Ratio Of Grain Diameter Research Articles

Grain Growth of AZ31 Magnesium Alloy Based on Three‐Dimensional Cellular Automata

Based on the thermodynamic conversion mechanism and energy transition principle, a three‐dimensional cellular automata model of grain growth is established from the aspects of grain orientation, grain size distribution, grain growth kinetics, and grain topology. Also, the effect of temperature on the three‐dimensional grain growth process of AZ31 magnesium alloy is analyzed. The results show that the normal growth of three‐dimensional grains satisfies the Aboav‐weaire equation, the average number of grain planes is between 12 and 14 at 420°C and 2000 CAS, and the maximum number of grain planes is more than 40. Grains of different sizes are distributed normally at different times, most of which are grains with the ratio of grain diameter to average grain diameter R/Rm ≈ 1.0, which meets the minimum energy criterion of grain evolution. The grain of AZ31 magnesium alloy increases in size with the increase of temperature, and the number of grains decreases with the increase in time. The angle between the two‐dimensional slices of three‐dimensional grains is approximately 120°, which is consistent with that of the traditional two‐dimensional cellular automata. The relative error of grain size before and after heat preservation is in the range of 0.1–0.6 μm, which indicates that the 3D cellular automata can accurately simulate the heat preservation process of AZ31 magnesium alloy.

Deviation of permeable coarse‐grained boundary resistance from Nikuradse's observations

AbstractNikuradse's (1933) rough pipe study is enormously influential in the understanding of flow resistance over a sediment bed. However, the rough boundary employed in Nikuradse's study differs from permeable sediment beds in rivers. This implies that the results derived from the rough pipe experiments may not be applicable for flows over a permeable coarse‐grained bed. The present study aimed to explore to what extent the flow resistance of a permeable coarse‐grained boundary deviates from the Nikuradse's observations. Experiments were conducted with rough pipes, which were prepared by overlaying the inner wall with one to four layers of spherical beads. The single layer roughness resembles the experimental setup reported in Nikuradse's study, while the multilayer of grains allows significant flow to pass through the porous roughness layer. In addition, the ratio of grain diameter, k, to pipe diameter, d, was chosen to be one to two orders greater than the range (0.001 < k/d < 0.033) adopted in Nikuradse's experiments. The data show that the friction factor deviates significantly from the prediction based on Nikuradse's rough pipe relation. For hydraulically rough pipes, the friction factor is found to be proportional to the squared ratio of the grain diameter to nominal pipe diameter. This result is different from the one‐third power function as implied by Nikuradse's rough pipe relation or the Manning‐Strickler formula but agrees well with laboratory observations of open channel resistance in the presence of large‐scale roughness. The measurements also suggest the existence of a laminar flow regime, in which the friction factor is inversely proportional to the Reynolds number. The observed variations in the flow resistance are attributed to both wall permeability and large‐scale roughness.

Correlation of morphological anisotropy and Lankford value of deep drawing sheets hot-rolled by compact strip production

Cold-rolled steel sheets in automotive applications require an excellent deep draw ability, which is characterized by the Lankford value (r-value). In this study, a correlation was identified between r-value and pancake-shaped grain flatness which is indicated as the ratio of grain diameter in the rolling direction (RD) and normal direction (ND) of sheets (dr/dn). A mathematical model \(\left( {r = e^{0.345\left( {d_n^{ - 1/2} - d_r^{ - 1/2} } \right)} } \right)\) was developed to calculate r-value by the microstructure of steel sheets hot-rolled by compact strip production (CSP). It is shown that the r-value is higher, if the microstructure of steel sheet is of pancake-shaped grains elongated in the rolling direction. The calculated r-value is confirmed to fit exactly to the measured one from the large-scale production.

Estimation of Bed Load Transport Rate Based on Grain Froude Similarity Considering the Existence of Sand Waves

It is very important for reservoir management to estimate the sedimentation amount deposited in a reservoir. Firstly, the formula for estimating the bed load transport rate in the bed of sand waves of prototype by model experiment was derived based on the similarity of grain Froude number; Secondly, several model experiments that the bed forms is similar with the prototype were carried, and the formula was verified. As a result, when the ratio of grain diameter in the prototype and model is great enough, and the bed forms in the model is similar with that in the prototype, a satisfactory result can be obtained by using the estimation formula for estimating the bed load transport rate of the prototype that sand waves occur in the bed.

Abnormal Grain Growth During Rapid Annealing of Sol–Gel Alumina Thin Film Deposited on Ni‐Based Superalloy

A ∼50 nm thick alumina layer was deposited on an Ni‐based superalloy substrate by a sol–gel method. α‐AlOOH particles presented in the layer after drying at 140°C transformed mostly to α‐Al2O3 grains within ∼1 min at 1100°C under a low oxygen partial pressure annealing environment. During the same time period, the α‐Al2O3 grains grew significantly in the lateral direction, resulting in the aspect ratio of grain diameter to thickness of ∼20. The presence of a preferred orientation in the α‐Al2O3 layer suggested that the mechanism for the lateral growth was abnormal. The lateral growth mechanism appeared to become very slow when a critical thickness (∼100 nm) was reached.

Morphological differentiation of Betula (birch) pollen in northwest North America and its palaeoecological application

Lake sediments from arcto-boreal regions commonly contain abundant Betula pollen. However, palaeoenvironmental interpretations of Betula pollen are often ambiguous because of the lack of reliable morphological features to distinguish among ecologically distinct Betula species in western North America. We measured the grain diameters and pore depths of pollen from three tree-birch species (B. papyrifera, B. kenaica and B. neoalaskana) and two shrub-birch species (B. glandulosa and B. nana), and calculated the ratio of grain diameter to pore depth (D/P ratio). No statistical difference exists in all three parameters between the shrub-birch species or between two of the tree-birch species (B. kenaica and B. papyrifera), and B. neoalaskana is intermediate between the shrub-birch and the other two tree-birch species. However, mean pore depth is significantly larger for the tree species than for the shrub species. In contrast, mean grain diameter cannot distinguish tree and shrub species. Mean D/P ratio separates tree and shrub species less clearly than pore depth, but this ratio can be used for verification. The threshold for distinguishing pollen of tree versus shrub birch lies at 2.55 μm and 8.30 for pore depth and D/P ratio, respectively. We'applied these thresholds to the analysis of Betula pollen in an Alaskan lake-sediment core spanning the past 800 years. Results show that shrub birch increased markedly at the expense of tree birch during the‘Little Ice Age’; this patten is not discernible in the profile of total birch pollen.

A sandpile experiment and its implications for self-organized criticality and characteristic earthquake

We have performed an experiment in which a conical sandpile was built by slowly dropping sand onto a circular disk through a funnel with a small outlet. Avalanches (sand dropping off the disk) occurred, the size and the number of which were observed. It was seen that the behavior of avalanches (frequency-size distribution) was determined solely by the ratio of grain size to disk size, which is consistent with earlier studies. We categorize the behavior into three types: (1) the self-organized criticality (SOC) type (obeying Gutenberg-Richter’s law), (2) the characteristic earthquake (CE) type where only large avalanches are almost periodically generated, and (3) the transition type. The transition from SOC to CE type drastically occurs when the ratio of grain diameter to disk radius is reduced to about 0.02. The underlying mechanism to cause the transition is considered. Results of simulation by cellular automaton models, an experimental result showing that a conical pile has a stress dip near its center, and a two-dimensional simulation building up a conical pile, all suggest that the transition occurs due to a change in stress profile inside and near the surface of the pile. Although we are unfortunately not able to understand the detailed mechanism at the present stage, it seems very important to further investigate the underlying physics of the transition because it presumably provides us a clue to understand the mechanism of the periodicity of large characteristic earthquakes and may open a way for earthquake prediction.

Dispersion effects on thermal convection in porous media

The influence of hydrodynamic dispersion on thermal convection in porous media is studied theoretically. The fluid-saturated porous layer is homogeneous, isotropic and bounded by two infinite horizontal planes kept at constant temperatures. The supercritical, steady two-dimensional motion, the heat transport and the stability of the motion are investigated. The dispersion effects depend strongly on the Rayleigh number and on the ratio of grain diameter to layer depth. The present results provide new and closer approximations to experimental data of the heat transport.