Size effects in the constrained deformation of metallic foams

The constrained deformation of an aluminium alloy foam sandwiched between steel substrates has been investigated. The sandwich plates are subjected to through-thickness shear and normal loading, and it is found that the face sheets constrain the foam against plastic deformation and result in a size effect: the yield strength increases with diminishing thickness of foam layer. The strain distribution across the foam core has been measured by a visual strain mapping technique, and a boundary layer of reduced straining was observed adjacent to the face sheets. The deformation response of the aluminium foam layer was modelled by the elastic-plastic finite element analysis of regular and irregular two dimensional honeycombs, bonded to rigid face sheets; in the simulations, the rotation of the boundary nodes of the cell-wall beam elements was set to zero to simulate full constraint from the rigid face sheets. It is found that the regular honeycomb under-estimates the size effect whereas the irregular honeycomb provides a faithful representation of both the observed size effect and the observed strain profile through the foam layer. Additionally, a compressible version of the Fleck-Hutchinson strain gradient theory was used to predict the size effect; by identifying the cell edge length as the relevant microstructural length scale the strain gradient model is able to reproduce the observed strain profiles across the layer and the thickness dependence of strength. © 2002 Elsevier Science Ltd. All rights reserved.

Mode I crack growth resistance of metallic foams

A Dugdale-type cohesive zone model is used to predict the mode I crack growth resistance (R-curve) of metallic foams, with the fracture process characterized by an idealized traction-separation law that relates the crack surface traction to crack opening displacement. A quadratic yield function, involving the von Mises effective stress and mean stress, is used to account for the plastic compressibility of metallic foams. Finite element calculations are performed for the crack growth resistance under small scale yielding and small scale bridging in plane strain, with K-field boundary conditions. The following effects upon the fracture process are quantified: material hardening, bridging strength, T-stress (the non-singular stress acting parallel to the crack plane), and the shape of yield surface. To study the failure behaviour and notch sensitivity of metallic foams in the presence of large scale yielding, a study is made for panels embedded with either a centre-crack or an open hole and subjected to tensile stressing. For the centre-cracked panel, a transition crack size is predicted for which the fracture response switches from net section yielding to elastic-brittle fracture. Likewise, for a panel containing a centre-hole, a transition hole diameter exists for which the fracture response switches from net section yielding to a local maximum stress criterion at the edge of the hole.

Correlation of transport and magnetic critical currents in melt-processed YBa2Cu3O7-δ thick films

Transport critical current measurements have been carried out on melt-processed thick films of YBa2Cu3O7-δ on yttria-stabilized zirconia in fields of up to 8 T both within grains and across grain boundaries. These measurements yield Jc values of ∼3000 A cm-2 at 4.2 K and zero magnetic field and 400 A cm -2 at 77 K and zero magnetic field, taking the entire sample width as the definitive dimension. Optical and scanning electron microscopy reveals that the thick-film grains consist typically of a central "hub" region ∼50 μm in diameter, which is well connected to radial subgrains or "spokes" which extend ∼1 mm to define the complete grain structure. Attempts have been made to correlate the transport measurements of inter- and intra-hub-and-spoke (H-S) critical current with values of this parameter derived previously from magnetization measurements. Analysis of the transport measurements indicates that current flow through H-S grains is constrained to paths along the spokes via the grain hub. Taking the size of the hub as the definitive dimension yields an intra-H-S grain Jc of ∼60 000 A cm-2 at 4.2 K and 0 T, which is in reasonable agreement with the magnetization data. Experiments in which the hub is removed from individual grains confirm that this feature determines critically the J c of the film.