Set Of Grains Research Articles

Numerical study on effects of microstructure randomness on fatigue fracture of non-oriented electrical steel

Advances in battery technology and electrical drive systems has allowed for more versatility in mobile applications found in automotive, logistics and aerospace engineering. Rotor cores used for electrical motors are often made from thin sheet metals with a maximum thickness of 0.5 mm. During operation, this material is subjected to variable dynamic loading conditions. As a consequence, fatigue testing is required for a more complete material characterisation. However, experiments on thin metals are generally more challenging as they require finer testing equipment that can apply low loads with high precision. Therefore, a micro-fatigue machine can be implemented to identify the high cycle fatigue behaviour of thin electrical steel sheets. Further, the manufacturing process of electrical steels often results in non-oriented grain structures. In other words, the material properties can vary between adjacent grains at the surface, thereby influencing the fatigue crack initiation mechanism. To investigate this effect, a finite element analysis is performed that includes a randomly generated set of grains with different elastic material behaviour. Using a critical plane approach the impact on the fatigue life prediction is assessed.

Quantifying the effect of macrozones on the cold-dwell fatigue response of UD-rolled Ti-6Al-4V using high-energy X-ray diffraction

High-energy X-ray diffraction is used to investigate the evolution of elastic lattice strains in rolled Ti-6Al-4V specimens during cyclic loading in-situ with and without the inclusion of a 120s dwell period. A 1mm segment of the gauge section is monitored throughout the first 100 cycles for specimens extracted along the rolling direction (RD), the transverse direction (TD) and 45° between the two, to explore the effects of texture on the evolution of the micromechanical response. Five families of lattice planes from the hexagonal α phase are analysed with emphasis on lattice strain measured at the peak of each cycle, while macroscopic strain accumulation is simultaneously monitored via Digital Image Correlation. In cyclic loading conditions including a dwell period at load, a prominent increase in elastic strains is observed in prismatic and basal lattice planes with the specimen loaded 45° from the rolling direction. In the absence of dwell, both RD and TD specimen orientations exhibited subtle cyclic hardening in all families of lattice planes probed despite negligible evolution in accumulated macroscopic plastic strain. Estimations of lattice orientation-dependent stresses are also presented using directional moduli to examine redistribution of load across sets of grains with the increasing cycle count.

The Concept of Optimal Compaction of the Charge in the Gravitation System Using the Grains Triangle for Cokemaking Process

Two isomorphic sets of grains, small and large, were analysed—without specifying their dimensions—under the acronym CMC (Curve of Maximum Compression) and taking into account the effects of segregation CMCS. The proposal is particularly valuable for optimal blend preparation in the gravity system in cokemaking. The main advantage of this work is the proposal of using the grains triangle, which limits the values calculated by the relations: bulk density-share of coarse/fine grains, for different levels of moisture content. Each system of changing shares of coarse grains is characterised by a constant C, but there is no need to determine it. Compliance of the calculated value with the experimentally determined value means that the given arbitrary grain set has reached its maximum density called the “locus”. The grains triangle practically covers the vast majority of laboratory and industrial test results, and geometrically or computationally indicates the ability of a given particle size distribution to reach maximum bulk density. This paper presents analysis of the results of tests on crushing, coal briquettes, and grinding coal blend in selected mechanical systems. Results of tests on coke quality (CRI, CSR) in connection with the grain size triangle are discussed.

Towards an understanding of surface finishing with compliant tools using a fast and accurate simulation method

Surface finishing with compliant tools is a widely used technology that still relies heavily on the trial-and-error approach. To predict surface evolution, one should ideally consider the tool as a set of grains and take into account the cutting action of each grain. In practice, the small size of abrasives renders this approach unpractical for industrial application. In this paper, the various aspects playing a role in surface generation, from micro-scale abrasives to macro-scale tool deformation as well as the time-dependent nature of compliant processes, are rationalized and modelled in a Folding Space (FS) rather than a classic geometrical space. This approach drastically reduces the computation time, and is found to be quite realistic as in each position the tool shape is distorted, taking into account the compliance level between the tool and local surface topography. Firstly, the concept of FS and methodology for physical representation of surfaces and processing by compliant tools in the FS are detailed. Next, predictions from the finishing model are analyzed for a variety of compliant grinding and polishing tools typically used in industry. Experimental testing confirms the accuracy and usefulness of the proposed method. To conclude, the model is exploited to offer a better understanding of finishing operations with compliant tools, while the limits and future possibilities of FS simulation method are discussed.

Domain wall conductivity as the origin of enhanced domain wall dynamics in polycrystalline BiFeO3

Despite their primary importance in modern nanoelectronics, conductive domain walls (DWs) can also have a marking effect on the macroscopic response of polycrystalline ferroelectrics. In particular, a large nonlinear piezoelectric response at sub-Hz driving-field frequencies has been previously observed in BiFeO3, which was linked to the conductive nature of the DWs but whose exact origin has never been explained. In this study, by carefully designing the local conductivity in BiFeO3 using chemical doping, we found that the low-frequency piezoelectric nonlinearity is only observed in the sample with a large fraction of conductive DWs. Supported by nonlinear Maxwell–Wagner modeling, we propose that this large response originates from DW displacements inside a specific set of grains or grain clusters in which the internal electric fields are enhanced due to M-W effects. We thus show that these effects likely arise due to the pronounced local anisotropy in the electrical conductivity, varying from grain to grain, whose origin lies in the conductive DWs themselves. The results demonstrate the possibility of controlling the global nonlinear properties of polycrystalline ferroelectrics by engineering local properties.

Image based Particle Shape Analysis Toolbox (IPSAT)

Shape analysis can provide vital information regarding the origin, transport and deposition history of grains. Particle shape measurement has been an active area of research for sedimentologists since the 20th century. With advancement in the field of computation and image analysis, shape analysis can be done in a faster and much more accurate way compared to manual measurements. The results obtained are reproducible as compared to visual qualitative analysis. However, there is a lack of image analysis software tools aimed at the field of sedimentology where the fine details of a particle boundaries are required. Image based Particle Shape Analysis Toolbox (IPSAT) developed in the Mathematica environment for the quantitative characterisation of sedimentary grains in 2-dimensions is presented here. This image analysis toolbox can be used to analyse consolidated as well as loose sediment samples. A total of 12 parameters are available for shape measurement comprising conventional shape parameters (roundness, angularity, circularity and irregularity), mathematically complex shape parameters (fractal dimension and Fourier descriptors) and common geometrical shape parameters (aspect ratio, convexity, solidity, mod ratio, rectangularity and compactness). Additionally, IPSAT offers to compute 6 particle size measurement parameters. Furthermore, 2-D particle size distribution can be transformed to a 3-D size distribution for thin section analysis. Example analyses have been carried out on a sandstone and a loose sediment sample. The toolbox presented here aims to establish a textural analysis methodology to be used by geologists and sedimentologists in particular. It will allow users to quantitatively characterise a large set of grains with a fast, cheap and robust methodology.

Diffracting-grain identification from electron backscatter diffraction maps during residual stress measurements: a comparison between the sin2ψ and cosα methods

X-ray diffraction (XRD) is a widely used technique to evaluate residual stresses in crystalline materials. Several XRD measurement methods are available. (i) The sin2ψ method, a multiple-exposure technique, uses linear detectors to capture intercepts of the Debye–Scherrer rings, losing the major portion of the diffracting signal. (ii) The cosα method, thanks to the development of compact 2D detectors allowing the entire Debye–Scherrer ring to be captured in a single exposure, is an alternative method for residual stress measurement. The present article compares the two calculation methods in a new manner, by looking at the possible measurement errors related to each method. To this end, sets of grains in diffraction condition were first identified from electron backscatter diffraction (EBSD) mapping of Inconel 718 samples for each XRD calculation method and its associated detector, as each method provides different sets owing to the detector geometry or to the method specificities (such as tilt-angle number or Debye–Scherrer ring division). The X-ray elastic constant (XEC) ½S 2, calculated from EBSD maps for the {311} lattice planes, was determined and compared for the different sets of diffracting grains. It was observed that the 2D detector captures 1.5 times more grains in a single exposure (one tilt angle) than the linear detectors for nine tilt angles. Different XEC mean values were found for the sets of grains from the two XRD techniques/detectors. Grain-size effects were simulated, as well as detector oscillations to overcome them. A bimodal grain-size distribution effect and `artificial' textures introduced by XRD measurement techniques are also discussed.

The measure of friction angles for different types of granular material

The aim of this research is to deepen the knowledge of the role of friction on the dynamics of granular media; in particular the friction angle is taken into consideration as the physical parameter that drives stability, motion and deposition of a set of grains of any nature and size. The idea behind this work is a question: is the friction angle really that fundamental and obvious physical parameter which rules stability and motion of granular media as it seems from most works which deal with particle dynamics? The experimental study tries to answer this question with a series of laboratory tests, in which different natural and artificial granular materials have been investigated in dry condition by means of a tilting flume. The characteristic friction angles, both in deposition (repose) and stability limit (critical) conditions, were measured and checked against size, shape, density and roughness of the considered granular material. The flume tests have been preferred to “classical” geotechnical apparatuses (e.g. shear box) since the flume experimental conditions appear closer to the natural ones of many situations of slope stability interest (e.g. a scree slope). The results reveal that characteristic friction angles depend on size and shape of grains while mixtures of granules of different size show some sorting mechanism with less clear behaviour.

Study of crushing of grains of limestone under the effect of cyclic loading with the fractal dimension

The grains can be of very diverse nature (size, shape, mineralogy, etc), indeed even if each grain is a fairly simple object, the set of grains is a very complex system in which the geometrical and physical properties of the grains, their forces and their orientations play a crucial role in their mechanical behavior. The measurement of their shape in soil mechanics has historically required the use of standards and diagrams to which the different grains can be compared. However, these methods are approaches and remain insufficient and incomplete for the actual measurement of their form and the understanding of their behavior remains a task far from being completed.
 This work is in this context and proposes to analyze the shape and size of the grains with the fractal theory using the Box Counting method. It also makes it possible to study their influence on the crushing of the grains of the calcareous material under the effect of the cyclic loading-unloading during the oedometer test. The obtained results show that the variation of the fractal dimension, corresponding to the crushing effect of the grains, is strongly influenced by their shape, their size, their particle size distribution and the variation in the number of loading-unloading cycles.

A micromechanical experimental study of highly/completely decomposed tuff granules

In this paper, an experimental micromechanical study is presented investigating the contact mechanics and tribological behaviour of highly/completely decomposed tuff granules. The parent material was taken from two locations—named the top and bottom—from a recent landslide in Hong Kong, and in this study the tested granules were obtained from the parent material after drying and sieving processes. Basic material characterisation was conducted quantifying the particle shape, the surface roughness and the strength of a set of grains. A set of twenty-nine monotonic inter-particle shearing tests were conducted on pairs of granules taken from the top and bottom of the landslide. It was found that the granules had very high friction angles at their contacts, in general greater in comparison with other materials reported in the literature. The slightly greater inter-particle friction for the granules taken from the top of the landslide might be because of their higher roughness in comparison with the ones from the bottom. Additional experiments were conducted to investigate the normal and tangential load–displacement response of the granules subjected to cyclic loading. A good curve fitting for the normal load–displacement response could be obtained by using very low apparent Young’s moduli in the Hertzian model. In general, the decomposed tuff granules showed significant plastic response during the first normal load cycle, and this plastic behaviour continued for the subsequent third and fourth cycles. In the cyclic inter-particle shearing tests, the nonlinearity and hysteresis increased for larger cyclic displacements, but the effect of the number of shearing cycles on the energy loss was generally small. Finally, a limited discussion is presented on the applicability of a theoretical model on the tangential load–displacement behaviour of the granules.

Microchemical signature of alluvial gold from two contrasting terrains in Cameroon

The microchemical signature of alluvial gold particles has wide application in constraining their primary sources. In this study, we apply this concept to investigate the composition of gold-bearing alloys from alluvial samples draining two geologically distinct terrains in southern and eastern Cameroon where the search for primary gold has remained elusive. The first set of gold grains (Lom grains) are from the Lom river drainage system with predominantly metasedimentary Pan-African rocks in the catchment region while the second set of grains (Nyong grains) are from the Mbal and Ebap tributaries of the Nyong river draining over a Paleoproterozoic complex comprising metamorphosed ultramafic rocks, amphibolites and granulitic gneisses. The gold grains recovered from these fluvial networks after panning were first studied under an electron microscope in order to evaluate their morphological features and subsequently embedded in epoxy resin, polished, and their compositions determined by both electron microprobe (EMPA) and laser ablation (LA-ICP-MS) techniques. The Lom grains are irregular to sub rounded with extensively pitted surfaces while the Nyong grains are predominantly rounded, oblong and with smooth surfaces. Nyong grains are devoid of inclusions while galena and pyrite are entombed in the Lom grains. Both set of grains are essentially Au–Ag alloys although the Ag content of the cores of the Nyong grains from both EMPA and LA-ICP-MS analytical techniques are significantly lower (0.05–6.07 wt% Ag; 93.54–99.29 wt% Au) than for Lom gold (0.06–22.75 wt% Ag; 78.76–99.86 wt% Au). X-ray element distribution maps do not show any zonal variation in core composition suggesting the gold grains derived from lode sources with single episode of hydrothermal gold deposition. Also the Nyong grains have significant amounts of Pt, Pd and Cr suggesting a link with ultramafic rocks while the Lom grains have substantial Sb and Zn levels pointing to hydrothermal quartz veining as the possible primary mineralization system. The grains from both localities have Ag-depleted rims. The results demonstrate that the microchemical signature of gold is useful to study the hypogene environment of a given area and a field for hydrothermal-orogenic gold is proposed on the ternary Au–Ag–Hg and Au–Ag–Cu plots.

Development of a stress-induced martensitic transformation criterion for a Cu–Al–Be polycrystalline shape memory alloy undergoing uniaxial tension

This study presents a criterion for predicting the martensitic variants (MVs) that appear during the stress-induced martensitic transformation (SIMT) in a polycrystalline sample of Cu–11.5% wt. Al–0.5% wt. Be under simple tension. Our criterion is based on crystallographic parameters, such as the crystal orientation and Schmid factor (SF). The displacement vector fields (DVFs) were obtained in the observation system by a mathematical model and were used to distort the boundary of a set of grains. From the DVF, the strain tensor for each grain was obtained, and the strain ratio (SR) in the observation system was calculated. Electron backscattering diffraction (EBSD) measurements were performed to determine the crystal orientation of the grains. The inverse SF was used to determine the in-plane stress transformation diagrams (STDs) for each studied grain. The combination of a balance criterion (BC) and STD provided a criterion that allowed us to predict the possible order of stress-induced MVs formed as a function of the crystal orientation and thermomechanical parameters of the shape memory alloy (SMA) with higher accuracy than when using the criteria separately. To validate our criteria, we tested other researchers’ published results. Our results were in agreement and were capable of predicting the stress-induced MVs in a polycrystalline SMA.

Deformation mechanism study of a hot rolled Zr-2.5Nb alloy by transmission electron microscopy. I. Dislocation microstructures in as-received state and at different plastic strains

Thin foil dog bone samples prepared from a hot rolled Zr-2.5Nb alloy have been deformed by tensile deformation to different plastic strains. The development of slip traces during loading was observed in situ through SEM, revealing that deformation starts preferentially in certain sets of grains during the elastic-plastic transition region. TEM characterization showed that sub-grain boundaries formed during hot rolling consisted of screw ⟨a⟩ dislocations or screw ⟨c⟩ and ⟨a⟩ dislocations. Prismatic ⟨a⟩ dislocations with large screw or edge components have been identified from the sample with 0.5% plastic strain. Basal ⟨a⟩ and pyramidal ⟨c + a⟩ dislocations were found in the sample that had been deformed with 1.5% plastic strain, implying that these dislocations require larger stresses to be activated.

Evolution of lattice strain and phase transformation of β III Ti alloy during room temperature cyclic tension

An in situ high-energy X-ray diffraction cyclic tension test was carried out on a β III Ti alloy to study its micromechanical behavior and the stress-induced phase transformation. Pre-strained material showed a microscopic multi-stage re-loading behavior following the sequence of elastic deformation, stress-induced martensite (SIM) transformation, a second stage of elastic deformation followed by a final stage of SIM transformation. Based on the relationship of internal strains and diffraction intensities between the β phase and the SIM, it is concluded that after a small strain deformation, the austenite is divided into two different sets of grains with different properties. Those that previously experienced phase transformation have a lower critical stress for the SIM transformation due to residual martensite and dislocations, while the rest have a higher trigger stress and only transform to martensite after the stress is back to levels comparable to where transformation was seen in the previous cycle. The different properties within the same austenite grain family cause the multistage re-loading behavior. The reverse phase transformation during unloading was impeded by the combination of increased dislocation density in the austenite and the increased tensile strain in the martensite prior to unloading.

Universal grain size distribution, most chaotic microstructures and tessellation condition

In this paper the probability distribution of grain sizes in the self-similar regime of grain growth is derived from the assumption that the grain boundary structure is the most chaotic. The grain size distribution obtained in this way does not contain fitting parameters and describes reasonably well the experimental data. The derivation is based on the suggested in the paper tessellation condition, the necessary and sufficient condition for a set of grains to fill the space without gaps and overlapping. The tessellation condition yields an infinite chain of constraints on the geometrical parameters of the grains. The derivation of the most chaotic grain size distribution employs only a few of these constraints, and, thus, the resulting distribution is approximate. It is checked that the incorporation of a few more constraints does not change the resulting distribution. Another aspect of the derivation is the notion of most chaotic microstructures as applied to polycrystal grains. This notion is introduced in accord with the Laplace principle of insufficient reasoning. Satisfactory description of experimental data indicates that the grain boundary structures developed in the self-similar regime of grain growth can be viewed as the most chaotic.

Grain Orientation Spread Values in if Steels after Plastic Deformation and Recrystallization

From an EBSD map made on a polycrystal one can define a set of grains using a criterion of misorientation between the adjacent pixels. Once such a list of grains is obtained, various quantities can be associated to each grain such as its size, (mean) orientation, GOS (Grain Orientation Spread) etc... The GOS associated to one grain is the mean value of the misorientations between all the pixels of the grain and the mean orientation of the grain. This value is quite sensitive to the state of the material (degree of plastic deformation, degree of recrystallization for example). Therefore it can help in interpreting the evolution of a microstructure during thermomechanical treatments. It is the purpose of this presentation to provide GOS values for an IF steel after several degrees of plastic deformation as well as after several annealing treatments which lead to partially or totally recrystallized states. The sources of influence on GOS values (as grain detection limit or grain size) are analyzed. The link between the values and the state of the material will be discussed at a global stage for a given population of grains.

On the Use of EBSD to Study the Heterogeneity of Plastic Deformation

This paper deals with the study of plastic heterogeneity. It aims to study the role of both grain size and orientation distributions in the development of such heterogeneity. The considered material is an IF steel. EBSD maps have been made on the same areas before and after several degrees of extension. Parameters such as GOS (Grain Orientation Spread) or GOS/D (D the diameter of the grain) or GND (Geometrically Necessary Dislocation) densities have been determined for the whole set of grains as well as for subpopulations (smallest grains, largest grains for example). It appears that the character of neighboring grains plays a more important role than any of these parameters alone.

The H-microdirectional model: Accounting for a mesoscopic scale

Solving boundary value problems requires implementation of sufficiently robust constitutive models. Most models try to incorporate a great deal of phenomenological ingredients, but this refining often leads to overcomplicated formulations, requiring a large number of parameters to be identified. A powerful alternative can be found with micromechanical models, where the medium is described as a distribution of elementary sets of grains. The complexity is not related to the constitutive description, but to the multiplicity of contacts oriented along all the directions of the physical space. This paper proposes an advanced micromechanical model that introduces an intermediate scale (mesoscopic scale): elementary hexagonal patterns of adjoining particles. This is advantageous with respect to current micromechanical models that generally describe the material through a single distribution of contacts. This new approach makes it possible to take many constitutive properties into account in a very natural way, such as the occurrence of diffuse failure modes. These preliminary results are presented in order to give clear insights into the capability of such multiscale approaches.

Micro-Structure Study on Collapsibility Loess with SEM Method

To study the micro-structure of collapsibility loess, the triaxial shear test under pressure of 10MPa to 100MPa and consolidation test under 1000kPa, 2000kPa and 4000kPa were respectively used on collapsibility loess here to imitate the working condition of dynamic compaction. Micro-images of the soil samples in above tests and undisturbed soil samples were collected by SEM at 500 enlarge. The results of images analysis are that the flocculated structure is destroyed drastically under compaction; the macrovoids and large set of grains are destroyed and recombined with tamping energy’s increase and the primary unordered sank is recombined and more dense and directional.

Molecular Modeling of Chemicals Products Inhibitors of Growth Struvite Crystal

Struvite (MgNH4PO46H2O) crystals were produced by infection associated with urea generating organ- isms.The aim of this study is to examine the interactions between the enzyme urease and two inhibitors, the first is an inhibitor monoatomic: Aluminum and the second is a polyatomic: Citrate by the methods of molecular modeling: molecular mechanics, molecular dynamics (MM+, AMBER) and molecular docking (FleX). Supersaturated solutions induce crystallization by nucleation and subsequent crystal growth .The mechanisms for the formation of calcium phosphate urinary stones are still not understood. Chemicals prod- uct has been studied extensively as inhibitors and has been observed in the attachment of crystals to in vitro study. As a complement we have using an electron microscope Hitachi TM1000, we examined specimens of crystals struvite. The various figures show a set of grains of sizes of the order of 20 µm. The majority of these particles present regular forms. This suggests the crystal growing. This result to an alteration in the expression of these faces and the development of a characteristic architectural struvite morphology. Similar changes were observed in the presence of identical concentrations of citrate acid, and Alluminuium, emphasizing the unique interaction of phosphocitrate with the struvite crystal.