Cell structure formation in a two-dimensional density-based dislocation dynamics model

Cellular patterns formed by self-organization of dislocations are a most conspicuous feature of dislocation microstructure evolution during plastic deformation. To elucidate the physical mechanisms underlying dislocation cell structure formation, we use a minimal model for the evolution of dislocation densities under load. By considering only two slip systems in a plane strain setting, we arrive at a model which is amenable to analytical stability analysis and numerical simulation. We use this model to establish analytical stability criteria for cell structures to emerge, to investigate the dynamics of the patterning process and establish the mechanism of pattern wavelength selection. This analysis demonstrates an intimate relationship between hardening and cell structure formation, which appears as an almost inevitable corollary to dislocation dominated strain hardening. Specific mechanisms such as cross slip, by contrast, turn out to be incidental to the formation of cellular patterns.

High temperature nanoindentation as a tool to investigate plasticity upon phase transformations demonstrated on Cobalt

A new field of application for high temperature nanoindentation as a complimentary method to understand the mechanics of plasticity upon bulk phase transformations in thermodynamic equilibrium is introduced. The feasibility is outlined on polycrystalline Cobalt involving a low-temperature hexagonal closed packed phase, and above 700K, a high-temperature face centered cubic phase, which was conventionally characterized by means of differential scanning calorimetry and high temperature X-ray diffraction. Strain rate sensitivity, activation volume and activation energy of plastic deformation were determined up to 873 K to identify the rate-controlling deformation mechanism. From RT to 473 K plasticity was found to be controlled by lattice friction on the basal plane, where dislocations have to overcome the Peierls barrier and deformation twinning was apparent in the hexagonal phase. The thermal activation of cross slip lead to reduced twinning actions when the phase transition temperature is approached. In the high temperature face centered cubic phase deformation was found to be controlled by cutting of forest dislocations and no deformation twinning was observed.

Correlation between anelastic response and microstructure of 5N-Al thin foils

The anelastic behavior of 5N-Al thin foils with three different thicknesses (10, 50 and 125 µm) was investigated in the temperature range from 300 to 720 K through Mechanical Spectroscopy (MS) measurements performed by using a completely automated vibrating reed analyser. Two relaxation peaks P1 and P2 and a relevant high temperature background were observed in the thinnest samples whereas only the grain boundary peak (PGB) was observed in the thickest ones. Detailed TEM observations and X-ray diffraction (XRD) measurements indicate that defective structures depend on foil thickness and suggest that the origin of P1 and P2 peaks is connected to the vibration dynamics of isolated dislocations not organized in networks. P1 has been attributed to the combination of dislocatio n motion through the stress field of other dislocations and thermally activated cross slip, while P2 is due to the movement of jogs assisted by pipe diffusion. In addition to anelastic effects due to dislocation vibration, permanent grain boundary sliding seems to contribute to the high temperature background observed in the thinnest foils.

Description of plane strain deformation of FCC crystals by a gradient theory of crystal plasticity

A higher-order gradient crystal plasticity theory applicable to three-dimensional problems is reduced to a plane strain version to be used for the analysis of the deformation of face-centered cubic (FCC) crystals at a particular orientation that the out-of-plane plastic deformation cancels out. Plane strain conditions have been frequently quoted in the literature on theoretical crack problems and experimental studies on FCC crystals since effective information on the fundamental deformation behavior of such materials under multiaxial states of stress and strain is obtained. The present plane strain theory is formulated with planar pseudo slip systems that are contractions of the crystallographic slip systems 111110 of FCC crystals. The resultant theory is purely two-dimensional, but it involves the nature of FCC crystal deformation, i.e., effects of latent hardening, cross slip, and backstresses (equivalently, internal stresses with the opposite sign) associated with the distribution of the edge and screw components of the geometrically necessary dislocations.

On the implementation of dislocation reactions in continuum dislocation dynamics modeling of mesoscale plasticity

The continuum dislocation dynamics framework for mesoscale plasticity is intended to capture the dislocation density evolution and the deformation of crystals when subjected to mechanical loading. It does so by solving a set of transport equations for dislocations concurrently with crystal mechanics equations, with the latter being cast in the form of an eigenstrain problem. Incorporating dislocation reactions in the dislocation transport equations is essential for making such continuum dislocation dynamics predictive. A formulation is proposed to incorporate dislocation reactions in the transport equations of the vector density-based continuum dislocation dynamics. This formulation aims to rigorously enforce dislocation line continuity using the concept of virtual dislocations that close all dislocation loops involved in cross slip, annihilation, and glissile and sessile junction reactions. The addition of virtual dislocations enables us to accurately enforce the divergence free condition upon the numerical solution of the dislocation transport equations for all slip systems individually. A set of tests were performed to illustrate the accuracy of the formulation and the solution of the transport equations within the vector density-based continuum dislocation dynamics. Comparing the results from these tests with an earlier approach in which the divergence free constraint was enforced on the total dislocation density tensor or the sum of two densities when only cross slip is considered shows that the new approach yields highly accurate results. Bulk simulations were performed for a face centered cubic crystal based on the new formulation and the results were compared with discrete dislocation dynamics predictions of the same. The microstructural features obtained from continuum dislocation dynamics were also analyzed with reference to relevant experimental observations.

Effect of plastic bending on high temperature creep resistance of molybdenum single crystals

Using molybdenum single crystals, it is shown how plastic bending multiplies the high-temperature strength of products for pipelines and tube shells of small diameter (10–30 mm), which are subjected to high internal pressure. It is very convenient to do this when the plastic bending process is included in the manufacturing technology of such products, for example, in the form of spiral winding a strip into a pipe. It has been established that during 1000 h, the creep rate of a pre-bent Mo single crystals at 1633 K and an applied stress of 10 MPa permanently decreases by 4–5 orders of magnitude as compared to an unstrengthened single crystal. Using light microscopy, X-ray diffractometry, and transmission electron microscopy, changes in the dislocation structure and the mechanism leading to such strengthening have been found. During the creep test, the edge components of dislocations are depleted and disappear, and the cross slip of screw dislocations is blocked by numerous loops and helicoids that were formed under bending and transformed during the creep process. As a result, dislocation creep gradually turns into diffusion creep during one test. It is safe to assume that similar effects will be observed in polycrystals when the dominant texture direction will correspond to the required bending axis.