Dislocation Channel Formation Research Articles

Experimental and modeling study on irradiation effect of A508-Ⅲ steel

Irradiation can induce microscopic defects in reactor pressure vessel (RPV) steel, resulting in macroscopic hardening and embrittlement. This paper proposes a micro-meso-macroscale calculation framework for the mechanical properties of irradiated RPV steel based on experimental and numerical investigations. The mean size and number density of Fe-ion-irradiation-induced dislocation loops were measured using transmission electron microscopy (TEM). These parameters were described by a power-function relationship with the irradiation dose at various temperatures and were used as input parameters for the crystal plasticity finite element model (CPFEM). Nano-indentation tests of A508-Ⅲ steel under different irradiation conditions were successfully simulated. In addition, microstructural characterization and molecular dynamics (MD) simulations revealed the phenomenon of dislocation pinning and the sweeping of irradiation defects during dislocation migration, implying that the dislocation-loop interactions could be responsible for the formation of dislocation channels and curved dislocation lines. Furthermore, increase in yield stress and the ductile-brittle transition temperature (DBTT) at various temperatures were investigated. Results indicated that yield stress, DBTT, and the degree of irradiation hardening and embrittlement increased with the irradiation dose and decreased with irradiation temperature. Finally, the adjusted reference temperature (ART), a significant design parameter for nuclear reactors, was calculated and evaluated using the multiscale framework. The framework can serve as a reference text for extending the life of nuclear reactors.

Heterogeneous distribution of isothermal ω precipitates prevents brittle fracture in aged β-Ti alloys

Isothermal ω (ωiso) precipitates in β Ti-alloys can increase the yield strength of the material, but unfortunately at a dramatic cost of the ductility. The embrittlement is mainly attributed to the suppression of twinning-induced plasticity (TWIP) and transformation-induced plasticity (TRIP) effects, as well as the formation of dislocation channels associated with localized deformation. To address this issue, we propose a heterogenous microstructure in Ti-15Mo-3Al alloy using conventional rolling method, in which the heterogeneous distributions of both Mo element and ωisoprecipitates are realized after aging. Both the nano-hardness and elastic modulus of ωisorich (Mo-lean) regions are larger than that of ωisodepleted (Mo-rich) regions. A four-time increase in tensile ductility is achieved in the heterogeneous microstructure without a loss of tensile strength, compared with the homogeneous counterpart. The ductility improvement can be ascribed to the blocking effect of ωisodepleted regions against the propagation of dislocation channels which later evolve into micro-cracks.

A concurrent irradiation-mechanics multiscale coupling model

• A novel concurrent irradiation-mechanical multiscale coupling model is developed. • Models of irradiation defect kinetics and irradiation hardening are established. • The difference between post irradiation and concurrent irradiation-deformation tests are disclosed. • Dislocation channel formation is not always correlated with yield drop. The vast majority of our current knowledge regarding the basic mechanisms controlling irradiation effect on mechanical properties is based almost entirely on the results of post-irradiation experiments or theoretical models. However, the concurrent effects of irradiation, mechanical stress, and thermal damage on the failure phenomena of materials and components remain largely unexplored due to its internal multiscale-multiphysics coupling nature. We present here a concurrent irradiation-mechanics multiscale coupling model. The concurrent evolutions of nanoscale irradiation defect clusters, microscale dislocation configurations, and mechanical responses are well captured based on coupling cluster dynamics, discrete dislocation dynamics, and the finite element methods using an effective time marching scheme. Model predictions of defect densities and size are in general agreement with experimental observations. Irradiation hardening is shown to take place also in samples undergoing concurrent irradiation-mechanical loading, similar to samples tested post-irradiation. However, the occurrence of plastic flow localization and dislocation channel formation is not accompanied with apparent yield drop (softening) under concurrent irradiation-mechanical loading conditions, which is different from the post-irradiation case.

Continuum modeling of dislocation channels in irradiated metals based on stochastic crystal plasticity

As a common feature observed in irradiated metallic materials, the formation of dislocation channels has been extensively studied and is considered to play a key role in irradiation embrittlement. However, modeling dislocation channels with the conventional crystal plasticity theory has been a theoretical challenge due to the difficulty of capturing microstructural inhomogeneities. Here a continuum crystal plasticity framework incorporating a stochastic distribution model of critical resolved shear stress (CRSS) is developed to describe the formation of dislocation channels and further plastic flow localization in irradiated materials. We show that the stochastic model is capable of capturing the heterogeneity of microscale plastic strain, which is an inherent feature of metallic materials during plastic deformation. It acts as an important microscale perturbation to trigger the dislocation channel nucleation in irradiated metals, especially for single crystals that lack mesoscale perturbations such as intergranular incompatibility and grain anisotropy. Without predetermining the potential nucleation position of dislocation channels, the stochastic irradiation crystal plasticity framework successfully simulates the dislocation channel formation and plasticity localization in both irradiated single- and polycrystalline copper (Cu), and further indicates the irradiation defect density threshold for the dislocation channel formation. This stochastic model broadens the application of the conventional crystal plasticity framework, and might provide new insights for other studies on plasticity localization, including shear bands formation of metals, mechanical behaviors with heterogeneous deformation and so on.

Plasticity of irradiated materials at the nano and micro-scales

We review here our recent work on plastic deformation in irradiated materials at the nano- and micro-scales, as revealed by Discrete Dislocation Dynamics (DDD) simulations. Two methods of including irradiation effects in the DDD framework are presented. The first directly captures the atomistic interaction mechanisms, while the second can effectively study high-dose irradiation. Computer simulations lead to new understanding of the dynamics of collective dislocation-irradiation defect interactions, as well as the quantitative analysis of the temporal and spatial characteristics associated with plastic instabilities. Based on these insights, theoretical models are developed to predict the critical conditions for dislocation channel formation. A simple probability model is proposed and demonstrated to predict the width of dislocation channels in bulk irradiated materials with good agreement with experimental data. The fundamental understanding of the origins of plastic flow localization in irradiated materials sheds light on the design of future generations of radiation-resistant materials.

Gum-like mechanical behavior of a partially ordered Al5Nb24Ti40V5Zr26 high entropy alloy

Microstructure and mechanical behavior of a new bcc Al5Nb24Ti40V5Zr26 high-entropy alloy in the as-cast, cold-rolled and recrystallized conditions were studied. In the as-cast condition, the Al5Nb24Ti40V5Zr26 alloy had a single bcc phase coarse-grained (~80 μm) structure. After cold rolling to a total thickness strain 80% the alloy demonstrated typical of deformed metals tensile behavior with a short hardening stage and early necking. Annealing at 800 °C resulted in recrystallization of the matrix and formation of a small fraction of C14 type Laves phase particles. After annealing at 1100 °C, a partial B2 ordering of the matrix phase was found. In the annealed condition, the alloy showed some typical of gum metals features associated with low work hardening and large elongation. The manifestation of a gum-like behavior can be ascribed to the formation of dislocation channels due to the local disordering of the bcc matrix in shear planes. In addition, an unusual (inverse) dependence of yield strength on the recrystallized grain size was observed, most possibly due to a different degree of ordering of the matrix phase.

Suppression of Localized Plastic Flow in Irradiated Materials

Suppressing deformation localization caused by dislocation channels is crucial in the reliable service of irradiated materials. Through 3D Discrete Dislocation Dynamics simulations, the evolution of deformation localization extent is quantitatively studied, and the effect of internal dislocation structure and slip mode are revealed. Results show that to inhibit dislocation channel formation, the material is required to be pretreated so as to enhance short-range dislocation interactions. This can be attained by introducing a homogeneously dense dislocation structure before irradiation, and by loading along orientations that activate multiple slip systems. Implications for the design of radiation-resistant materials are discussed.

A coupled dislocation dynamics-continuum barrier field model with application to irradiated materials

A new computational methodology for 3-dimensional (3D) Discrete Dislocation Dynamics (DDD) in barrier-strengthened materials is developed. We couple the discrete 3D DDD framework with the Finite Element Method (FEM) solution of a continuum field equation for the evolution of dispersed barriers. Coupled model parameters are obtained from detailed statistical analysis of 3D DDD simulations of single dislocation-barrier interactions. We develop a crystal lattice based continuum material point arrangement method to precisely distribute localized plastic strain as a result of dislocation-barrier interactions, enabling the method to be crystal-structure sensitive. The model is demonstrated by an application to the study of the physics of dislocation channel formation and plastic instability phenomena in irradiated materials. The results are shown to be in agreement with experiments on the magnitude of radiation hardening and the onset of plastic instability. Plastic flow localization in irradiated materials was shown to be more prevalent at high irradiation dose. The method enables future studies of the plastic deformation in precipitation-strengthened alloys, hydrogen-embrittled materials, and the plasticity of irradiated materials.

Modeling of dislocation channel width evolution in irradiated metals

Defect-free dislocation channel formation has been reported to promote plastic instability during tensile testing via localized plastic flow, leading to a distinct loss of ductility and strain hardening in many low-temperature irradiated materials. In order to study the underlying mechanisms governing dislocation channel width and formation, the channel formation process is modeled via a simple stochastic dislocation-jog process dependent upon grain size, defect cluster density, and defect size. Dislocations traverse a field of defect clusters and jog stochastically upon defect interaction, forming channels of low defect-density. Based upon prior molecular dynamics (MD) simulations and in-situ experimental transmission electron microscopy (TEM) observations, each dislocation encounter with a dislocation loop or stacking fault tetrahedron (SFT) is assumed to cause complete absorption of the defect cluster, prompting the dislocation to jog up or down by a distance equal to half the defect cluster diameter. Channels are predicted to form rapidly and are comparable to reported TEM measurements for many materials. Predicted channel widths are found to be most strongly dependent on mean defect size and correlated well with a power law dependence on defect diameter and density, and distance from the dislocation source. Due to the dependence of modeled channel width on defect diameter and density, maximum channel width is predicted to slowly increase as accumulated dose increases. The relatively weak predicted dependence of channel formation width with distance, in accordance with a diffusion analogy, implies that after only a few microns from the source, most channels observed via TEM analyses may not appear to vary with distance because of limitations in the field-of-view to a few microns. Further, examinations of the effect of the so-called “source-broadening” mechanism of channel formation showed that its effect is simply to add a minimum thickness to the channel without affecting channel dependence on the given parameters.

Formation of dislocation channels in neutron irradiated molybdenum

The formation of deformation-induced dislocation channels in neutron irradiated molybdenum and the loop-dislocation interactions were investigated using transmission electron microscopy. It is suggested that the irradiation-induced defect - microstructure is unstable with respect to the stress. Under the influence of the stress, loops start gliding on their glide cylinders in transition region of a cascade where vacancies and interstitials may coexist. Results indicate that loop-loop interactions have a significant role in the early stage of channel formation; dislocations are not seen either within or at the ends of the embryonic channels. There are two consequences of loop-loop interactions: the reduction in the loop density due to their mutual annihilation in localized regions and the increase in the loop sizes due to the coalescence of loops having the same nature. On further stressing, the segments of the larger loops could serve as the source of mobile dislocations. The yielding may occur when the stress level is high enough to activate the coalescence-produced glide sources. Furthermore, results on the attractive loop-dislocation interactions suggest that they may not have a significant role in eliminating defect clusters. On the other hand, the repulsive interactions may have a substantial role in altering the microstructure of the irradiated metals.

Deformation localization and dislocation channel dynamics in neutron-irradiated austenitic stainless steels

The dynamics of deformation localization and dislocation channel formation were investigated in situ in a neutron-irradiated AISI 304 austenitic stainless steel and a model 304-based austenitic alloy by combining several analytical techniques including optic microscopy and laser confocal microscopy, scanning electron microscopy, electron backscatter diffraction, and transmission electron microscopy (TEM). Channel formation was observed at ∼70% of the polycrystalline yield stress of the irradiated materials (σ0.2). It was shown that triple junction points do not always serve as a source of dislocation channels; at stress levels below the σ0.2, channels often formed near the middle of the grain boundary. For a single grain, the role of elastic stiffness value (Young’s modulus) in channel formation was analyzed; it was shown that in the irradiated 304 steels the initial channels appeared in “soft” grains with a high Schmid factor located near “stiff” grains with high elastic stiffness. The spatial organization of channels in a single grain was analyzed; it was shown that secondary channels operating in the same slip plane as primary channels often appeared at the middle or at one-third of the way between primary channels. The twinning nature of dislocation channels was analyzed for grains of different orientation using TEM. In the AISI 304 steel, channels in grains oriented close to 〈001〉||TA (tensile axis) and 〈101〉||TA were twin free and grain with 〈111〉||TA and grains oriented close to a Schmid factor maximum contained deformation twins.

Modeling plastic deformation of post-irradiated copper micro-pillars

We present here an application of a fundamentally new theoretical framework for description of the simultaneous evolution of radiation damage and plasticity that can describe both in situ and ex situ deformation of structural materials [1]. The theory is based on the variational principle of maximum entropy production rate; with constraints on dislocation climb motion that are imposed by point defect fluxes as a result of irradiation. The developed theory is implemented in a new computational code that facilitates the simulation of irradiated and unirradiated materials alike in a consistent fashion [2]. Discrete Dislocation Dynamics (DDD) computer simulations are presented here for irradiated fcc metals that address the phenomenon of dislocation channel formation in post-irradiated copper. The focus of the simulations is on the role of micro-pillar boundaries and the statistics of dislocation pinning by stacking-fault tetrahedra (SFTs) on the onset of dislocation channel and incipient surface crack formation. The simulations show that the spatial heterogeneity in the distribution of SFTs naturally leads to localized plastic deformation and incipient surface fracture of micro-pillars.

Continuum modeling of localized deformation in irradiated bcc materials

A continuum constitutive crystal plasticity framework is implemented to model the post-irradiation tensile behavior of bcc structural materials, accounting for localized deformation due to the formation of dislocation channels. Both the mechanical response and deformed microstructure of the material are modeled for quasi-static tensile loading. The latter is studied to identify the stages of dislocation channel formation during localization, specifically with respect to the evolution of dislocations and irradiation-induced defects. Parametric studies of the cross-slip and flow softening (due to annihilation of irradiation-induced defects) models are performed to study their effects on the localization behavior. Results are compared to available experimental data.

The role of irradiated microstructure in the localized deformation of austenitic stainless steels

Localized deformation has emerged as a potential factor in irradiation-assisted stress corrosion cracking of austenitic stainless steels in LWR environments and the irradiated microstructure may be a critical factor in controlling the degree of localized deformation. Seven austenitic alloys with various compositions were irradiated using 2–3 MeV protons to doses of 1 and 5 dpa at 360 °C. The irradiated microstructure consisting of dislocation loops and voids was characterized using transmission electron microscopy. The degree of localized deformation was characterized using atomic force microscopy on the deformed samples after conducting constant extension rate tension tests to 1% and 3% strain in argon. Localized deformation was found to be dependent on the irradiated microstructure and to correlate with hardening originating from dislocation loops. Dislocation loops enhance the formation of dislocation channels and localize deformation into existing channels. On the contrast, voids mitigate the degree of localized deformation. The degree of localized deformation decreases with SFE with the exception of alloy B. Localized deformation was found to have similar dependence on SFE as loop density suggesting that SFE affects localized deformation by altering irradiated microstructure.

Dislocation channel formation process in V–Cr–Ti alloys irradiated below 300 °C

Atomic force microscopy was applied to study the slip band evolution of neutron-irradiated V–Cr–Ti alloys deformed in a tensile test. Quantitative data were obtained on the changes of the surface topography of dislocation channels and on the kinetics of dislocation channel growth up to the ultimate tensile stress. As stress approached the ultimate tensile strength, the slip bands nucleated and propagated across the specimens. As the stress increased, the interval spacing between slip bands decreased and became constant. On the other hand, the slip step height continued to increase, and indicated that the growth of individual dislocation channels occurred continuously. The conjugated and multi-slip bands in a grain were seldom observed. The evolution of dislocation channels may induce the significant loss of ductility after the UTS in V–Cr–Ti alloys.

Formation of Dislocation Channels in Neutron Irradiated Molybdenum

The evolution of dislocation channels in irradiated metals during deformation can be envisaged to occur in three stages: (i) formation of embryonic cluster free regions, (ii) growth of these regions into microscopically observable channels and (iii) termination of their growth due to the accumulation of dislocation damage. The first two stages are particularly intriguing, and we have attempted to follow the early stages of channel formation in polycrystalline molybdenum, irradiated to 5×1019 n. cm−2 (E > 1 Mev) at the reactor ambient temperature (∼ 60°C), using transmission electron microscopy. The irradiated samples were strained, at room temperature, up to the macroscopic yield point.Figure 1 illustrates the early stages of channel formation. The observations suggest that the cluster free regions, such as A, B and C, form in isolated packets, which could subsequently link-up to evolve a channel.