Finite Element studies on indentation size effect using a higher order strain gradient theory

In this work, a Finite Element implementation of a higher order strain gradient theory (due to Fleck and Hutchinson, 2001) has been used within the framework of large deformation elasto-viscoplasticity to study the indentation of metals with indenters of various geometries. Of particular interest is the indentation size effect (ISE) commonly observed in experiments where the hardness of a range of materials is found to be significantly higher at small depths of indentation but reduce to a lower, constant value at larger depths. That the ISE can be explained by strain gradient plasticity is well known but this work aims to qualitatively compare a gamut of experimental observations on this effect with predictions from a higher order strain gradient theory. Results indicate that many of the experimental observations are qualitatively borne out by our simulations. However, areas exist where conflicting experimental results make assessment of numerical predictions difficult. © 2012 Elsevier Ltd. All rights reserved.

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.

The microstructure and mechanical properties of ball-milled stainless steel powder: The effect of hot-pressing vs. laser sintering

The microstructure and mechanical properties of sintered stainless steel powder, of composition AISI 420, have been measured. Ball-milled powder comprising nanoscale grains was sintered to bulk specimens by two alternative routes: hot-pressing and microlaser sintering. The laser-sintered alloy has a porosity of 6% and comprises a mixture of delta ferrite and tempered martensite, and the relative volume fraction varies along the axis of the specimen due to a thermal cycle that evolves with progressive deposition. In contrast, the hot-pressed alloy has a porosity of 0.7% and exhibits a martensitic lath structure with carbide particles at the boundaries of the prior austenite grains. These differences in microstructure lead to significant differences in mechanical properties. For example, the uniaxial tensile strength of the hot-pressed material is one-half of its compressive strength, due to void initiation at the carbide particles at the prior austenite grain boundaries. Nanoindentation measurements reveal a size effect in hardness and also reveal the sensitivity of hardness to the presence of mechanical polishing and electropolishing. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Size effects in the conical indentation of an elasto-plastic solid

The size effect in conical indentation of an elasto-plastic solid is predicted via the Fleck and Willis formulation of strain gradient plasticity (Fleck, N.A. and Willis, J.R., 2009, A mathematical basis for strain gradient plasticity theory. Part II: tensorial plastic multiplier, J. Mech. Phys. Solids, 57, 1045-1057). The rate-dependent formulation is implemented numerically and the full-field indentation problem is analyzed via finite element calculations, for both ideally plastic behavior and dissipative hardening. The isotropic strain-gradient theory involves three material length scales, and the relative significance of these length scales upon the degree of size effect is assessed. Indentation maps are generated to summarize the sensitivity of indentation hardness to indent size, indenter geometry and material properties (such as yield strain and strain hardening index). The finite element model is also used to evaluate the pertinence of the Johnson cavity expansion model and of the Nix-Gao model, which have been extensively used to predict size effects in indentation hardness. © 2012 Elsevier Ltd.

Tensile response of passivated films with climb-assisted dislocation glide

The tensile response of single crystal films passivated on two sides is analysed using climb enabled discrete dislocation plasticity. Plastic deformation is modelled through the motion of edge dislocations in an elastic solid with a lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation incorporated through a set of constitutive rules. The dislocation motion in the films is by glide-only or by climb-assisted glide whereas in the surface passivation layers dislocation motion occurs by glide-only and penalized by a friction stress. For realistic values of the friction stress, the size dependence of the flow strength of the oxidised films was mainly a geometrical effect resulting from the fact that the ratio of the oxide layer thickness to film thickness increases with decreasing film thickness. However, if the passivation layer was modelled as impenetrable, i.e. an infinite friction stress, the plastic hardening rate of the films increases with decreasing film thickness even for geometrically self-similar specimens. This size dependence is an intrinsic material size effect that occurs because the dislocation pile-up lengths become on the order of the film thickness. Counter-intuitively, the films have a higher flow strength when dislocation motion is driven by climb-assisted glide compared to the case when dislocation motion is glide-only. This occurs because dislocation climb breaks up the dislocation pile-ups that aid dislocations to penetrate the passivation layers. The results also show that the Bauschinger effect in passivated thin films is stronger when dislocation motion is climb-assisted compared to films wherein dislocation motion is by glide-only. © 2012 Elsevier Ltd.

Plane-strain discrete dislocation plasticity with climb-assisted glide motion of dislocations

A small-strain two-dimensional discrete dislocation plasticity (DDP) framework is developed wherein dislocation motion is caused by climb-assisted glide. The climb motion of the dislocations is assumed to be governed by a drag-type relation similar to the glide-only motion of dislocations: such a relation is valid when vacancy kinetics is either diffusion limited or sink limited. The DDP framework is employed to predict the effect of dislocation climb on the uniaxial tensile and pure bending response of single crystals. Under uniaxial tensile loading conditions, the ability of dislocations to bypass obstacles by climb results in a reduced dislocation density over a wide range of specimen sizes in the climb-assisted glide case compared to when dislocation motion is only by glide. A consequence is that, at least in a single slip situation, size effects due to dislocation starvation are reduced. By contrast, under pure bending loading conditions, the dislocation density is unaffected by dislocation climb as geometrically necessary dislocations (GNDs) dominate. However, climb enables the dislocations to arrange themselves into lower energy configurations which significantly reduces the predicted bending size effect as well as the amount of reverse plasticity observed during unloading. The results indicate that the intrinsic plasticity material length scale associated with GNDs is strongly affected by thermally activated processes and will be a function of temperature. © 2013 IOP Publishing Ltd.

The effect of hole size upon the strength of metallic and polymeric foams

Tensile and compressive tests have been performed on centre-hole panels, made from three types of metallic foams and two polymeric foams. In compression, the foams fail in a ductile, notch-insensitive manner, in support of a "net section strength" criterion. In tension, a ductile-brittle transition is observed for some of the foams at sufficiently large specimen sizes: for a small hole diameter the net section strength criterion is obeyed, whereas for a large hole a local stress criterion applies and the net section strength is reduced. For a number of the foams, the panel size was not sufficiently large to observe this ductile-brittle switch in behaviour. The predictions of a cohesive zone model are compared with the measured strengths and are found to be in good agreement. © 2001 Elsevier Science Ltd. All rights reserved.