Creep of polycrystalline alumina,pure and doped with transition metal impurities

Grain size effects were used to evaluate the relative contributions of aluminium lattice and oxygen grain boundary diffusion to the high temperature (1350 to 1550° C) steady state creep of polycrystalline alumina, pure and doped with transition metal impurities (Cr, Fe). Divalent iron in solid solution was found to enhance both aluminium lattice and oxygen grain-boundary diffusion. Large concentrations of divalent iron led to viscous Coble creep which was rate-limited entirely by oxygen grain-boundary diffusion. Nabarro-Herring creep which was rate-limited by aluminium lattice diffusion was observed in pure and chromium-doped material. Chromium additions had no effect on diffusional creep rates but significantly depressed non-viscous creep modes of deformation. Creep deformation maps were constructed at various iron dopant concentrations to illustrate the relative contributions of aluminium grain boundary, aluminium lattice, and oxygen grain-boundary diffusion to the diffusional creep of polycrystalline alumina.     

Enhancement of the diffusional creep of polycrystalline Al2O3 by simultaneous doping with manganese and titanium

The effect of simultaneous doping with manganese and titanium on diffusional creep was studied in dense, polycrystalline alumina over a range of grain sizes (4–80m) and temperatures (1175–1250° C). At a total dopant concentration of 0.32–0.37 cation %, diffusional creep rates were enhanced considerably such that the temperature at which cation mass transport was significant was suppressed by at least 200° C compared to that observed in undoped material. The Mn-Ti (and Cu-Ti) dopant couple was far more effective in enhancing creep rates and suppressing sintering temperatures than the Fe-Ti couple. The enhanced mass transport kinetics are believed to be caused by significant increases in both aluminium lattice and grain-boundary diffusion. When aluminium grain-boundary diffusion is enhanced by increasing the concentration of divalent impurity (Mn²⁺, Fe²⁺) or by creep testing at low temperatures, creep deformation is Newtonian viscous.     

An evaluation of the grain-boundary sliding contribution to creep deformation in polycrystalline alumina

The occurrence of grain-boundary sliding during creep in fine grained alumina was examined by inscribing marker lines on the tensile surfaces of specimens, prior to testing in four-point bending mode. There was considerable microstructural evidence for the occurrence of grainboundary sliding and grain rotation during creep deformation. Experimental measurements of the offsets in the marker lines at grain boundaries reveal that the grain-boundary sliding contribution to the total strain during creep deformation is 70 ± 6.2%. The extensive grain boundary sliding observed, together with the other mechanical properties, suggests that polycrystalline alumina exhibits superplastic characteristics. Several possible rate controlling mechanisms are examined critically in light of the present results and it is concluded that creep occurs either by an independent grain-boundary sliding mechanism or by an interface controlled diffusion mechanism.     

Effect of dynamic recrystallization on the importance of grain-boundary sliding during creep

During creep of polycrystalline materials at elevated temperatures, a certain amount of the strain is accommodated by grain-boundary sliding (GBS). The relative importance of GBS depends on the stress and grain size and sometimes temperature. During high-strain deformation, dynamic recrystallization often occurs with the resultant grain size only related to the stress. In this situation the importance of GBS is then dependent only upon stress and sometimes temperature. In dynamically recrystallized Magnox Al80 deformed atT>0.8T _m, 16 to 23% of the imposed strain is accommodated by GBS. A comparison has been made between the experimental results and some theoretical models for the importance of GBS during creep, modified to take account of recrystallization. The best fit to the data is obtained with the modified form of Langdons model. Deformation mechanism maps constructed with this model suggest that dynamic recrystallization can cause a switch of mechanism from dislocation creep to dominant GBS at intermediate temperature (T<673 K) and low stress. Deformation mechanism maps have also been constructed for calcite based on the data of Schmidet al. These suggest that GBS is an important mechanism in calcite deformed under geological conditions.     

Creep in non-ductile ceramics

The effect of a transition in creep behaviour in non-ductile ceramics (i.e. those with limited slip systems available) from diffusion controlled creep, to a mechanism involving non-viscous grain-boundary sliding and localized crack propagation is examined. Localized crack propagation is considered as a transition between diffusional creep and instantaneous fracture, and the fracture strength is used as a guide to predict the conditions necessary for the onset of this high strain-rate creep mechanism. In this way the variation in stress, temperature and grain size dependencies of creep rate reported in the literature for these materials may be explained and experimental evidence in support of the present hypothesis is presented.     

Analysis of mass transport in the diffusional creep of polycrystalline MgO-FeO-Fe2O3 solid solutions

An analysis of mass transport in the diffusional creep of iron-doped, polycrystalline MgO was conducted. Creep regimes in which magnesium grain boundary, oxygen grain boundary, and magnesium-lattice diffusion were rate-controlling were identified. An analytical procedure was developed for the estimation of the diffusion constants for these three processes.     

The incorporation of ambipolar diffusion in deformation mechanism maps for ceramics

Ambipolar diffusion gives rise to four distinct types of diffusion creep in ceramic materials, depending on whether the processes of lattice and grain-boundary diffusion creep are controlled by the anions or cations, respectively. These four processes are incorporated in a deformation mechanism map for diffusion creep in pure Al₂O₃, using a new form of map which is independent of the selected stress level. This map may be used to determine the rate-controlling mechanism for diffusion creep under any selected experimental conditions. By superimposing dislocation creep on to the map, it is possible to estimate the highest permissible stress and the lowest feasible temperature for experimental observation of any of the diffusion creep processes.     

On the initiation of wedge-type cracks at grain-boundary triple junctions during high-temperature creep

The typical grain boundary cracks are often formed at the grain-boundary triple junction as a result of blocking of grain-boundary sliding. However, a theoretical discussion has not fully been made on the nucleation of grain corner cracks at high temperatures where diffusional recovery occurs. In this study, a continuum mechanics model which incorporated the recovery effect by diffusion of atoms has been developed to explain the initiation of wedge-type cracking during high-temperature creep. A good agreement was found between the result of calculation based on this model and experimental results in austenite steels. It was considered that there is a critical creep rate for wedge-type cracking. The model was also applied to the prediction of the rupture life in creep.     

On Grain Size Dependence of Minimum Creep Rate

The available experimental results have beensummarized concerning the effect of grain size onminimum creep rate.There are two types of creeprate-grain size relations.One is that there is a criti-cal grain size above which creep rate is independentof grain size,below which creep rate increases withthe decrease of grain size.The other is that there isan intermediate grain size at which creep resistanceis optimum.The first relation usually occurs athigher temperatures(>0.5 T_m),and intermediatestress ranges,while the second relation at interme-diate temperature ranges(0.4-0.5 T_m)and higherstresses.For the two types of creep rate-grain sizerelations,the increase of the creep rates with the de-crease of grain size for small grain sizes is all due tograin boundary sliding.For large grain sizes,a dis-location climb mechanism is dominant in creepdeformation for the first relation,while aHall-Perch grain boundary strengthening effect isbelieved to play an important role by dislocationglide mechanism for the second relation.     

Creep of polycrystalline sodium chloride containing a dispersion of alumina

The creep of polycrystalline NaCl contaning a fine dispersion of Al₂O₃ particles is analysed in terms of dependence on stress, temperature, volume fraction and size of dispersion, and grain size of samples. Compressive creep experiments around 0.8 Tm show that the dispersion inhibits diffusive creep. The creep is characterized by a threshold stress above which the creep rate increased linearly with applied stress. The threshold stress decreases with increasing temperature and is proportional to the volume fraction of the dispersion in agreement with a model proposed by Burton. The activation energy corrected for the temperature dependence of the threshold stress falls within a narrow range consistent with grain-boundary diffusion of chlorine in sodium chloride. The grain-size dependence is not consistent with a modified diffusive creep model but it is suggested that it may be controlled by inhibited grain-boundary sliding according to a new model.     

Effects of the creep deformation on the fractal dimension of the grain boundaries in an austenite steel

The change in the fractal dimension of the grain boundaries during creep was investigated using an austenitic SUS304 steel at 973 K. The fractal dimension of the grain-boundary surface profile (the fractal dimension of the grain boundaries, D, 1 < D < 2) in the plane parallel to the tensile direction (in the parallel direction) and in the transverse direction, was examined on specimens deformed up to rupture (about 0.30 creep strain). Grain boundaries became serrated and the fractal dimension of the grain boundaries increased with increasing creep strain, because the density of slip lines which formed ledges and steps on grain boundaries increased as the creep strain increased. The increase in the fractal dimension due to creep deformation was slightly larger under the higher stress (118 MPa) than under the lower stress (98 MPa), while the increase of the fractal dimension with strain was a little larger in the specimens tensile-strained at room temperature (293 K) than in the crept specimens. These results were explained by the grain-boundary sliding and the diffusional recovery near grain boundaries, which lowered the increase of the fractal dimension with the creep strain. The fractal dimension of the grain boundaries in the parallel direction was slightly larger than that in the transverse direction in both creep at 973 K and tensile deformation at room temperature, especially at the large strains. This could be correlated with the shape change of the grains by creep or plastic deformation. Grain-boundary cracks were principally initiated at grain-boundary triple junctions in creep, but ledges, steps and carbide precipitates on serrated grain boundaries were not preferential nucleation sites for the cracks.     

A simple method of constructing an Ashby-type deformation mechanism map

An Ashby-type deformation mechanism map may be considerably simplified by plotting in the form of normalized stress versus the reciprocal of the homologous temperature. In this form, the boundaries separating the various fields appear as straight lines and the constant strain rate contours may be approximated as straight lines. Representative maps are presented for conditions of high temperature creep, and a simple procedure is outlined for constructing several maps for the same material at different grain sizes.     

Creep in pure and two phase nickel-doped alumina

Creep in pure and two phase nickel-doped alumina has been investigated in the stress range 0.70 to 4.57 kgf mm^–2 (1000 to 6500 psi), and temperature range 1450 to 1800° C, for grain sizes from 15 to 45 m (pure alumina) and 15 to 30 um, (nickel-doped alumina). The effect of stress, grain size and temperature on the creep rate suggests that diffusion controlled grain-boundary sliding is the predominant creep mechanism at low stresses and small grain sizes. However, the stress exponents show that some non-viscous boundary sliding occurs even at the lowest stresses investigated. This mechanism is confirmed by metallographic evidence, which shows considerable boundary corrugation in the deformed aluminas. At higher stresses and larger grain sizes the localized propagation of microcracks leads to high stress exponents in the creep rate equation. The nickel dopant, which introduces an evenly distributed spinel second phase into the alumina matrix, increases the creep rate and enhances boundary sliding and localized crack propagation. The weakening effect of the second phase increases with grain size, and tertiary creep occurs at strains of 0.5% and below in large grained material.     

A technique for the measurement of diffusion creep from marker line displacements

A procedure is presented which allows the determination of the relative displacement of grains across a common grain boundary during diffusional creep deformation. This relative displacement comprises the strain produced by accretion of material at the grain boundary and by grain-boundary sliding. The only measurements necessary are of marker line displacements across the grain boundary.     

Mechanisms of interdiffusion in Pd-Cu thin film diffusion couples

Interdiffusion in sputter-deposited polycrystalline Pd-Cu bilayers (thickness of each sublayer: 50 nm) was studied in the temperature range 175 °C-250 °C by sputter-depth profiling in combination with Auger electron spectroscopy. X-ray diffraction and transmission electron microscopy investigations revealed that the layers are polycrystalline, consisting of columnar grains separated by grain boundaries oriented more or less perpendicularly to the film surface. Considerable diffusional intermixing occurred in the studied temperature range, which was accompanied by the sequential formation of (ordered) phases Cu₃Pd and CuPd. Volume interdiffusion coefficients were determined using the so-called ‘centre-gradient’ and ‘plateau-rise’ methods. Grain-boundary diffusion coefficients of Pd through Cu grain boundaries were determined by the Whipple-Le Claire method and grain-boundary diffusion coefficients of Cu through Pd grain boundaries were determined by the Hwang-Balluffi method. It was found that both volume and grain-boundary diffusion coefficients decreased roughly exponentially with annealing time. Activation energies were determined which pertain to the same (defect) microstructure at each temperature. The differences with literature results for macroscopic diffusion couples were discussed.     

The effect of the diffusion creep behavior on the TSV-Cu protrusion morphology during annealing

As through-silicon vias (TSVs) are key structural elements of 3D integration and packaging, creep deformation, which causes TSV-Cu protrusion, is critical for TSV reliability. Here, the effect of the diffusion creep behavior on the TSV-Cu protrusion morphology is analyzed using experiment and simulation. The protrusion morphology of TSV-Cu after annealing treatment is examined using a white light interferometer. The diffusion creep mechanism of TSV-Cu is determined by observation of the TSV-Cu microstructure using a scanning electron microscopy and a focused ion beams. The TSV-Cu grain size is measured using an electron backscatter diffraction system. The diffusion creep rate model of TSV-Cu is deduced based on the energy balance theory and is introduced into the finite element model to clarify the influence of diffusion creep on TSV-Cu protrusion. It is determined that the diffusion creep of TSV-Cu is mainly caused by grain boundary diffusion and grain boundary sliding. The diffusion creep strain rate is positively correlated with the ambient temperature and the external load but negatively correlated with the grain size. The amount of TSV-Cu protrusion increases with decreasing grain size. The simulation results show that the “donut”-shaped protrusion morphology is more likely to occur in TSV-Cu with smaller grain sizes near the sidewall region of the via.     

Superplastic deformation and microstructure evolution in PM IN-100 superalloy

The superplastic deformation behaviour of PM IN-100 alloys consolidated by hot isostatic pressing (HIP) was investigated in compression tests at temperatures between 1323 and 1373K. The microstructural changes were observed using scanning electron microscopy. In the high strain rate region, grain refinement occurs due to dynamic recrystallization, resulting in the work softening type stress-strain curves. At low strain rates, grain growth occurs during deformation corresponding to work hardening. The strain rate sensitivity index,m, reaches a maximum value (m = 0.6) at the optimum strain rate which depends on the test temperature. The grain size dependence coefficient,p, was determined to be 2.0. The activation energy for deformation was 348kJ mol^–1. The rate-controlling mechanism of superplasticity in as HI Ped IN-100 seems to be the grain-boundary sliding controlled by volume diffusion rather than grain-boundary diffusion.     

Conductivity and creep in acceptor-dominated polycrystalline Al2O3

Ionic and electronic conductivity and compressive creep of hot-pressed polycrystalline acceptor-dominated Al₂O₃ were measured as a function of oxygen partial pressure and grain size varying from 3 to 200 m. Hole conduction shows a slight preference for grainboundaries; ionic conduction is slightly hindered by grain boundaries, indicating that fast oxygen grain-boundary diffusion involving charged species does not occur. Conductivity and creep are accounted for on the basis of a model in which there is fast grain-boundary migration by a neutral oxygen species.     

Newtonian flow process in polycrystalline silicon carbides: diffusional creep or Harper-Dorn creep?

Some previous studies on hot-pressed and sintered SiC polycrystalline materials have been reexamined. Mechanical data and microstructures strongly suggest that the Newtonian creep behaviour observed in these SiC materials was induced by a dislocation process operating in Harper-Dorn creep, rather than by diffusional creep as concluded before. The supporting evidence for this suggestion includes extensive development of dislocation substructures, no dependence of creep rate upon grain size, and the measured creep rates being far faster than those predicted by the model of diffusion creep, but consistent with those estimated by the model of Harper-Dorn creep.     

High-temperature deformation behaviour of YBa2Cu3O7−x

High-temperature compression tests were performed in air for YBa₂Cu₃O_7–x polycrystals with grain sizes of 3 and 7 m at various strain rates between 1.3×10^–5 and 4×10^–4s^–1 and at temperatures between 1136 and 1253 K. Steady state deformation appeared above 1203 K for both samples. A stress exponent of 1.3 and an activation energy of 150 kJ mol^–1 were evaluated. The compression tests and microstructural observations revealed that there was a difference in deformation mechanism above and below 1203 K. The dominant mechanism was diffusional creep associated with grain-boundary sliding above 1203 K, and dislocation glide accompanied with grain-boundary sliding below 1203 K. The growth of anisotropic grains and their preferred arrangement were enhanced by deformation.