Rishi Raj

On grain boundary sliding and diffusional creep

The problem of sliding at a nonplanar grain boundary is considered in detail. The stress field, and sliding displacement and velocity can be calculated at a boundary with a shape which is periodic in the sliding direction (a wavy or stepped grain boundary): a) when deformation within the crystals which meet at the boundary is purely elastic, b) when diffusional flow of matter from point to point on the boundary is permitted. The results give solutions to the following problems. 1) How much sliding occurs in a polycrystal when neither diffusive flow nor dislocation motion is possible? 2) What is the sliding rate at a wavy or stepped grain boundary when diffusional flow of matter occurs? 3) What is the rate of diffusional creep in a polycrystal in which grain boundaries slide? 4) How is this creep rate affected by grain shape, and grain boundary migration? 5) How does an array of discrete particles influence the sliding rate at a grain boundary and the diffusional creep rate of a polycrystal? The results are compared with published solutions to some of these problems.

Intergranular fracture at elevated temperature

Abstract The kinetic problem of intergranular fracture at elevated temperatures by the nucleation and growth of voids in the grain boundary is analysed in detail. Diffusional transport accounts for the void growthrat in the analysis, and the nucleation-rate is obtained by using the concepts of classical nucleation theory. The two are compounded to calculate the time-to-fracture. The influence of grain size, strainrate, temperature, second phase particles and interface energies is taken into account. Particular attention is given to the presence of inclusions in the boundary; the role of the stress concentration at the interface between the inclusion and the matrix, and the energy of this interface is investigated.

Measurement of the ultimate shear strength of a metal-ceramic interface

Abstract The ultimate shear strength of a metal-ceramic interface has been measured by depositing a thin film of the ceramic on a ductile, metal substrate. As the metal is plastically stretched the ceramic film develops cracks that are oriented transverse to the pulling direction. The density of the cracks (the number per unit length) increases as more and more plastic strain is applied to the metal substrate. Eventually the crack density reaches a constant value and is not influenced by further plastic deformation of the metal. Theoretical analysis of the problem prescribes that the minimum and the maximum spacing between the cracks should differ by a factor of two. Also, the ultimate shear strength of the metal-ceramic interface is related to the tensile fracture strength of the ceramic film and the largest spacing between the cracks; both of these quantities are measured in this simple technique. Experiments performed with 60 nm thick films of silica bonded to pure copper substrates show the tensile fracture strength of the film to be in the range 3.4–6.7 GPa, and the ultimate shear strength of the interface to lie in the range 0.56–1.67 GPa.

Solution-precipitation creep in glass ceramics

Abstract The deformation rate of polycrystalline ceramics that contain a residual glass phase is analysed in terms of material transport through the liquid phase. Molecules are transported and deposited in the direction of the positive normal traction gradient along the interfaces. This produces a change in the shape of the grains such that they become elongated in the direction of the tensile stress. It is suggested that the steady state kinetics of this process is controlled either by the rate of dissolution and precipitation reaction at the glass-crystal interfaces, or by the rate of transport through the liquid phase. An island structure of the grain boundary is assumed to model the atomistics of the transport process. The results of creep experiments in a β-spodumene glass ceramic are shown to be in agreement with the model for interface reaction controlled creep.

Development of a Processing Map for Use in Warm-Forming and Hot-Forming Processes

A fracture initiation map is developed which should be useful in fast forming operations at strain rates greater than about 10-3 s-1 at elevated temperatures. Two types of cavitation mechanisms, one pertaining to cavity formation at second phase particles, as in ductile fracture, and the other pertaining to wedge type microcracking at grain boundaries, are considered. In addition, dynamic recrystallization and adiabatic heating effects are considered. When these concepts are applied to aluminum, it is shown that there may be an intermediate region in the strain rate and temperature field in which neither of these mechanisms should operate and within which the material would, therefore, be safe from fracture.

The effect of particle size on the thermal conductivity of ZnS/diamond composites

We have observed that the thernal conductivity of zincsulphide is increased by adding large particles of highly conducting diamond, but lowered by the addition of sub-micron size particles of diamond. This effect is explained in terms of the interfacial thermal resistance which becomes increasingly dominant as the particles becomes smaller (because that increases their surface to volume ratio). A phenomonological model in which the interface resistance is expressed as an effective Kapitza radius, ak, is presented. The conductivity of the composite is analyzed for different values of α, which is defined to be equal to the Kapitza radius divided by the particle radius. If α = 1, that is, the actual particle radius is equal to ak then the effective thermal conductivity of the particles is equal to that of the matrix. If α > 1, that is the particles are very small, then the contribution of the particles to the thermal conductivity of the composite is dominated by interfaces; if α < 1 then the bulk property of the particles is important. Our measurements yield ak ≈ 1.5 μm for the ZnS-diamond interface.

Nucleation of cavities at second phase particles in grain boundaries

Abstract A kinetic approach is used, to explain the nucleation of cavities in grain boundaries at elevated temperature. Under the influence of a tensile stress, vacancies cluster together and form cavities. However a free energy barrier exists for the nucleation of a cluster which is stable. Heterogeneous nucleation, especially at the junctions of grain boundaries and second phase particles, is favored. Also an incubation time is required to form a vacancy cluster of critical size. Its duration depends upon the volume of the cluster and the diffusivity of vacancies. In this manner a stress and time condition for the nucleation of cavities in grain boundaries is obtained.

Sintering behavior of bi-modal powder compacts

Abstract Time dependent sintering of a bi-modal powder compact, consisting of two regions which sinter at different rates, is analyzed in detail. Complete solutions are obtained for the internal stress and for the densification rate. The important feature of the analysis is that it combines densification with deviatoric creep, since creep serves to relax the stress concentration produced by incompatible densification. The structure of the bi-modal compact is assumed to consist of a sphere of one type of material embedded in a matrix of the other material. Two cases are considered. In one case the matrix, and in the other the sphere, is assumed to sinter faster. The maximum tensile stress generated by incompatible sintering is found to be sensitive to a parameter, β, which is the ratio of the rate constant for creep, and the rate constant for densification. A large value of β reduces the magnitude of the stress. The generation of flaws as a result of this stress is considered. The influence of inhomogeneous sintering on the overall rate of shrinkage is calculated; we find that unless β is large the densification rate of the composite will deviate significantly from the simple rule-of-mixtures.

CREEP FRACTURE IN CERAMICS CONTAINING SMALL AMOUNTS OF A LIQUID PHASE

Abstract Even small quantities of a fluid phase, say a few volume percent, can have a dominant influence on fracture behavior of polycrystalline ceramics. It is possible to conceive of several reasons why: 1. (i) the liquid film in two grain junctions can promote grain boundary sliding, 2. (ii) since the liquid is often constrained in pockets at triple grain junctions, it can become stressed in hydrostatic tension, and as a result cavitate. 3. (iii) grain boundaries can become separated by the lateral growth of penny shaped bubbles in the fluid film when a tensile stress is applied across the interface, and 4. (iv) the fluid may lead to accelerated crack growth along the interface if the meniscus along the crack front becomes unstable and breaks up into a finger-like morphology. This paper is an attempt to synthesize the results from published literature on these separate topics and apply them to fracture in polycrystalline ceramics, with an emphasis on quantifying properties and phenomena of engineering interest such as modulus of rupture, creep crack-growth and superplastic flow. Also some other relevant issues such as multiaxial or mixed mode fracture, fracture from small flaws vs large flaws, and the question of localized microcrack damage near crack tips vs more general cavitation damage, are discussed.

Fabrication of SiCN MEMS by photopolymerization of pre-ceramic polymer☆

This paper describes the use of photopolymerization of a liquid polysilazane as a novel, versatile and cost-effective means of fabricating SiCN ceramic MEMS. SiCN is a new class of polymer-derived ceramics whose starting material is a liquid-phase polymer. By adding a photo initiator to the precursor, photolithographical patterning of the pre-ceramic polymer can be accomplished by UV exposure. The resulting solid polymer structures are then crosslinked under isostatic pressure, and pyrolyzed to form an amorphous ceramic capable of withstanding over 1500°C. By adding and curing successive layers of liquid polymer on top of one another, multi-layered ceramic MEMS can be easily fabricated. The use of photopolymerization can also be used to make thin, membrane-like ceramic structures. Key issues concerning the fabrication process are discussed. By combining photopolymerization with other in-house developed techniques such as polymer-based bonding and flip-chip bonding, three SiCN MEMS devices for high-temperature applications have been fabricated: an electrostatic actuator, a pressure transducer, and a combustion chamber. These represent a wide range of MEMS, demonstrating the versatility of this technique.