Obstacle Strength Research Articles

Effect of helium bubbles on the mobility of edge dislocations in copper

Abstract Helium bubbles can form in materials upon exposure to irradiation. It is well known that the presence of helium bubbles can cause changes in the mechanical behavior of materials. To improve the lifetime of nuclear components, it is important to understand deformation mechanisms in helium-containing materials. In this work, we investigate the interactions between edge dislocations and helium bubbles in copper using molecular dynamics (MD) simulations. We focus on the effect of helium bubble pressure (equivalently, the helium-to-vacancy ratio) on the obstacle strength of helium bubbles and their interaction with dislocations. Our simulations predict significant differences in the interaction mechanisms as a function of helium bubble pressure. Specifically, bubbles with high internal pressure are found to exhibit weaker obstacle strength as compared to low-pressure bubbles of the same size due to the formation of super-jogs in the dislocation. Activation energies and rate constants extracted from the MD data confirm this transition in mechanism and enable upscaling of these phenomena to higher length-scale models.

Atomic-scale three-dimensional irradiation-induced defect kinetics models for bcc Fe-based alloys

The interaction between irradiation defects and dislocations could lead to macroscopic hardening and embrittlement. In this study, molecular dynamics (MD) and machine learning were conducted to study three-dimensional void- and Cu-cluster-induced kinetics models under interaction with dislocations in body-centered cubic Fe-based alloys. MD Results show that dislocation climb and shear are two types of interaction mechanism based on the defect size. Combined MD results and machine learning, it was found that the dislocation length increased linearly with an increase in the size of the defects after the interaction. In addition, the number of atoms in the Cu-rich cluster and the reduced number of vacancies in the voids had a square relationship with the defect size where 0.85D2 is for Cu-rich cluster and 0.50D2 is for void. Furthermore, atomic-scale three-dimensional irradiation-induced defect kinetics models were developed and incorporated into the crystal plasticity finite element model (CPFEM). We also analyzed the contributions of various defects to the increase in the yield stress during CPFEM simulation. Compared with DBH model, the prediction of MD data-driven CPFEM matches better with the experimental data. Cluster contributed the most to hardening with low obstacle strength due to the higher number density compared with dislocation loops and voids. The loops also contributed to hardening; however, their contribution was smaller than that of the clusters. Although the number density and size of voids were minimized, they may have contributed because of the high obstacle strengths. This work can indeed deepen the understanding of irradiation effect in Fe-based alloys.

Atomistic simulations of the interaction of edge dislocations with β-Nb precipitates in Zr-Nb alloys

Experiments have shown that precipitation can affect the mechanical properties of zirconium alloy, but the interaction mechanism between dislocations and Nb precipitates in zirconium alloys is still unclear. Thus, a systematic molecular dynamics study was performed to investigate the interaction between edge dislocations and Nb precipitates. It was found that the dislocation passed through Nb precipitate by shear mechanism or bypass mechanism of forming jogs, and the critical resolved shear stress increased with the diameter of the precipitate. After completion of the interaction, dislocations formed jogs due to climb when the precipitates were larger than 2 or 3 nm. Some atoms in the precipitate were more disordered after dislocation shearing, and dislocation fragments were generated around the precipitate, both of which lead to the precipitate hardening. The calculation of obstacle strength further confirmed that unsheared Nb precipitates until hundreds of nanometers were the weak obstacle for dislocations.

A spatially resolved analysis of dislocation loop and nanohardness evolution in proton irradiated Zircaloys

Proton irradiation is increasingly used as a surrogate for neutron irradiation, providing similar damage structures at significantly lower costs and less time compared to neutron irradiation. However, in contrast to neutrons, protons produce a depth dependent damage profile that incorporates a plateau region and a Bragg peak in the tens of microns region depending on the material and proton energy. Here we demonstrate that this depth dependent damage can be utilised to obtain new understanding about irradiation induced damage at different dose levels from a single sample by combining spatially resolved micro-beam synchrotron X-ray diffraction-based dislocation analysis and nanoindentation. For this purpose, and to study the damage evolution starting from very early stages, we have investigated microstructure evolution and hardening behaviour of Zircaloy-2 and Zircaloy-4 proton irradiated samples between 0.01 dpa and 17 dpa at 350 °C. The results highlight good agreements of SRIM-based damage depth predictions with irradiation-induced dislocation appearance and nanohardness. However, at even relatively low damage levels within the plateau region, dislocation line density and nanohardness profiles appear saturated across the entire irradiated region, even when the dpa levels differed significantly. When relating dislocation loop line densities to nanohardness, it was found that from a certain point hardness increased only very slightly with increasing line densities. This apparent discrepancy can be explained by a decreasing loop size for the highest line densities identified by from the diffraction line profile analysis and the application of a Dispersed Barrier Hardening model that relates obstacle strength to dislocation loop size.

The effects of different factors on obstacle strength of irradiation defects: An atomistic study

In this work we study the effects of different factors of dislocation loop on its obstacle strength when interacting with an edge dislocation. At first, the interaction model for dislocation and dislocation loop is established and the full and partial absorption mechanism is obtained. Then, the effect of temperature, size and burgers vector of dislocation loop are investigated. The relation between the obstacle strength and irradiation dose has been established, which bridges the irradiation source and microscale properties. Except that, the obstacle strength of C, Cr, Ni, Mn, Mo and P decorated dislocation loop is studied. Results show that the obstacle strength for dislocation loop decorated by alloy element decreases in the sequence of Cr, Ni, Mn, C, P and Mo, which could be used to help parameterize and validate crystal plasticity finite element model and therein integrated constitutive laws to enable accounting for irradiation-induced chemical segregation effects.

A robust dislocation line tension model considering obstacle strength distribution for yield strength prediction of an Al–Cu–Li alloy

In this study, the yield strength of AA2195 (Al–Cu–Li) alloy as a function of ageing time was determined using a dislocation line tension model. The model simulates the dislocation motion through an array of point obstacles, which represent forest dislocations and semi-coherent precipitates (T1 and θ’). These obstacles were distributed within the simulation environment according to experimentally derived areal densities of the T1 and θ’ precipitates and the forest dislocations. Point obstacles symbolizing T1 and θ’ precipitates were assigned a strength value derived from a log–normal approximation of the size distribution of the precipitates as observed using transmission electron microscopy. A notable agreement between experimental and simulated results emerged when the strength distribution of point obstacles representing precipitates was considered in the simulations. Conversely, simulations that assumed uniform strength of point obstacles led to an underestimation of the yield stress. This work proposes a framework that contemplates both spatial and strength distribution of point obstacles, offering an advance approach that outperforms previous yield strength models based on a linear superposition of strengthening mechanisms.

Dislocations generated by pre-strain dominate the subsequent plastic deformation

Plasticity of sub-micron scale metals is well known to be controlled by dislocation source. Here, we report an in-situ study of how the dislocation structures generated by pre-strain in submicron-sized copper affect the subsequent plastic deformation by conducting nanocompression testing in a transmission electron microscope. The results show that short isolated dislocations first undergo directional intermittent jumping motion along specific glide directions under the applied force. And the jumping frequency and jumping distance of dislocation motion can be determined by the density and strength of obstacles distributed in the crystal. Then, the dislocation wall formed by dislocation pileup and entanglement during pre-strain can effectively pin the mobile dislocation in the early stages of compression, but at high stress levels it will perform overall motion in the form of dislocation avalanches and lead to the strain burst emissions of the material. The in-situ dynamic evolution of dislocation avalanche reveals the emitted dislocations and associated glide planes introduced by pre-strain can preferentially trigger dislocation avalanches of the dislocation wall.

Radiation-induced hardening of ion-irradiated Zircaloy-2 at 573 K under applied stress

The microstructural evolution and hardening of Zircaloy-2 under low-dose irradiation (<1.0 dpa) with 3.2 MeV Ni3+ ions under applied stress at 573 K were investigated using transmission electron microscopy (TEM) examination and nano-indentation measurements in this study. The irradiation doses ranged from 0.05 to 1 dpa. The formation of < a > loops was observed at doses below 0.05 dpa, and the density was found to be saturated at about 0.1 dpa. The < a > loops then grew and intersected with adjacent loops to become entangled at doses above 0.4 dpa. Radiation-induced hardening was confirmed in Zircaloy-2 at the early stage of irradiation below 0.1 dpa, and the hardening effect was attributed to the nucleation and growth of < a > loops. The Orowan equation was used to estimate the contribution of dislocation loops to the hardening, and the estimated values were in good agreement with the experimental results, with the obstacle strength factor of < a > loops as 0.25. Furthermore, the effect of applied stress of 1 dpa irradiated tensile samples on radiation-induced hardening was also discussed. This study provides dislocation loop formation and hardening behavior of Zircaloy-2 under low-dose irradiation at 573 K with stress conditions.

Investigation of irradiation defects and hardening of cold-worked vanadium alloys

Irradiation defects of V-5Cr-5Ti alloys with different pre-irradiation treatment after irradiation to 0.5 dpa at 100 °C with energetic Fe ions were investigated. For the cold-worked specimens, dislocation loops decrease in size while increasing in number density with the increase of the deformation percentage. For the annealed specimens, dislocation loops have minor difference in size whilst the number density decreases with the increasing deformation percentage. Meanwhile, dislocation loops decorating dislocations were observed. The obstacle strength factor (α) is calculated according to the dispersion barrier hardening model (DBH). For the cold-worked specimens, α increases with increasing size of dislocation loops. A linear relation, α=0.075*d−0.074 is established. At a similar size, dislocation loops in the annealed specimens have a greater α than the cold-worked specimens, possibly due to the lock of the tangled network dislocations and/or the hinder of the segmented movement of the tangled network dislocations by dislocation loops.

Interaction between an edge dislocation and faceted voids in body-centered cubic Fe

Irradiation defects cause mechanical property degradation in reactor materials. The relationship between dislocations and defects in these materials is of particular importance to mechanical strength. In the current study, we investigate the interaction between an edge dislocation and different faceted void geometrical combinations using molecular dynamics to clarify the cutting mechanism and void effects on irradiation hardening in pure iron. We elucidate the difference in obstacle strength and the cutting process between spherical voids and faceted voids, especially for different faceted void configuration types. The highest critical shear stress in the type-a faceted void configuration is observed from the lower to upper void region, whereas that in the type-b faceted void configuration is observed at the void center, with the critical shear stress decreasing with increasing and decreasing normalized distance from the void center (dnorm). As for the type-c faceted void configuration, the highest critical shear stress is observed at the lower region of the void. The difference in the cutting process is due to the faceted plane; the highest critical shear stress is observed at the region where the dislocation cuts the {110} plane of the faceted void. The {110} plane is the close packed plane of the body center cubic structure, and therefore the largest amount of energy is required to cut the atomic binding and slip the next equivalent {110} plane compared to other planes.

Vortex shedding frequency of a moving obstacle in a Bose–Einstein condensate

We experimentally investigate the periodic vortex shedding dynamics in a highly oblate Bose–Einstein condensate using a moving penetrable Gaussian obstacle. The shedding frequency f v is measured as a function of the obstacle velocity v and characterized by a linear relationship of f v = a(v − v c) with v c being the critical velocity. The proportionality constant a is linearly decreased with a decrease in the obstacle strength, whereas v c approaches the speed of sound. When the obstacle size increases, both a and v c are decreased. We discuss a possible association of a with the Strouhal number in the context of universal shedding dynamics of a superfluid. The critical vortex shedding is further investigated for an oscillating obstacle and found to be consistent with the measured f v. When the obstacle’s maximum velocity exceeds v c but its oscillation amplitude is not large enough to create a vortex dipole, we observe that vortices are generated in the low-density boundary region of the trapped condensate, which is attributed to the phonon emission from the oscillating obstacle.

The combined effect of carbon and chromium enrichment on 〈1 0 0〉 loop absorption in iron

In this work we study the effects of C and Cr enrichment of 〈100〉 dislocation loops (DL) on their absorption and obstacle strength when interacting with an edge dislocation. To do so, we have i) developed a C-Cr cross potential based on density functional theory data as part of a ternary FeCrC interatomic potential; ii) performed exchange Monte Carlo simulations employing the developed interatomic potential to obtain the distribution of the solutes enriching the DL in the energetically optimum configurations; iii) performed large scale molecular dynamics simulations employing the interatomic potential to characterize the interaction between an edge dislocation line and the decorated DL. We found that the obstacle stress scales to the same obstacle strength regardless the DL density. On the other hand, we found that C, the level of Cr enrichment, loop size and interaction temperature have a significant impact on the obstacle strength and level of absorption of the loops. The presented results can be used to help parameterize and validate discrete dislocation dynamics codes and therein integrated constitutive laws to enable accounting for irradiation-induced chemical segregation effects.

Distinct He-induced damage evolution in nickel-based alloys irradiated at elevated temperatures

The nickel-based alloy Inconel 617 and Alloy 800H have been envisaged as the leading candidate for the higher-temperature Molten Salt Reactors (MSRs) due to their superior high-temperature properties. To evaluate their potential applications, both alloys were irradiated by He ion at 750 and 850 °C with corresponding He ion fluence. Same irradiation tests were performed on Hastelloy N alloy to study its microstructure evolution at elevated irradiation temperature, as well as being the reference alloy to reveal candidate alloys irradiation tolerance. Transmission electron microscopy (TEM) reveals the depth distribution of irradiation induced He bubbles and Frank loops. The TEM graphs and quantitative analysis shows that when irradiated at 850 °C, the formation of precipitated clusters lead to denser and boarder distribution of He bubbles in Inconel 617, while the bubble-loop complexes form and contribute to larger volume fraction of He bubbles in Hastelloy N alloy. The nanoindentation technique is used to measure their mechanical changes, and the results show that the Alloy 800H has the lowest degree of irradiation induced hardening when irradiated at 850 °C, whereas that of all alloys irradiated at 750 °C are basically similar. Further, the yield strength increment is calculated and deviations between experimental and calculated values are caused by the formation of precipitated clusters in Inconel 617 and the selection of smaller obstacle strength in Hastelloy N alloy. By comparison, the Alloy 800H demonstrates a greater potential to function as the structural material for higher-temperature MSRs due to smaller volume fraction and better resistance to irradiation induced hardening.

Change in nanoindentation hardness of polycrystalline tungsten irradiated with Fe ions or electrons by hydrogen gas charging

The effects of hydrogen atoms on the hardnesses of unirradiated, ion-irradiated, and electron-irradiated polycrystalline tungsten samples were investigated using nanoindentation tests. The bulk equivalent hardnesses of the unirradiated and electron-irradiated tungsten samples did not change upon hydrogen charging. The bulk equivalent hardness of the ion-irradiated tungsten increased upon the hydrogen charging. The number of hydrogen atoms trapped at dislocation loops was very small. We estimated that the hydrogen occupancy in vacancy clusters was 0.24−0.45 (in the case of tri-vacancies, the number of hydrogen atoms trapped per vacancy (H/V) is 1.04−1.95). Because of the irradiation temperature of 573 K, the density and size of irradiation-induced defects did not change during hydrogen charging at 543 K. Therefore, the hardening was mainly caused by an increase of approximately 8 − 11% in the obstacle strength α of vacancy clusters containing hydrogen atoms. The ion-irradiated area hardened upon the hydrogen charging and changed the configuration of the pile-up. Observation of the dislocation structure is required to clarify the mechanism of hardening caused by hydrogen charging.

Irradiation hardening of stainless steel model alloy after Fe-ion irradiation and post-irradiation annealing treatment

Microstructural observation with atom probe tomography, transmission electron microscopy, and mechanical examination with a nano-indenter were performed on stainless steel model alloy that had been irradiated with Fe ions and subjected to post-irradiation annealing treatment (PIA). Significant irradiation hardening occurred in the as-irradiated specimen and irradiation hardening recovery occurred at 400 °C of cumulative PIA, Tiny black dots, Frank loops and Ni-Si clusters formed in the as-irradiated specimen and their recovery was observed with the cumulative PIA. A classic dispersed-barrier hardening model was used to evaluate irradiation hardening connected to microstructural information by applying the density and size of defect variants. Ni-Si clusters and Frank loops contributed substantially to the increase of irradiation hardening, whereas the black dots contributed little for the stainless steel model alloy. The barrier strength factor of Ni-Si clusters, αSC, was obtained as 0.029 and 0.015 for two different obstacle strength model, which suggests that an individual Ni-Si cluster is a weak barrier obstacle to mobile dislocation on the dispersed-barrier hardening model, but that the dense formation of Ni-Si clusters controls irradiation hardening behavior. A quantitative analysis was performed of the increase in strength from the Ni-Si clusters that was caused by coherency strains, and an irradiation hardening mechanism for the stainless steel, including the solute atom clusters, is discussed.

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.

A dislocation-based flow rule with succinct power-law form suitable for crystal plasticity finite element simulations

The physical interpretation of the power-law flow rule from the classic Kocks model suggests that strain rate sensitivity is determined by an empirical parameter that differs from the zero-stress activation energy. This paper proposes a dislocation bow-out model that seeks to further interpret the physical significance of strain rate sensitivity of face-centered cubic (fcc) metals without involving empirical terms. Interestingly, strain rate sensitivity is found to rely on the ratio of the obstacle strength to the zero-stress activation energy. The values of strain rate sensitivity obtained from our calculations match well with the experimental data for pure fcc metals. The resulting flow rule maintains a mathematically concise power-law form with parameters having clear physical meanings and sufficient accuracy. The concise power-law form of the present model enables its easy implementation in the crystal plasticity finite element method and offers flexibility to simulate stress-strain curves of fcc metals deformed at a wide range of temperatures and strain rates.

Interaction mechanism of an edge dislocation with a void in Fe–Ni–Cr concentrated solid-solution alloy

The interactions of a 1/2<110>{111} edge dislocation with a void in Fe10Ni20Cr and Fe33Ni33Cr concentrated solid-solution alloys are investigated by using molecular dynamics simulation method. The edge dislocation dissociates into two shockley partial dislocations with stacking fault in both alloys. Compared to the Fe10Ni20Cr alloy, the dislocation motion becomes difficult in Fe33Ni33Cr alloy due to the big fluctuation of stacking fault energy. The obstacle strength for a void with diameter of 2 nm in Fe33Ni33Cr alloy is slightly weaker than that in Fe10Ni20Cr alloy at temperature range from 300K to 800K. It is attributed to easy vacancies migration in Fe33Ni33Cr alloy. Interestingly, a significant increase of obstacle strength for void at 900K is noted only in Fe10Ni20Cr alloy because of the transformation from void to stacking fault tetrahedra (SFT). It is found that the compress strain upon the edge dislocation glide plane promotes the transformation from void to SFT at 900K in Fe10Ni20Cr alloy. While in Fe33Ni33Cr alloy, sluggish diffusion induced by atomic-level heterogeneity suppresses the transition from void to SFT. Consequently, Fe33Ni33Cr concentrated solid-solution alloy exhibits better irradiation hardening resistance than Fe10Ni20Cr alloy, especially at high temperature.

Repulsion leads to coupled dislocation motion and extended work hardening in bcc metals

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. We demonstrate here that the high activation barrier for screw dislocation glide motion in tungsten results in repulsive interactions between screw dislocations, and triggers dislocation motion at applied loading conditions where it is not expected. In situ transmission electron microscopy and atomistically informed discrete dislocation dynamics simulations confirm coupled dislocation motion and vanishing obstacle strength for repulsive screw dislocations, compatible with the kink pair mechanism of dislocation motion in the thermally activated (low temperature) regime. We implement this additional contribution to plastic strain in a modified crystal plasticity framework and show that it can explain the extended work hardening regime observed for [100] oriented tungsten single crystal. This may contribute to better understanding the increase in ductility of highly deformed bcc metals.

Microstructural evolution and hardening effect in low-dose self-ion irradiated Zr–Nb alloys

Self-ion irradiation-induced hardening behavior and microstructural evolution in dilute Zr–Nb alloys after exposure to low-dose irradiation have been investigated using nano-indentation measurement, EBSD analysis, and TEM examination. Two types of Zr–Nb alloys, i.e., solute-type Zr0.2Nb with only solute Nb atoms and precipitate-type Zr2Nb with both solute and excessive Nb atoms, are utilized to elucidate how the addition of Nb influences microstructural and mechanical property changes upon irradiation. Significant irradiation-induced hardening was confirmed for both alloys, and the extent of hardening was slightly greater in Zr2Nb relative to Zr0.2Nb. The irradiation-induced hardening at [0001] orientation exhibited the lowest value, which gradually intensified as the orientation deviated from [0001] axis to [101¯0] and [21¯1¯0]axes, irrespective of the concentration of Nb. This tendency is ascribed to the slip-system-dependent loops-dislocation interaction. The signs that the doping of Nb can suppress irradiation defect formation were evidenced by the strong sinking effects verified at the particle–matrix interface and grain boundary. With the application of the dispersed barrier hardening model and quantitative characterization of microstructure features, it is revealed that the <a>-loops are mostly responsible for the hardening in both alloys and a rational obstacle strength of <a>-loop in α-Zr is derived as ∼0.33–0.36.