Julie A. Yeomans

A model for the sintering of spherical particles of different sizes by solid state diffusion

Abstract In this paper the numerical scheme developed by Pan and Cocks (Acta metall. 43, 1395–1406, 1995) is used to simulate the co-sintering process of two spherical particles of different sizes by coupled grain-boundary and surface diffusion. The numerical analysis reveals many interesting features of the co-sintering process. For example, it is found that the shrinkage between the two particles is not affected significantly by the size difference of the two particles as long as the difference is less than 50%. Based on the numerical results, empirical formulae for the characteristic time of the co-sintering process and for the shrinkage rate between the two particles are established. The empirical formulae can be used to develop constitutive laws for early-stage sintering of powder compacts which take into account the effect of particle size distribution. To demonstrate this, a densification rate equation for compacts with bimodal particle size distributions is derived.

The toughening of alumina with iron : Effects of iron distribution on fracture toughness

Two composites have been fabricated by hot pressing powder blends of alumina with 20 volume percent of ductile iron particles. The composites differ in the shape, size and distribution of the iron particles. The fracture toughness of each composite has been obtained in situ, by testing inside a scanning electron microscope, using a double cantilever beam technique modified specifically for small ceramic specimens. Observation of the crack-particle interactions has enabled information to be gained about the toughening mechanisms occurring and hence the parameters for microstructural tailoring of these materials have been deduced. Results showed that the fracture toughness of the composites differed greatly due to the distribution of the iron throughout the microstructure, which in turn affected the type and degree of observed toughening mechanism. These material-specific toughening parameters were then used to fabricate a third alumina/iron composite with a more optimised fracture toughness.

Microstructure and fracture toughness of nickel particle toughened alumina matrix composites

Al2O3-Ni composite materials have been made by a hot pressing technique. Two composite microstructures, i.e. a dispersive distribution of nickel particles and a network distribution of nickel particles in an alumina matrix, have been produced. The fracture toughness of the composite materials has been measured by a double cantilever beam method. Both composites are tougher than the virgin alumina matrix. The fracture toughness of the composite with a network microstructure is much higher and has a more desirable R-curve behaviour than the composite with a microstructure of dispersed particles. For the particulate dispersion microstructure, the main limitation to toughening is the lack of plastic deformation of the ductile nickel due to the pull out of nickel particles, indicating weak bonding at the Al2O3/Ni interface. For the network microstructure composite, the gauge length of the ductile phase is much larger, allowing the ductile nickel to stretch to failure between the crack faces. A large extent of nickel plastic deformation has been observed, and the weak bonding at the Al2O3/Ni interface can promote partial debonding and contribute further to toughening.

The thermal shock behaviour of ductile particle toughened alumina composites

Over recent years, it has been established that the incorporation of metallic particles into a ceramic matrix can lead to enhanced fracture properties. Relatively few attempts, however, have been made to establish whether or not the improved fracture toughness typically observed in such composite systems can offer improved performance in demanding environments. The current study is concerned with the thermal shock behaviour of a ceramic matrix composite consisting of an alumina matrix containing 20 vol% of discrete iron particles. The composite material has been produced by both hot pressing and conventional sintering techniques. The hot pressed composite shows a greater resistance to thermal shock than the monolithic matrix, both in terms of the critical temperature differential and retained strength, whereas the sintered material has been found to behave as a typical low strength refractory ceramic. The calculation of thermal shock resistance parameters for the composites and the monolith has indicated possible explanations for the differences in thermal shock behaviour.

Effect of pore clustering on the mechanical properties of ceramics

The reduction in strength and, to a lesser extent, Youngs modulus with increased amounts of discrete pores is frequently greater than that predicted by models based on a homogenous pore distribution. The effect of pore distribution has been examined in the present work by producing samples containing a non-homogenous distribution of pores and comparing the results with data reported for samples containing homogenously distributed pores. Youngs modulus and, to a greater extent, strength were shown to have stronger dependencies on the porosity content than would be predicted for homogeneous samples. By considering the material as a composite consisting of a pore-rich continuous phase containing a dispersion of pore-free material, various models were used to predict behaviour. It was found that the strength of the material is likely to be governed by the properties of the continuous phase, while the Youngs modulus is a function of the properties of the two phases, with the porous phase being described by the Spriggs equation. The implications of the different dependencies of strength and Youngs modulus in terms of the resistance to crack propagation following a thermal shock were then considered. Predictions of retained strength were in good agreement with those observed after water quenching.

Spatially resolved electron energy-loss studies of metal–ceramic interfaces in transition metal/alumina cermets

Composites consisting of an alumina matrix and 20 vol.% transition metal (Ni or Fe) particles, prepared by hot pressing powder blends, have been studied using spatially resolved transmission electron energy‐loss spectroscopy (EELS), and, to a lesser extent, by high‐resolution electron microscopy (HREM). Particular attention was paid to the elucidation of the chemical bonding mechanisms at the metal‐ceramic interface; EELS spectra from interfacial regions being obtained via a spatial difference technique. From both qualitative and quantitative interpretation of EELS near‐edge structures, as well as observed HREM images, the data appear to be consistent with the presence of an Al‐terminated alumina at the interface and the formation of direct transition metal – aluminium bonds in Al(O3M) (M = Ni or Fe) tetrahedral units, possibly as a result of the dissolution and interfacial reprecipitation of Al during processing. These results correlate well with similar model studies on diffusion‐bonded Nb/Al2O3 interfaces and may, in the light of recent theoretical electronic structure calculations, have implications for the resultant interfacial bond strength in such materials.

Thermal shock behaviour of unidirectional silicon carbide fibre reinforced calcium aluminosilicate

Unidirectional silicon carbide fibre-reinforced calcium aluminosilicate (CAS) has been subjected to a variety of thermal regimes. Microscopy has been used to assess the degree of matrix damage. Thermal shock induced matrix cracking was first seen on the end faces of the composite, perpendicular to the fibre direction at a temperature differential of 400°C. At more severe thermal shocks the next damage was observed on faces parallel to the fibre direction in the form of cracking in the matrix perpendicular to the fibre direction. Matrix cracking damage increased, initially, with increasing severity of thermal shock, but then became less extensive at the highest temperature differentials (800°C) used. Thermal shock-induced crack densities were correlated with literature data for cracking under quasi-static loading using a simple thermal shock analysis incorporating a stress reduction factor. The suitability of applying a modified Aveston, Cooper and Kelly (ACK) model [1] to predict critical temperature differentials for matrix cracking onset in the unidirectional composite has also been tested. The method was found to be valid for the unidirectional material providing that some key parameters were determined independently.

A combined finite element and finite difference scheme for computer simulation of microstructure evolution and its application to pore–boundary separation during sintering

Abstract This paper presents two new developments to the numerical technique previously developed by Pan and Cocks [cf. J. Pan, A.C.F. Cocks, A numerical technique for the analysis of coupled surface and grain-boundary diffusion, Acta Metall. 43 (1995) 1395–1406; J. Pan, A.C.F. Cocks, S. Kucherenko, Finite element analysis of coupled grain-boundary and surface diffusion with grain-boundary migration, Proc. R. Soc. London A 453 (1998) 2161–2184] for the computer simulation of microstructure evolution of materials. Coupled grain-boundary diffusion, surface diffusion and grain-boundary migration are considered as the underlying mechanisms for the evolution. The first development is that a set of “link elements” are developed to link the finite difference scheme of Pan and Cocks (1995) with the finite element scheme of Pan et al. (1998) for the surface diffusion and grain-boundary migration parts of the problem respectively. Unlike the method used in Pan and Cocks (1995), these link elements are designed to link the two discretisation schemes away from the interface junction so that the dihedral angle can be maintained in the variational sense at the junction while the finite difference scheme can still be used for most of the interface network. Such a combined scheme is more efficient than the full finite element scheme because most of the degrees of freedom for surface diffusion and grain-boundary migration no longer contribute to the global linear simultaneous equations. The second development is that an implicit time integration method is implemented. In general the implicit time integration method allows much larger timesteps to be used than that allowed by an explicit method. The two new developments together significantly improved the efficiency of the numerical scheme. Several test cases are provided to verify the numerical scheme. As an example of application, the effect of pore shrinkage on pore-boundary separation is investigated using the numerical scheme. It is shown that the existing separation criteria significantly over-predict separation.

Microstructure and mechanical properties of chromium and chromium/nickel particulate reinforced alumina ceramics

A range of Al2O3-Cr and Al2O3-Cr/Ni composites have been made using either pressureless sintering in the presence of a graphite bed or hot pressing. Examination of the microstructures shows that they are fully dense (typically 98–99% of the theoretical density) and that the micrometre-scale metallic particles remain discrete and homogeneously dispersed in all composites. All of the hot pressed specimens had higher flexural strengths than the sintered materials. Within each processing route, the composites had slightly lower strength values than the equivalent monolithic alumina specimens. This was attributed to weak interfacial bonding. Fracture toughness behaviour was investigated using indentation and double cantilever beam methods. All of the composites were found to be tougher than the parent alumina and to show resistance-curve behaviour. For the composites, maximum fracture toughness values were 5–6 MPa m1/2 (about double the value for alumina) for process zone sizes of a few millimetres, although steady state was not reached in the limited number of specimens tested. Examination of fracture surfaces and indentation cracks showed that the toughening potential of the metal particles was not exploited to any significant extent. This was mainly due to weak metal-Al2O3 interfaces, but also because of carbon embrittlement of the metallic particles in which chromium was the major constituent.

Aspects of residual thermal stresses in continuous-fibre-reinforced ceramic matrix composites

Abstract An analytical model is presented that predicts the thermal stresses which arise from mismatch in coefficients of thermal expansion between a fibre and the surrounding matrix in a continuous fibre composite. The model consists of two coaxial isotropic cylinders. Stress transfer between the fibre and the matrix near an unstressed free surface has been modelled by means of a shear-lag analysis. Away from the free surface the theoretical approach satisfies exactly the conditions for equilibrium and continuity of stress at the fibre-matrix interface. Application of the model to a composite consisting of a glass-ceramic calcium alumino-silicate (CAS) matrix containing unidirectional Nicalon fibres points to a strong dependence of stress on fibre volume fraction. Surface effects are significant for depths of the order of one fibre diameter. Near-surface shear stresses resulting from cooling from the stress-free temperature are sufficiently high to suggest that a portion of fibre close to the surface is debonded at room temperature. Experimental results acquired with a scanning electron microscope (SEM) equipped with a heating stage are consistent with this prediction. Consequently, the model has been modified in a simple way to incorporate frictional slip at the interface, according to the Coulomb friction law. Although detailed measurements are limited by the resolution of the technique, experimental evidence suggests that the transfer length is within an order of magnitude of the model prediction.