Effect of precipitate type and morphology on high-temperature creep and internal stress in Al-Li based alloys

The tensile creep of a series of aluminium-lithium-based alloys, two binary alloys containing precipitate, and the 2090 alloy containing and T₁ precipitate, has been studied over a range of stresses at 150°C. In some cases the internal stress developed during creep has been determined using the strain transient dip test. The results have been compared with similar data previously obtained for the 8090 alloy containing and S precipitates. The solid solution alloy and the binary alloy containing shearable particles exhibited normal Class II behaviour, with the development of sub-grains and a stress dependence of the creep rate given by a single stress exponent,n, between 4 and 5 at all applied stresses. The alloys containing particles not easily sheared by dislocations, coarse , S and T₁, exhibited similar stress dependencies of the creep rate at low stresses but exhibited large values ofn, between 18 and 35 at high stresses. The internal stress, _i, in these alloys was found to be approximately constant at high stresses possibly due to partial shearing of the coarse , T₁, and the S on sub-boundaries. The stress dependence of the minimum creep rate, , could be represented at all applied stresses, _a, by , where (_a–_i) is the effective stress driving dislocations during creep, andn is a single stress exponent of between 5 and 6 for all applied stresses. The internal stress, which increases with applied stress, at least at a low applied stress, arises from inhomogeneity of plastic deformation, due to hard sub-boundaries or hard particles which are Orowan looped. These two types of contribution to the internal stress are of similar magnitude in the alloys containing coarse and T₁ but the majority of the internal stress in the 8090 alloy may arise as a result of the hardening of sub-boundaries by the S precipitate.     

Precipitate strengthening mechanisms in magnesium zinc alloy single crystals

The mechanical behaviour of Mg-5.1 wt % Zn alloy single crystals was studied in the 4.2 to 300° K temperature range. Quenched crystals have activation energies and volumes best associated with the cutting of small clusters of Zn atoms by dislocations. Fully hardened crystals contain fine ₁ and occasional ₂ precipitates with an average ₁ interparticle spacing of 330 to 660 Å. Strengthening in these crystals is mainly ascribed to the cutting of ₁ particles by dislocations. In the overaged condition ₁, ₂ and equilibrium particles are present and lead to a considerable temperature-dependence unusual for an overaged condition. Analysis of this temperature-dependence suggests that below 77° K the relatively easy cutting of ₁ particles by dislocations takes place in addition to the cutting of ₂ and particles. Above 77° K the difficult cutting of ₂ and particles alone controls the deformation, ₁ being more easily cut with the aid of thermal fluctuations.     

Repeated θ′ precipitation at dislocations in Al-4 wt% Cu

Repeated precipitation of the phase has been observed to occur on dislocations on {110} planes of an Al-4 wt % Cu alloy, particularly when the alloy was in the reverted state. It is shown that is nucleated at prismatic dislocation loops, the climb of which determines the growth of the precipitates in the matrix.     

High-temperature creep of the particlehardened commercial Al-Li-Cu-Mg alloy 8090

Creep of the particle-hardened commercial Al-Li 8090 alloy has been studied at temperatures of 425 and 445 K. The measured stress sensitivity of the minimum creep rates changes abruptly at a given applied stress with stress exponents being around 4–6 at low stresses and 30–40 at high stresses. Creep activation enthalpies were determined by both temperature cycling and by comparing creep rates at two temperatures at a given applied stress, the results from both gave the same unrealistically high values. The internal stresses, _i, developed during creep were determined using the strain-transient dip test. These increased linearly with the applied stress, _a, at low stresses and were effectively constant at high stresses. The minimum creep rate was found to be a simple function of the effective stress, _a-_i, with a stress exponent of between 5 and 6, at all applied stresses. The dislocation and precipitate structure of the alloy was examined before and after creep using thin-film electron microscopy. The initial structure consisted of pancake grains with a well-developed {1 1 0}1 1 2 type texture. The grains contained well-developed sub-cells and and S precipitates. The structure developed during creep consisted of dislocation pairs, single dislocations and dislocations loops. There was evidence to suggest that slip took place on both {1 0 0} and {1 1 1} planes. The dislocation loops were most likely to have been Orowan in character and around the rodlike S precipitate, with the coherent precipitate being sheared by pairs of dislocations. The measured internal stresses result from inhomogeneity of plastic deformation. These stresses increase continuously with applied stress up to the observed macroscopic yield stress, and then become constant. The internal stresses are likely to have arisen from the Orowan loops around S and the behaviour of sub-grain boundaries. The increases in internal stress may have resulted from an increased loop density with increasing applied stress. This rate of increase is likely to slow down if S particles are sheared or fractured at high applied stresses.     

Influence of rhenium on the microstructures and mechanical properties of a mechanically alloyed oxide dispersion-strengthened nickel-base superalloy

The influence of a 3 wt% Re addition on the creep strength and microstructure of a mechanically alloyed and oxide dispersion-strengthened nickel-base superalloy was investigated. Two alloys, Ni–8Cr–6.5Al–6W–3Ta–1.5Mo–6Co–1Ti–3Re–0.15Zr–0.05C–0.01B–0.9Y₂O₃ (3Re alloy) and a non-rhenium containing (0Re) alloy were prepared for this study.The 3Re alloy showed two-fold improvement in creep life compared with that of 0Re alloy, presumably due to a change in the mode of the precipitate-dislocation interaction. For the 3Re alloy, finer, more cuboidal and aligned precipitates are formed, which force the mobile dislocations at the – interfaces to cut precipitates in order to proceed. Shearing of precipitates is evinced by the existence of stacking faults and results in an increase of creep strength. In constrast, lower creep strength was observed for 0Re alloy because a dislocation looping mode is dominant with coarser and more irregularly shaped precipitates present in this alloy. Another possible explanation for an improved creep strength of 3Re alloy is related to the tangled dislocation structure formed by the interaction between glide dislocation and interfacial dislocation, which also acts as an effective barrier for further glide dislocation motion. A 3 wt% Re addition significantly retards coarsening kinetics. Rhenium acts as a rate-controlling species upon the volume diffusion-controlled coarsening process because it is a heavy elemenet and also it almost solely partitions to the matrix. X-ray diffraction experiments showed that the magnitude of the lattice mismatch between and increased with the 3 wt% Re addition from 0% to –0.26% at room temperature. Increased lattice mismatch for 3Re alloy causes the formation of more aligned and cuboidal precipitates rather than random and odd-shaped precipitates for 0Re alloy, and it also accelerates the coalescence between cuboidal precipitates.     

Extended defects in sintered AIN

Extended defects in the AIN grains of sintered material have been studied by transmission electron microscopy (TEM) as a function of the concentration of sintering additives (Y₂O₃). Evidence of dislocations and planar defects has been found. Using the weak beam technique, dislocations were found to be dissociated in the basal plane. The deduced reduced stacking fault energy,, has been found to confirm the correlation between and the charge redistribution index in III–V and II–VI compounds. The formation of planar defects during sintering is also discussed.     

Grain-boundary de-segregation and intergranular cohesion in Si-Al-O-N ceramics

The influence of heat-treatment on high-temperature creep and sub-critical crack growth in hot-pressed Si-Al-O-N ceramics has been analyzed from microstructural evidence and determination of stress exponents and activation energies. The most significant change is the suppression of cavitation during creep and of the cavity-interlinkage mechanism for slow crack propagation. A creep mechanism of grain-boundary diffusion is characterized by stress exponent n=1 and unusually high activation energy >820 kJ mol^–1. The microstructural origin of the transformation in grain-boundary dominated properties is mainly the removal of triple-junction glassy residues within which cavities are nucleated. This is caused by grain-boundary diffusion of metallic impurities (Mg, Mn, Ca) into a surface silica oxidation layer, and consequent crystallization of the remaining glass components as . There is a continued improvement in grain-boundary cohesion and increased difficulty of grain-boundary diffusion following the stage at which triple-junction glass is removed. The resultant ceramics, in addition to superior mechanical behaviour, have an increased temperature for application due to a marked reduction in susceptibility to dissociation above 1400° C.     

Synthesis,characterization and thermal studies of polyamide esters containing aryl-azo,azomethine and thianthrene units

New polyamide esters containing aryl-azo, azomethine and thianthrene tetraoxide units in the backbone and also having different aromatic moieties, were synthesized by reacting 4,4-ozodibenzoyl, 3,3-ozodibenzoyl, 4,4[1,4-phenylenebis(methylidynenitrilo)] dibenzoyl chlorides, 2,7-dichloroformyl-thianthrene-5-5,10,10-tetraoxide, 4,4-diphenic, isothaloyl and terephthaloyl dichlorides with ethanediamide-N,N-bis(2-hydroxyethyl) using the lowtemperature solution polycondensation technique. The yields and the values of reduced viscosity of the produced polyamide esters were found to be unaffected by the type of organic solvent used. In order to characterize the polymers, a model compound was prepared from ethanediamide-N,N-bis(2-hydroxyethyl) and benzoyl chloride and investigated by infrared, nuclear magnetic resonance and elemental analysis. The synthesized polymers were confirmed by infrared, ultraviolet, nuclear magnetic resonance spectroscopy, elemental analyses and viscosity measurements. The effect of the nature of different units on the thermal properties of polymers was evaluated by thermogravimetric analysis: the data showed that the thermal stabilities of the polymer were remarkably affected by the introduction of these groups.     

The tensile strength and ductility of continuous fibre composites

The plastic instability approach has been applied to the tensile behaviour of a continuous fibre composite. It is shown that the combination of two components with different strengths and degrees of work-hardening produces a new material with a new degree of work-hardening, which may be determined by the present analysis. Expressions for the elongation at rupture and the strength of a composite have been obtained and the results of the calculation are compared with some experimental data.List of symbols V _f volume fraction of fibres in composite - , , true strain of fibre, matrix and composite - s true stress - , , nominal stress on fibre, matrix and composite - _*, _*, _* critical stress of fibre, matrix and composite (ultimate tensile strength) - _*, _* critical strain of separate fibre and matrix - _* critical strain of composite - Q external load - A cross-sectional area - A ₀ initial value of area     

Microstructure and mechanical properties of metastable lath martensite wires in the Fe-Ni-Cr-Al-C system produced by melt spinning in rotating water

Metastable lath martensite ( _L ) phase wires with high strengths have been produced in the Fe-Ni-Cr-Al-C alloy system by melt spinning in rotating water. These wires have a circular cross section and a white lustre and the wire diameter is in the range of 100 to 140m. The width and length of each lath in the _L phase are as small as about 0.3 and 2m, respectively. The _y, _f and _p are about 900 and 1650 MPa and 2.0% for the _L wires. The subsequent annealing causes an increase in _p as well as _y and _f and the attained values are about 1000 and 1700 MPa and 3.0% for Fe-10Ni-10Cr-6.5 Al-1.0C wire annealed at 773 K for 1 h owing to the precipitation strengthening of a very fine unidentified carbide and to a high density of dislocations and lath boundaries in the _L phase. Further annealing causes a significant decrease in _p through decomposition of _L to+M₇C₃+M₂₃C₆. Therefore, the high strength combined with relatively good ductility for the _L wires is interpreted as due to the suppression of the phase transformation of _L to a mixed structure of+M₇C₃+M₂₃C₆ by melt quenching.     

Coarsening of δ′ (Al3Li) and composite precipitates in an Al-2.5% Li-0.15% Zr alloy

The early stage coarsening behaviour of (Al₃Li) precipitates and composite precipitates, consisting of (Al₃Zr) core enveloped by a shell, in an Al-2.5% Li-0.15% Zr alloy has been studied at 443, 473 and 503 K by conventional transmission electron microscopy using superlattice dark-field images. Coarsening kinetics of precipitates was found to exhibit considerable deviation from the t ^1/3 law corresponding to diffusion control at 473 and 503 K. This deviation may be explained either by the operation of a surface-reaction controlled coarsening mechanism represented by t ^1/2 law, or by the presence of a slower precoarsening stage preceding diffusion-controlled coarsening. The particle-size distributions of precipitates were not in accordance with either the earlier theoretical predictions or the normal distribution. They were symmetrical or slightly skewed to the left, and particle sizes twice the average were observed. The coarsening kinetics of composite precipitates, was found to be rather different from that of ; a diffusion model which yields t ^1/n law with n changing from 1/4 to 1/6 as the coarsening progresses, was predicted. The composite precipitates have exhibited quite a narrow and rather symmetrical size distribution.     

Microstructural study of ε-iron-carbonitrides formed by a glow discharge technique

The microstructure and phase transformations occurring in-iron-carbonitrides have been studied by means of X-ray and electron diffraction, electron microscopy and Mössbauer spectrometry. Ordering of the interstitial atoms, N or C, results in a hexagonal unit cell for Fe₃(C, N) with parametersa=a3 andc=c wherea andc are the lattice parameters of the hexagonal close-packed (h c p) iron unit cell. Stacking faults on (0001) planes and partial dislocations with Burgers vector b=1/31 0 ¯1 0 are observed in quenched-Fe₄ (C, N). After quench-aging, the carbonitrides show a structural hardening due to the precipitation of a metastable phase. Slow cooling of-carbonitrides with less than 25 at% interstitials leads to the precipitation of-carbonitride and ferrite in-phase grains which allows the orientation relationships between the-,- and-phases to be defined and a model of the-phase--phase transformation to be proposed.     

Energetic and kinetic evaluations conducted in Cu-3.34 at % Sn through differential scanning calorimetry

Microcalorimetric enthalpy measurements associated with the different peaks appearing during linear heating of Cu-3.34 at % Sn were made in a 50% cold-rolled alloy. Unlike the situation in the deformed material, quenched and furnace-cooled alloys do not exhibit thermal events at any of the heating rates employed in the temperature range scanned. In the cold-rolled condition, from the energetic and kinetic analysis of the first exothermic peak, designated Stage 1, and of the endothermic peak, designated Stage 3, it was consistently inferred that they correspond, respectively, to the growth on dislocations of a metastable phase and to its subsequent dissolution prior to recrystallization. Such inference was also supported by Vickers microhardness and yield-stress determinations. The calculated volume fraction for after Stage 2 goes to completion, is about 0.02. A suitable expression previously developed for enthalpy release due to the pinning of solute atoms to partial dislocations was applied to compute dislocation density from the exothermic peak (Stage 2). The calculated value is in excellent agreement with those obtained from the analysis of the recrystallization trace (Stage 4) and from tensile tests, thus confirming that the second DSC trace actually corresponds to the solute segregation process. It is also suggeseted that additional dislocation-induced formation of might take place as a consequence of the enhanced solute concentration around partial dislocations. The non-isothermal dissolution kinetics of was adequately described by an integrated kinetic model function essentially appropriate for application in one-dimensional diffusion situations.     

A note on the solution of a differential equation arising in boundary-layer theory

Summary The differential equation f + ff + f² = 0 (where dashes denote differentiation with respect to the independent variable ) subject to the boundary conditions f(0)=0, f()=0 and either f(0)=1 or f(0)=–1 is considered. It is shown that by using pf as dependent variable and =C–f (where C=f()) as independent variable and then expanding in powers of , a very good approximation to the solution can be obtained using only a few terms in the expansion.     

Morphological and crystallographic features of γ-γ′ Ni-Al and Ni-Al-Ti two-phase bicrystals

Several- Ni-Al and Ni-Al-Ti two-phase bicrystals were made by the solid-state diffusion couple method. Each couple consisted of a-phase single crystal and a pure-Ni polycrystal, and was annealed at 1473 K in an Ar gas atmosphere. Single crystal layers of-phase with uniform thickness always grow into the parent-phase single crystals. The resultant/ interface has no voids or facets regardless of the orientation of interface and the chemical composition of the-phase. Porosity formation due to the Kirkendall effect is observed in the diffused region. Concentration profiles exhibit nearly constant gradients in-phase. The orientation relationship between both phases is found to be 001//001, that is, the-phase grows epitaxially along the crystal orientation of-phase.     

Defect distribution near abraded surface of III–V compound semiconductors

Microstructures of damaged layers near the abraded surface of GaP, GaAs_0.6P_0.4 and GaAs single crystals have been observed with a transmission electron microscope. The damage due to 0.3 m Al₂O₃ abrasion consists of dislocations. Dislocation densities in the abrasion band and other regions are larger than 5×10¹¹ cm^–2 and about 10¹¹ cm^–2, respectively. Dislocation density decreases with increasing distance (depth) from the abraded surface. The depths of the damage layers for GaP, GaAs_0.6P_0.4 and GaAs are about 0.4, 0.55, and 0.8 m, respectively. The Burgers vector of dislocations is a/2[1 1 0], and A and B dislocations are observed. During annealing, the dislocations are rearranged and eliminated by the reaction of the dislocations with different Burgers vectors and climbing motion. The rearrangement temperatures for dislocations in GaP and GaAs are about 500 and 450° C, respectively. Electrical resistance changes in the damaged layer of GaP are recognized by electrical resistance measurements.     

Negatively isotone optimal policies for random walk type Markov decision processes

Summary This paper considers a random walk type Markov decision process in which the state spaceI is an integer subset of IR ^m , and the action spaceK is independent ofi I. The natural order, overI, and a quasi order,, overK, is assumed, together with aconditional convexity assumption on the returns {r _i ^k }, and certain other assumptions about these rewards and the transition probabilities in relationship to the orders and.A negatively isotone policy is one for whichi i(i))(i) (i.e.(i) (i) or(i) i)). It is shown that, under specified conditions, a negatively isotone optimal policy exists. Some consideration is given to computational implications in particular relationship to Howard's policy space method.

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Zusammenfassung Wir betrachten einen Markovschen Entscheidungsprozeß vom random walk Typ. Der ZustandsraumI sei eine Teilmenge des IR^m, wobeii I ganzzahlige Komponenten habe. Die MengeK der zulässigen Aktionen ini I sei unabhängig voni I. Sei die natürliche Ordnung aufI und sei eine Quasiordnung aufK. Die Erträge {r _i ^k }seienbedingt konvex, darüberhinaus seien weitere Voraussetzungen über diese Erträge und die Übergangswahrscheinlichkeiten in Bezug auf die Ordnungen und erfüllt. Eine Politik heißt negativ isoton, falls ausi i folgti(i) (d. h.(i) (i) oder(i)(i)). Wir zeigen, daß unter gewissen Voraussetzungen einenegativ isotone optimale Politik existiert: Auch diskutieren wir einige Folgerungen für die Numerik, insbesondere hinsichtlich Howards Politikiteration.

     

Coarsening of precipitates and dispersoids in aluminium alloy matrices: a consolidation of the available experimental data

Experimental data on the coarsening of precipitates and dispersoids in aluminium-based matrices are reviewed. Available data are tabulated as K=(r ³–r ₀ ³ )/t where r ₀ is the initial particle radius and r is its value after time t at temperature T, and then plotted as log (KT) against 1/T for consolidation and assessment. The considerable body of data for -A₃Li in Li-containing alloys is well represented by K=(K ₀/T) exp (–Q/RT) with K ₀=(1.3 _–0.5 ^+3.0 ) × 10^–13m³Ks^–1 and Q=115±4kJ mol^–1. The relatively limited data for and in Cucontaining alloys are representable by the same relationship with K ₀4 × 10^–8 and — 4 × 10^–10 m³ Ks^–1, respectively, and Q — 140 kJ mol^–1. Available data for coarsening of L1₂ ^– Al₃(Zr, V) and related phases in Zr-containing alloys and of Al₁₂Fe₃Si and related phases in Al-Fe based alloys indicate (i) rates of coarsening at 375 to 475 °C (0.7 to 0.8T_m) five to eight orders of magnitude less than would be expected for , and in this temperature range, and (ii) high activation energies of 300 and 180 kJ mol^–1, respectively.     

The Ni3Al-Ni3Cr-Ni3Ru section of the Ni-Cr-Al-Ru system

An investigation is reported of the 75 at% nickel section of the Ni-Cr-Al-Ru system at 1523 and 1273 K. Constitutional data obtained by electron probe microanalysis, X-ray diffraction and microscopical examination are presented as partial isothermal sections. At 1523 K, the major part of the section consists of phase, while the aluminium-rich region contains a and+ region; the extent of the solid solution of chromium and ruthenium in totals ~ 4 at%. The ruthenium-rich corner of the section shows a two-phase region consisting of + ruthenium-rich solid solution. At 1273 K the,+ and + ruthenium regions increase in extent. The/ mismatch values in the equilibrated alloys studied lie in the range ~ –0.08 to –0.39%. Constitutional features of as-cast alloys are also reported.     

High temperature mechanical properties of single phase alumina

The creep properties of a commercial, single phase aIurnina have been determined in the temperature range of 1623 to 1723 K. The stress exponent,n, in the relationship ⁿ was determined to be 1.9 and the true activation energy was found to be 635 kJ mol^–1. Normal primary stage creep transients were observed up to strains of 1%. At low stresses, steady-state conditions were not obtained due to the occurrence of concurrent grain growth. It is shown that the steady state creep results are consistent with the occurrence of an interface controlled diffusionaI creep mechanism.