Analysis of electro-permeation of hydrogen in metallic alloys.

A reaction-diffusion type modelling framework is presented to analyse both electro-permeation (EP) and thermal desorption spectrometry (TDS) measurements of hydrogen in metallic alloys. It is assumed that the kinetics of hydrogen motion is governed by diffusion through the lattice, along with trapping/detrapping at specific sites such as dislocations, grain boundaries, etc. It is shown that the trapping and detrapping rates are typically much faster than the diffusion rate, and consequently a simplification of the governing equations suffices such that local equilibrium exists between lattice and trapped hydrogen. Using this local equilibrium assumption, we then present an asymptotic analysis of the governing kinetic equation for the EP test. This asymptotic analysis reveals that four regimes of behaviour exist, ranging from negligible trapping to the complete filling of deep traps. The analysis suggests that EP tests should be so-arranged that three regimes of behaviour are spanned, in order to extract the relevant material properties associated with hydrogen transport. The numerical solutions presented in this study support the asymptotic analysis. The hydrogen kinetics framework is also deployed to analyse both EP and TDS tests on the same martensitic steel. The EP measurements all lie in regime I and are thus insufficient to uniquely determine both the trap density and binding energy. Reasonable agreement is obtained between measurements and numerical predictions of TDS tests using parameters estimated from the EP tests. Further improvements in measurements are required to confirm the fidelity of this modelling approach.This article is part of the themed issue 'The challenges of hydrogen and metals'.

Prediction of failure in notched carbon-fibre-reinforced-polymer laminates under multi-axial loading.

A damage-based finite-element model is used to predict the fracture behaviour of centre-notched quasi-isotropic carbon-fibre-reinforced-polymer laminates under multi-axial loading. Damage within each ply is associated with fibre tension, fibre compression, matrix tension and matrix compression. Inter-ply delamination is modelled by cohesive interfaces using a traction-separation law. Failure envelopes for a notch and a circular hole are predicted for in-plane multi-axial loading and are in good agreement with the observed failure envelopes from a parallel experimental study. The ply-by-ply (and inter-ply) damage evolution and the critical mechanisms of ultimate failure also agree with the observed damage evolution. It is demonstrated that accurate predictions of notched compressive strength are obtained upon employing the band broadening stress for microbuckling, highlighting the importance of this damage mode in compression. This article is part of the themed issue 'Multiscale modelling of the structural integrity of composite materials'.

Convective Assembly of a Particle Monolayer.

Recently, the steady-state process of convective assembly has emerged as a viable production route for colloidal monolayers. The present study models the regions of particle assembly: Region I comprises convective concentration of a particle suspension in a liquid below a meniscus, Region II comprises permeation of fluid through the dense particle monolayer, and Region III comprises capillary densification. For each region, the dominant physics and nondimensional groups are identified, and quantitative models are derived to describe the evolution of microstructure in terms of the main process parameters. The concentration profile within the assembly zone of Region I is predicted, including the role of a concentration-dependent diffusion constant and the shape of the meniscus. The fluid flow through the assembled monolayer is treated in Region II, along with a stability calculation to reveal that isolated particle clusters do not survive on top of the monolayer. The physics of capillary crystallization is addressed in Region III, with an emphasis on the density of cracks that emerge. The Peclet number and Capillary number both play important roles but in different regions of the assembly process.

Wave propagation in two-dimensional periodic lattices.

Plane wave propagation in infinite two-dimensional periodic lattices is investigated using Floquet-Bloch principles. Frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies: hexagonal honeycomb, Kagomé lattice, triangular honeycomb, and the square honeycomb. These topologies exhibit dramatic differences in their long-wavelength deformation properties. Long-wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices. The slenderness ratio of the constituent beams of the lattice (or relative density) has a significant influence on the band structure. The techniques developed in this work can be used to design lattices with a desired band structure. The observed spatial filtering effects due to anisotropy at high frequencies (short wavelengths) of wave propagation are consistent with the lattice symmetries.