Behaviour of cellular materials under impact loading

The paper describes experimental and computational testing of regular open‐cell cellular structures behaviour under impact loading. Open‐cell cellular specimens made of aluminium alloy and polymer were experimentally tested under quasi‐static and dynamic compressive loading in order to evaluate the failure conditions and the strain rate sensitivity. Additionally, specimens with viscous fillers have been tested to determine the increase of the energy absorption due to filler effects. The tests have shown that brittle behaviour of the cellular structure due to sudden rupture of intercellular walls observed in quasi‐static and dynamic tests is reduced by introduction of viscous filler, while at the same time the energy absorption is increased. The influence of fluid filler on open‐cell cellular material behaviour under impact loading was further investigated with parametric computational simulations, where fully coupled interaction between the base material and the pore filler was considered. The explicit nonlinear finite element code LS‐DYNA was used for this purpose. Different failure criteria were evaluated to simulate the collapsing of intercellular walls and the failure mechanism of cellular structures in general. The new computational models and presented procedures enable determination of the optimal geometric and material parameters of cellular materials with viscous fillers for individual application demands. For example, the cellular structure stiffness and impact energy absorption through controlled deformation can be easily adapted to improve the efficiency of crash absorbers.     

Dynamic crushing behavior of 3D closed-cell foams based on Voronoi random model

Dynamic crushing responses of three-dimensional cellular foams are investigated using the Voronoi tessellation technique and the finite element (FE) method. FE models are constructed for such closed-cell foam structures based on Voronoi diagrams. The plateau stress and the densification strain energy are determined using the FE models. The effects of the cell shape irregularity, impact loading, relative density and strain hardening on the deformation mode and the plateau stress are studied. The results indicate that both the plateau stress and the densification strain energy can be improved by increasing the degree of cell shape irregularity. It is also found that the plastic deformation bands appear firstly in the middle of the model based on tetrakaidecahedron at low impact velocities. However, the crushing bands are seen to be randomly distributed in the model based on Voronoi tessellation. At high impact velocities, the “I” shaped deformation mode is clearly observed in all foam structures. Finally, the capacity of foams absorbing energy can be improved by increasing appropriately the degree of cell shape irregularity.     

Mechanical response of cellular solids: Role of cellular topology and microstructural irregularity

Rapid advance in additive manufacturing techniques promises that, in the near future, the fabrication of functional cellular structures will be achieved with desired cellular microstructures tailored to specific application in mind. In this perspective, it is essential to develop a detailed understanding of the relationship between mechanical response and cellular microstructure. The present study reports on the results of a series of computational experiments that explore the effect topology and microstructural irregularity (or non-periodicity) on overall mechanical response of cellular solids. Compressive response of various 2D topologies such as honeycombs, stochastic Voronoi foams as well as tetragonal and triangular lattice structures have been investigated as functions of quantitative irregularity parameters. The fundamental issues addressed are (i) uniqueness of mechanical response in irregular microstructures, and effects of (ii) specimen size, (iii) boundary morphology, (iv) cellular topology, and (v) microstructural irregularity on mechanical response.     

On crushing response of the three-dimensional closed-cell foam based on Voronoi model

The crushing response of the three dimensional closed-cell foams is investigated using mesoscale numerical models based on Voronoi tessellation. The crushing stress at the impact and stationary sides of the Voronoi structures are obtained. The effects of the impact velocity, the cell shape irregularity degree, the relative density, inertia of cell walls and the dependence of the base material on the crushing stress are discussed. Meanwhile, the contention of the rate dependency of cellular materials are expounded by the comparison of numerical results of the Voronoi model and solid continuum model as well as the shock wave theory, in which the densification strain and plateau stress are calculated using the energy absorption efficiency approach.     

The mechanical behaviour of aluminium foam structures in different loading conditions

The use of foam has the potential for energy absorption enhancement. Many types of materials can be produced in the form of foams, including metals and polymers. Of the metallic based foams, aluminium based are among the most advanced. Aluminium foams couple good specific mechanical properties with high thermal stability. Among the various aspects still to be investigated regarding their mechanical behaviour is the influence of a hydrostatic state of stress on yield strength. Unlike metals, the hydrostatic component affects yields. Therefore, different loading conditions have to be considered to fully identify the material behaviour. Another important issue in foam structure design is the analysis of composite structures. The mechanical behaviour of an aluminium foam has been examined. The foam was subjected to uniaxial, hydrostatic stress, pure deviatoric stress, and combinations thereof. Results obtained will be presented as quasi-static and dynamic uniaxial compression and quasi-static bending and shear loading. Moreover, composite structures were made by assembling the foam into aluminium cold extruded closed section 6060 aluminium tubes. The results show that the energy absorption capability of the composite structures is much greater than the sum of the energy absorbed by the two components, the foam and the tube.     

Effects of statistics of cell’s size and shape irregularity on mechanical properties of 2D and 3D Voronoi foams

In the study of the mechanical properties of metallic foam, the relative density (or porosity) and the average size of cells are two key parameters of the meso-geometry, but it is also well known experimentally that the two parameters alone are not enough since the mechanical properties of metallic foams are different even with the same initial relative density and average cell size. In this paper, we have classified the irregularity of cells into two types to describe polygonal and polyhedral cells in 2D and 3D metallic foams, which are called size irregularity and shape irregularity, respectively. The former reflects the deviation of the size of a cell from the average cell size in the foam and the latter reflects the deviation of the shape of a cell from a circle with the same area (2D) or a globe with the same volume (3D). With the two kinds of definitions, effects of the irregularity of cells in aluminum foam on mechanical properties are investigated using the Voronoi tessellation technique and the finite element method. The well- designed 2D and 3D Voronoi models are constructed, of which the statistic distributions of size and shape irregularity are presented. The compression simulations of Voronoi-based models indicate that the yield stress of metallic foam is seldom affected by the size irregularity, but significantly affected by the shape irregularity. The more regular the foams, the higher will be their yield plateau at constant overall relative density and average cell size.     

Comparison between RVE and full mesh approaches for the simulation of compression tests on cellular metals

Metal foams are materials of recent development and application that show interesting combinations of physical and mechanical properties. Many applications are envisaged for such materials, particularly in equipments of passive safety, because of their high capacity of energy absorption under impact conditions. The damage analysis in metallic foams is a complex problem and must be performed in a finite strain context. Considering that compression is the dominant loading in impact situations, a finite deformation simulation including damage effects of a compression test on a cellular metal sample is shown in this work. The main objective of the paper is to compare simulations considering periodic boundary conditions, by means of a representative volume element (RVE) approach, with results obtained using full meshes. It is shown that, when the imposed deformation is high, the use of RVE does not describe in a proper manner the deformation that occurs at the walls of cells. This characteristic of RVE approach results in a too stiff behavior when considering load‐displacement relations. A comparison with experimental results is also presented.     

Properties of Ti–6Al–4V non-stochastic lattice structures fabricated via electron beam melting

This paper addresses foams which are known as non-stochastic foams, lattice structures, or repeating open cell structure foams. The paper reports on preliminary research involving the design and fabrication of non-stochastic Ti–6Al–4V alloy structures using the electron beam melting (EBM) process. Non-stochastic structures of different cell sizes and densities were investigated. The structures were tested in compression and bending, and the results were compared to results from finite element analysis simulations. It was shown that the build angle and the build orientation affect the properties of the lattice structures. The average compressive strength of the lattice structures with a 10% relative density was 10 MPa, the flexural modulus was 200 MPa and the strength to density ration was 17. All the specimens were fabricated on the EBM A2 machine using a melt speed of 180 mm/s and a beam current of 2 mA. Future applications and FEA modeling were discussed in the paper.     

Dynamic behaviour of high strength steel parts developed through laser assisted direct metal deposition

High strength steel alloys are good candidates for many engineering applications particularly those involving high strains and impact loads. Such applications in energy absorption devices require materials that can sustain dynamic loading and remain strong under demanding conditions. But the processing cost of these alloys has been a prohibitive factor, thus re-enforcing the research on porous and cellular structures made of stainless steels. Direct metal deposition (DMD) is a process which employs the power of a CO₂ laser to melt and deposit metallic powders onto steel substrates. Such structures offer advantages of creating novel configurations only by computer control of laser “tool path”. This research investigates the mechanical behaviour of solid and porous parts with prismatic cavities under quasi-static and dynamic compressive loading. Apart from two main deficiencies of relatively large variations of properties among the test specimen and sufficiently low modulus of elasticity, the stress strain behaviour is very close to the commercial grades of stainless steel produced by rolling and forming. The energy absorption behaviour of porous specimen is also very encouraging and renders DMD as a suitable process for manufacturing of customized sandwich and graded structures that can be used as a substitution for many engineering applications such as monolithic compression plates and explosion shields.     

Characterisation of aluminium matrix syntactic foams under drop weight impact

It is a challenging task to develop a lightweight, and at the same time, strong material with high energy absorption for applications in military vehicles, which are able to withstand impact and blast with minimum injury to occupants. This paper presents a study on aluminium matrix syntactic foams as a possible core material for a protection system on military vehicles. Experimental work was first carried out which covers sample preparation through pressure infiltration and impact tests on aluminium matrix syntactic foams manufactured. Numerical models were then developed using commercial finite element code ABAQUS/Explicit to simulate the dynamic behaviour of the foam. The effect of strain rate on their compressive behaviour was investigated as these properties are vital in terms of the applications of these materials. Characterisation of the foam behaviour under low velocity impact loading and an identification of the underlying failure mechanisms were also carried out to evaluate the effective mechanical performance. It was found that samples subjected to drop weight impact offered a 20–30% higher plateau stresses than those of the samples subjected to quasi-static compression loading. The degree of correlation between the numerical simulations and the experimental results has been shown to be reasonably good.     

Fatigue and damage accumulation in open cell aluminium foams

Open‐cell aluminium foams are a relatively new material with interesting uses in different engineering applications. This study investigates the fatigue behaviour and damage accumulation of metal foams via a fatigue analysis (Weibull E‐N model), a failure criterion (the relation among the prepeak compressive and tensile slopes, the reduction in the tensile stress, or the reduction in the compressive stress), and a mathematical approach (linear, quadratic, or exponential). As a result of combining the 3 mathematical approaches and 3 failure criteria, different approaches are obtained, analysed, and validated by using experimental data. Finally, the proposed approaches can be used to directly obtain the damage accumulation level for open‐cell metal foams under fully reversed cyclic loading as a function of the number of cycles applied, the total strain amplitude, and the initial damage accumulation condition.     

Investigation on the Static Response and Failure Process of Metallic Open Lattice Cellular Structures

Abstract: The response of three different cellular core types, suitable for manufacturing crashworthiness sandwich cellular structures, is investigated in this paper. A methodology is developed, comprising linear static and eigenvalue buckling analysis, as well as nonlinear material elastoplastic analysis. The methodology is used to study the structural response and failure process of open lattice metallic cellular cores and derive the most important structural properties of the cellular core, i.e. elasticity modulus, plateau stress and compaction strain. The critical elastoplastic buckling stress of the metallic struts is approximated by analytical solutions, while a simple engineering approach is applied for the estimation of the compaction strain. The influence of core basic design parameters, i.e. strut aspect ratio (radius/length), unit‐cell spatial configuration and unit‐cell size on the structural behaviour is assessed.     

Effect of strain rate and density on dynamic behaviour of syntactic foam

The final objective of this study is to improve the mechanical behaviour of composite sandwich structures under dynamic loading (impact or crash). Cellular materials are often used as core in sandwich structures and their behaviour has a significant influence on the response of the sandwich under impact. Syntactic foams are widely used in many impact-absorbing applications and can be employed as sandwich core. To optimize their mechanical performance requires the characterisation of the foam behaviour at high strain rates and identification of the underlying mechanisms.Mechanical tests were conducted on syntactic foams under quasi-static and high strain rate compression loading. The material behaviour has been determined as a function of two parameters, density and strain rate. These tests were complemented by experiments on a new device installed on a flywheel. This device was designed in order to achieve compression tests on foam at intermediate strain rates. With these test machines, the dynamic compressive behaviour has been evaluated in the strain rate range up [6.7 · 10⁻⁴ s⁻¹, 100 s⁻¹].Impact tests were conducted on syntactic foam plates with varying volume fractions of microspheres and impact conditions. A Design of Experiment tool was employed to identify the influence of the three parameters (microsphere volume fraction, projectile mass and height of fall) on the energy response. Microtomography was employed to visualize in 3D the deformation of the structure of hollow spheres to obtain a better understanding of the micromechanisms involved in energy absorption.     

Finite element modelling of the mechanism of deformation and failure in metallic thin-walled hollow spheres under dynamic compression

Recent interest in lightweight metallic hollow sphere foams for aerospace applications requires a better physical understanding of dynamic properties of single spheres. Finite element modelling supported by high rate experiments was developed to investigate the underlying deformation and failure mechanisms of electrodeposited nickel thin-walled hollow spheres. Parametric simulation was performed to further explore the effect of sphere geometry (wall thickness to diameter ratio) and loading rate. It was found that decreasing the ratio of wall thickness to diameter tends to transit the side wall failure mode from bending to buckling. For a thin-walled sphere (the thickness to diameter ratio less than a critical value), the macroscopic dynamic behaviour is primarily dominated by the two deformation and failure mechanisms: (1) buckling failures of wall materials and (2) self-contacts of wall surfaces and wall-anvil contacts. At higher impact velocity (greater than a critical velocity), inertia effect due to dynamic localisation of wall crushing arises and significantly influences the deformation/failure mode of the sphere, resulting in an increased initial crushing strength and asymmetric deformation. Finally, the behaviour of hollow spheres was correlated to explore the power law behaviour of bulk foams with respect to the relative density; it was found that metallic thin-walled hollow sphere foams can be better approximated as open-cell rather than closed-cell foams.     

Process Control in Aluminum Foam Production Using Real‐Time X‐ray Radioscopy

Aluminum alloy foams were created by expanding foamable precursors containing a gas‐releasing blowing agent in a dense metallic matrix. The precursors were prepared in two different ways: either by hot‐compaction of powder mixtures or by thixocasting of billets obtained by cold compaction of powder blends. Foam evolution was visualized by means of real‐time X‐ray radioscopy with image frequencies ranging up to 18 Hz and spatial resolutions down to 10 μm. The difference in pore formation between the two processing routes could be studied. Rupture of cell walls during foam expansion could be visualized, critical rupture thickness measured, and the time‐scale of the rupture process estimated. By manufacturing foam precursors in which defects were incorporated deliberately, the question of the origin of very large pores in solid metal foams could be examined. By forced cooling of liquid metal foams while recording their structure, the importance of solidification‐induced changes of foam morphology was illustrated.     

Strategic Advances in Formation of Cell‐in‐Shell Structures: From Syntheses to Applications

Single‐cell nanoencapsulation, forming cell‐in‐shell structures, provides chemical tools for endowing living cells, in a programmed fashion, with exogenous properties that are neither innate nor naturally achievable, such as cascade organic‐catalysis, UV filtration, immunogenic shielding, and enhanced tolerance in vitro against lethal factors in real‐life settings. Recent advances in the field make it possible to further fine‐tune the physicochemical properties of the artificial shells encasing individual living cells, including on‐demand degradability and reconfigurability. Many different materials, other than polyelectrolytes, have been utilized as a cell‐coating material with proper choice of synthetic strategies to broaden the potential applications of cell‐in‐shell structures to whole‐cell catalysis and sensors, cell therapy, tissue engineering, probiotics packaging, and others. In addition to the conventional “one‐time‐only” chemical formation of cytoprotective, durable shells, an approach of autonomous, dynamic shellation has also recently been attempted to mimic the naturally occurring sporulation process and to make the artificial shell actively responsive and dynamic. Here, the recent development of synthetic strategies for formation of cell‐in‐shell structures along with the advanced shell properties acquired is reviewed. Demonstrated applications, such as whole‐cell biocatalysis and cell therapy, are discussed, followed by perspectives on the field of single‐cell nanoencapsulation.     

An investigation on the dynamic response of polymeric,metallic, and biomaterial foams

Mechanical characterization of foams at varying strain rates is indispensable for the selection of foam as core material for the proficient sandwich structure design at dynamic loading application. Both servo-hydraulically controlled Material Testing System (MTS) and Instron machines are generally considered for quasi-static testing at strain rates on the order of 10⁻³ s⁻¹. Split Hopkinson pressure bar (SHPB) with steel bars is typically utilized for characterizing metallic foams at high strain rates, however modified SHPB with polycarbonate or soft martial bars are used for characterizing polymeric and biomaterial foams at high strain rates on the order of 10³ s⁻¹ for impedance match between the foam specimens and bars. This paper reviews the effect of strain rate of loading, density, environmental temperature, and microstructure on compressive strength and energy absorption capacity of various closed-cell polymeric, metallic, and biomaterial foams. Compressive strength and energy absorption capacity increase with the increase in both strain rate of loading and density of foams, but decrease with the increase in surrounding temperature. Foams of same density can have different strength and can absorb unequal amount of energy at the same strain rate of loading due to the variation of microstructure.     

The quasi-static and blast loading response of lattice structures

A range of metallic lattice structures have been manufactured using the selective laser melting (SLM) rapid manufacturing technique. The lattice structures were based on [±45°] and [0°, ±45°], unit-cell topologies. Initially, the structures were loaded in compression to investigate their progressive collapse behaviour and associated failure mechanisms. Tests were then undertaken at crosshead displacement rates up to 3 m/s in order to characterise the rate-dependent properties of these architectures. A series of blast tests were then undertaken on a ballistic pendulum in order to investigate the behaviour of lattice structures under these extreme loading conditions.     

Mechanical modelling of the creep behaviour of Hollow-Sphere Structures

Hollow-Sphere Structures could represent an alternative to classical cellular materials (like metal foams or honeycombs) for numerous structural applications, for instance in which mechanical energy absorption in case of impact is important. The present work explores the main mechanisms that govern the viscous behaviour of Hollow-Sphere Structures in view of their potential high-temperature applications, and more specifically under creep loading. It aims at understanding how elastic, plastic and viscous properties of the constitutive material contribute to the effective behaviour of the structure. In the computational framework mechanical properties can be deliberately varied in order to make their effects stand out clearly. The results show a strong strain rates heterogeneity in the structure because of stress concentration phenomena. Hence the architecture causes an additional non-linearity in the overall mechanical response that has to be taken into account in order to correctly capture overall creep mechanisms.     

A Unit‐Cell Approach of Finite Element Analysis for Transverse Impact Damage of 3‐D Biaxial Spacer Weft‐Knitted Composite

Abstract: This paper evaluates the transverse impact damage of a 3‐D biaxial spacer weft‐knitted composite using experimental results and complimentary finite element analysis. The load–displacement curves and damage morphologies during impact loading were obtained to analyse energy absorption and impact damage mechanisms of the knitted composite. A unit‐cell model based on the microstructure of the 3‐D knitted composite was established to calculate the deformation and damage evolution when the composite is impacted by a hemisphere‐ended steel rod. An elastoplastic constitutive equation is incorporated into the unit‐cell model and the critical damage area failure theory developed by Hahn and Tsai has been implemented as a user‐defined material law (VUMAT) for commercial available finite element code ABAQUS/Explicit. The load–displacement curves, impact damages and impact energy absorption obtained from ABAQUS/Explicit are compared with those FROM experiments. The good agreement of the comparisons supports the validity of the unit‐cell model and user‐defined subroutine VUMAT. The unit‐cell model can also be extended to evaluate the impact crashworthiness of engineering structures made out of the 3‐D knitted composites.