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The structure of high purity (99.99%) aluminium processed by equal channel angular pressing in the as pressed state after different number of passes was examined using various stereological methods. An extreme inhomogeneity and complicated anisotropy was observed along the body of rod-like specimens.

Powder of tool steel STN 19830 with 1.9 wt.% of Nb addition was prepared by atomization. Compact material was prepared using of hot isostatic pressing (HIP) and followed by heat treatment to improve the carbides distribution. The aim of this work was to evaluate and quantify the influence of heat treatment parameters on size, shape and spatial distribution of the carbides. Light optical microscopy and image analysis was used to obtain relevant data. Area fraction of carbides was used as parameter of carbide distribution in steel matrix. Sensitivity and accuracy of this method was compared with technique based on Voronoi tessellation. Result shows that size characteristics of tessellation and area fraction analysis are both sufficiently sensitive to indicate the deviation between different states of the respective material and could be used for quantification of size and spatial distribution of the carbides in PM tool steels. Positive effect of used heat treatment on size and distribution of carbides was verified.

The regularities of the influence of the number of passes under equal-channel angular pressing on the mechanical properties and defect structure of an aluminum alloy have been elucidated. It has been established that the degradation of the mechanical properties (a decrease in the durability) is associated with the formation of nanoregions of an excess free volume in the course of severe plastic deformation under equalchannel angular pressing. A correlation between the nucleation of excess free volume regions and the formation of high-angle grain boundaries under equal-channel angular pressing has been revealed. The nature of the influence of severe plastic deformation on the elastic modulus, the vibration decrement, and the microplastic flow stress has been analyzed.

The attractive metallographic electron backscatter diffraction (EBSD) method is used to describe the effect of the number N of passes on the subgrain and grain structures of pure aluminium and copper processed by equal channel angular pressing (ECAP). The remarkable feature of the aluminium structure is the lack of high angle boundaries after a low number (N = 2, 4) of passes and this remains preserved even after a relatively long annealing time. On the other hand, the boundary structure of copper is relatively stable and high angle boundaries always prevail.

Very few reports describing the creep behaviour of materials processed by equal-channel angular pressing (ECAP) have shown that there are both similarities and differences between the creep behaviour of coarse-grained metals and alloys and their ultrafine-grained counterparts. This paper examines these differences and evaluates some factors affecting the creep behaviour of pure aluminium, pure copper, and the binary Al-0.2 wt.% Sc alloy processed by ECAP. It was found that the creep behaviour of pressed material depends strongly on the number of ECAP passes and successive passes result in a gradual decrease in the creep resistance which may be attributed to microstructural changes, homogenization of the microstructure and the microtexture, nanoporosity induced by the ECAP procedure and thermal instability of the pressed material during creep exposure.

The creep life of pure ultrafine-grained aluminum produced by equal-channel angular pressing and examined at 473 K, 15–20 MPa, continually decreases with the increasing number N of passes in spite of a considerable grain refinement. In order to explain this behavior, a detailed microstructural study has been carried out by means of electron backscatter diffraction at four different lower bounds of subgrain boundary misorientation Δ = 2°, 5°, 10° and 15°. At low N = 1, 2, the misorientation of the majority of boundaries is very low ( Δ Δ ≥ 15°) area do not exceed 10% and the creep strain is very slow. With the increasing N , the mutual misorientation of neighboring subgrains grows, the deformation processes can proceed faster and the creep life is substantially shortened (the creep fracture elongation grows only slowly).

Significant developments have been made in recent years in the description of microstructure evolution and its effects on the creep behaviour in advanced 9-12%Cr steels. However, data available for assessing the predictability of the creep behaviour are somewhat scarce since creep testing has generally been for constant temperature and load conditions. The present investigation was conducted on three advanced 9-12%Cr martensitic/ferritic steels (P91, P92 and E911) in an effort to obtain more complete description and understanding of the role of degradation processes in high temperature creep during intermittent heating. A comparison between the creep characteristics of non-steady and monotonously loaded creep specimens has revealed no significant deterioration of the creep strength and fracture resistance of the steels P91, P92 and E911 under non-steady loading in power-law (dislocation) creep. The final part of this paper deals with detailed experimental microstructural and fractographic investigations of crept specimens to explain the observed creep behaviour. Special attention is paid to the thermodynamic calculations using the software package Thermo-Calc, that have been used to predict precipitation reactions during intermittent heating of 9-12% chromium steels. The results of the thermodynamic calculations are in a good agreement with experimental data.

The results of intercept and profile counts are commonly interpreted as a suitable estimates of the mean grain size as represented e.g. by the grain density V. The term grain size is not explicitly defined even when some relation to grain volume and/or mean grain breadth (the mean Ferret diameter) is tacitly assumed. However, the intercept count L is directly related to the mean value of grain boundary area per unit volume SV and the profile count A is, under relatively general assumptions, directly related to the mean value of grain junctions per unit volume LV. Their relation to V can be generally written as V = c¢(A)3/2 = c²(L)3, but the coefficients c¢ and c² strongly depend on the structural characteristics like grain size dispersion, anisotropy etc. and their evaluation is far from being simple. Consequently, whereas the reliable estimates of SV and LV result from intercept and profile counts, the estimate of grain density based on them requires a careful consideration.

In an analogy to the 3D tool of tessellation classification – w−s diagram, a similar graphical device is proposed for 2D tessellations. Any tessellation is represented by a point in the Cartesian coordinate system with the axes Ep (the mean cell perimeter) and CV a (the coefficient of cell area variation). Images of tessellations and p−CV a diagrams for selected tessellations with low and high values of CV a are shown as examples.

The estimators proportional to (NA(x,y)NA(x,z)NA(y,z))1/2 and (NL(x)NL(y)NL(z)) obtained by profile and intercept counts are recommended by ASTM Standards E 112 for 3D grain intensity l of anisotropic grain structures (NA(•) are estimated in three mutually perpendicular planes suitably oriented with respect to the prevailing anisotropy direction and NL(•) are intercept intensities along three suitably selected mutually perpendicular directions). However, l is also related to the profile and intercept intensities l', l', namely l= c'(l')3/2= c'(l')3. The induced intensities are estimated by arithmetic means NA = (NA(x,y)+NA(x,z)+NA(y,z))/3, NL = (NL(x)+NL(y)+NL(z))/3. A simple model isdeveloped, in which the role of geometric and arithmetic means of profile and intercept counts in the grain size estimation is elucidated. Its results are compared with computer simulated random tessellations with prevailing rod-like and plate-like cells and applied to anisotropic grain structures of pure Al produced by ECAP and to platinum based composite Pt - 0.5 Y2O3.

The grain structure of pure aluminium processed by equal channel angular pressing (ECAP) was examined electron backscattered diffraction (EBSD) in the as pressed state and after heating preceding the creep deformation using various stereological methods. Area intensities of grain and subgrain boundaries, length intensities of triple grain and subgrain junctions, structural homogeneity and its thermal stability are strictly dependent on the number of passes.

This paper deals with an experimental investigation of the effect of various microdefects induced by equal-channel angular pressing (ECAP) on mechanical and creep properties of ultrafinegrained pure aluminium, an Al-0.2%Sc alloy and copper.

The effect of ECAP technology on the subgrain structure of coarse-grained pure aluminium is described by means of the orientation imaging microscopy (the selected lower bounds of misorientation (disclination) are = 2o, 5o, 10o and 15o). Standard profile and intercept counts carried out in three suitably oriented and mutually perpendicular section planes and along 18 systematically oriented directions, resp., are used to examine the subgrain and grain structures after the number of passes N = 2, 4, 8, 12 as well the effect of subsequent annealing (several hours at 473K). The local and overall non-homogeneity and anisotropy of boundary structures have also been evaluated.

The presence of nanopores formed during the equal-channel angular pressing of aluminum is revealed using small-angle x-ray scattering. The parameters of nanopores are determined, and a correlation between the level of nanoporosity and the fraction of high-angle grain boundaries is found. The data obtained indicate that the level of nanoporosity can affect the tensile durability of fine-crystalline aluminum in the creep mode. The data on the regularities in the development of nanopores under deformation of the fine-crystalline aluminum-based alloy in the superplasticity mode are obtained.

Critical high temperature components of machines and structures are often subjected to complicated load and temperature histories. The closest laboratory simulation of service loading conditions involves creep under nonsteady temperatures and stresses. For example, the start up and shut down cycles can be well simulated by temperature variation by use of intermittent heating tests. Such approach is illustrated by recent experimental results on advanced high creep strength 9- 12%Cr ferritic-martensitic steels (P91, P92 and E911). A comparison between the creep characteristics of nonsteady and monotonously creep specimens has revealed no significant deterioration of the creep strength and fracture resistance of these steels in power-law (dislocation) creep.

This paper examines the effect of equal-channel angular pressing (ECAP) on creep behaviour of pure aluminium, binary Al-0.2wt.%Sc alloy and ternary Al-3wt.%Mg-0.2wt.%Sc alloy. The ECAP was conducted at room temperature with a die that had a 90° angle between the channels and 8 repetitive ECAP passes followed route BC. Constant stress compression creep tests were performed at 473 K and stresses ranging between 16 to 80 MPa on ECAP materials and, for comparison purposes, on the initial coarse-grained materials. The results showed that the creep resistance of the ECAP processed Al-Sc and Al-Mg-Sc alloys was markedly deteriorated with respect to unpressed coarse-grained materials.

Considerable structural inhomogeneity and anisotropy were found even after eight ECAP passes in high purity aluminium and the creep loading of ECAP material at 473K, 15MPa resulted in scattered fracture times ~ 20-60 hours. The structure revealed by orientation imaging microscopy with different disclination bounds was analysed by stereological methods. The effect of inhomogeneity and grain orientation on the creep fracture time was assessed.

High purity (99.99%) pure aluminium processed by equal channel angular pressing (ECAP) was examined in terms of the ECAP microstructure inhomogeneity and its creep behaviour. The results indicate that an inhomogeneity of the ECAP microstructure in mesoscopic scale may influence the creep behaviour of the pressed material.

A new point process is proposed which can be viewed either as a Boolean cluster model with two cluster modes or as a p-thinned Neyman-Scott cluster process with the retention of the original parent point. Voronoi tessellation generated by such a point process has extremely high coefficients of variation of cell volumes as well as of profile areas and lengths in the planar and line induced tessellations. An approximate numerical model of tessellation characteristics is developed for the case of small cluster size; its predictions are compared with the results of computer simulations. Tessellations of this type can be used as models of grain structures in steels.

Voronoi tessellations generated by various point processes including translation and displaced translation lattices are examined as models of grain structures. The computer-simulated cell systems are sectioned by random planes and lines, and the assumptions used in the standard grain size classifications are tested.

Zbyněk Sidak, the chief editor of the Applications of Mathematics, an outstanding Czech statistician and probabilist, died on November 12, 1999, aged 66 years. This article is devoted to memory of him and outlines his life and scientific work.

TEM images of thin foils with quasi-globular particles are examined by means of two methods of spatial statistics. The spatial arrangement of particle reference points is described by means of quadrat count statistics and by polygonal method (the analysis of the Voronoi mosaic generated by patterns of particle reference points). A good agreement between the both approaches is found, the polygonal method is more sensitive and its results are more conclusive.

Summary. Boolean cluster point processes with various cluster distributions are exam­ ined by means of their spherical contact distribution function. Special attention is paid to clusters with strong independence properties (Poisson clusters) and regular clusters.

Oscillating point patterns are point processes derived from a locally finite set in a finite dimensional space by i.i.d. random oscillation of individual points. An upper and lower bound for the variation distance of the oscillating point pattern from the limit stationary Poisson process is established. As a consequence, the true order of the convergence rate in variation norm for the special case of isotropic Gaussian oscillations applied to the regular cubic net is found. To illustrate these theoretical results, simulated planar structures are compared with the Poisson point process by the quadrat count and distance methods.

TEM images of thin foils with quasi-globular particles are examined by means of two methods of spatial statistics. The spatial arrangement of particle reference points is described by means of its shape with quadrat count statistics and by polygonal method (the analysis of the Voronoi mosaic generated by patterns of particle reference points). A good agreement between the both approaches is found, the polygonal method is more sensitive and its results are more conclusive.

Four applications of computer simulations in stereology are discussed and demonstrated: 1 systematic graphical classification of 3D tessellations with application to the grain size estimation based on the combination of profile and intercept counts with the coefficient of profile area variation 2 simulation and estimation of double stochastic processes with application to cavity formation under high-temperature creep loading 3 simulation of the intercrystalline fracture and stereology of fracture surfaces 4 estimation of the anisotropy of simulated spatial fibre processes.

The standard metallographic methods of the estimation of the degree of intergranular damage (cavitation) based on the quantitative microscopy are rather unsatisfactory since the typical feature of cavitation is its pronounced inhomogeneity. This work attempts to highlight the problem areas just in this respect. The attention is focused on the semiquantitative and quantitative investigation of inhomogeneities in the spatial distribution of cavities and the proposed approaches are illustrated by recent experimental results. The total of acquired information gives the detailed quantitative picture of cavitation in different stages of loading and can be used in constitutive models of creep fracture process. The critical amount of creep damage accumulation is defined and demonstrated experimentally. Finally, the application of the percolation model of cavitation to explain theoretically the critical amount of cavitation has been used.

A simple theoretical model is proposed to describe the anisotropic distribution of internal stresses in poled PZT ceramics. The anisotropic distribution of grain-boundary microcracks observed in poled coarse-grained PZT type ceramics is explained and characterized using the quantitative methods of stereology. Finally, the observed anisotropy of bending strength is discussed.

The spatial distribution of intergranular cracks in poled coarse-grained PZT ceramics is found to be non-homogeneous with a higher density of cracks in the central region of the specimen and a lower density near the electrodes. As the cracks are formed by internal stresses (due to motion of 90° walls) it is also concluded that the distribution of internal stresses (even in fine-grained transducers without any cracks) is non-homogeneous on a macroscopic scale with the highest peak stress values in the central region.

A graphical method for the estimation of the anisotropy of planar fibre systems based on the Steiner compact set is proposed and discussed. Upper bounds for the deviation in probability of the graphical estimate of the Steiner compact are given and a consistency theorem is proved.