Initial Grain Size Distribution Research Articles

Investigation on the existence of a ‘Hillert regime’ in normal grain growth

The existence of a ‘Hillert regime’ in 3D normal grain growth, where the grain size distributions (GSDs) at different time-steps match the Hillert distribution during parabolic grain growth, is investigated for different initial GSDs using large-scale phase-field simulations. The short-lived ‘Hillert regime’ was present in the early-stage only in few cases. The GSDs obtained at a later-stage for all cases are self-similar over long period; independent of the initial GSDs; and wider than the Hillert distribution. Also, the topological properties in the ‘Hillert regime’ were different from that in the later-stage self-similar regime.

Mechanical twinning in E2412 electrical steel

The deformation of fine-grain E2412 steel containing 3.63% Si, with different grain size is considered. Twinning predominates in its deformation. The samples are extended on an Instron-5565 machine at strain rates \(\dot \varepsilon \) ≈ 0.002–0.660 s–1 at 183–393 K. Samples of two types are investigated: with around 80% of the grains in the ranges 1.5–9.0 mm and 0.025–0.225 mm. (The mean grain sizes are d me1 = 3.55 mm and d me2 = 0.12 mm, respectively.) The relation between the number of twins and the types of steps formed on the strain and strain-rate diagrams in loading is established for the grains with d me1 = 3.55 mm. At small loading rates, on account of the high growth rate of the twins, step formation on the strain diagrams is accompanied by marked decrease in the load. With increase in the loading rate, the spread of the load is reduced; Δσ changes sign at a strain rate \(\dot \varepsilon \) ≈ 0.04 s–1. In fine-grain steel (d me2 = 0.12 mm), there are no visible jumps in the load with the appearance of twins. In the fine-grain steel, the growth time of twins in the grain is small. On account of their high rate of development, the number of twins is also small. The distribution of twinned grains is plotted as a function of the grain size, at different temperatures and loading rates. The peak in the size distribution of the twinned grains is shifted to larger grains in comparison with the overall grain-size distribution of the polycrystal. There is some optimal grain size that facilitates twinning. As a rule, it is higher than the mean grain size determined from the initial grain-size distribution. The number of twins in a particular grain depends on the test temperature and the strain rate. There is a deformation temperature at which the number of twins in the grain is constant at the strain rates employed.

Weibull Distribution to Describe Grading Evolution of Materials with Crushable Grains

This work presents a study on the evolution of the Grain Size Distribution (GSD) of an artificial granular material with crushable grains and its relation with the observed mechanical behaviour. The main aim of the work is to find a relationship between the initial GSD, its evolution and the mechanical behaviour. The artificial material used is a Light Expanded Clay Aggregate (LECA) subject to one-dimensional compression at various stress levels with eight initial GSDs characterised by four coefficients of uniformity and two mean diameters. The evolution of the GSD is characterised by a double mechanism depending on the initial GSD and on the applied stress level. A link between the evolution of the GSD, breakage and the compressibility curves is observed. A bimodal Weibull distribution function is proposed to describe the GSD before and after testing. The long term objective of the work is to link the evolution of breakage, from moderate to high stress, with the mechanical behaviour and to formulate a constitutive model able to describe the observed behaviour.

Experimental tsunami deposits: Linking hydrodynamics to sediment entrainment, advection lengths and downstream fining

A goal of paleotsunami research is to quantitatively reconstruct wave hydraulics from sediment deposits in order to better understand coastal hazards. Simple models have been proposed to predict wave heights and velocities, based largely on deposit grain size distributions (GSDs). Although seemingly consistent with some recent tsunamis, little independent data exist to test these equations. We conducted laboratory experiments to evaluate inversion assumptions and uncertainties. A computer-controlled lift gate instantaneously released ~6.5m3 of water into a 32m flume with shallow ponded water, creating a hydraulic bore that transported sand from an upstream source dune. Differences in initial GSDs and ponded water depths influenced entrainment, transport, and deposition. While the source dune sand was fully suspendable based on size alone, experimental tsunamis produced deposits dominated by bed load sand transport in the upstream ~1/3 of the flume and suspension-dominated transport downstream. The suspension deposits exhibited downstream fining and thinning. At 95% confidence, a published advection-settling model predicts time-averaged flow depths to approximately a factor of two, and time-averaged downstream flow velocities to within a factor of 1.5. Finally, reasonable scaling is found between flume and field cases by comparing flow depths, inundation distances, Froude numbers, Rouse numbers and grain size trends in suspension-dominated tsunami deposits, justifying laboratory study of sediment transport and deposition by tsunamis.

STUDY ON LOCAL SCOUR AND VARIATION OF BED COMPOSITION AROUND NON-SUBMERGED SPUR DYKE

Several studies have been made on local bed scour by movable bed experiments. Researches taking into account non-uniform sediment transport are still very few, in particular in case of the involvement of spur dykes. In this paper, we carried out movable bed experiments around an impermeable spur dyke under non-submerged condition. Both uniform and non-uniform sediment beds with similar mean diameter used and the changes of the bed configuration and bed surface composition have been considered. In addition, we used color sediment which is divided in three ranges of diameter with different colors in order to clarify the spatial differences of bed surface composition through pictures and visual observation. We focused on the relation between initial grain-size distribution and the final scour hole depth and the influence of vortices around a spur dyke on bed surface composition.

Sedimentation of volcanic particles

AbstractVolcanic eruptions present many hazards including pyroclastic flows and volcanic mud flows (lahars) that together have caused the death of more than 65000 people in the last two centuries (e.g. eruptions of Tambora 1815, Mount Pelee 1902 and Nevado del Ruiz 1985). However tephra (volcanic rock and glass fragments) can be transported in the atmosphere for long times and distances after the eruptive event, representing one of the most widespread hazards with significant human health consequences and the potential to significantly affect crucial economical sectors such as agriculture, social services, tourism and industry. In addition, the associated deposits retain a considerable amount of information of the generating processes, such as total erupted mass, initial grainsize distribution and also important constraints on plume dynamics and eruption intensity. As a result, the study of tephra fallout is crucial to the understanding of volcanic processes and to the hazard assessment of volcanoes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modelling the effects of grain-size gradients on necking in superplastic forming

A step-bar model is developed and used to investigate the effects of grain-size gradients, geometrical irregularities and deformation rates on the necking of Ti–6Al–4V at 927 °C. A necking map, which indicates the necking mode for a range of deformation rates under various initial cross-sectional area and grain-size combinations, is obtained. Finite-element simulations of a superplastic gas-blow forming process are carried out to investigate the effects of initial grain-size distributions on the non-uniform thinning of a formed structural component. The effects of grain sizes on the gas-pressure history required to maintain a forming rate is also studied.

Transformation of cataclastically deformed rocks to pseudotachylyte by pervasion of frictional melt: inferences from clast-size analysis

Optical contrast between clasts and surrounding dark-coloured matrix in thin sections has been used in a computer-aided method which has been applied for clast-size analysis of pseudotachylyte exposed in a 25-km-long brittle deformation zone in the Precambrian terrain of western India. While the number of clasts ( N 2) equal to or coarser than size u shows a power-law distribution ( N 2∝ u − D ), the area ( A 1) occupied by the clasts of different size fractions shows a log-normal distribution. The clast-size distribution pattern indicates transformation of cataclastically deformed rocks to pseudotachylytes by pervasion of a rock melt generated at the frictional slip planes. It is inferred that the melt pervaded the permeable cataclastically damaged zones and so occupied the intergranular space. This melt, mixed with the comminuted material, flowed further as a slurry to form the pseudotachylyte veins. The clast-laden final product retained the grain-size distribution pattern of the parent comminuted material with minor modifications. Fusion of clast rinds due to heat transfer from the melt slightly modified the initial grain-size distribution pattern. Because of the short duration of the heat-transfer process, combined with the low conductivity and high specific heat of rocks, the temperature at the centre of the coarse grains remained at the initial temperature T i and reduction w of radius r by fusion was a negligible fraction of r. As a consequence, the population of coarse clasts retained the pre-fusion size distribution pattern. In contrast, w/ r of the smaller grains was considerable. The initial grain-size distribution pattern did not survive in the finer fraction of the clasts. This difference in thermal response of the smaller versus larger grains to the heat-transfer process is revealed in clast-size distribution graphs for the pseudotachylytes. Moreover, the observed proportion of matrix can not be explained by cataclasis alone. The extent of comminution in the parent material and size of the openings, through which the clast-laden melt flowed to form veins, controlled the clast/matrix ratio in the pseudotachylytes.

The effect of initial grain size distribution on abnormal grain growth in single-phase materials

A model that describes the temporal evolution of an initial grain size distribution (GSD) has been used to analyze the effect of initial GSD on grain growth. Based upon the work of Hillert, and Hunderi and Ryum, this model uses a finite difference technique to numerically solve the continuity equation. A formal method has been developed to create synthetic GSDs. The model is used to study the evolution of both continuous and discontinuous GSDs. For either case, two parameters describe the deviation from steady state: u max is the ratio of the largest grain radius to the critical grain radius, and F o is the initial fraction of grains larger than twice the critical radius. The analysis is applied to lognormal GSDs obtained from experimental results. It is shown that, for all initial GSDs with nonzero F o, a transient period of abnormal grain growth characterizes the initial stages of growth. F o and u max allow approximate prediction of the duration and extent of abnormal grain growth.

Grain-size variation of tephra derived from volcanic umbrella clouds

The relationships among the thickness and grain-size of tephra-fall deposits and the volumetric flow rate of their source umbrella clouds are analytically obtained. The logarithm of the ratio of the probability distribution function based on grain size (InR f) in fall deposits at two localities from the vent (r 1 and r 2, respectively) has a linear relationship with the particle-settling velocity, v, as: In $$1n R_f = - \frac{{\pi (r_2^2 - r_1^2 ) \nu }}{Q} + 1n A,$$ where Q is the volumetric flow rate of the umbrella cloud and A is a constant for a given pair of localities. The volumetric flow rate of the umbrella cloud can be estimated from granulometric data using this formula. Generally, the thickness-distance relationship of tephra-fall deposits depends on the initial grain-size distribution and the volumetric flow rate of the umbrella cloud. The empirical relationship of the exponential thinning behaviour can be extrapolated towards infinite distance only for a specific initial grain size which is similar to a log-normal distribution with σφ=2.5, otherwise it holds only in a limited range of distances. In applying these results to the 1991 eruption of Mt. Pinatubo, it is shown that the volumetric flow rate of the umbrella cloud during the climactic phase of 15 June was approximately 5x1010 m3/s, which is fairly consistent with the expansion rate of the umbrella cloud observed in the satellite images.

On conditions for secondary recrystallization in a material with random orientation

The initial value and the time dependence of the pinning force which are necessary for the secondary recrystallization in a material with known initial microstructure and random orientation were determined by means of computer simulation. Secondary recrystallization was shown to take place only when the pinning force varies with time exponentially. The results obtained are in satisfactory agreement with the experimental data. The value of the pinning force which corresponds to the end of the induction period was determined. The induction period and the rate of secondary recrystallization are found to depend not only on the pinning force but also on both the average grain size and the width of the initial grainsize distribution. The secondary recrystallization behaviour in a sheet was also investigated.

Particle-size characteristics of Pyroclastic Tuffs

Size-frequency distributions of volcanic tuffs precisely characterize several types of deposits and provide a means for evaluating the mechanism of transport and deposition. Particulate size analyses may be visually interpreted when plotted on arithmetic probability paper in phi notation. As with sedimentary clastic units, four statistical moments describe size distributions: phi mean, standard deviation, skewness, and kurtosis. Relationships between size-frequency distributions and transport energies exist for rhyolitic ash flow, rhyolitic air fall, rhyolitic base surge, basaltic air fall, and basaltic base-surge deposits. The three energy environments, which singly, or in combination control the grain-size populations of air-transported tephra, are: fallout, suspended load, and bed load. Pyroclastic deposits that closely approximate single-mode, log-normal distributions (or their skewed and kurtic variations) result from deposition in a predominantly single-energy environment. Polymodal distributions are mixed populations that represent transitions from one transport energy to another. The few tephra samples that have single-mode distributions closely approximating Rosin's law of crushing are ambiguous cases and may not have undergone enough transport to modify the initial grain-size distribution produced by volcanic explosion.