Search

This study investigates the mechanical behaviour of nanocrystalline Cu-Ag alloys using molecular dynamics simulations combined with detailed analyses of dislocation densities, atomic populations, and deformation characteristics. Shear tests were conducted across three different atomic compositions at temperatures ranging from 10 K to 500 K. The influence of temperature and Ag impurities on the mechanical properties of nanocrystalline Cu is explored. Elevated temperatures are found to promote plastic deformation by increasing atomic mobility, resulting in reduced dislocation densities and flow stresses. Increasing Ag content correlates with lower dislocation densities, highlighting enhanced plastic activity between grain and grain boundaries. Structural population analysis underscores the significant impact of Ag species on the mechanical response of nanocrystalline Cu. Further investigations are warranted to explore additional deformation mechanisms. These findings contribute to a deeper understanding of nanocrystalline Cu-Ag alloys, informing the design of novel materials with tailored mechanical properties. [ABSTRACT FROM AUTHOR]

An edge dislocation with a time-dependent Burgers vector in an orthotropic plane is analyzed. The stress field caused by a dynamic point force in the intact plane is determined. The displacement discontinuity of dislocation and direction of point load are at arbitrary angles with the Material Principal Axes (MPA), the general orthotropic plane. The density of dislocations is employed to construct integral equations for orthotropic planes weakened by several interacting cracks, making arbitrary angles with the MPA. The numerical solution of integral equations results in the density of dislocations on a crack surface. The results are employed to determine time-dependent Stress Intensity Factors (SIFs) at the tips of a crack and Crack Opening Displacement (COD). In the problem of general orthotropic planes containing cracks subjected to dynamic loads, crack orientations may cause their partial/total closing. Under the hypothesis of frictionless contact, we devise an iterative procedure to handle crack closing, as well. By contrast to cracks in the directions of MPA, expressions for the two modes of SIFs contain the density functions of both the climb and glide of the edge dislocation. Therefore, mode I SIF at an open tip of a crack may not be positive. Conversely, positive mode I SIF may occur at a closed crack tip. Numerical results of the SIFs and COD for several examples of orthotropic planes under dynamic point loads, while weakened by single and double parallel cracks, are presented. Moreover, in double cracks cases, the interaction between cracks is studied. [ABSTRACT FROM AUTHOR]

Herein, we explore the effect of dynamic strain aging (DSA) on dislocation evolution using nanoindentation and transmission electron microscopy (TEM). DSA is primarily manifested as serrations on the load-displacement curves at lower strain rates (10−2 and 10−3 s−1), whereas these serrations are substantially less at higher strain rate (10−1 and 100 s−1). Interestingly, despite variations in strain rates and DSA occurrence, detailed TEM observations beneath the indentations reveal no discernible differences in dislocation density and substructure. The present study indicates that although DSA can increase the gliding resistance of dislocations, it does not affect the evolution of dislocation. [ABSTRACT FROM AUTHOR]

Equal Channel Angular Pressing (ECAP) is one of the severe plastic deformation methods that is applied to metals, alloys and composite materials in order to convert the normal grain structure into ultra-fine grain structure, so as to increase the strength of the metal and its ductility. The uniqueness of ECAP is that the severe plastic deformation apply large strains on the material without affecting the original dimensions of material. ECAP process was chosen among the other severe plastic deformation methods, because of its cost-effectiveness and simplicity. Die angle, corner angle, ECAP routes, number of passes and heat treatments have great impact on the micro-structure and mechanical properties of various materials. The grain refinement enhances the yield strength, tensile strength, hardness, ductility and corrosion resistance on ECAPed materials, which are commonly used for engineering and bio-medical applications. Many researchers have contributed greatly to this method. This article mainly focuses on the effect of ECAP die orientations and on novel ECAP methods that exclusively combines ECAP with heat treatment or hot working on aluminium, magnesium, titanium and other materials. [ABSTRACT FROM AUTHOR]

In the current investigation, cold work influence on mechanical strength, microstructure, hardness and ductile to brittle transition (DBT) in pure (P) 304 L-stainless steel (SS) (with ultra-low content of sulphur (0.001%) and phosphorus (nil) at several levels of cold work (5%, 10%, 20% and 30%) are reported, which provide valuable information regarding beneficial effects of reduced level of sulphur for the material selection in structural design. The cold work results in dual-phase (γ + ${\rm{\alpha {^{\prime}}}}$ α ′ ) with distinct values of dislocation densities and grain size that are used in the modified Hall-Petch equation to obtain the corresponding change in yield strength. Cold working up to 30% increased yield strength (${{\rm{\sigma }}_y}$ σ y ) from 280 to 900 MPa, whereas ultimate tensile strength (${{\rm{\sigma }}_u}$ σ u ), increased from 620 to 950 MPa, i.e. an increase of 34.73%. The hardness values increased from 172 to 360 Hv, i.e. an enhancement of 110.5% for a cold work of 30%. The material showed a remarkable enhancement in the impact energy absorption from 200 to 390 J for a temperature change from 77 to 473 K. It is observed that cold working at 5% level reduces the impact energy absorption from 390 to 250 J, i.e. reduction of 35.89% at 298 K. The value of impact energy absorbed by P-304 L-SS was 37% higher than the commercial grade 304 L-SS (sulphur (0.03%), phosphorous (0.04%). The study succinctly brings out the importance of reduced content of sulphur and phosphorus in obtaining superior mechanical properties through cold work. [ABSTRACT FROM AUTHOR]

Dislocation evolution in multilayered Ti/Nb composites processed by accumulative roll bonding under uniaxial tension was quantitatively evaluated by high-energy X-ray diffraction. The composites with different heterogeneous microstructures show distinct dislocation activities in Ti, which majorly contributes to their different ductility. For the composite in which extensive shear bands have formed before loading, the stable fraction of 〈c+a〉 dislocations and the suppressed activation of 〈c〉 dislocations contribute to its uniform deformation. We emphasize that tracking the dynamic evolution of dislocations is fundamental for understanding ductility of the multilayers, whereas the increased 〈c+a〉 dislocations found by post-mortem analysis do not necessarily dominate. IMPACT STATEMENT: Dynamic evolution of dislocations, rather than only dislocation densities obtained by post-mortem analysis, is found to explain ductility of multilayered composites, which can be tailored by adjusting heterogeneous microstructures. [ABSTRACT FROM AUTHOR]

AbstractThe strain hardening behavior of friction stir welded AA7039 (Al-4.2Zn-3.1 Mg) alloy was explored in terms of dislocation density, crystallite size, hardening capacity, hardening exponent, and strain hardening rate. Strain hardening behavior was analyzed for base metal and friction stir welded specimens. Four different models were used to calculate the dislocation density viz., Scherrer model, uniform strain model (USM), uniform stress distribution model (USDM), and uniform strain energy distribution model (USDEM). Maximum dislocation density was obtained in base metal for all models (maximum for USM, 3.9 ×1015m−2) with a minimum crystallite size of 15.81 nm. The low dislocation density in FSW samples is due to the higher heat input in the FSW process. Strain hardening stages were shown by Kocks–Mecking type plots. Lower strain hardening capacity was obtained for BM, i.e. 0.427 as compared to FSW samples, due to the higher dislocation density of BM. It was determined that there is an inverse relationship between the strain hardening capacity and the strain hardening exponent. Strain hardening rate was higher for BM than FSW specimens, and similar results were obtained from mathematical relations that indicate the adequacy of the results. The ultimate tensile strength was 2.5% higher than the BM at a rotational speed of 1325 rpm, 35 mm/min of welding speed and 1.65° tilt angle. The maximum strength friction stir-welded specimen showed a more ductile fracture surface than the BM because the grain boundary phase disappeared or broke up in the thermomechanical affected zone. [ABSTRACT FROM AUTHOR]

In the present study, we systematically analyze the relationship between the surface microstructural evolution and rolling contact fatigue (RCF) damage behavior of the ER9 wheel tread. In the unfatigued zone (Zone A), where the shear stress was low, a thin plastic deformation layer with low hardness formed. The ferrite grains exhibited obvious plastic flow; however, these grains were not refined, and the cementite showed no significant fragmentation or dissolution. Additionally, the dislocation density remained low on the wheel surface in Zone A. Conversely, in the fatigue zone (Zone B), where the shear stress was high, a thicker plastic deformation layer with increased hardness developed. The ferrite grains in this zone were notably refined, and a substantial amount of lamellar cementite fragmented and dissolved, leading to a high dislocation density on the wheel surface. The severe plastic deformation in Zone B facilitated the formation of fatigue wear cracks on the wheel, which initiated the RCF crack in Zone B. Furthermore, the interface between pearlite and proeutectoid ferrite grains in the wheel accelerated the RCF crack propagation, ultimately leading to RCF failure. [ABSTRACT FROM AUTHOR]

A prominent strengthened Y2O3 stabilized t-ZrO2 (YSTZ)/MgO nanocomposite coating is achieved by the plasma electrolytic oxidation (PEO) process and in-situ synthesized YSTZ reinforced phase with a quantitative control approach. The idea of activating double slip systemic semi-coherent interface dislocations in YSTZ/MgO nanocomposite coating to realize crack self-healing is proposed. High dislocation densities are associated with {101} < 101> YSTZ slip and {111} < 101> MgO slip system to coordinate interfacial deformation to stop crack initiation and propagation. This crack propagation path can absorb more fracture energy, providing more opportunities for crack deflection and bridge, which closes crack and realizes crack self-healing. This paper reveals semi-coherent interface dislocation of double slip systems in nanocomposite coating stop crack initiation and propagation is proposed to realize crack self-healing. [ABSTRACT FROM AUTHOR]

This study addresses effect of shotpeening on surface characteristics of AA6061-SiCP composite. Aluminium composites with reinforcements of solitary and multiple particles are widely employed in the transportation, aerospace, and automotive sectors due to their exceptional properties, such as strength, stiffness, and wear resistance. However, the surface characteristics such as hardness, wear, and frictional properties are not improved much. To attain better surface properties, surface modification has become necessary. Therefore, shotpeening is employed with selected parameters to analyse surface topography before and after shotpeening using optical and scanning electron microscopes. Then, the average crystalline size (ACS), dislocation densities, and micro-strain are calculated with the X-ray diffraction (XRD) analysis and then correlated with the hardness of shot peened AA6061-SiCP composites in comparison with the untreated surface. The results demonstrate that increasing the shotpeening exposure durations improves surface characteristics compared to untreated AA6061-SiCP composites. At 140 s of exposure time, the micro-hardness is increased to approximately 143HV, crystallite size is refined to approximately 33.7 nm, micro-strain is enhanced by about 3.1 × 10−3, and dislocation density is increased by about 19.2 × 10−14 m−2. Severity of the shotpeening develops severe plastic deformation results in surface fracture and an increase in roughness of AA6061-SiCP composites. [ABSTRACT FROM AUTHOR]

In this paper, the contact heating technology was combined with the warm and hot stamping process of high-strength aluminum alloy, and the corresponding experimental device was developed. For the contact heating-warm stamping process, it's found that as the heating temperature increases, the mechanical properties of the parts first decrease and then increase, while the springback decreases. Meanwhile, for the contact heating-hot stamping process, it's found that the aluminum alloy sheets experience large plastic deformation during contact heating, resulting in the refinement of microstructure and the increase in dislocation density, and the performance of the formed parts is improved. [ABSTRACT FROM AUTHOR]

The Geometrically Necessary Dislocation (GND) density was estimated from Electron Backscatter Diffraction (EBSD) data for an AZ31/Mg-0.6Gd (wt.%) hybrid material fabricated by high-pressure torsion (HPT) at room temperature through an equivalent strain range of ϵeq = 0.3–144 using Kernel Average Misorientation (KAM) and the Nye tensor approaches. The results show that generally the GND densities are significant at the beginning of the deformation (ϵeq = 0.3) and decrease in both alloys when ϵeq increases. The Mg-0.6Gd alloy exhibits a lower GND density due to rapid dynamic recrystallization. These results were compared to the GND densities measured in AZ31 and Mg-0.6Gd mono-materials processed separately by HPT under the same experimental conditions. In these mono-materials the GND densities increase with increasing equivalent strain up to 7 and then decrease with further straining. The Mg-0.6Gd and AZ31 regions of the hybrid material exhibit higher GND densities than the mono-materials particularly at low strain where the disc thickness and the bonding of the AZ31/Mg-0.6Gd interfaces cause more deformation heterogeneity in the hybrid material. It is shown that the GND density evolution as a function of ϵeq has the same tendency for the KAM and the Nye approaches but the average values are significantly higher with the Nye approach. An analysis suggests that the Nye approach overestimates the GND density of the Mg-based alloys. [ABSTRACT FROM AUTHOR]

This work investigates the synergy between texture evolution and grain refinement in ultra-low carbon body-centred cubic (BCC) ferritic steel. In this regard, experiments and polycrystal plasticity for ambient compressive deformation in low (up to ϵ≈0.22) and moderate (ϵ≈0.22−0.69) strain regimes were carried out. The tests were interrupted at intermediate strains for microstructure and texture characterisation. It was observed that the change in texture to ${\rm \gamma }$ γ -fibre ($\lcub {111} \rcub \parallel$ { 111 } ∥ Compression direction ${\rm \; }\lpar {{\rm CD}} \rpar$ (CD)) and the formation of ${\rm \theta }$ θ -fibre $\lpar \lcub {100} \rcub \parallel {\rm CD}\rpar$ ({ 100 } ∥ CD) up to ${\rm \varepsilon }\approx 0.22$ ϵ ≈ 0.22 contributes towards lattice bending, resulting in grain size reduction from $\sim 104\lpar {23} \rpar {\rm \mu m}$ ∼ 104 (23) μ m to $\sim 23\lpar 6 \rpar {\rm \mu m}.$ ∼ 23 (6) μ m. Simultaneously, crystallite size decreases, and statistically stored dislocations (SSD) and geometrically necessary boundaries (GNB) increase rapidly. Thus, resulting in an abrupt decrease in strain hardening rate (SHR). From ${\rm \varepsilon }\approx 0.22-0.69$ ϵ ≈ 0.22 − 0.69 , the ${\rm \gamma }$ γ and ${\rm \theta }$ θ -fibre broadens and ${\rm \theta }$ θ -fibre intensity increases. The low GNB density increase indicates insignificant deformation-induced lattice curvature formation within grains, resulting in SSD intensification. Thus, leading to elongated grains with sluggish grain size decrease to $\sim 17\lpar 4 \rpar {\rm \;\mu m}$ ∼ 17 (4) μ m and a lesser decrease in SHR. The ${\rm \alpha }$ α -fibre could not evolve due to the dispersion of $110$ 110 axes along the axisymmetric radial direction due to axial deformation. The polycrystal model could appropriately simulate strain-hardening behaviour and texture evolution. [ABSTRACT FROM AUTHOR]

P92 (9Cr-1.8W–0.5Mo-NbV) martensite steel is widely used in high-temperature pipes of ultra-supercritical boilers in China. During high-temperature operation, microstructural evolution of the heat affected zone (HAZ) across welded joint leads to type IV cracking failure. In this article, microstructural evolution and type IV cracking of P92 steel welded joint in an actual 605℃ supercritical boiler were analysed. The results show the cracking appeared in the fine-grained heat affected zone (FGHAZ). Laves phase and M23C6 phase clustered around the cavity. Their precipitation and coarsening promote the nucleation and growth of cavities. The Z phase was also observed in the heated affected zone. Compared with other zones, FGHAZ has lower dislocation density and more degeneration of tempered martensite lath, the coarsening of Laves phase and M23C6 phase is more severer in FGHAZ. These factors led to the deterioration of the creep properties and type IV cracking. [ABSTRACT FROM AUTHOR]

Several contents of silicon in AlSi coatings, and substrate nature, were investigated in this present research. For this purpose, thin films were deposited by Physical Vapour Deposition onto three substrates: The effect of silicon content on the microstructure and mechanical properties of the coatings was studied. The microstructural observations showed that the coating carried out with 7 wt-%. silicon reduced the porosities by making the microstructures more homogeneous and denser. Also, the influence of substrate characteristics on the evolution and distribution of the microstructure formed during coating is important. Content of 13 wt-% eutectic enhanced the mechanical properties. The crystallite size evolves in a completely opposite way to that of the dislocation density and micro-deformation, with a minimum for the same values of silicon content (10–12 wt-%). The microstructural analysis allowed us to highlight the importance of silicon in the formation of intermetallic compounds. [ABSTRACT FROM AUTHOR]

The origin and mechanisms responsible for incipient plasticity in metals are still poorly understood. Moreover, the reasons for the recently reported large scattering of the initial pop-in load remain unclear. Hence, this study addresses these issues through a combination of nanoindentation tests and electron channelling contrast imaging characterisation considering a CrCoNi medium-entropy alloy. Experimental findings were also supported by elastic calculations that consider both the indentation and dislocation stress fields. A wide scatter in the maximum shear stress underneath the indenter, as expected, was observed for the analysis based on dislocation density. As a consequence, the spatial arrangement of dislocations within the indented region or local dislocation configuration is introduced as a new parameter to overcome overly simple analysis based on the dislocation density. The maximum shear stress underneath the indenter increased from 6 GPa for dislocation closer to the indentation axis to 11 GPa at 600 nm for dislocation far away from it. Additionally, elastic calculations revealed that the response to the incoming nanoindenter was different for dislocations with different configurations. Thus, the complex interactions of stress fields due to configurations of dislocations and indentation account for the large scatter of the maximum shear stress beneath the indenter. [ABSTRACT FROM AUTHOR]

Solid solution strengthened (SSS) Ni-based superalloys, such as A617, show superior creep resistance at 700°C. Established for many years in land- and aero-based gas turbines, these materials are increasingly being considered for use in high-temperature thermal power plants. Apart from SSS, the creep strength in A617 stems from γ' and carbide precipitates. In this work, a microstructurally based creep model for A617 is presented. Mobile dislocations in the model interact with fine grain-interior precipitates, and grain boundaries act as dislocation sources/sinks. The model is capable of simulating creep curves and time-to-rupture (TTR) diagrams based on the evolution of mobile dislocations. At lower stresses, the accuracy of modelled TTR can be improved by adding diffusion creep to dislocation creep. The simulated evolution of dislocation densities is realistic compared to the literature data. The reduction of area of ruptured samples was included in a damage factor, enabling the consideration of creep ductility. [ABSTRACT FROM AUTHOR]

We demonstrate a dislocation density-based crystal plasticity (CP) model approach for simulating mesoscale deformation and damage. The existing CP framework is extended to be compatible with the oxygen-free phosphorous copper microstructure that is the focus of this study. The key aim is to introduce relevant plastic deformation mechanisms and to develop a failure model capable of depicting creep damage in the material. The effect of local variations in material is evaluated, and the model response is compared with experiments and characterisation. The basis of this work is CP material modelling, including grain orientation and size, obtained using electron backscatter diffraction and experimental test data of real relaxation test specimens. This will yield a realistic description of texture and grain shape and, ultimately, accurate stress–strain response at the microstructural level for further evaluation of performance with respect to material creep(−fatigue) damage. [ABSTRACT FROM AUTHOR]

The present experimental study introduced NTA-WAAM system for fabricating thin-layered structures using ER70S-6 wire. The study is directed towards determining the Sw in the manufactured parts, considering varying level of TS (0.17, 0.19, and 0.24 m/min) and BL (2, 3, 7 layers). The Sw is computed through image processing using canny edge detection method. Increasing the BL from 2 to 7 and reducing TS from 0.24 to 0.17 m/min, the resulting Sw is increased from 1.05 to 2.69 mm. So with high BL, TS should be more to suitably control the Sw because of high heat dissipation and low fluidity of molten pool. In addition to the morphological attributes, microstructural evolution, XRD, Rietveld refinement, tensile, and wear testing are incorporated to present the feasibility and stability of part fabricated through NTA-WAAM. Crystallite size, dislocation density, and residual stress are computed through XRD. It is observed that when approaching the top section from bottom zone of deposition, crystallite size is reduced from 23.43 to 21.85 nm, whereas dislocation density (2.83 × 1012 to 6.52 × 1012m−2) and residual stress (−263.72 to −300.12 MPa) are increased. It indicates the adverse effect of crystallite size towards dislocation density and residual stress, which is primarily attributed to varying level of heat transfer during deposition. The deposit exhibits an ideally refined crystal structure than initial filler wire as χ2≈1 (from Rietveld analysis). Compressive residual stress development further improves the fabricated part's tensile characteristics. Formation of equiaxed dimples, characterises the ductile failure phenomena, whereas the enhancement in their dimensions reflects the improvement in ductility. [ABSTRACT FROM AUTHOR]

Nanocrystalline magnesium oxide powders (MgO) were prepared using a hydrothermal method. In various fuel-to-oxidizer ratios (F/O) and precursor solutions with pH levels from 8 to 12, magnesium nitrate hexahydrate Mg(NO3)2 was utilized as an oxidizer and polyvinyl alcohol (PVA) as a fuel. To improve crystallinity and phase purity, these materials were annealed for two hours at varied temperatures. XRD, FTIR, EDS, FESEM and DRS were used to study the MgO nanopowders' structure, vibration, elemental and optical properties. The fuel-to-oxidizer ratios, annealing temperatures and pH values greatly affected the samples' properties. The synthesized powders had a particle size distribution in the range of 18–49 nm. The XRD results showed that the crystallite percent of the MgO phase grew with an increase in the F/O from 0.5 to 0.75, and then, it decreased at F/O = 1. The maximum percent of crystallites was observed at pH = 8. By increasing the annealing temperatures, the crystallite size of the samples increased from 22.82 nm to 49.06 nm, while the specific surface area and dislocation density decreased from 20.59 m2/g to 7.83 m2/g and 0.0006 nm−2 to 0.0001 nm−2, respectively. FTIR spectra results indicated that the MgO band peaking at (418–688 cm−1) was high at pH value 8, then it reduced at pH 10 and finally, this peak had the smallest size at pH = 12. Further confirmation of MgO presence and its homogeneity in the final product was approved through EDS measurements. DRS spectra were used to obtain energy gap using Kubelka–Munk relation and noticed in the range of 5.72–5.89 eV for MgO NPs. [ABSTRACT FROM AUTHOR]

Nanotwinned exist in crystals as coherent interfaces with low interfacial energy, which can not only improve the strength of metal materials, but also increase the ductility. In this manuscript, we have performed molecular dynamics simulations of the mechanical properties of a nano-columnar crystalline Cu-Ni alloy with different twin boundary spacing. It is found that the model without twin has a stacking fault tetrahedron composed of stair-rod dislocations, which results in a small change in dislocation density at the later stage of deformation, and the average stress after yielding is lower than that of the model with twin. During the deformation process, with the increase of Other atoms, the dislocation slip barrier is enhanced, the tensile strength is increased, and the yield phenomenon is delayed, which is more obvious with the decrease of twin boundary spacing. The dislocation density decreases with the decrease of the spacing of the twin boundary, and the dislocation segments become shorter. When the twin boundary spacing is 0.625 nm, the tensile strength is increased by about 71% compared with the model without twin structure. [ABSTRACT FROM AUTHOR]

To improve the cutting performance and prolong the service life of a carbide-coated tool in the process of ductile iron machining, an electromagnetic coupling treatment (EMCT) was carried out. The cutting experiments show that the cutting force and cutting temperature are reduced after EMCT, and the roughness of the machined surface is reduced. It is found that after EMCT with optimal parameters the dislocation density, microscopic strain, microhardness and bonding strength of an alumina coating increase by 109.2%, 28.2%, 28.3% and 26.6%, respectively. Using the actual machining of a differential housing to verify the tool life, it is found that after EMCT, a single tool can process 18.4 more workpieces or in other words, the tool life increased by 44%. EMCT can promote element diffusion, optimize coating properties and have great potential in coating tool life extension. [ABSTRACT FROM AUTHOR]

The study investigates the impact of microstructure modifications on the corrosion, passivation, and plasma-nitriding behaviour of 316L steel. Microstructure modifications are achieved through the laser powder bed fusion (L-PBF) process and surface mechanical attrition treatment (SMAT). Three scanning strategies (concerning the orientation of the sample surface with scanning directions) are used in the L-PBF process, and the corresponding samples are labelled as HNS (0°), INS (45°), and VNS (90°). The scanning strategies have altered the average grain size (maximum for HNS and minimum for VNS) and porosity (HNS has the highest). Porosity disappears after SMAT. The surface of the SMATed specimen (VS) has equiaxed austenite nanograins (∼32 nm) with a fine distribution of α'-martensite, nanotwins, and high dislocation density. Microstructure affects the passivation, corrosion, and nitriding behaviour of the steel. The VNS has the lowest corrosion rate, decreasing further after SMAT. The SMATed sample exhibits the lowest nitrided layer thickness (∼65 μm). SMAT followed by nitriding causes a gradient-structured layer (with improved hardness) consisting of a nitrided layer, SMATed layer, and core. The nitrided HNS sample (∼78 μm thick nitrided layer) is dominated by γ'-Fe4N, while the nitrided VNS and VS samples have a relatively higher proportion of expanded austenite. [ABSTRACT FROM AUTHOR]

Cerium substituted BCZT ceramic samples for x = 0, 0.05–0.020 were prepared by conventional method. These samples were sintered through microwave sintering. The structural properties were studied with XRD, SEM, and FTIR. The crystallinity was calculated by using Scherrer's, particle density was calculated with Smith and Wijn formulae, micro strain and dislocation densities were calculated from Williamson–Hall (W–H) plots and Nelson–Riley (N–R) plot for finding lattice parameters. The average size of the particle is increased whereas the lattice parameters, densities, and porosity were decreased with the increasing concentration of Ce. FTIR shows broad peaks for all concentrations of Ce. [ABSTRACT FROM AUTHOR]

Nitrogen ion implantation with different dose rates was conducted on 8Cr4Mo4V-bearing steel in the present study. The effects of high-dose-rate nitrogen plasma immersion ion implantation (N-PIII) on the microstructure and nanohardness of the 8Cr4Mo4V-bearing steel were studied. The surface morphology, phase microstructure, lattice parameters and nanohardness were investigated by scanning electron microscopy (SEM), X-ray diffraction (XRD) and nanoindentation tests. The results showed that finer crystallite size, higher micro-strain and dislocation density can be achieved under high-dose-rate ion implantation and the dislocation density reaches the highest level of 1.71 × 1016 m−2 at a dose rate of 5.23 × 1017 ions cm−2 h−1. In addition, the high-dose-rate ion implantation results in changes in phase composition in the surface layer, and the Fe(M) peaks slightly shift to a lower angle. Moreover, the nanohardness of implanted samples improved notably, especially at a dose rate of 8.64 × 1017 ions cm−2 h−1, reaching the high value of 15.8 GPa, which is 42.1% higher than that of a non-implanted sample (11.1 GPa), implying that the properties of the samples were strongly affected by the implantation dose rate of nitrogen. [ABSTRACT FROM AUTHOR]

Severe plastic deformations under high pressure are used to produce nanostructured materials but were studied ex-situ. Rough diamond anvils are introduced to reach maximum friction equal to yield strength in shear and the first in-situ study of the evolution of the pressure-dependent yield strength and radial distribution of nanostructural parameters are performed for severely pre-deformed Zr. ω-Zr behaves like perfectly plastic, isotropic, and strain-path-independent and reaches steady values of the crystallite size and dislocation density, which are pressure-, strain- and strain-path-independent. However, steady states for α-Zr obtained with smooth and rough anvils are different, causing major challenge in plasticity theory. In-situ study of severe plastic deformation of ω-Zr with rough diamond anvils revealed that pressure-dependent yield strength, crystallite size, and dislocation density are getting steady and plastic strain- and strain-path-independent. [ABSTRACT FROM AUTHOR]

Influence of configurational design of single crystal Al-Al90Sm10 metallic glass nanolaminates on torsion deformation behaviour of Al/Al90Sm10 nanolaminate (Configuration 1) and Al90Sm10/Al nanolaminate (Configuration 2) from a structural evolution aspect have been analysed by employing Molecular Dynamics for a torsion speed of 1/600 revolution/ps. Adaptive common neighbour (a-CNA) analysis, Dislocation extraction algorithm (DXA), atomic shear strain analysis, and Voronoi Polyhedral (VP) analysis have been carried out to reveal the structural evolution in the nanolaminates specimen subjected to torque. As a consequence of dislocation density localisation under torsional loading in Al/Al90Sm10 nanolaminate high atomic strain gradient is developed in the nanolaminate specimen causing torsional buckling of the Al/Al90Sm10 nanolaminate. The localisation of dislocation density rings induces the formation of dislocation substructure in Al/Al90Sm10 nanolaminate. The crystalline/amorphous interface serves as a free surface and encourages the formation of such dislocation substructure. The collective nucleation, coalescence, and growth of shear transformation zones (STZs) leading to the formation of thick shear bands on either end of Al90Sm10/Al nanolaminate inducing an almost homogenous atomic strain gradient across the surface of the nanolaminate specimen thereby averting torsional buckling. The C/A interface serves as a nucleation site for the generation STZs in Al90Sm10/Al nanolaminate. VPs such as <0, 0, 4, 6>, <0, 3, 6, 4>, <0, 3, 6, 5> <0, 2, 8, 2> have the load bearing capacity and are resistant to fragmentation under the subjugation of torsion loading. [ABSTRACT FROM AUTHOR]

The fracture behavior of a cracked functionally graded piezoelectric plane was investigated under in-plane mechanical and electrical loading. The electro-elastic properties of the plane exponentially varied along the y-axis. Employing the Fourier transform, stress analysis containing a Volterra edge dislocation in a functionally graded piezoelectric plane was carried out. These solutions were used to derive a system of Cauchy singular integral equations for analyzing the straight and curved cracks. Linear, arc, parabolic and sine wave-shaped cracks were evaluated. The integral equations were numerically solved using the Lobatto–Chebyshev integration formula for dislocation density functions on the crack face which were employed to calculate field intensity factors. The effects of the shaped crack, loading parameters, and non-homogeneity parameter on the stress and electric intensity factors were considered. [ABSTRACT FROM AUTHOR]

Friction stir welding (FSW) of AA2014 alloy requires cooling to prevent the dissolution of precipitates. The sustainable minimum quantity lubrication technique with graphene nanofluid is employed in this study for cooling purposes. FSW was carried out at 1200 rpm and 72 mm/min. A tool with a square pin was used. The microstructural evolution of the FSW joint under uniaxial tensile load is explored in detail for the first-time using electron backscatter diffraction. The results show that the grains undergo discontinuous dynamic recrystallisation during FSW and continuous dynamic recrystallisation during tensile deformation. Pole figures reveal the shear texture formed by plastic deformation. Tensile deformation has reduced local grain misorientation remarkably and thereby the dislocation accumulation. A significant increase of 94.5% is observed in grain size. Tensile deformation transforms a significant number of sub-grains with low-angle grain boundaries into stable grains with high-angle grain boundaries. The stable recrystallized grains with HAGBs and subgrains with LAGBs significantly influence the mechanical properties of the weld. [ABSTRACT FROM AUTHOR]

Based on the modified KM (Kock–Mecking) model, a cutting constitutive model of AA7050-T7451 considering anisotropy is established in this article. With the aid of high-speed cutting FEM simulation and experiment, the micro-influence mechanism of anisotropy on high-speed cutting hardening of AA7050-T7451 was studied from three aspects: micro-morphology, residual strain, and plastic deformation. By analyzing the macro-micro correlation mechanism of dislocation density, work hardening, and cutting temperature, a "Three-Stage" model of work hardening is put forward. The results show that the work-hardening behavior of high-speed cutting AA7050-T7451 shows obvious anisotropic characteristics. And the work hardening degree is less than 0° and 90° at the material forming angle of 45°. At the 45° forming angle, the material dislocation density is the highest, and the grains are most prone to the dislocation slip. The macroscopic properties show that the microhardness of the material is small. The "Three-stage" model reveals the micro-evolution mechanism of work-hardening behavior. It is found that the dislocation density dominates the work-hardening behavior in stages I and II, and cutting temperature dominates the work-hardening behavior in stage III. The microhardness of the material increases sharply at first and then tends to be flat. [ABSTRACT FROM AUTHOR]

A novel idea of precisely constructing gradient heterogeneous microstructure was proposed to greatly improve the formability of Al-Zn-Mg-Cu alloy by coupling multi-process firstly. After coupling control of the heterogeneous distribution of precipitates, strain energy storage and dislocation number density, a gradient distribution of coarse/fine grains can be constructed in the pre-aged alloy, resulting in a greatly enhanced average plastic strain ratio of 0.716. This work opens up a new frontier for achieving super-high room temperature formability without sacrificing the high strengths for Al-Zn-Mg-Cu alloys. This paper reports a gradient heterogeneous structure in Al-Zn-Mg-Cu alloys by coupling control of precipitates, strain energy storage and dislocation number density, resulting in a greatly enhanced average plastic strain ratio of 0.716. [ABSTRACT FROM AUTHOR]

A cost-effective process for preparation of aluminum nitride was developed by using single-source precursor tris (N,N dimethylethylenediamine)AlCl3, which was prepared from anhydrous aluminum chloride and N,N dimethylethylenediamine (DMEDA) in 1:3 molar ratio at room temperature under N2. The pyrolysis of the precursor was carried out at various temperatures, pressures, and flow of gases (N2 and Ar) to optimize parameters. The resultant pyrolyzed residues were investigated using various instrumental techniques. X-ray diffraction (XRD) showed that AlN crystallizes in mixed-phase (hexagonal/cubic) and the grain size was estimated to be in the range of 4–10 nm. The band gap of AlN was investigated by UV-Vis spectroscopy and found to be ∼5.7 eV (6.1 eV bulk); TEM showed agglomerated crystallites of AlN. [ABSTRACT FROM AUTHOR]

In the present study, mode III dynamic stress intensity factors (DSIFs) for the multiple axisymmetric interfacial cracks in an orthotropic layer with FGM orthotropic coating under transient torsional loading are formulated. It is assumed that the mass density and the shear modulus of the FGM orthotropic coating vary exponentially and power-law form along the thickness of the layer. At first, the solution for Somigliana-type dynamic rotational ring dislocation in the layer and its coating is obtained by using the Laplace and Hankel transforms. Then, the dislocation solution is used to derive a set of singular integral equations for a system of coaxial axisymmetric interfacial cracks, including penny-shaped and annular cracks. The integral equations are of Cauchy singular type, which are solved by Erdogan's collocation method for dislocation density on the surface of interfacial crack and the results are used to determine DSIFs for axisymmetric interfacial cracks. Finally, several examples are provided to study the effects of the non-homogeneity constant, orthotropy parameter and thickness of FGM coating as well as the interaction of multiple interfacial cracks on the DSIFs. [ABSTRACT FROM AUTHOR]

AM30 magnesium alloy was subjected to annealing at temperatures ranging from 200 to 450°C for 1–1440 min to evaluate the microstructure and texture evolution during grain growth. The grain growth exponent of n = 9 and activation energy of Q = 105.6 KJ/mol were observed. Precipitates, such as Mg17Al12, Al8Mn5 and Al11Mn4 were observed in the alloy, and they were found to be reduced with increasing the annealing temperature/time. The precipitates further appeared to be dissolved at a higher annealing temperature of 450°C, leading to abnormal grain growth in the alloy. The effects of solute drag and dislocation density on the grain growth behaviour, estimated through a mesoscale model based on cellular automata, were found to be insignificant during annealing. The strong basal texture in the starting material was observed to be weakened up to 480 mins of annealing, and on further increasing the annealing time to 1440 min, the alloy regained its basal texture. It was found that both normal and abnormal grain growth promoted basal texture during the annealing of the alloy. [ABSTRACT FROM AUTHOR]

Nickel oxide (NiO) is a transparent conductive oxide material that has interesting physical properties, making it one of the most promising materials for a variety of modern technological applications. The interest of this work is to study the structural and optical properties of pure and Li doped NiO thin films deposited using spray pyrolysis on glass substrates. The samples were prepared at 480 °C with various concentrations of Li doping (1, 2, 3, and 5%). X-Ray Diffraction (XRD) was employed to study the structural characteristics including the crystallite size, dislocation density, and lattice strain. Meanwhile, UV visible spectroscopy was used to study the optical properties. The results revealed a polycrystalline cubic structure with (200) crystal plan being the preferred orientation for the produced films. On the other hand, (Li: NiO) films have shown a high transmittance ranging between 60 and 80%. Also, the bandgap values (Eg), were found to be significantly affected by the Li doping ratios to take values from 3.38 to 3.66 eV. Furthermore, diverse linear and nonlinear optical properties were examined. It was found that the nonlinear properties values of χ1, χ3, and n2 to were improved when lithium doping is incorporated into the NiO lattice. [ABSTRACT FROM AUTHOR]

The change in microstructure and mechanical properties ofTi–6Al–4V alloy due to 160 MeV O6+ ion irradiation has been reported here. Detailed X-ray diffraction line profile analyses have been used to evaluate the microstructural parameters and characterize the nature of defects and their arrangements. The results indicate saturation of size of the coherent region, the dislocation density and its arrangement with dose, which points to an optimized final microstructure of irradiated material. This was also supported by the Vicker's microhardness measurements. Electron back scattered diffraction study was used to assess the changes in microstructure in terms of the evolution of misorientation boundaries within the grains due to irradiation-induced defects. All the results support the radiation resistance nature of Ti–6Al–4V alloy. Finally, comparison has been made with earlier proton irradiation results, and the difference has been related to the nature of the displacement cascade produced by light and heavy ions. [ABSTRACT FROM AUTHOR]

A precipitation hardening high-entropy alloy (HEA) (FeCoNi)86Al7Ti7 was fabricated by selective laser melting (SLM) and ageing treated under different temperatures and time conditions. Yield strength of the aged HEA increases substantially from 710 to 934 and then to 1203 MPa. Theoretical analyses reveal that the coherent L12 precipitate contributes most of the improved strength for the aged HEAs, whereas recovery during ageing causes the decrease of dislocation density thus exerts a softening effect. In addition, it is found that ductility decreases with increasing volume fraction of the incoherent L21 precipitates. Based on a void growth model, the trend is qualitatively explained. Moreover, a new fracture mode, intercellular fracture, is proposed to account for the strong dependence of fracture dimple size on the dislocation cells, also directly validated by delicate microstructural examination. The findings provide an effective strengthening method and propose a unique fracture mechanism for the additively manufactured HEA. [ABSTRACT FROM AUTHOR]

This report presents the synthesis of cobalt ferrite (CoFe2O4) by co-precipitation method and its subsequent characterization by using X-ray diffraction (XRD), atomic force microscope (AFM), TG-DTA and Fourier transform infrared spectroscopy (FTIR) techniques. XRD results confirm the formation of single phase cubic spinel structure, having lattice constant from 8.4029 Å to 8.3744 Å. We also report hopping length (LA and LB), strain (ɛ) and dislocation density (ρD) of ferrite sample. AFM images show the microstructure of ferrite samples. The TG-DTA of sample CoFe2O4 of pH 8, confirms the formation of final product at 683 °C. The FTIR curves for CoFe2O4 series shows two major peaks near 492 cm−1 and 442 cm−1 which are assigned to the tetrahedral and octahedral sites, respectively, in a spinel structure. [ABSTRACT FROM AUTHOR]

Eutectic high-entropy alloys (EHEAs) feature attractive strength–ductility balance at both ambient and cryogenic temperatures. Nevertheless, microstructural origins underpinning these balanced mechanical properties remain elusive. Here the deformation mechanisms of a recently-reported Al19Co20Fe20Ni41 EHEA were comparatively investigated at 298 and 77 K, which revealed a high frequency and density of dislocation multi-slip scenario in the soft eutectic lamellae and the corresponding compatible co-deformation in the adjacent hard lamellae that collectively endowed strong hetero-deformation-induced (HDI) hardening and excellent forest-dislocation hardening. Therefore, better ductility and tensile strength, in comparison to the other widely-studied EHEA system, could be sustained even at liquid-nitrogen temperatures. We identify a new eutectic HEA system with superior strength–ductility combination at liquid-nitrogen temperatures, and provide critical microstructural insights and mechanisms into its enhanced cryogenic properties. [ABSTRACT FROM AUTHOR]

The (FeCoNi)86Ti7Al7 multi-principal-element alloy with a dual heterogeneous microstructure was successfully fabricated by selective laser melting, exhibiting an excellent combination of strength (ultimate tensile strength, 1085.2 ± 23.2 MPa) and ductility (30.5 ± 2.6%). It is evidenced that the joint effects of the hetero-deformation induced hardening from grains with heterogeneous geometrically necessary dislocations densities, in-situ formed B2 phase, and the coherent precipitation hardening from in-situ formed nano L12 phase were responsible for the strength. This work sheds light on the feasibility of simplifying the production of multi-mechanism strengthened alloys within one step and paves a new avenue to produce high-performance complex-shaped components. (FeCoNi)86Ti7Al7 multi-principal-element alloy exhibiting heterogeneity on the grains structure and in-situ precipitation was successfully fabricated by selective laser melting. It shows both good tensile strength and ductility. [ABSTRACT FROM AUTHOR]

A composite with periodically distributed particulate reinforcements is usually preferred in some industrial engineering areas to enhance the damage resistance of materials. The bonding of the matrix and enhancements may be fractured during manufacturing or operating by cracks that are evenly distributed. In this study, a cracked composite is simplified as an infinite plane with repeatedly distributed units containing inhomogeneities and cracks. The inhomogeneities can be in arbitrary shapes and cracks are assumed horizontally oriented. In formulating the governing equations, each inhomogeneity is homogenized according to the Equivalent Inclusion Method with equivalent eigenstrains to be determined, and each crack of mixed modes I and II is modeled as a distribution of climb and glide dislocations using the Distributed Dislocation Technique with dislocation densities to be determined. The fast Fourier transform is used to speed up the calculation while taking into account the interactions of the inhomogeneities and cracks in the plane. Effective moduli of the composites are obtained from average stresses and strains and samples are reported to demonstrate the generality of the model. [ABSTRACT FROM AUTHOR]

Modelling the flow behaviour enables to understand the underlying deformation mechanisms underneath the various conditions imposed during the thermo-mechanical processing. Thus, herein flow stress response of 64.7Ni–31.96Cu alloy with different grain size is modelled at varying temperatures and strain rates, employing a dislocation density reliant physical model. The model takes account of immobile dislocations and assimilates strain hardening effect, Hall–Petch effect and the short-range interactions. Furthermore, the model addresses the static and dynamic recovery as key aspects during plastic deformation. In this advanced approach, the influence of twin boundaries has been incorporated and modelled flow curves show reasonable agreement with the experimental ones. The effect of different grain sizes and connected changes in the amount of twins on the flow stress can be obtained from the model. Predicted final dislocation densities and cell size are in the range of 6.91–10.26 × 1014 m−2 and 0.59–0.80 μm, respectively, for varying test conditions. It was observed that there is a sharp increase in dislocation density at the commencement of deformation. Concomitantly, hardening is also more profound during initial deformation. The investigation also revealed that excluding the twin boundaries in this physical-based approach would lead to underestimation of flow stress. This model also makes it possible to evaluate the relative contributions from different strengthening mechanisms. [ABSTRACT FROM AUTHOR]

In this work, the continuous hot-compaction behavior of Quinary-FeCrCuMnTi, Senary-FeCrCuMnTiV, and Septenary-FeCrCuMnTiVZn equiatomic nanostructured high-entropy alloys (HEAs) was studied from 0 to 550 MPa pressure in a universal testing machine. These alloys were synthesized by mechanical alloying and characterized by HRSEM and HRTEM. The synthesized powders were compacted at different temperatures (RT to 525°C) using a universal testing machine operated at 10 mm per minute. Microstructural results demonstrated that multiphase solid solutions were obtained in all the HEAs. Septenary-FeCrCuMnTiVZn HEA has produced a higher amount of FCC phase compared to other alloys due to the incorporation of low melting Zn atoms enhancing solid solutions leading to produce a lower value of FCC phase crystallite size (7.8 nm). The continuous hot-compaction results explained that the percentage relative density was increased drastically after 225°C due to the elimination of internal stress, and decreased dislocation density. Senary-FeCrCuMnTiV HEA exhibited a higher percentage of relative density in all operating conditions due to more crystallite size, lower value of powder particle sizes, and the domination of BCC-V atoms in addition to high-configurational entropy. The experimental relative density-pressure data were fitted linearly using the Panelli and Ambrozio Filho equation for exploring the plastic deformation ability of developed powder particles. [ABSTRACT FROM AUTHOR]

The hot compression of A-100 steel at 850–1150°C and strain rate of 0.01–10 s−1 was tested on a Gleeble-3800 thermal simulation machine to determine the corresponding true stress–strain curve. Based on theoretical calculation, the dislocation density factor was introduced into the Avrami equation and thereby a dynamic recovery physical constitutive relational model based on dislocation density theory was established. Then the hot deformation behaviour of A-100 steel was predicted (correlation coefficient R = 0.9964 with an average absolute relative error AARE = 4.0923%). The structures after hot compression were observed by electron backscattered diffraction and found to be lath-shaped martensite and austenite. With an increase of temperature and deceleration of strain rate, the proportions of large-angle boundaries and substructures increased and the softening mechanism became dominated by dynamic recovery. [ABSTRACT FROM AUTHOR]

In this research, 1 wt% carbon nanotubes/aluminum 5 wt% Mg (CNTs/Al-Mg) composites were fabricated using powder metallurgy and hot pressing method. Dislocation density increases and dislocation cell structure is formed in Al-Mg particles for the repeared flattening, cold welding, fracturing and rewelding during ball milling. The horizontal stirring high-energy ball milling method can uniformly disperse 1 wt% CNTs in Al-Mg matrix powders, and can form an effective composite interface bonding. Some parts of the carbon nanotubes are twisted to form carbon nanoonions. After 90 min of ball milling, the tensile strength of the composite material obtained by hot pressing reached the maximum value, which was 244 MPa, which was increased by 31% compared with the composite materials none milled. [ABSTRACT FROM AUTHOR]

This study concerns the effect of bicrystal spatial orientation on the iron Σ5 boundary under nanoindentation tests. The orientation of the bicrystal is changed relative to the indenter by the parameter "nanoindentation angle" to create dislocation collisions with grain boundary in different directions and to determine the possibility of transmission of these dislocations through the grain boundary. Simulations were carried out for nanoindentation angles between −90° and 90° with a resolution of 18°. Molecular dynamics with EAM atomic potential functions are employed for the simulations. The effect of nanoindentation angle on the crystals Young's modulus, shear stress, hardness, and Poisson's ratio were determined. Due to the periodicity which has been observed in all of the aforementioned quantities of the rotated crystal, analytical equations were extracted by adapting the Fourier series expansion on the calculated data. Some explanations were provided for the dislocation behaviors based on the physics of the problem and also by the results reported in the literature. Simultaneous effects of Poisson's ratio and pile-ups on each other were also investigated and interpreted. [ABSTRACT FROM AUTHOR]

This paper reports the degradation behaviour of Super304H during the creep process. The failure mechanism of this Super304H is the typical intergranular damage, the creep voids and micro-crack are mainly concentrated on the GBs and triple point GBs. Meanwhile, there is a lot of precipitates inside void chain, those particles are the M23C6 phase, which indicate that the coarsening and growth of M23C6 phase are detrimental to the microstructural property of Super304H. Besides, the GND density of Super304H increased remarkably at the creep acceleration period, and the dislocation structure also changed from the pattern of straight-line to the zigzag. In addition, the nonlinear ultrasonic measurement results showed that there is a general upward trend of nonlinear parameter β' of Super304H during creep. The increase of the nonlinearity effect in Super304H could be due to several factors such as the precipitates precipitation, dislocation density/structure change, and the microdefects formation. [ABSTRACT FROM AUTHOR]

To raise the efficiency of thermal power plants, operation temperature and pressure must be increased by improving the creep performance of materials such as martensitic Cr-steels. To understand the underlying mechanisms of degradation, physical creep modelling provides a detailed and profound insight into microstructural processes. For such a physically based dislocation creep model, it is demonstrated that based on a parameter set found for one experimental creep curve, numerous creep curves on different stress levels can be simulated without any additional experimental data. These simulation results are then used for constructing a TTR diagram of P92. We succeeded in extrapolating rupture times for variations in both applied stress and temperature. In all cases, microstructural evolution of the simulated material is considered, including dislocation density, subgrain size and precipitates. The obtained rupture times in the simulated TTR diagram are compared to reference data, achieving good agreement. [ABSTRACT FROM AUTHOR]

This work represents a facile synthesis of ZnO and Ba-doped ZnO (BaZnO) for using as photocatalysts. ZnO and BaZnO are sub-micron particles and nanoparticles, respectively, with similar hexagonal wurtzite polycrystalline structures. Even the size of the lower particles and crystals of BaZnO, compared with ZnO, correspond to the improved specific surface area and dislocation density. The existence of surface chemical defects was detected for both ZnO and BaZnO. For use as photocatalysts, both ZnO and BaZnO were dispersed into a carbaryl solution activated with ultra-violet irradiation. The BaZnO had a higher degradation rate constant of 17.34 × 10−2 min−1 than ZnO (12.40 × 10−2 min−1), an improvement of 39.8%. The improvement is facilitated by the synergistic effects of high specific surface areas and defects caused by small particle sizes and high dislocation density, respectively. Therefore, it can be demonstrated that Ba is an effective dopant for modifying suitable BaZnO nanoparticles to enhance photocatalytic degradation of the toxic carbaryl insecticide. [ABSTRACT FROM AUTHOR]

The theory of anisotropic generalised plane strain of line forces and dislocation lines is embedded in the three-dimensional elasticity of point forces and dislocation densities. Embedding in real space is achieved by slicing in reciprocal space using the projection-slice theorem. [ABSTRACT FROM AUTHOR]