N.A. Fleck

STRAIN GRADIENT PLASTICITY: THEORY AND EXPERIMENT

Abstract Dislocation theory is used to invoke a strain gradient theory of rate independent plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocation. The density of the geometrically necessary dislocations scales with the gradient of plastic strain. A deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening. The theory is a non-linear generalization of Cosserat couple stress theory. Tension and torsion experiments on thin copper wires confirm the presence of strain gradient hardening. The experiments are interpreted in the light of the new theory.

Metal Foams: A Design Guide

Introduction Making Metal Foams Characterization Methods Properties of Metal Foams Design Analysis for Material Selection Design Formulae for Simple Structures A Constitutive Model for Metal Foams Design for Creep with Metal Foams Sandwich Structures Energy Management: Packaging and Blast Protection Sound Absorption and Vibration Suppression Thermal Management and Heat Transfer Electrical Properties of Metal Foams Cutting, Finishing and Joining Cost Estimation and Viability Case Studies Suppliers of Metal Foams Web Sites Index .

A phenomenological theory for strain gradient effects in plasticity

Abstract A Strain Gradient Theory of plasticity is introduced, based on the notion of statistically stored and geometrically necessary dislocations. The strain gradient theory fits within the general framework of couple stress theory and involves a single material length scale l. Minimum principles are developed for both deformation and flow theory versions of the theory which in the limit of vanishing l, reduce to their conventional counterparts: J2 deformation and J2 flow theory. The strain gradient theory is used to calculate the size effect associated with macroscopic strengthening due to a dilute concentration of bonded rigid particles; similarly, predictions are given for the effect of void size upon the macroscopibic softening due to a dilute concentration of voids. Constitutive potentials are derived for this purpose.

A reformulation of strain gradient plasticity

A class of phenomenological strain gradient plasticity theories is formulated to accommodate more than one material length parameter. The objective is a generalization of the classical J2 3ow theory of plasticity to account for strain gradient e4ects that emerge in deformation phenomena at the micron scale. A special case involves a single length parameter and is of similar form to that proposed by Aifantis and co-workers. Distinct computational advantages are associated with this class of theories that make them attractive for applications requiring the generation of numerical solutions. The higher-order nature of the theories is emphasized, involving both higher-order stresses and additional boundary conditions. Competing members in the class of theories will be examined in light of experimental data on wire torsion, sheet bending, indentation and other micron scale plasticity phenomena. The data strongly suggest that at least two distinct material length parameters must be introduced in any phenomenological gradient plasticity theory, one parameter characterizing problems for which stretch gradients are dominant and the other relevant to problems when rotation gradients (or shearing gradients) are controlling. Flow and deformation theory versions of the theory are highlighted that can accommodate multiple length parameters. Examination of several basic problems reveals that the new formulations predict quantitatively similar plastic behavior to the theory proposed earlier by the present authors. The new formulations improve on the earlier theory in the manner in which elastic and plastic strains are decomposed and in the representation of behavior in the elastic range. ? 2001 Elsevier Science Ltd. All rights reserved.

Isotropic constitutive models for metallic foams

The yield behaviour of two aluminium alloy foams (Alporas and Duocel) has been investigated for a range of axisymmetric compressive stress states. The initial yield surface has been measured, and the evolution of the yield surface has been explored for uniaxial and hydrostatic stress paths. It is found that the hydrostatic yield strength is of similar magnitude to the uniaxial yield strength. The yield surfaces are of quadratic shape in the stress space of mean stress versus effective stress, and evolve without corner formation. Two phenomenological isotropic constitutive models for the plastic behaviour are proposed. The first is based on a geometrically self-similar yield surface while the second is more complex and allows for a change in shape of the yield surface due to differential hardening along the hydrostatic and deviatoric axes. Good agreement is observed between the experimentally measured stress versus strain responses and the predictions of the models.

Effective properties of the octet-truss lattice material

The effective mechanical properties of the octet-truss lattice structured material have been investigated both experimentally and theoretically. Analytical and FE calculations of the elastic properties and plastic yielding collapse surfaces are reported. The intervention of elastic buckling of the struts is also analysed in an approximate manner. Good agreement is found between the predictions of the strength and experimental observations from tests on the octet-truss material made from a casting aluminium alloy. Moreover, the strength and stiffness of the octet-truss material are stretching-dominated and compare favourably with the corresponding properties of metallic foams. Thus, the octet-truss lattice material can be considered as a promising alternative to metallic foams in lightweight structures.

The topological design of multifunctional cellular metals

Abstract The multifunctional performance of stochastic (foamed) cellular metals is now well documented. This article compares such materials with the projected capabilities of materials with periodic cells, configured as cores of panels, tubes and shells. The implementation opportunities are as ultra-light structures, for compact cooling, in energy absorption and vibration control. The periodic topologies comprise either micro-truss lattices or prismatic materials. Performance benefits that can be expected upon implementing these periodic materials are presented and compared with competing concepts. Methods for manufacturing these materials are discussed and some cost/performance trade-offs are addressed.

Compressive failure of fibre composites

Abstract A review of experimental data and elementary theoretical formulas for compressive failure of polymer matrix fibre composites indicates that the dominant failure mode is by plastic kinking. Initial local fibre misalignment plays a central role in the plastic kinking process. Theoretical analyses and numerical results for compressive kinking are presented, encompassing effects of strain-hardening, kink inclination, and applied shear stress. The assumption of rigid fibres is assessed critically, and the legitimacy of its use for polymer matrix composites is established.

Fabrication and structural performance of periodic cellular metal sandwich structures

Metallic sandwich panels with periodic, open-cell cores are important new structures, enabled by novel fabrication and topology design tools. Fabrication protocols based on the sheet forming of trusses and shell elements (egg-boxes) as well as textile assembly have allowed the manufacture of robust structures by inexpensive routes. Topology optimization enables control of failure mechanisms at the truss length scale, leading to superior structural performance. Analysis, testing and optimization have demonstrated that sandwich panels constructed with these cores sustain loads at much lower relative densities than stochastic foams. Moreover, the peak strengths of truss and textile cores are superior to honeycombs at low relative densities, because of their superior buckling resistance. Additional benefits of the truss/textile cores over honeycombs reside in their potentially lower manufacturing cost as well as in their multifunctionality.

Foam topology: bending versus stretching dominated architectures

Abstract Cellular solids can deform by either the bending or stretching of the cell walls. While most cellular solids are bending-dominated, those that are stretching-dominated are much more weight-efficient for structural applications. In this study we have investigated the topological criteria that dictate the deformation mechanism of a cellular solid by analysing the rigidity (or otherwise) of pin-jointed frameworks comprising inextensional struts. We show that the minimum node connectivity for a special class of lattice structured materials to be stretching-dominated is 6 for 2D foams and 12 for 3D foams. Similarly, sandwich plates comprising of truss cores faced with planar trusses require a minimum node connectivity of 9 to undergo stretching-dominated deformation for all loading states.