Dislocation-defect Interaction Research Articles

A self-consistent plasticity theory for modeling the thermo-mechanical properties of irradiated FCC metallic polycrystals

A self-consistent theoretical framework is developed to model the thermo-mechanical behaviors of irradiated face-centered cubic (FCC) polycrystalline metals at low to intermediate homologous temperatures. In this model, both irradiation and temperature effects are considered at the grain level with the assist of a tensorial plasticity crystal model, and the elastic-visocoplastic self-consistent method is applied for the scale transition from individual grains to macroscopic polycrystals. The proposed theory is applied to analyze the mechanical behaviors of irradiated FCC copper. It is found that: (1) the numerical results match well with experimental data, which includes the comparison of results for single crystals under the load in different directions, and for polycrystals with the influences of irradiation and temperature. Therefore, the feasibility and accuracy of the present model are well demonstrated. (2) The main irradiation effects including irradiation hardening, post-yield softening, strain-hardening coefficient (SHC) dropping and the non-zero stress offset are all captured by the proposed model. (3) The increase of temperature results in the decrease of yield strength and SHC. The former is attributed to the weakened dislocation–defect interaction, while the latter is due to the temperature-strengthened dynamic recovery of dislocations through the thermally activated mechanism. The present model may provide a theoretical guide to predict the thermo-mechanical behaviors of irradiated FCC metals for the selection of structural materials in nuclear equipment.

A size-dependent tensorial plasticity model for FCC single crystal with irradiation

In this paper, effects of irradiation damage and crystal size on the mechanical behaviors of FCC single crystals are explored. By treating the spatial dependent interaction between dislocations and irradiation-induced stacking fault tetrahedrons (SFTs) as a tensorial form and taking into account the influence of dislocation source limitation at submicron (∼100nm to ∼1μm), a unified size-dependent tensorial plasticity model for irradiated single crystals is developed. The feasibility and accuracy of this model are well validated by comparing numerical results with corresponding experimental data. It is found that (1) the yield strength of unirradiated FCC copper increases with the decrease of crystal size, which mainly attributed to the mechanism shifting from dislocation forest strengthening to dislocation source limitation strengthening. (2) For large crystal copper, the yield strength increases with the amount of irradiation, which is attributed to the increase of irradiation-induced SFTs and enhancement of dislocation–defect interaction. The phenomenon of yield dropping is observed when the irradiation is strong. (3) The competition between the irradiation effect and size effect induces the existence of a critical crystal size. Below the critical size, the yield hardening is controlled by size effect. Otherwise, it is controlled by irradiation effect. Furthermore, the proposed model can easily predict this critical crystal size, which may provide a quick guideline to distinguish different hardening mechanisms regarding different crystal sizes.

Atomistic simulation of the interaction between mobile edge dislocations and radiation-induced defects in Fe-Ni-Cr austenitic alloys

The classical molecular dynamics method is employed to simulate the interaction of edge dislocations with interstitial Frank loops (2 and 5 nm in diameter) in the Fe-Ni10-Cr20 model alloy at the temperatures T = 300–900 K. The examined Frank loops are typical extended radiation-induced defects in austenitic steels adapted to nuclear reactors, while the chosen triple alloy (Fe-Ni10-Cr20) has the alloying element concentration maximally resembling these steels. The dislocation-defect interaction mechanisms are ascertained and classified, and their comparison with the previously published data concerning screw dislocations is carried out. The detachment stress needed for a dislocation to overcome the defect acting as an obstacle is calculated depending on the material temperature, defect size, and interaction geometry. It is revealed that edge dislocations more efficiently absorb small loops than screw ones. It is demonstrated that, in the case of small loops, the number of reactions accompanied by loop absorption increases with temperature upon interaction with both edge and screw dislocations. It is established that Frank loops are stronger obstacles to the movement of screw dislocations than to the movement of edge ones.

Mapping strain rate dependence of dislocation-defect interactions by atomistic simulations

Probing the mechanisms of defect-defect interactions at strain rates lower than 10(6) s(-1) is an unresolved challenge to date to molecular dynamics (MD) techniques. Here we propose an original atomistic approach based on transition state theory and the concept of a strain-dependent effective activation barrier that is capable of simulating the kinetics of dislocation-defect interactions at virtually any strain rate, exemplified within 10(-7) to 10(7) s(-1). We apply this approach to the problem of an edge dislocation colliding with a cluster of self-interstitial atoms (SIAs) under shear deformation. Using an activation-relaxation algorithm [Kushima A, et al. (2009) J Chem Phys 130:224504], we uncover a unique strain-rate-dependent trigger mechanism that allows the SIA cluster to be absorbed during the process, leading to dislocation climb. Guided by this finding, we determine the activation barrier of the trigger mechanism as a function of shear strain, and use that in a coarse-graining rate equation formulation for constructing a mechanism map in the phase space of strain rate and temperature. Our predictions of a crossover from a defect recovery at the low strain-rate regime to defect absorption behavior in the high strain-rate regime are validated against our own independent, direct MD simulations at 10(5) to 10(7) s(-1). Implications of the present approach for probing molecular-level mechanisms in strain-rate regimes previously considered inaccessible to atomistic simulations are discussed.

Effects of hydrogen on interaction between dislocations and radiation-induced defects in austenitic stainless steels

Effects of solute hydrogen on slip deformation behavior and dislocation–defect interaction were investigated by using Fe ion-irradiated stainless steels. Types 304 and 316 stainless steel (304SS and 316SS) specimens irradiated to 10dpa with 2.8MeV Fe ions were strained in tension to 2% plastic strain at 573K in 3 or 75MPa hydrogen and 1atm argon gas atmospheres, and then slip line spacing and height measurements and cross-sectional microstructure observations were conducted. Slip concentration into dislocation channels due to irradiation was suppressed in the presence of solute hydrogen because solute hydrogen is suggested to promote sweeping of dislocation loops by dislocation glide. Such effects of solute hydrogen would mitigate slip localization in neutron-irradiated stainless steels. The effects of solute hydrogen were not observed for 316SS specimens, probably due to insufficient hydrogen concentration, because hydrogen-carrying dislocations could more readily cross-slip in steels with high stacking fault energies resulting in less accumulation of solute hydrogen at dislocation–defect interaction points.

Predicting plastic flow and irradiation hardening of iron single crystal with mechanism-based continuum dislocation dynamics

Continuum dislocation dynamics (CDD) with a novel constitutive law based on dislocation density evolution mechanisms was developed to investigate the deformation behaviors of single crystals. The dislocation density evolution law in this model is mechanism-based, with parameters predicted by lower-length scale models or measured from experiments, not an empirical law with parameters back-fitted from the flow curves. Applied on iron single crystal, this model was validated by experimental data and compared with traditional single crystal constitutive models using a Hutchinson-type hardening law or a dislocation-based hardening law. The CDD model demonstrated higher fidelity than other constitutive models when anisotropic single crystal deformation behaviors were investigated. The traditional Hutchinson type hardening laws and other constitutive laws based on a Kocks formulated dislocation density evolution law will only succeed in a limited number of loading directions. The main advantage of CDD is the novel physics-based dislocation density evolution laws in describing the meso-scale microstructure evolution. Another advantage of CDD is on cross-slip, which is very important when loading conditions activate only one primary slip system. In addition to the dislocation hardening, CDD also takes into consideration dislocation defect interactions. Irradiation hardening of iron single crystal was simulated with validation from experimental results.

In Situ and Electron Tomography Observations of Dislocation-Defect Interactions in Ion Irradiated Austenitic Stainless Steels

Extended abstract of a paper presented at Microscopy and Microanalysis 2011 in Nashville, Tennessee, USA, August 7–August 11, 2011.

Mesoscale thermodynamic analysis of atomic-scale dislocation–obstacle interactions simulated by molecular dynamics

Given the time and length scales in molecular dynamics (MD) simulations of dislocation–defect interactions, quantitative MD results cannot be used directly in larger scale simulations or compared directly with experiment. A method to extract fundamental quantities from MD simulations is proposed here. The first quantity is a critical stress defined to characterise the obstacle resistance. This mesoscopic parameter, rather than the obstacle ‘strength’ designed for a point obstacle, is to be used for an obstacle of finite size. At finite temperature, our analyses of MD simulations allow the activation energy to be determined as a function of temperature. The results confirm the proportionality between activation energy and temperature that is frequently observed by experiment. By coupling the data for the activation energy and the critical stress as functions of temperature, we show how the activation energy can be deduced at a given value of the critical stress.

Stacking fault energy and plastic deformation of fully austenitic high manganese steels: Effect of Al addition

Dependence of the dislocation glide mode and mechanical twinning on the stacking fault energy (SFE) in fully austenitic high manganese steels was investigated. Fully austenitic Fe–22Mn– xAl–0.6C ( x = 0, 3, and 6) steels with the SFE in the range of 20–50 mJ/m 2 were tensile tested at room temperature, and their deformed microstructures were examined at the different strain levels by optical microscopy and transmission electron microscopy. Deformation of all steels was dominated by planar glide before occurrence of mechanical twinning, and its tendency became more evident with increasing the SFE. No dislocation cell formation associated with wavy glide was observed in any steels up to failure. Dominance of planar glide regardless of the SFE is to be attributed to the glide plane softening phenomenon associated with short range ordering in the solid solution state of the present steels. Regarding mechanical twinning, the higher the SFE is, the higher the stress for mechanical twinning becomes. However, in the present steels, mechanical twinning was observed at the stresses lower than those predicted by the previous model in which the partial dislocation separation is considered to be a function of not only the SFE but also the applied stress. An analysis revealed that, of the various dislocation–defect interactions in the solid solution alloy, the Fisher interaction tied to short range ordering is qualitatively shown to lower the critical stress for mechanical twinning.

Atomistic simulation of He bubble in Fe as obstacle to dislocation

Degradation of mechanical properties due to nanometric irradiation induced defects is one of the challenging issues in designing materials for future fusion reactors. Various types of defects such as voids and He bubbles may be produced due to high dose of neutron irradiation due to fusion reaction. We study the influence of He bubble on the mobility of an edge dislocation in pure bcc-Fe using molecular dynamics simulation as a function of bubble size, He density and temperature. It appears that low contents He bubbles are penetrable defects, which size and temperature rise make them harder and softer, respectively. At high He contents a size dependent loop punching is observed, which at larger bubble sizes leads to a multistep dislocation-defect interaction. It also appears that the bubble surface curvature and temperature are the main parameters in the screw segments annihilation needed for the release of the dislocation from the bubble.

Effect of interatomic potential on the behavior of dislocation-defect interaction simulation in α-Fe

Molecular dynamics simulation is one of the most useful methods to model defect generation and subsequent change in mechanical properties in material that will suffer irradiation in the future fusion reactors. This work is aimed at showing the influence of the empirical interatomic potential for the Fe–Fe interaction on the simulated shearing of α-Fe containing one edge dislocation interacting with one nanometric void sitting on its glide plane. The recent potentials derived by Ackland et al. [G.J. Ackland, D.J. Bacon, A.F. Calder, T. Harry, Philosophical magazine a-physics of condensed matter structure defects and mechanical properties 75 (1997) 713], Mendelev et al. [M.I. Mendelev, S. Han, D.J. Srolovitz, G.J. Ackland, D.Y. Sun, M. Asta, Philos. Mag. 83 (2003) 3977] and Dudarev–Derlet [S.L. Dudarev, P.M. Derlet, J. Phys. Condens. Matter 17 (2005) 7097] are used to identify critical parameters. The stress–strain responses are obtained under imposed strain rate and at temperatures ranging from 10 to 700 K at constant volume. It appears that different potentials give different strengths and rates of decrease of obstacle strength with increasing temperature. Results are analyzed in terms of dislocation core structure and thermal expansion. Implications for the choice of the potential are given.

Mechanical and energetical analysis of molecular dynamics simulations of dislocation–defect interactions

In this paper, we present a method of analysis on the continuum scale of molecular dynamics simulations of dislocation–defect interactions. It is shown how the applied work can be decomposed into its elementary components: the elastic strain energy, the dissipated work against the Peierls stress and the curvature energy needed to enable the dislocation, pinned by the defect, to bow out. While the dissipated work is entirely extracted from the system in molecular statics, the elastic and curvature energies contribute to a large increase in the internal energy. The curvature energy is evaluated and compared with predictions of the line tension model. This analysis allows the calculation of the dislocation–defect interaction energy and the determination of the predominant features in the unpinning process.

Dynamic observations and atomistic simulations of dislocation–defect interactions in rapidly quenched copper and gold

Dislocation interactions with quenched-in defects, which are either partial or complete stacking-fault tetrahedra, in copper and gold have been studied by combining static and dynamic transmission electron microscope studies with molecular dynamics computer simulations. The interaction of a dislocation with a stacking-fault tetrahedron can result in the tetrahedron being sheared into two defects, converted to another defect type, or annihilated. These observations provide insight into defect interaction and annihilation mechanisms that are responsible for creating the defect-free channels in deformed irradiated material.

Dislocation defect interaction in irradiated Cu

Pure Cu single crystals irradiated at room temperature to low doses with 590 MeV protons have been deformed in situ in a transmission electron microscope in order to identify the basic mechanisms at the origin of hardening. Cu irradiated to 10 −4 dpa shows at room temperature a yield shear stress of 13.7 MPa to be compared to the 8.8 MPa of the unirradiated Cu. Irradiation induced damage consists at 90% of 2 nm stacking fault tetrahedra, the remaining being dislocation loops and unidentified defects. In-situ deformation reveals that dislocation–defect interaction can take several forms. Usually, dislocations pinned by defects bow out under the applied stress and escape without leaving any visible defect. From the escape angles obtained at 183 K, an average critical stress of 100 MPa is deduced. In some cases, the pinning of dislocations leads to debris that are about 20 nm long, which formation could be recorded during the in situ experiment.

On dislocation–defect interactions and patterning: stochastic discrete dislocation dynamics (SDD)

The problem of dislocation patterning and interaction of threading dislocations with immobile dislocation loops and defects is investigated analytically and computationally based on a statistical analysis and a recently developed model of discrete stochastic dislocation dynamics (SDD), respectively. The statistical analysis is based on the Friedel–Kocks model and shows the validity of the Friedel relation for the critical resolved stress while a power law with different stress dependence is obtained for the average pinning distance on a stable dislocation array. The difference of the stress dependence is attributed to each model assumptions, such as stable dislocation configurations in athermal system or meta-stable configurations in thermally activated system. The SDD computational study includes thermal and strain fluctuation, predicting non-trivial fractal instability of the plastic strain. The height difference correlations of the plastic strain show that the external load causes a multifractality, and enhances the instability at higher order moments.

Second IEA fusion materials agreement workshop on modeling and experimental validation

The present workshop dealt both theoretically and experimentally with issues of primary damage and irradiation induced defect evolution, helium and other impurities, dislocation–defect interactions, deformation to large plastic strains and fracture. It was focused on the bcc structure (Fe, V and their alloys), but a number of presentations and discussions were centred around results in the fcc and hcp structures.

Multiscale Dislocation Dynamics Plasticity

A recently developed discrete dislocation dynamics (DD) model for crystalline materials coupled with finite elements (FE) analysis is reviewed. The three-dimensional continuum-based FE formulation for elastoviscoplasticity incorporates the DD simulation, replacing the usual plasticity constitutive relationships, leading to what is called multiscale dislocation dynamics plasticity (MDDP). The coupling involves a nontrivial homogenization to obtain local plastic strains from the contributions of discrete plastic events captured in DD. The superposition principle is used in order to find the effects of the boundaries (free, rigid, or interfaces) on the dislocation movement. The developed computer code can efficiently handle size-dependent small-scale plasticity phenomena and related material instabilities at various length scales ranging from the nano-microscale to the mesoscale. The DD modeling is based on the fundamental physical laws governing dislocation motions and their interactions with various defects, interfaces, and external loadings. The multiscale frame of consideration merges the two scales of nano-microscale, where plasticity is determined, and the continuum scale, where the energy transport is based. In order to illustrate the usefulness of this approach in investigating a wide range of plasticity phenomena, results for a set of case studies are presented. This includes the deformation and dislocation structure during nano-indentation in bcc and fcc single crystals, analyses pertaining to the formation of dislocation boundaries during heavy deformation, dislocations interaction with shock-waves during impact loading conditions, and dislocation–defect interaction.

In-situ transmission electron microscopy observations and molecular dynamics simulations of dislocation-defect interactions in ion-irradiated copper

An in-situ transmission electron microscopy straining technique has been used to investigate the dynamics of dislocation-defect interactions in ion-irradiated copper and the subsequent formation of defect-free channels. Defect removal frequently required interaction with multiple dislocations, although screw dislocations were more efficient at annihilating defects than edge dislocations were. The defect pinning strength was determined from the dislocation curvature prior to breakaway and exhibited values ranging from 15 to 175 MPa. Pre-existing dislocations percolated through the defect field but did not show long-range motion, indicating that they are not responsible for creating the defect-free channels and have a limited contribution to the total plasticity. Defect-free channels were associated with the movement of many dislocations, which originated from grain boundaries or regions of high stress concentration such as at a crack tip. These experimental results are compared with atomistic simulations of the interaction of partial dislocations with defects in copper and a dispersed-barrier-hardening crystal plasticity model to correlate the observations to bulk mechanical properties.

Mechanisms of dislocation-defect interactions in irradiated metals investigated by computer simulations

During irradiation, mobile defects, defect clusters and impurity atoms segregate on dislocations. When an external stress is applied, plastic flow is initiated when dislocations are unlocked from segregated defects. Sustained plasticity is achieved by continuation of dislocation motion, overcoming local forces due to dispersed defects and impurities. The phenomena of flow localization, post-yield hardening or softening and jerky flow are controlled by dislocation-defect interactions. We review here computational methods for investigations of the dynamics of dislocation-defect interactions. The influence of dislocations on the motion of glissile self-interstitial atoms (SIAs) and their clusters is explored by a combination of kinetic Monte Carlo and dislocation dynamics. We show that dislocation decoration by SIAs is a result of their 1-D motion and rotation as they approach dislocation cores. The interaction between dislocations and immobilized SIA clusters indicates that the unlocking mechanism is dictated by shape instabilities. Finally, computer simulations for the interaction between freed dislocations and stacking fault tetrahedra in irradiated Cu, and between dislocations and microvoids in irradiated iron are presented, and the results show good agreement with experimental observations.

Dislocation-defect interactions in nuclear reactor pressure-vessel steels investigated by means of internal friction

A study of pressure-vessel steel embrittlement mechanisms by means of temperature-dependent and amplitude-dependent internal friction has been carried out within the framework of commercial surveillance of nuclear reactor components. An inverted torsion pendulum operating at ∼1 Hz has been employed to study a wide variety of pressure-vessel steels and an IAEA reference material in various conditions. This contribution will discuss the results for the JRQ reference material only and serve as a basis on which to interpret the data from real pressure-vessel steels. The temperature-dependent experiments evidence a reduction in the dislocation mobility as a result of neutron irradiation and prove that the technique is sensitive to thermal ageing involving changes in the dislocation mobility and type of dislocation-defect interaction. Amplitude-dependent internal friction provides a means to determine the yield strength of the material. The importance of the influence of dislocation dragging on the yield stress is highlighted.