EXPERIMENTAL AND SIMULATED COMPRESSIVE PROPERTIES OF WORK-HARDENED X-TYPE LATTICE TRUSS STRUCTURES

The expauded metal sheets were folded with 11％ work-hardening.These were subsequently used with resistance welding to construct X-type lattice truss sandwich panels having a core relative density of 0....     

Compressive response of a sandwich plate containing a cracked diamond-celled lattice

The compressive strength is determined for a sandwich plate containing a centre-cracked core made from an elastic–brittle, diamond-celled lattice. It is assumed that the lattice fails when the major component of principal stress anywhere in the lattice attains the compressive or tensile strength of the solid, or when local buckling intervenes. First, analytical and numerical predictions are given for the unnotched strength of the core and for the compressive fracture toughness of the lattice K_IC. Second, finite element simulations and analytical models are reported for the fracture response of the sandwich plate with cracked core. The active failure mechanism in the cracked core is sensitive to core height, crack length, lattice geometry and material choice; this is illustrated by means of material-property charts.     

Mechanical properties of lattice grid composites

An equivalent continuum method only considering the stretching deformation of struts was used to study the in-plane stiffness and strength of planar lattice grid com- posite materials. The initial yield equations of lattices were deduced. Initial yield surfaces were depicted separately in different 3D and 2D stress spaces. The failure envelope is a polyhedron in 3D spaces and a polygon in 2D spaces. Each plane or line of the failure envelope is corresponding to the yield or buckling of a typical bar row. For lattices with more than three bar rows, subsequent yield of the other bar row after initial yield made the lattice achieve greater limit strength. The importance of the buckling strength of the grids was strengthened while the grids were relative sparse. The integration model of the method was used to study the nonlinear mechanical properties of strain hardening grids. It was shown that the integration equation could accurately model the complete stress-strain curves of the grids within small deformations.     

Dynamic failure of metallic pyramidal truss core materials – Experiments and modeling

The quasi-static and dynamic compressive behavior of pyramidal truss cores made of 304 stainless steel were investigated using a combination of experimental techniques. Quasi-static tests were performed using a miniature loading stage while a Kolsky bar apparatus was used to investigate intermediate deformation rates. High deformation rates were examined using a light gas gun. Optical imaging of the sample deformation was performed in real time by means of high-speed photography. In this article, we provide a quantification of load-deformation response and associated failure modes across the sample as captured by high-speed photography. A finite element model is formulated and thorough simulations performed to understand the roles of material strain rate hardening and structural microinertia. Deformation modes were identified from acquired images, force-deformation histories and numerical modeling. Comparison between force-deformation histories under quasi-static and Kolsky bar loading reveals a moderate microinertia effect as manifested by a small increase in peak compressive stress. At high deformation rates, gas gun experiments, a totally different deformation mode is manifested with a major increase in peak compressive stress. In this case, the inertia associated to the bending and buckling of truss struts played a significant role. This effect appears to dominate the early truss core response because of two effects: (i) the propagation of a plastic wave along the truss members; (ii) buckling induced lateral motion. These findings are consistent with prior theoretical and computational work carried out by Vaughn et al. (2005) [Vaughn, D. Canning, M., Hutchinson, J.W., 2005. Coupled plastic wave propagation and column buckling. Journal of Applied Mechanics 72 (1), 1–8]. At larger deformations, the material strain rate hardening contribution to the total energy is as pronounced as the contribution arising from microinertia effect.     

Dynamic buckling of an inclined strut

The dynamic compressive response of a sandwich plate with a metallic corrugated core is predicted. The back face of the sandwich plate is held fixed whereas the front face is subjected to a uniform velocity, thereby compressing the core. Finite element analysis is performed to investigate the role of material inertia, strain hardening and strain rate hardening upon the dynamic collapse of the corrugated core. Three classes of collapse mode are identified as a function of impact velocity: (i) a three-hinge plastic buckling mode of wavelength equal to the strut length, similar to the quasi-static mode, (ii) a ‘buckle-wave’ regime involving inertia-mediated plastic buckling of wavelength less than that of the strut length, and (iii) a ‘stubbing’ regime, with shortening of the struts by local fattening at the front face. The presence of strain hardening reduces the regime of dominance of the stubbing mode. The influence of material strain rate sensitivity is evaluated by introducing strain rate dependent material properties representative of type 304 stainless steel. For this choice of material, strain rate sensitivity has a more minor influence than strain hardening, and consequently the dynamic collapse strength of a corrugated core is almost independent of structural dimension.     

Tensile failure of two-dimensional quasi-brittle foams

Stress redistribution caused by damage onset and the subsequent local softening plays an important role in determining the ultimate tensile strength of a cellular structure. The formation of damage process zones with struts dissipating a finite amount of fracture energy will require the macroscopic stress to be increased in order to continue structural damage. The goal of this paper is to investigate the influence of the fracture energy of the solid on the tensile fracture strength and the strain to fracture in quasi-brittle two-dimensional foams using a microstructural model. We analyze the mesoscopic damage and failure mechanisms in uniaxial tension. Relative density, strut cross-sectional profile, solid’s fracture strain, and fracture energy are varied systematically. The effect of the specific fracture energy on the peak behavior has been shown to be captured by the ratio of the fracture energy to the stored elastic energy. We have also explored the net section strength variation in the presence of a central crack at two different fracture energies. Comparison is made between two structurally identical quasi-brittle and ductile strain hardening foams to identify the differences in the damage mechanisms.     

One-dimensional response of sandwich plates to underwater shock loading

The one-dimensional shock response of sandwich plates is investigated for the case of identical face sheets separated by a compressible foam core. The dynamic response of the sandwich plates is analysed for front face impulsive loading, and the effect of strain hardening of the core material is determined. For realistic ratios of core mass to face sheet mass, it is found that the strain hardening capacity of the core has a negligible effect upon the average through-thickness compressive strain developed within the core. Consequently, it suffices to model the core as an ideally plastic-locking solid. The one-dimensional response of sandwich plates subjected to an underwater pressure pulse is investigated by both a lumped parameter model and a finite element (FE) model. Unlike the monolithic plate case, cavitation does not occur at the fluid-structure interface, and the sandwich plates remain loaded by fluid until the end of the core compression phase. The momentum transmitted to the sandwich plate increases with increasing core strength, suggesting that weak sandwich cores may enhance the underwater shock resistance of sandwich plates.     

Structural response of pyramidal core sandwich columns

An experimental and analytical investigation is carried out to examine the in-plane compressive response of pyramidal truss core sandwich columns. The identified failure mechanisms include Euler buckling, shear buckling and face wrinkling. The operative mechanism is dependent on the properties of the bulk material and geometry of the sandwich columns and analytical formulae are derived for each of these modes. Failure maps are constructed for sandwich columns made from an elastic ideally-plastic material and AISI 304 stainless steel which has a strongly strain hardening response. Pyramidal core sandwich columns made from 304 stainless steel have been designed using these mechanism maps and the measured responses are compared with the analytical predictions. Finally, optimal single layer and multi-layer pyramidal sandwich column designs that minimize the weight for a given load carrying capacity are calculated using the developed analytical models for the failure of the sandwich columns. The results demonstrate that pyramidal core sandwich columns outperform the currently used hat-stiffened column design.     

Scaling laws of nanoporous gold under uniaxial compression: Effects of structural disorder on the solid fraction,elastic Poisson's ratio,Young's modulus and yield strength

In this work the relationship between the structural disorder and the macroscopic mechanical behavior of nanoporous gold under uniaxial compression was investigated, using the finite element method. A recently proposed model based on a microstructure consisting of four-coordinated spherical nodes interconnected by cylindrical struts, whose node positions are randomly displaced from the lattice points of a diamond cubic lattice, was extended. This was done by including the increased density as result of the introduced structural disorder. Scaling equations for the elastic Poisson's ratio, the Young's modulus and the yield strength were determined as functions of the structural disorder and the solid fraction. The extended model was applied to identify the elastic–plastic behavior of the solid phase of nanoporous gold. It was found, that the elastic Poisson's ratio provides a robust basis for the calibration of the structural disorder. Based on this approach, a systematic study of the size effect on the yield strength was performed and the results were compared to experimental data provided in literature. An excellent agreement with recently published results for polymer infiltrated samples of nanoporous gold with varying ligament size was found.     

The stiffness and strength of the gyroid lattice

Recently, a nanoscale lattice material, based upon the gyroid topology has been self-assembled by phase separation techniques (Scherer et al., 2012) and prototyped in thin film applications. The mechanical properties of the gyroid are reported here. It is a cubic lattice, with a connectivity of three struts per joint, and is bending-dominated in its elasto-plastic response to all loading states except for hydrostatic: under a hydrostatic stress it exhibits stretching-dominated behaviour. The three independent elastic constants of the lattice are determined through a unit cell analysis using the finite element method; it is found that the elastic and shear modulus scale quadratically with the relative density of the lattice, whereas the bulk modulus scales linearly. The plastic collapse response of a rigid, ideally plastic gyroid lattice is explored using the upper bound method, and is validated by finite element calculations for an elastic-ideally plastic lattice. The effect of geometrical imperfections, in the form of random perturbations to the joint positions, is investigated for both stiffness and strength. It is demonstrated that the hydrostatic modulus and strength are imperfection sensitive, in contrast to the deviatoric response. The macroscopic yield surface of the imperfect lattice is adequately described by a modified version of Hill’s anisotropic yield criterion. The article ends with a case study on the stress induced within a gyroid thin film, when the film and its substrate are subjected to a thermal expansion mismatch.     

The microstructural origin of strain hardening in two-dimensional open-cell metal foams

This paper aims at elucidating the microstructural origin of strain hardening in open-cell metal foams. We have developed a multiscale model that allows to study the development of plasticity at two length scales: (i) the development of plastic zones inside individual struts (microscopic scale) and (ii) the formation of plastic localization bands at the scale of the cellular architecture (mesoscopic scale). We address how plasticity at both scales contribute to the macroscopic yielding and strain hardening of cellular metals. One of the important results is that, in contrast to strain hardening in dense metals, strain hardening in cellular metals consist of a synergistic contribution of two sources: (i) strain hardening of the solid material (microscopic scale) and (ii) geometric hardening due to strut reorientation (mesoscopic scale). We show that the synergy of the two leads to an enhanced macroscopic hardening capacity. Our results are in qualitative agreement with experimental studies and elucidate the microstructural origin of plastic hardening in this class of materials.     

Metallic sandwich panels subjected to multiple intense shocks

The mechanical response and fracture of metal sandwich panels subjected to multiple impulsive pressure loads (shocks) were investigated for panels with honeycomb and folded plate core constructions. The structural performance of panels with specific core configurations under multiple impulsive pressure loads is quantified by the maximum transverse deflection of the face sheets and the core crushing strain at mid-span of the panels. A limited set of simulations was carried out to find the optimum core density of a square honeycomb core sandwich panels under two shocks. The panels with a relative core density of 4%–5% are shown to have minimum face sheet deflection for the loading conditions considered here. This was consistent with the findings related to the sandwich panel response subjected to a single intense shock. Comparison of these results showed that optimized sandwich panels outperform solid plates under shock loading. An empirical method for prediction of the deflection and fracture of sandwich panels under two consecutive shocks – based on finding an effective peak over-pressure – was provided. Moreover, a limited number of simulations related to response and fracture of sandwich panels under multiple shocks with different material properties were performed to highlight the role of metal strength and ductility. In this set of simulations, square honeycomb sandwich panels made of four steels representing a relatively wide range of strength, strain hardening and ductility values were studied. For panels clamped at their edge, the observed failure mechanisms are core failure, top face failure and tearing at or close to the clamped edge. Failure diagrams for sandwich panels were constructed which reveal the fracture and failure mechanisms under various shock intensities for panels subjected to up to three consecutive shocks. The results complement previous studies on the behavior and fracture of these panels under high intensity dynamic loading and further highlights the potential of these panels for development of threat-resistant structural systems.     

Mechanical Behaviors and Bending Effects of Carbon Fiber Reinforced Lattice Materials

To acquire materials of higher specific stiffness and strength, stretching dominated lattice materials reinforced by carbon fibers were designed and manufactured. The mechanical behaviors were predicted and experimented. The imperfections of lattice materials, such as the waviness of the struts, non-circular cross-sections and cantilever ribs, greatly influenced their performance. The bending effects of the imperfections were predicted and compared with the experiment results. Although influenced by the imperfections, carbon reinforced lattice materials are still much stiffer and stronger than foams and honeycombs.     

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.     

The response of clamped sandwich plates with lattice cores subjected to shock loading

The dynamic response of clamped circular monolithic and sandwich plates of equal areal mass and thickness has been measured by loading the plates at mid-span with metal foam projectiles. The sandwich plates comprise AISI 304 stainless steel face sheets and either AL-6XN stainless steel pyramidal core or AISI 304 stainless steel square-honeycomb lattice core. The resistance to shock loading is quantified by the permanent transverse deflection at mid-span of the plates as a function of projectile momentum. It is found that the sandwich plates have a higher shock resistance than monolithic plates of equal mass, and the square-honeycomb sandwich plates outperform the pyramidal core plates. Three-dimensional finite element simulations of the experiments are in good agreement with the experimental measurements. The finite element calculations indicate that the ratio of loading time to structural response time is approximately 0.5. Consequently, the tests do not lie in the impulsive regime, and projectile momentum alone is insufficient to quantify the level of loading.     

Analytical solution for a Mode III crack in a 3D beam lattice

The brittle fracture behavior of an open cell foam is considered. The foam is modeled by an infinite lattice composed of elastic straight-line beam elements (struts) having uniform cross-sections and rigidly connected at the nodal points. The beams are parallel to the three mutually orthogonal lattice vectors thus forming a microstructure with rectangular parallelepiped cells.A semi-infinite Mode III crack is embedded in the lattice and, for the considered antiplane deformation, each node has three degrees of freedom, namely, the displacement parallel to the crack front and two rotations about the axes perpendicular to this direction. The analysis method hinges on the discrete Fourier transform, which allows to formulate the crack problem by means of the Wiener–Hopf equation. Its solution yields closed-form analytical expressions for the forces and the displacements at any cross-section, and, in particular, at the crack plane. An eigensolution for the traction-free crack faces and K-field remote loading is derived from the solution for the loaded crack using a limiting procedure. An analytical expression for the fracture toughness is derived from the eigensolution by comparing the remote stress field and the stresses in the near-tip struts. The obtained expression is found to be consistent with the known analytical and experimental results for Mode I deformation. It appears, that the dependence of the fracture toughness upon shape anisotropy ratio of the lattice material is non-monotonic. The optimal value of this parameter, which provides the maximum crack arresting ability is determined.     

Bounds and estimates for the effect of strain gradients upon the effective plastic properties of an isotropic two-phase composite

Predictions are made for the size effect on strength of a random, isotropic two-phase composite. Each phase is treated as an isotropic, elastic-plastic solid, with a response described by a modified deformation theory version of the Fleck-Hutchinson strain gradient plasticity formulation (Fleck and Hutchinson, J. Mech. Phys. Solids 49 (2001) 2245). The essential feature of the new theory is that the plastic strain tensor is treated as a primary unknown on the same footing as the displacement. Minimum principles for the energy and for the complementary energy are stated for a composite, and these lead directly to elementary bounds analogous to those of Reuss and Voigt. For the case of a linear hardening solid, Hashin-Shtrikman bounds and self-consistent estimates are derived. A non-linear variational principle is constructed by generalising that of Ponte Castañeda (J. Mech. Phys. Solids 40 (1992) 1757). The minimum principle is used to derive an upper bound, a lower estimate and a self-consistent estimate for the overall plastic response of a statistically homogeneous and isotropic strain gradient composite. Sample numerical calculations are performed to explore the dependence of the macroscopic uniaxial response upon the size scale of the microstructure, and upon the relative volume fraction of the two phases.     

Fracture toughness of open-cell Kelvin foam

Brittle fracture behavior of a perfect open-cell Kelvin foam is considered. The foam is modeled as a spatial lattice consisting of brittle elastic struts rigidly connected to each other at the nodal points. The fracture toughness is determined from the analysis of a quasi-plane problem for a slice of the foam with an embedded finite length crack generated by broken struts. The crack plane is chosen on the basis of a previous study of crack nucleation phenomenon, and the crack length, which assures the self-similar K-field in the tip vicinity, is established by numerical experiments. For the considered densities range the crack includes several hundreds of broken struts and, consequently, the portion of the foam to be considered in the analysis has a very large number of nodal degrees of freedom. The computational cost is reduced significantly by using for the analysis the representative cell method based on the discrete Fourier transform. As a result, the initial problem for the foam slice is reduced to the problem for the repetitive cell which includes 12 struts.