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This paper is an investigation on the failure mechanism involved in underground power transmission cables with their life limited by corrosion of phosphor bronze reinforcing tapes. In the present work, a detailed analysis of failed bronze tapes in an ammonium free environment has been undertaken and corrosion fatigue failure mechanism has been identified. A detailed examination of the tape samples is carried out using 2D and 3D optical microscopy and SEM. It follows a mechanical approach that confirms corrosion fatigue as the failure mechanism. SEM images reveal that the pits present on the surface could be the starting point for the crack that eventually leads to failure. Stress calculation shows that the tape could fail only if corrosion pits are present on the tape surface. Presence of corrosion pits, multi cracks and striations on the fractured surface demonstrates corrosion fatigue cracking as the failure mechanism across the tape samples.

In the sintering of ceramics, cracks are inevitably encountered after sintering. But very few studies have been presented in the literature for qualifying and quantifying effects of inhomogeneity on sintering kinetics. Therefore, a series of detailed sintering variables such as grain size, surface tension and diffusivity are chosen to study the effects of their inhomogeneity on sintering kinetics through a computational model calculated by computer.Furthermore, there are two main achievements in this computational model that first one is providing a numerical solution for the curvature at triple junction (pore tip) of microscopic particles, and second one is considering the effect of surface diffusion on first-stage sintering where diffusion mechanism is coupled by grain-boundary and surface diffusion.

Phosphor bronze tape is a key protection component of underground power transmission cables. During the service life, it is affected by both corrosion and fatigue effects, leading to the failure of material and eventually the failure of cables. In the present work, the combined effect on the cable failure is studied in five stages: pit initiation, pitting corrosion control, pit-crack transfer, crack propagation control, and material failure. The cable time to failure is defined as the time needed for a corrosion pit on the tape surface to transfer into a crack resulting from a cyclic fatigue load condition. The pit-crack transfer is described statistically by a pitting corrosion to crack propagation transfer probability function. The result shows that a life prediction model can convey the long-term data of cables and can predict the years of failure. Subsequently, the life prediction model is extended and tested to include crack transfer probability function.

Phosphor bronze tapes used in underground power transmission cables are affected by pitting corrosion that can lead to cable failures. In the present work, the probability distribution of corrosion...

In this paper we examine how the operation of an interface reaction influences the response of a body which deforms as the result of the transportation of material around the grains by grain-boundary diffusion. A characteristic material length scale λ is identified. If λ is much less than a suitably chosen physical length scale for a problem then the rate of diffusion controls the overall rate of the process. If, however, λ is comparable with the physical length scale then the interface reaction dominates the response. A range of problems are examined which provide a number of different possible physical length scale.

This paper presents a numerical study on contact law between extremely fine particles taking into account of the effect of adhesion force and surface roughness. The adhesion force between two particles is calculated from the Erkoc inter-atomic potential. This force is incorporated into a material point model for the dynamic impact between the two particles. Unlike a molecular dynamics model, atoms in the model are embedded in the continuum solid such that they can only move relatively to each other as the continuum solid deforms. The model is numerically efficient while taking into account of the adhesion effect at the same time . Numerical study using this model shows that the Maugis theory ( Maugis, 1992 ) is valid for spherical particles as small as 50 nm in size. The numerical study also shows that a slight change in surface roughness can alter the impact behaviour completely. Therefore an uncertainty in using the Maugis contact law for real particles is how to determine the effective specific surface energy for particles of different surface roughness. Because of the uncertainty, full numerical analysis may have to be used to obtain the adhesive contact law.

Die compaction of powders is a process which involves filling a die with powder, compaction using rigid punches to form a dense compact and ejection from the die. The process can be treated as a large deformation plasticity problem. The challenge is to develop and implement appropriate constitutive models that capture the evolution of the powder from a loose state into a dense compact. In this paper we describe data analysis procedures and calibrate classic incremental plasticity models, such as Cam-Clay, Drucker-Prager cap models. The complexity of the models is increased from models with a hardening law to more complex constitutive models using density as state variable. The compaction behaviour of a range of powder materials is characterized experimentally. Numerical simulation of the compaction of simple parts and complex parts is demonstrated. The merits of various models are evaluated in terms of the balance between complexity and practicality. The discussion is illustrated with case studies exploring the applicability of the models specific to various powder pressing scenarios.

The paper presents a molecular dynamics study on the interactions between nanoparticles at elevated temperatures. The emphasis is on the comparison between the molecular dynamics model and the continuum model using solid state physics. It is shown that the continuum model is unable to capture the sintering behaviour of nanoparticles. This is not because the continuum theory does not apply at the nano-scale but because the nanoparticles behave in so many different scenarios of the continuum theory that a meaningful model has to predict these scenarios, using the molecular dynamics for example. In the MD simulation, it is observed that the particles reorient their crystalline orientations at the beginning of the sintering and form different types of “necks” between different particles. This leads to different mechanisms of matter redistribution at the different necks. It is also observed that the particles can switch the mechanism of matter transportation half-way through the sintering process. It would be very difficult, if not impossible, to handle these complexities using the continuum model. However assuming the right scenario, the continuum theory does agree with the MD simulation for particles consisting of just a few thousands atoms.

Predicting the sintering deformation of ceramic powder compacts is very important to manufactures of ceramic components. In theory the finite element method can be used to calculate the sintering deformation. In practice the method has not been used very often by the industry for a very simple reason – it is more expensive to obtain the material data required in a finite element analysis than it is to develop a product through trial and error. A finite element analysis of sintering deformation requires the shear and bulk viscosities of the powder compact. The viscosities are strong functions of temperature, density and grain-size, all of which change dramatically in the sintering process. There are two ways to establish the dependence of the viscosities on the microstructure: (a) by using a material model and (b) by fitting the experimental data. The materials models differ from each other widely and it can be difficult to know which one to use. On the other hand, obtaining fitting functions is very time consuming. To overcome this difficulty, Pan and his co-workers developed a reduced finite element method (Kiani et. al. J. Eur. Ceram. Soc., 2007, 27, 2377-2383; Huang and Pan, J. Eur. Ceram. Soc., available on line, 2008) which does not require the viscosities; rather the densification data (density as function of time) is used to predict sintering deformation. This paper provides an overview of the reduced method and a series of case studies.

This paper presents a numerical model for the early stage sintering of powder compact taking into account of the separation of contact necks. The neck separation or damage may occur in a powder matrix which contains large second phase inclusions. A damage parameter is introduced and a variational principle for the sintering deformation of the matrix is developed using the damage parameter as a control variable. The sintering problem is therefore modelled by the minimisation of a quadratic functional under the control of a Kuhn–Tucker condition of damage growth. A sequential quadratic programming algorithm is used to solve the minimisation problem, giving temporal evolution of the stresses, strains, damage parameter and deformation of the matrix material. A range of numerical examples are given and the results are qualitatively compared with experimental observations made by Sudre et al. [Sudre, O., Bao, G., Fan, B., Lange, F.F., Evans, A.G., 1992. Effects of inclusions on densification. II: Numerical model. Journal of the American Ceramic Society 75, 525–531] and by Lange [Lange, F.F., 1989. Densification of powder ring constrained by dense cylindrical core. Acta Metallurgica 37, 697–704].

The sintering kinetics of large pores in a dense polycrystalline solid is studied using computer simulation. Coupled grain-boundary diffusion, surface diffusion and grain-boundary migration are assumed as the underlying mechanisms for the microstructural evolution. A numerical method developed by Ch’ng and Pan [Ch’ng, H.N., Pan, J., 2004. Cubic spline elements for modelling microstructural evolution of materials controlled by solid state diffusion and grain-boundary migration. Journal of Computational Physics 196, 724], which is an improved version of that developed by Pan et al. [Pan, J., Cocks, A.C.F., Kucherenko, S., 1997. Finite element formulation of coupled grain-boundary and surface diffusion with grain-boundary migration. Proceedings of the Royal Society, London A 453, 2161], is used for the computer simulation. A well-known textbook theory due to Kingery and Francois [Kingery, W.D., Francois, B., 1967. The sintering of crystalline oxides. I. Interaction between grain boundaries and pores. In: Kuczynski, G.C., et al. (Eds.), Sintering Related Phenomena. Goedon and Breach, New York, p. 471] predicts that a critical coordination number exists above which a pore does not shrink. The computer simulation demonstrates that this is not a general rule and that the critical coordination number only exists if one assumes that the pore is surrounded by identical grains. This numerical finding explains the contradiction between existing experimental observations and the critical coordination number theory. The numerical results also support the analytical expression developed by Ma [Ma, J., 1997. Constitutive modelling of the densification of porous ceramic components. PhD thesis, Engineering Department, Cambridge University] and Cocks [Cocks, A.C.F., 2001. Constitutive modelling of powder compaction and sintering. Progress in Materials Science 46, 201] for the sintering potential of powder containing large pores.

This paper presents a model for the evolution of creep damage by the nucleation, growth and coalescence of multiple cavities at a grain-boundary. Coupled grain-boundary and surface diffusion is assumed as the mechanism of cavity growth. At the core of the model is a simplified finite element formulation of cavity growth. Each cavity is modelled using a cavity element, these can be assembled together to construct a grain-boundary network with an evolving distribution of cavities. The cavity element is an extension of our previous model for the growth of a single cavity (Westwood et al., 2000). Continuous nucleation and coalescence of cavities are integrated into the model through remeshing the grain-boundary at a nucleation or coalescence event. The finite element formulation is tested using a series of cases for which the solutions are known. The finite element model is then compared with the smeared out model which was first proposed by Tvergaard (1983) and later adopted by Onck and van der Giessen (1997, 1999). It is shown that the two models only agree with each other at either a unrealistically high level of applied stress or extremely low rate of the nucleation. Under realistic values of applied stress and relative diffusivity, the smeared-out model tends to over-predict the damage growth rate. Finally the effect of relative diffusivity on creep damage is investigated. It is confirmed that materials with fast surface diffusivity possess a high resistance to diffusional damage growth, but this effect is only significant at a relatively high level of applied stress.

This paper presents a numerical scheme for solving the governing equations of the phase field model for microstructural evolution of materials. Grain-growth is used as an example but the scheme can be applied to any general phase field model. The numerical scheme is a Galerkin scheme using Daubechies wavelets as the trial and weight functions. Multi-level Daubechies wavelets with six vanishing moments are used. Using the wavelets as the trial and weight functions has the advantage of focusing the numerical calculation to where the field variable has high gradient, i.e. the interfacial boundaries. The numerical scheme therefore overcomes the problem of computational inefficiency in the phase field models. In this paper we first explain the wavelet-Galerkin scheme using a one-dimensional example for its simplicity and then extend the scheme to three-dimensional problems. By comparing the wavelet-Galerkin scheme with a classical finite difference scheme for both one and three-dimensional problems, the wavelet-Galerkin scheme is verified and its computational efficiency is demonstrated especially for three-dimensional problems.

Following a model for the sintering of a row of grains by Sun et al. (1996), a simplified model is developed for cavity growth along a grain-boundary by surface and grain-boundary diffusion. The cavity surface is approximated by two arcs of equal radius truncated by the grain-boundary. The arcs evolve by changing the radius and the intersection angle they make with the grain-boundary. A variational principle for the coupled diffusion problem is used to obtain the rate equations for the two degrees of freedom which are numerically integrated to follow the cavity growth. The simplified model can be reduced to the well established equilibrium cavity growth model for the limiting case of fast surface diffusion. A validity map for the model is constructed by comparing the approximate solutions with full numerical solutions over a wide range of values of relative diffusivity, initial dihedral angles and applied stresses. It is found that the simplified solution can be used under most of the practical conditions. The model described here is two dimensional although the approach can be easily extended to axisymmetric cases.

In this paper, a numerical procedure is described to simulate the grain structure evolution of fine grain materials during superplastic deformation. The basic assumption is that the dominant mechanism for the deformation of the material under mechanical loading is grain-boundary sliding accomodated by grain-boundary diffusion. At each time step, the full set of equations which control the grain-boundary diffusion process are solved by the numerical technique suggested by Cocks [1–2] with a further extension to the situation of grains with arbitrary sizes and shapes. The grain boundary network is updated according to grain velocities obtained from the numerical analysis. Any four-rayed grain boundary junction is supposed to be unstable. Therefore a vanishing grain-boundary will lead to either a “neighbour-switching” [3] or “grain vanishing” event. It is demonstrated that the computer simulation based on these few assumptions is able to capture the main characteristics of microstructural evolution in fine grain materials during superplastic deformation. Most importantly, the grain size increases slightly and the grain shape is essentially preserved, remaining equiaxed after a hundred percent elongation.

Heterogeneities in a green film made from a powder compact is considered to be one of the major reasons for the generation of sintering cracks. Stresses are generated in a film due to the constraint of the substrate. Instabilities in the sintering process can occur at sites of these heterogeneities resulting in the generation of multiple cracks, which can propagate through the thickness of the film. The classical finite element method is fundamentally ill-suited to studying this multiple-cracking problem. This paper presents a simple and robust numerical method for the computer modelling of sintering and multiple cracking. The method is based on the so-called material point method, which was initially developed for large deformation problems in plasticity. A parallel computing algorithm is implemented and a simple scheme for modelling the initiation and propagation of multiple cracks is proposed. The numerical scheme is then validated by simulating a simple geometric problem for which an analytical solution can be obtained. Finally, the robust performance of the numerical method is demonstrated by modelling the sintering response of a film which contains different types of heterogeneities.

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.

The resistance of bacteria toward antibacterial drugs is a rising problem. This threat is a major concern for space stations, where antibacterial surfaces would be ideal for materials which also need to be corrosion-resistant, hard and durable. Accordingly, the purpose of this work is to investigate novel coatings that have superhydrophobic mushroom microstructures. The microstructures are made of nickel deposited on a substrate which is composed of a gold layer on top of the silicon. The microstructures were fabricated with UV-light assisted nanoimprint lithography. These superhydrophobic microstructures have a well-defined alignment and shape which does not have any detrimental effect on the plastic deformation of the substrate. Similar structures were coated with carbon by hot-filament chemical vapour deposition (HFCVD) for a duration varying from 30 min to 120 min. Raman spectroscopy shows that the coating is composed of graphite, due to nickel-induced graphitisation during the deposition process. The antibacterial evaluation shows the bare nickel microstructures offer no antibacterial properties despite their superhydrophobic behaviour. On the other hand, the graphitic coated microstructures demonstrate significant antibacterial properties. Especially, 30 min HFCVD coated samples was antibacterial against E. coli and S. aureus with Gram-dependence and dependent on the coating deposition duration. Keywords: Microstructures, Antibacterial, Graphite, Diamond, Coating, Superhydrophobic