Polygonization Process Research Articles

Phase and structural transformations in U and U-Nb alloy upon severe deformation and heat treatments

Transmission electron microscopy was used to analyze the twin and dislocation structure of samples of commercial uranium in the initial (undeformed) state and after severe deformation using explosive loading by plane and spherical waves of various intensity. It has been shown that an increase in the intensity of explosive loading by a plane wave leads, first, to an increase in the density of randomly distributed dislocations and twins and, then, to the development of polygonization processes with the formation of a subgrain structure of the α phase. Crystallographic analysis of the initial and deformation-induced twins in uranium has shown the presence of predominantly {130} twins of mixed type and, in singular cases, {172} and {176} twins of the second kind. It has been established that the retained spherical shells have a distinctly pronounced zonal structure, which contains information on the forward and reverse martensitic phase transformations of uranium (α ↔ β(γ) ↔ L, etc.) that occur under shock-wave loading by spherical waves. Conditions are determined for the manifestation of structural heredity in the U-6 wt % Nb alloy with recovery of the size and shape of grains of the initial high-temperature γ phase during the forward γ → α″ martensitic transformation upon cooling and during reverse α″ → γ transformation upon heating. Elimination of the structural heredity with significant grain refinement of the high-temperature γ phase occurs in the process of repeated quenching from 700°C after one type of preliminary treatments (cold deformation of α″ martensite, recrystallization of the deformed α″ phase, high-temperature aging of the initial α″ martensite, and eutectoid decomposition).

Microstructural Aspects of Low Cycle Fatigue of Aged GX12CrMoVNbN9-1 Cast Steel

The paper presents the results of research on the changes in microstructure of GX12CrMoVNbN9-1 cast steel subject to aging at the temperature of 600°C and holding time of 8000 hours, followed by low-cycle fatigue. The characteristics of the microstructure of the examined cast steel after ageing and low-cycle fatigue was described using transmission electron microscopy (study of the dislocation microstructure) and morphology of precipitations. It has been shown that low cycle fatigue leads to the matrix softening as a result of the processes of recovery, polygonization and repolygonization. Moreover, the processes of precipitation of Laves phase and coagulation of M23C6 carbides were observed in the microstructure. Intensity of these processes depended not only on the temperature of fatigue tests, but also on the level of total strain amplitude εac.

Prior Structure Modification on Grain Refinement and Deformation Behavior of Medium Carbon Steel Processed by ECAP

The present work, deals with grain refinement of medium carbon steel AISI 1045 (0.45% C), having different initial ferrite–pearlite microstructure resulted from thermal and thermomechanical treatment (TM). The purpose of TM steel processing was to refine ferrite and modify pearlite lamellae structure. The final grain refinement of steel structure was then accomplished during warm Equal Channel Angular Pressing (ECAP) at 400°C. Employment of this processing route, in dependence of the applied effective strain ϵef, resulted in extensive deformation of ferrite grains and cementite lamellae fragmentation. When applying higher shear stress (ϵef = 4) the mixed structure of subgrains and ultrafine grains was formed within ferrite phase, regardless the initial steel structure morphology. In pearlite grains, modification of cementite lamellae due to shearing, bending, twisting, and breaking was found efficient as straining increased. Processes of dynamic polygonization and recrystallization in deformed structure also contributed to submicrocrystalline grains formation in deformed structure. Comparing results the course of lamellae cementite spheroidization was then more efficient in prior TM treated steel. The tensile deformation results confirmed the strength increase, however deformation behavior and strain hardening generally for different initial structural conditions of steel, showed diversity.

Heat treatment and properties of plastically deforming, highly coercive iron alloy (30% Cr, 15% Co, 2% W, 1% Mo, and 1% Ti)

The structural transformations of plastically deforming, highly coercive Kh30K15V2MT iron alloy (30% Cr, 15% Co, 2% W, 1% Mo, and 1% Ti) are studied, along with its magnetic and mechanical properties. Metallographic and X-ray data show that, besides the α solid solution that exists at 1220–1180°C, metastable α phase is present at 670–700°C. If the alloy is annealed at 670–700°C after cold deformation, no recrystallization occurs; only processes of recovery and polygonization are observed. The relation of the magnetic and mechanical properties to the initial state and structure of the single-phase α solid solution is established. Either good magnetic properties or good mechanical properties may be obtained, by adjusting the initial state of the single-phase α solid solution.

Evolution of Microstructure in Martensitic GX12CrMoVNbN9 – 1 Cast Steel after Low Cycle Fatigue

The paper presents the results of microstructural research on GX12CrMoVNbN91 cast steel in the as-received condition (after heat treatment) and after the process of low cycle fatigue at room temperature. The microstructural tests were carried out by means of transmission electron microscope and completed with quantitative study determining: the mean diameter of subgrains, density of dislocations and shape factor. Performed research has proved that in both states: the as-received one, as well as after fatigue, the investigated cast steel is characterized by lath microstructure of tempered martensite with numerous precipitations of the M23C6 and MX type. Fatigue in the low cycle scope leads to the processes of recovery and polygonization of the matrix, as a result of a decrease in the dislocation density and an increase in the subgrain width. Intensity of these processes depends not only on the temperature of testing, but also on the level of total strain amplitude εac. Stability of the substructure of the examined cast steel depends on the morphology of precipitates of M23C6, precipitated on the boundaries of grains/subgrains.

A study of softening processes in heating of cold-deformed sheets of low-alloy aluminum alloys

Processes of polygonization and recrystallization in aluminum alloys with 0.3 at.% magnesium, zinc, or copper and their structure and hardness are investigated. The temperature, time, and amplitude dependences of internal friction are determined. A comparative analysis of the dislocation structure in the alloys is conducted.

Effect of microadditions of magnesium and zinc in aluminum upon heating of cold-rolled sheets

Methods of structural investigations, measurements of hardness, temperature, time, and amplitude dependences of internal friction have been used to study processes of polygonization and recrystallization in Al-0.3 at % Mg and Al-0.3 at % Zn alloys. It has been established that the magnesium atoms more efficiently pin dislocations in the aluminum-based alloys as compared to zinc atoms. Therefore, in the alloy with zinc the process of polygonization occurs more intensely and the processes of softening upon recrystallization occur more slowly than those in the alloy with magnesium.

Effect of annealing on conversion efficiency of nanostructured CdS/CuInSe2 heterojunction thin film solar cell prepared by chemical ion exchange route at room temperature

We report, the effect of air annealing on solar conversion efficiency of chemically grown nanostructured heterojunction thin films of CdS/CuInSe2, such 100, 200 and 300°C air annealed thin films characterized for physicochemical and optoelectronic properties. XRD pattern obtained from annealed thin films confirms tetragonal crystal geometry of CuInSe2 and an increase in average crystallite size from 16 to 32nm. An EDAX spectrum confirms expected and observed elemental composition in thin films. AFM represents high energy induced grain growth and agglomeration due to polygonization process. Increase in optical absorbance strength and decrease in energy band gap from 1.36 to 1.25eV is observed. Increase in charge carrier concentration from 2×1016 to 8×1017cm−3 is observed as calculated from Hall effect measurements and an enhancement in solar conversion efficiency from 0.26 to 0.47% is observed upon annealing.

Asymptotic results for polygonal processes related to an autoregression

We establish functional central limit theorems for polygonal process constructed from consecutive estimators of a simple AR(1) model. We consider both stationary and unit root cases. The results are applied to change segment analysis.

On‐demand transmission model for remote visualization using image‐based rendering

SUMMARYInteractive distributed visualization is an emerging technology with numerous applications. However, many of the present approaches to interactive distributed visualization have limited performance because they are based on the traditional polygonal processing graphics pipeline. In contrast, image‐based rendering uses multiple images of the scene instead of a three‐dimensional geometrical representation, and so has the key advantage that the final output is independent of the scene complexity and depends on the desired final image resolution. Furthermore, the discrete nature of the light field dataset maps well to a hybrid solution, which can overcome the identified drawbacks. In this paper, we propose an on‐demand solution for efficiently transmitting visualization data to remote users/clients. This is achieved through sending selected parts of the dataset based on the current client viewpoint, and is done instead of downloading a complete replica of the light field dataset to each client, or remotely sending a single rendered view back from a central server to the user each time the user updates their viewing parameters. The on‐demand approach shows stable performance as the number of clients increases because the load on the server and the network traffic are reduced. Furthermore, detailed performance studies show that the proposed scheme outperforms the current solution in terms of interactivity measured in frames per second. Copyright © 2012 John Wiley & Sons, Ltd.

Industrial strength polygon clipping: A novel algorithm with applications in VLSI CAD

We present an algorithm to compute the topology and geometry of an arbitrary number of polygon sets in the plane, also known as the map overlay. This algorithm can perform polygon clipping and related operations of interest in VLSI CAD. The algorithm requires no preconditions from input polygons and satisfies a strict set of post conditions suitable for immediate processing of output polygons by downstream tools. The algorithm uses sweepline to compute a Riemann–Stieltjes integral over polygon overlaps in O ( ( n + s ) log ( n ) ) time given n polygon edges with s intersections. The algorithm is efficient and general, handling degenerate inputs implicitly. Particular care was taken in implementing the algorithm to ensure numerical robustness without sacrificing efficiency. We present performance comparisons with other polygon clipping algorithms and give examples of real world applications of our algorithm in an industrial software setting.

Effect of Polygonal Rotor Process on Solidification Structure of Lead-Free Bismuth Bronze

Semi-solid slurry with fine solid granules for rheocasting was made from lead-free bismuth bronze by passing the low-superheat melt through an opening between a rotating regular octagonal rotor and a circumscribed chill block. We mainly investigated the effect of rotational speed on the structure of a solidified small ingot. The ingot structures changed from the dendrite of rotor-free condition to the rosette at the rotational speed of 50rpm and to the granular with a mean grain size of about 50m at higher than100 rpm. If the slurry made at 100rpm was rheocast to a disk shape by the use of a high pressure casting machine, the disk had almost uniform granular structures from the center to the edge regions.

Types of twins and the dislocation structure of α uranium in the initial and explosion-deformed states

Transmission electron microscopy is used to study and analyze the twin and dislocation structures of commercial-purity uranium samples in the initial (undeformed) state and after severe deformation induced by shock loading by plane waves with various intensities. As the shock loading intensity increases, the density of chaotically distributed dislocations and twins first increases, and, then, polygonization processes develop and result in a subgrain structure. Crystallographic analysis of the initial and deformation twins in uranium reveals predominant twins of the compound type {130} and rare {172} and {176} second-type twins.

Effect of rolling-assisted deformation on the formation of an ultrafine-grained structure in a two-phase titanium alloy subjected to severe plastic deformation

The effect of rolling in the temperature range 450–650°C on the fragmentation of the primary phase in a hot-rolled VT6 alloy rod preliminarily subjected to severe plastic deformation by equal-channel angular pressing at 700°C (scheme B c, the angle between the channels is 135°, 12 passes) is studied. Rolling at 450°C without preliminary ECAP is shown not to cause α-phase fragmentation and to favor intense cold working of the alloy due to multiple slip. ECAP provides partial fragmentation of the initial structure of the α phase and changes the morphology of the retained β phase: it transforms from a continuous matrix phase into separated precipitates located between α particles. This transformation activates the fragmentation of the α phase during rolling at 550°C owing to the development of twinning and polygonization processes apart from multiple slip. Both a decrease (to 450°C) and an increase (to 625–650°C) in the rolling temperature as compared to 550°C lead to the formation of a less homogeneous and fragmented structure because of weakly developed recovery and intense cold working in the former case and because of the beginning of recrystallization and the suppression of twinning in the latter case. A relation between the structure that forms upon SPD followed by rolling and the set of its properties is found. A general scheme is proposed for the structural transformations that occur during ECAP followed by rolling at various temperatures.

Integration of combinatorial decompositions in the presence of collinearities

Many results in Combinatorial Integral Geometry are derived by integration of the combinatorial decompositions associated with finite point sets {P i } given in the plane ℝ2. However, most previous cases of integration of the decompositions in question were carried out for the point sets {P i } containing no triads of collinear points, where the familiar algorithm sometimes called the “Four indicator formula” can be used. The present paper is to demonstrate that the complete combinatorial algorithm valid for sets {P i } not subject to the mentioned restriction opens the path to various results, including the field of Stochastic Geometry. In the paper the complete algorithm is applied first in an integration procedure in a study of the perforated convex domains, i.e convex domains containing a finite array of non-overlapping convex holes. The second application is in the study of random colorings of the plane that are Euclidean motions invariant in distribution, basing on the theory of random polygonal windows from the so-called Independent Angles (IA) class. The method is a direct averaging of the complete combinatorial decompositions written for colorings observed in polygonal windows from the IA class. The approach seems to be quite general, but promises to be especially effective for the random coloring generated by random Poisson polygon process governed by the Haar measure on the group of Euclidean motions of the plane, assuming that a point P ∈ ℝ2 is colored J if P is covered by exactly J polygons of the Poisson process. A general theorem clearing the way for Laplace transform treatment of the random colorings induced on line segments is formulated.

Influence of Thermal Condition of ECAP on Microstructure Evolution in Low Carbon Steel

Commercial low carbon steel AISI 1010 was subjected to Equal Angular Channel Pressing (ECAP) at different temperatures. The paper describes the refinement of the coarse grained ferrite microstructure to submicrocrystalline range by large plastic strain. The steel was deformed in an ECAP tool with a channel angle φ = 90°, at different temperature in the ranging between 150 – 300°C. The number of passes at each temperature was N = 3. Optical microscopy, scanning electron microscopy (SEM) and transmission electron microscopy (TEM) were used to study the formation of substructure and ultrafine grains in the deformed specimens. The TEM study reveals that at the lowest ECAP temperature of 150°C extensively elongated ferrite grains with dense dislocation network dominate in the structure. The randomly scattered polygonized subgrains have been observed. The activation of dynamic recovery process, even at the lowest temperature of equal channel pressing, contributed to the formation of individual polygonized grains. As the temperature of ECAP processing was increased the process of dynamic polygonization and recrystallization occurred more effectively and the submicrocrystalline structure was formed by sectioning of elongated ferrite grains. The formation of such predominant submicrocrystalline structure resulted in strength increase of the low carbon steel.

New tests of heteroskedasticity in linear regression model

In this paper, we present a class of tests for heteroskedasticity of various types in the linear regression model. These tests are based on the limit behavior of the polygonal process constructed from squared residuals. The law of test statistics under the null hypothesis is established, and the consistency is proved. By means of simulations these tests are compared with two classical tests (likelihood-ratio and Breusch-Pagan) for two types of heteroskedasticity (changed-segment and the type where the error variance is proportional to one of the components of the design matrix).

Hölderian properties of partial sums of regression residuals

In this paper we investigate Holder convergence of polygonal line process based on residuals of linear regression model. Bootstrap counterpart is also studied. Our results provide additional tools for testing epidemic type structural changes in regression models.

Understanding of the concave polygon object in the shape understanding system

In this paper a method of understanding of the concave polygon object is presented. The proposed method of understanding the concave polygon object is part of the shape understanding method. The main novelty of the presented method is that the process of understanding of the concave polygon object is related to the visual concept represented as a symbolic name of the possible classes of shape. The possible classes of shape, viewed as hierarchical structures, are incorporated into the shape model. At each stage of the reasoning process that led to assigning of an examined object to one of the possible classes, the novel processing methods were used. These methods, implemented as modules of the shape understanding system (SUS) and tested on the broad classes of shapes, are very efficient because they deal with a very specific classes of shape. The system consists of different types of experts that perform different processing and reasoning tasks. The concave polygon class models and processing methods are also described.

Delta-ferrite recovery structures in low-carbon steels

The development of delta-ferrite recovery substructures in low-carbon steels has been observed in-situ utilizing laser scanning confocal microscopy (LSCM). Well-developed sub-boundaries with interfacial energies much smaller than that of delta-ferrite grain boundaries formed following transformation from austenite to delta-ferrite on heating. It is proposed that transformation stresses associated with the austenite to delta-ferrite phase transformation generate dislocations that subsequently recover into sub-boundaries by a process of polygonization. Experimental evidence in support of this proposal was found in a ferritic stainless steel. Thermal cycling through the high-temperature delta-ferrite/austenite/delta-ferrite phase transformation leads to the development of a well-defined recovery substructure, which, in turn, modifies the low-temperature austenite decomposition product from Widmanstatten to polygonal ferrite, with a commensurate change in hardness.