SUMMARYThe cohesive finite element method (CFEM) allows explicit modelling of fracture processes. One form of CFEM models integrates cohesive surfaces along all finite element boundaries, facilitating the explicit resolution of arbitrary fracture paths and fracture patterns. This framework also permits explicit account of arbitrary microstructures with multiple length scales, allowing the effects of material heterogeneity, phase morphology, phase size and phase distribution to be quantified. However, use of this form of CFEM with cohesive traction-separation laws with finite initial stiffness imposes two competing requirements on the finite element size. On one hand, an upper bound is needed to ensure that fields within crack-tip cohesive zones are accurately described. On the other hand, a lower bound is also required to ensure that the discrete model closely approximates the physical problem at hand. Both issues are analysed in this paper within the context of fracture in multi-phase composite microstructures and a variable stiffness bilinear cohesive model. The resulting criterion for solution convergence is given for meshes with uniform, cross-triangle elements. A series of calculations is carried out to illustrate the issues discussed and to verify the criterion given. These simulations concern dynamic crack growth in an Al 2 O 3 ceramic and in an Al 2 O 3 /TiB 2 ceramic composite whose phases are modelled as being hyperelastic in constitutive behaviour.

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Sintering is a processing technique which compacts powder materials into solids leading to microstructural evolution with reduced surface area and improved material density. Understanding the densification mechanism and grain growth kinetics during the powder compaction process during sintering is of immense importance in order to evaluate usability of the final materials in a wide range of applications. Current work focuses on capturing the microstructural changes as powder particles compact into a polycrystalline structure during sintering. A phase field modeling based approach is adopted in this study in order to predict consolidation kinetics during sintering. It is observed that at the initial stage of sintering interactions between powder particles are initiated due to surface diffusion. At later stage, densification is primarily governed by volume and grain boundary diffusion. Also individual grains increase in size under pressure until adjacent grains touch each other. Once grains start interacting with adjacent grains, grain boundary diffuses and average grain size stabilizes.

Dynamic fracture in two-phase Al 2 O 3 /TiB 2 ceramic composite microstructures is analyzed explicitly using a cohesive finite element method (CFEM). This framework allows the effects of microstructural heterogeneity, phase morphology, phase distribution, and size scale to be quantified. The analyses consider arbitrary microstructural phase morphologies and entail explicit tracking of crack growth and arbitrary fracture patterns. The approach involves the use of CFEM models that integrate cohesive surfaces along all finite element boundaries as an intrinsic part of the material description. This approach obviates the need for any specific fracture criteria and assigns models the capability of predicting fracture paths and fracture patterns. Calculations are carried out using idealized phase morphologies as well as real phase morphologies in actual material microstructures. Issues analyzed include the influence of microstructural morphology on the fracture behavior, the influence of phase size on fracture resistance, the effect of interphase bonding strength on failure, and the effect of loading rate on fracture.

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A continuum theory is used to study the interactions between nanoparticles suspended in nematic liquid crystals. The free energy functional that describes the system is minimized using an Euler-Lagrange approach and an unsymmetric radial basis function method. It is shown that nanoparticle liquid-crystal mediated interactions can be controlled over a large range of magnitudes through changes of the anchoring energy and the particle diameter. The results presented in this work serve to reconcile past discrepancies between theoretical predictions and experimental observations, and suggest intriguing possibilities for directed nanoparticle self-assembly in liquid crystalline media.

Nanoscale engineered materials with tailored thermal properties are desirable for applications such as highly efficient thermoelectric, microelectronic and optoelectronic devices. It has been shown earlier that by judiciously varying the interface thermal boundary resistance (TBR), thermal conductivity in nanostructures can be controlled. In the presented investigation, the role of TBR in controlling thermal conductivity at the nanoscale is analyzed by performing non-equilibrium molecular dynamics (NEMD) simulations to calculate thermal conductivity of a range of Si-Ge multilayered structures with 1-3 periods, and with four different layer thicknesses. The analyses are performed at three different temperatures (400, 600 and 800 K). As expected, the thermal conductivity of all layered structures increases with the increase in the number of periods as well as with the increase in the monolayer thickness. Invariably, we find that the TBR offered by the interface nearest to the hot reservoir is the highest. This effect is in contrast to the usual notion that each interface contributes equally to the heat transfer resistance in a layered structure. Findings also suggest that for high period structures the average TBR offered by the interfaces is not equal. Findings are used to derive an analytical expression that describes period-length-dependent thermal conductivity of multilayered structures.

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