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Characterization of the tip field of a discrete dislocation pileup for the development of physically based micromechanics

It is shown, on the basis of calculations by Eshelby et al. (1951), Armstrong et al. (1966), and Chou and Li (1969), that a single parameter, such as the force on the leading dislocation (F), the crack extension force, or the stress intensity factor, is capable of characterizing uniquely the entire tip field of a discrete dislocation pileup, including the positions of mobile dislocations behind the locked leading dislocation at the tip. Conversely, the position of the i-th mobile dislocation X(i) is related to the value of F and is capable of characterizing the entire stress, strain, and displacement fields at the tip of a discrete dislocation pileup. If the interactions between dislocations are linear elastic, the measured positions of the mobile dislocations can be used to determine the value of F, which can then be used as a quantitative measure of the strength of a dislocation barrier resisting the propagation of a microslip or the nucleation of a microfracture.

Gao, Q.↗

Single-parameter characterization of discrete-dislocation pileup tipfield and its application to physically based micro-mechanics

The equivalence between continuous dislocation pileups and cracks is reviewed. The force on the leading dislocation is defined and a general method of calculation of the force is proposed. The equivalence relations are given. Based on the analysis by Eshelby, Frank, and Nabarro and the numerical calculations by Chou and Li and Armstrong et al, it will be shown that the force, F, on the locked leading dislocation of a discrete pileup is capable of characterizing uniquely the stress, strain, and displacement fields at the tip of the pileup, including the positions of the discrete mobile dislocations behind the leading dislocation. Conversely, the positions of the mobile dislocations can be used to measure F. If the propagation of micro-slips and the initiation of micro-fractures at the tip of a pileup are controlled by resolved shear stress and normal cleavage stress respectively, the resolved shear stress intensity coefficient, ReSIC, and the resolved cleavage stress intensity coefficient, ReCIC, must be constant.

Liu, H. W.↗

Effect of a micro-scale dislocation pileup on the atomic-scale multi-variant phase transformation and twinning

In this paper, we perform concurrent atomistic–continuum (CAC) simulations to assess the contribution of the internal stress induced by the microscale dislocation pileup at an atomically structured interface to the atomic-scale phase transformations (PTs), reverse PTs, and twinning. The main novelty of this work is to unify the atomistic description of the interface and the coarse-grained (CG) description of the lagging dislocations away from the interface within one single framework. Our major findings are: (a) the interface dynamically responds to a pileup by forming steps/ledges, the height of which is proportional to the number of dislocations arriving at the interface; (b) the pileup-induced internal stress concentration profile follows neither the classical Eshelby model nor the super-dislocation model alone, but a combination of them; (c) when the pre-sheared sample is compressed, a direct square-to-hexagonal PT occurs ahead of the pileup tip and eventually grows into a wedge shape. The two variants of the hexagonal phases form a twin with respect to each other; (d) upon a further increase of the loading, part of the newly formed hexagonal phase transforms back to the square phase. The square product phase resulting from this reverse PT forms a twin with respect to the initial square phase. All phase boundaries (PBs) and twin boundaries (TBs) are stationary and correspond to zero thermodynamic Eshelby driving forces; and (e) the microscale dislocation pileup-induced internal shear stress and the structural change at the atomic-scale interface reduces the stress required for initiating a PT by a factor of 5.5, comparing with that in the sample containing no dislocations. This work is the first characterization of the behavior of PTs/twinning resulting from the reaction between a microscale dislocation slip and an atomically structured interface. In conclusion, the gained knowledge will advance our understanding of how the multi-phase material behaves in many complex physical processes, such as the synthesis of multi-phase high-entropy alloys or superhard ceramics under high-pressure torsion, deep mantle earthquakes in geophysics, and so on, which all involve dislocation slip, PTs, twinning, and their interactions across from the atomistic to the microscale and beyond.

36 MATERIALS SCIENCE↗

The development of physically based micro-mechanics - Based on the characteristic tip field of dislocation pileup

Based on the analytical solution by Eshelby et al. (1951) and the numerical calculations by Chou and Li (1969) and Armstrong et al. (1962), it is shown that the force, F, on the locked leading dislocation of a discrete dislocation pileup is capable of characterizing uniquely the stress, strain, and displacement field at the tip of the pileup, including the positions of the discrete mobile dislocations next to the leading dislocation. Conversely, the positions of the mobile dislocations can be used to measure F. The F thus measured can be used to study micro-plastic deformation and micro-fractures at grain boundaries or any other dislocation barriers.

Gao, Q.↗

Void growth via dislocation pileup impingement on grain boundary

In this work, the effect of edge dislocations, impinging on grain boundary in fcc Fe near a preexisting void on the volume of this void, was studied using MD simulation. It was found that virtually unlimited growth of the void via this mechanism is possible under certain conditions. To the best of our knowledge this is the first atomistic simulation study, demonstrating feasibility of this void growth mechanism.

36 MATERIALS SCIENCE↗

Correlating dislocation structures to basal and prismatic slip bands near grain boundaries in tensile-tested Mg–4Al using a multiscale electron microscopy approach

Dislocation structures where basal and prismatic slip bands meet grain boundaries in tensile-tested Mg with 4 wt% Al (Mg–4Al) were studied using a multiscale electron microscopy approach to explore the assumptions made for the dislocation pileup theory: a) slip bands consist of dislocation arrays piling up near grain boundaries, and b) stress concentration in the adjacent grain is solely caused by dislocation pileup. After post-testing electron backscatter diffraction (EBSD) scans, focused-ion-beam (FIB) lift-out specimens were prepared from regions of interest so that the specimen plane is parallel to the bulk sample surface to allow for direct correlation between mesoscale and microscale characterization. High dislocation density and the dislocation arrays in the slip bands corroborated with the first assumption. Evidence of plastic deformation in all grains, however, showed that the second assumption was false. Additionally, dislocation structures including crystal rotation boundaries and dislocations dissociating to the basal plane provide additional stress relief mechanisms near grain boundaries that are not accounted for in many crystal plasticity models, which requires auxiliary models to more accurately predict the stress and strain distribution in a microstructure.

36 MATERIALS SCIENCE↗

Tailoring composition and deformation modes at the microstructural level for next generation low-cost high-strength austenitic stainless steels

The objective of this project is to enable deliberate development of cost-effective, hydrogen resistant alloys by establishing detailed relationships specific to the effects of alloy composition, short-range order (SRO), and microsegregation in the presence of hydrogen on the transition between homogeneous deformation and localized plasticity in shear bands. In collaboration with the International Institute for Carbon-Neutral Energy Research, I2CNER, at Kyushu University in Japan, we conceptualized, designed, and manufactured four austenitic alloys that maintain corrosion resistance and ensure lower cost relative to baseline commercial alloys. The mechanical properties and deformation modes of the novel alloys (KU alloys) were assessed in the presence of hydrogen (H). Correlations between composition and performance revealed that two of the KU alloys are suitable replacements for 316 steel, while another is a viable replacement for 304 steel at room temperature. We found that, in the presence of other austenite stabilizing elements namely Mn and N, replacing Ni with Cu does not lead to martensite formation as has been previously reported.1–3 Furthermore, we found that the addition of Cu leads to an earlier onset of multiple slip resulting in an relative earlier onset of a higher work hardening rate (WHR). Greater understanding of the relationships between alloy composition and SRO required the development of a novel advanced electron diffraction methodology to characterize SRO in complex FCC alloys. This innovative approach, which combines fluctuation and correlation analyses of diffuse-scattering signals, successfully differentiated between SRO and long-range ordering (LRO). Further investigations into annealed austenitic stainless steels could provide insights into manipulating SRO and its effects on material properties. Atomistic simulations provided understanding of SRO behavior that was difficult to capture experimentally. This project created the first spin cluster expansion model that is able to capture and describe SRO effects in Fe-Ni-Cr FCC alloys, accounting for the non-negligible effects of magnetism. An automated computational workflow was established to provide reliable predictions of SRO in Fe-Ni-Cr austenitic alloys, both with and without the presence of H atoms. Analysis of the propensity for SRO in Fe-Ni-Cr alloys revealed that H tends to cluster with specific, well-defined SRO domains. The computational framework is general purpose and can be extended to realistic stainless steels across diverse composition ranges. With confidence that SRO is possible in austenitic stainless steels, we developed a discrete dislocation finite element code to understand the interaction of dislocations with SRO in the presence of H. By incorporating H effects on the dislocation emission and SRO stress field we show that the critical stress for the dislocation pileup to breakthrough the SRO domain decreases in the presence of H, which directly contributes localized deformation at the macroscale. Through the simulation of a uniaxial tension test, we demonstrated that H-induced weakening of SRO stress field and H-enhanced dislocation emission can lead to the onset of shear localization at lower macroscopic strains. As a whole, this project identified three novel alloys that show improvements in performance and cost efficiency for H-facing applications by studying correlations between alloy chemistry and deformation behavior. We also made significant advancements to experimental and computational methodologies necessary to study the chemistry and distribution of SRO across a range of alloys, which in turn allowed us to demonstrate how deformation mechanisms change due to the contributions of SRO in austenitic alloys in the presence of H. The combined advancements in fundamental understanding with novel alloy development in this project has increased the viability of next generation H-technologies for the broader public through accessible low-cost alloys and accelerated development towards future H-infrastructure.

08 HYDROGEN↗

Molecular dynamics simulation of vacancy and void effects on strain-induced martensitic transformations in Fe-50 at.% Ni model concentrated solid solution alloy

Strain-induced martensitic transformations can improve the strength and ductility of some face centered cubic (FCC) metals and alloys. Irradiation-induced defects such as vacancies, dislocation loops, and voids activate martensitic transformations over a wider range of mechanical loading conditions than in pristine material. Furthermore, the mechanisms underlying irradiation-enabled martensite transformations remain unclear. In this work, we use molecular dynamics simulations to study the effect of vacancies and voids on strain-induced martensitic transformations in a model concentrated solid solution alloy Fe-50 at.% Ni. It has been found that single vacancies have no resolvable effect on the transformation because they reduce the stacking fault energy by a relatively insignificant margin and do so only if the vacancy is located on the stacking fault plane. Voids, however, activate the martensite transformation through shear strain accumulation around the void due to dislocation pileup. The larger the void, the more pronounced this effect.

36 MATERIALS SCIENCE↗

Complexity of segregation behavior at localized deformation sites formed while in service in a 316 stainless steel baffle-former bolt

Here, post-irradiation evaluation was performed on a 316 stainless steel baffle former bolt harvested after 40 years of service in a pressurized water reactor. Microstructure analysis revealed the presence of defect-free dislocation channels and strain-induced twins, indicative of loading at a stress level close to yield stress at least once while in service. Primary radiation-induced Ni/Si precipitates were destroyed during channel and twin formation, and secondary, significantly coarser Ni/Si precipitates formed along newly formed Σ3 boundaries during the continued irradiation. Additionally, an elevated phosphorus level was observed inside the strain-induced twin. Complex chemistry inside the strain-induced feature may overlap with dislocation pileups and impact localized corrosion, material long-term performance, and safety.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A Comparison of Solidification Structures and Submicroscale Cellular Segregation in Rapidly Solidified Stainless Steels Produced via Two-Piston Splat Quenching and Laser Powder Bed Fusion

Fusion-based additive manufacturing techniques leverage rapid solidification (RS) conditions to create parts with complex geometries, unique microscale/nanoscale morphological features, and elemental segregation. Three custom composition stainless steel alloys with varying chromium equivalence to nickel equivalence ratio (Cr eq /Ni eq ) between 1.53 and 1.95 were processed using laser powder bed fusion (LPBF) and/or two-piston splat quenching (SQ) to produce solidification rates estimated between 0.4 and 0.8 m/s. Both scanning electron microscopy (SEM) and transmission electron microscopy (TEM) were utilized to collect high-resolution images, electron backscatter diffraction (EBSD) phase identification, and measure cellular segregation. Similar features were observed in both LPBF and SQ samples including phase and microstructure, nanoscale oxide particles, cell size, and segregation behavior. However, dislocation pileup was observed along the cell boundaries only in the LPBF austenite solidified microstructure. Targeted adjustment of the SQ feedstock Cr and Ni concentrations, within the ASTM A240 specification for 316L resulted in no observable impact on the cell size, oxide particle size, or magnitude of segregation. Also, the amount of Ni segregation in the ferrite solidified microstructures did not significantly differ, regardless of Cr/Ni eq or processing technique. Here, SQ is demonstrated as capable of simulating RS rates and microstructures similar to LPBF for use as an alternative screening tool for new RS alloy compositions.

42 ENGINEERING↗

The fine structure of slip lines in disordered Cu3Au.

The fine structure of the slip bands observed on the surface of a deformed Cu3Au single crystal is examined. The separation distance determined between the resolved individual slip lines is used to examine the calculations of other authors relating the passing stress of a dislocation past a dislocation pileup on a nearby parallel glide plane.

Salama, K.↗

Dislocation-density evolution and pileups in bicrystalline systems

Here, a dislocation-density crystalline plasticity (DCP) framework based on total and partial dislocation densities interactions was used to investigate the behavior of Cu/Pb bicrystals with a focus on GB effects. The modeling predictions were validated with bicrystal compression micropillar experiments. A key new aspect of the modeling approach is to account for partial dislocation-densities. A GB formulation that is directly linked to GB energies was used to monitor GB transmission and blockages, such that pileups can be monitored and predicted at the GB interfaces for misorientations. The predictions indicate that pileups can form due to fully and partially blocked slip-rates and perfect and partial dislocation-densities. As the nominal strain increases from five to fifteen percent, dislocation-densities and pileups significantly increase by almost an order of magnitude. The proposed validated approach provides a microstructural scale predictive framework that accounts for a myriad of defects related to the interactions of partial and perfect dislocation densities that interact at highly misoriented GBs; it is these interactions that are critical to the formation and evolution of dislocation-density pileups that can lead to physically limiting stress accumulations in bicrystals.

36 MATERIALS SCIENCE↗

Slip band characteristics in the presence of grain boundaries in nickel-based superalloy

Shear strain profiles along slip bands in a modified Rolls-Royce nickel superalloy (RR1000) were analyzed for a tensile sample deformed by 2%. The strain increased with distance away from a grain boundary (GB), with maximum shear strain towards the center of the grain, indicating that dislocation nucleation generally occurred in the grain interior. The strain gradients in the neighborhood of the GBs were quantified and generally correlated with rotation about the active slip system line direction. This leads to an ability to determine the active slip system in these regions. The dislocation spacing and pileup stresses were inferred. The dislocation spacing closely follows an Eshelby analytical solution for a single ended pileup of dislocations under an applied stress. The distribution of pileup stress values for GBs of a given misorientation angle follows a log-normal distribution, with no correlation between the pileup stress and the GB misorientation angle. Furthermore, there is no observed correlation between various transmissivity factors and slip band pileup stress. Hence it appears that the obstacle strength of any of the observed GBs is adequate to facilitate the dislocation pileups present in the slip bands. However, slip band transmission does correlate with transmissivity factors, with the current study focusing on the Luster and Morris m’-factor. Observation of strain profiles of transmitted bands indicate dislocation nucleation locations.

36 MATERIALS SCIENCE↗

Dislocation-graphene interactions in Cu/graphene composites and the effect of boundary conditions: a molecular dynamics study

Here, in this paper, systematic molecular dynamics simulations were employed to study dislocation-graphene interactions in Cu/graphene systems using two carefully selected configurations: (i) edge dislocations in the pileup interacting with graphene during nanoindentation and (ii) complex dislocations interacting with graphene in compression of layered nanopillars. The intrinsic and extrinsic size effects were investigated with respect to varying the Cu lamella thickness and pillar sizes, revealing an anomalous extrinsic size effect: the smaller, the weaker. To understand which boundary conditions are physically consistent, both free and periodic graphene were considered. It was seen that edge dislocations in the pileup continuously transmitted across the free graphene through Cu/graphene interfacial sliding and graphene reorientation, whereas transmission was very difficult for periodic graphene as its in-plane deformation was required. In compression of Cu/graphene nanopillars, the strengthening effect of free graphene was found to be less obvious than that of the periodic case, which could be attributed to free graphene edges acting as dislocation sources after the compressed Cu overflowed the graphene sheet from all directions. We therefore conclude that the strengthening effect of periodic graphene inclusions appears to be overestimated, such that free graphene should be more appropriate.

36 MATERIALS SCIENCE↗

Unusual plastic strain-induced phase transformation phenomena in silicon

Pressure-induced phase transformations (PTs) in Si, the most important electronic material, have been broadly studied, whereas strain-induced PTs have never been studied in situ. Here, we reveal in situ various important plastic strain-induced PT phenomena. A correlation between the direct and inverse Hall-Petch effect of particle size on yield strength and pressure for strain-induced PT is predicted theoretically and confirmed experimentally for Si-I→Si-II PT. For 100 nm particles, the strain-induced PT Si-I→Si-II initiates at 0.3 GPa under both compression and shear while it starts at 16.2 GPa under hydrostatic conditions. The Si-I→Si-III PT starts at 0.6 GPa but does not occur under hydrostatic pressure. Pressure in small Si-II and Si-III regions of micron and 100 nm particles is ~5–7 GPa higher than in Si-I. For 100 nm Si, a sequence of Si-I → I + II → I + II + III PT is observed, and the coexistence of four phases, Si-I, II, III, and XI, is found under torsion. Retaining Si-II and single-phase Si-III at ambient pressure and obtaining reverse Si-II→Si-I PT demonstrates the possibilities of manipulating different synthetic paths. The obtained results corroborate the elaborated dislocation pileup-based mechanism and have numerous applications for developing economic defect-induced synthesis of nanostructured materials, surface treatment (polishing, turning, etc.), and friction.

36 MATERIALS SCIENCE↗

Reversing inverse Hall-Petch and direct computation of Hall-Petch coefficients

A 2D bicrystal atomistic model of dislocation transmission through a Σ11<101>{131} symmetric-tilt grain boundary reveals details of Hall-Petch breakdown in the single dislocation regime in Al, Ni, and Cu. Partly based on a previous study, this research determines the stress required for a single dislocation to be transmitted through the Σ11 boundary and finds that single dislocation transmission typically deviates from Hall-Petch behavior because the leading partial dislocation becomes trapped in the boundary and emits glissile grain boundary disconnections that cause boundary sliding deformation at stresses well below boundary transmission stresses. Thus, mechanisms of inverse Hall-Petch, namely grain boundary shear and sliding, are shown to operate in lieu of grain boundary transmission in the single dislocation regime. However, by controlling the applied stresses, inverse Hall-Petch can be reversed and typical Hall- Petch grain boundary transmission regained. This, in turn, allows the direct computation of Hall-Petch coefficients. Further, a second dislocation on the same slip plane preserves typical Hall-Petch behavior for Al and Ni and does not lead to boundary sliding events, thus implying a critical grain size for Hall-Petch breakdown based on the pileup model.

36 MATERIALS SCIENCE↗