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Mechanical Behavior of Metallic Foams
Abstract
Metallic foams have a combination of properties that make them attractive for a number of engineering applications, including lightweight structural sandwich panels, energy absorption devices, and heat sinks. For many potential applications an understanding of the mechanical behavior of these foams is essential. Recently, there has been substantial progress in identifying the mechanisms of deformation and failure in metallic foams. Here, we summarize the current understanding of the elastic moduli, uniaxial strength, yield criterion, creep, and fatigue of metallic foams.
... In the last several years, researchers have focused their attention on the production of a wide range of metallic and polymeric cellular materials with the aim of developing lightweight structures with adequate stiffness and strength [1][2][3][4][5]. These cellular materials can be described as porous, consisting of a network of interconnecting elements. ...
... However, many CAD software packages work with the boundary representation (B-rep) and therefore are not able to directly work with the implicit geometry of Equation (1). For this reason, it is helpful to describe how to generate a CAD model of the fillet shape by dissecting Equation (2) to extract some main curves that serve as a basis to create a volume geometry using B-rep-based CAD software. Using the symmetry of the geometry, it is very useful to work only on an eighth of a unit cell and then generate the complete cell by mirroring. ...
... An eighth of a unit cell rests on the origin of the reference system, x, y, z; therefore, it is possible to identify four planes for each direction having as normal vectors the directions x, y and z. The four planes having normal vectors collinear to the z-axis are chosen at specific z * = {z 1 , z 2 , z 3 , z 4 } coordinates ( Figure 1) such that the sections of the external fillet surface, obtained by setting Equation (2) to equal zero, generate closed curves: ...
The goal of this paper is to improve the mechanical strength-to-weight ratios of metal cubic lattice structures using unit cells with fillet shapes inspired by triply periodic minimal surfaces (TPMS). The lattice structures here presented were fabricated from AA6082 aluminum alloy using lost-PLA processing. Static and dynamic flat and wedge compression tests were conducted on samples with varying fillet shapes and fill factors. Finite element method simulations followed the static tests to compare numerical predictions with experimental outcomes, revealing a good agreement. The TPMS-type fillet shape induces a triaxial stress state that significantly improves the mechanical strength-to-weight ratio compared to fillet radius-free lattices, which was also confirmed by analytical considerations. Dynamic tests exhibited high resistance to flat impacts, while wedge impacts, involving a high concentrated-load, brought out an increased sensitivity to strain rates with a short plastic deformation followed by abrupt fragmentation, indicating a shift towards brittle behavior.
... The foaming process plays an important role in the foam structure, and foam performance is directly influenced by its structure [6][7][8][9][10][11]. PET's low melt strength and viscoelasticity make it difficult to be foamed, which has been extensively discussed in the literature [12][13][14][15]. ...
... The compressive stress-strain behavior of foams has been systematically studied by Gibson et al. [6,7]. Subsequent researchers have also conducted numerous studies on various specific foams [22][23][24][25][26]. ...
... The curves can be divided into three different regions, i.e., the elastic region, plateau region, and densification region. Although PET foam exists with a honeycomb-shaped strand border, the global stress-strain curves demonstrate typical characteristics, which has been proved in conventional metal and polymer foams [6,7,29]. It also shows that extruded PET foams, although composed of foamed strands, can still be analyzed from a macroscopic point of view in terms of the relationship between the mechanical properties of the foam and its structure. ...
The cell structure and compressive properties of extruded polyethylene terephthalate (PET) foam with different densities were studied. The die of the PET foaming extruder is a special multi-hole breaker plate, which results in a honeycomb-shaped foam block. The SEM analysis showed that the aspect ratio and cell wall thickness of the strand border is greater than that of the strand body. The cells are elongated and stronger in the extruding direction, and the foam anisotropy of the structure and compressive properties decrease with increasing density. The compression results show typical stress–strain curves even though the extruded PET foam is composed of multiple foamed strands. The compression properties of PET foam vary in each of the three directions, with the best performing direction (i.e., extrusion direction) showing stretch-dominated structures, while the other two directions show bending-dominated structures. Foam mechanics models based on both rectangular and elongated Kelvin cell geometries were considered to predict the compressive properties of PET foams in terms of relative density, structure anisotropy, and the properties of the raw polymer. The results show that the modulus and strength anisotropy of PET foam can be reasonably predicted by the rectangular cell model, but more accurate predictions were obtained with an appropriately assumed elongated Kelvin model.
... Interest in metallic foams has significantly grown over the past few decades, largely due to their unique physical and mechanical properties [1][2][3][4]. Such properties include a high internal specific surface area (for open-cell foams), a high stiffness-to-weight ratio, a high strength-weight ratio, and an ability to absorb sound and energy [5][6][7][8][9][10][11]. There are two basic types of metallic foams, open-cell foams, where the pores are interconnected throughout the foam structure, and closed-cell foams, where pores are isolated inside the volume of the foam. ...
... Once all the pores have collapsed, the foam enters the densification stage, which is identified by a rapid increase in compressive stress. Gibson and Ashby state that the densification strain, ε d , can be predicted by Equation (1) [9]: ...
... These values are calculated using an assumed solid aluminum density of 2.7 g/cm 3 and a cell wall aluminum yield strength of 130 MPa [10]. The ideal open-and closed-cell foam compressive strengths are defined by Gibson in Equations (2) and (3), respectively [9]. ...
The powder metallurgy (PM) route for the production of closed-cell metallic foams has recently received a significant amount of attention. One of the major issues is the non-uniform and non-spherical nature of the cells produced, which can negatively affect the mechanical behavior. The current paper uses the PM route to process metallic foams for the first time using novel Al-TiH2 foamable precursor “particles” (FPPs). The effect of FPP content (0–10 wt.%) on the developed foam structure of aluminum and its mechanical properties is investigated. An increase in FPP content results in a decline in product density by forming uniform and near-spherical cells. The main advantage of the FPPs is the localization of the blowing agent TiH2 particle content within Al-TiH2 composite particles (i.e., giving rise to a higher local TiH2 content), which has led to the production of pores with relatively high circularities even at very low overall TiH2 contents. The foams produced displayed energy absorption capacities of 10–25 MJ/m3 at 50% strain, and maximum energy absorption efficiencies ranging from 0.6–0.7 (for 40–60% closed cell content)
... Cell size/pore size, describes the size of the typical unit cell or periodicity of a structure. Metalfoams made using traditional manufacturing techniques typically have a cell size in the range of 2mm to 10mm [10]. ...
... As outlined above cellular solids are traditionally categorised as open-cell or closed cell [10], and display a combination of bending dominated and/or stretch dominated behaviour. For strut-based lattices the Maxwell number M (Eq. ...
... 10: Sample GS-04-B25 shown after testing at ×20 (left) and ×100 (right) optical zoom. ...
Additive manufacturing (AM) is an emerging technology which has enabled unprecedented design freedom, allowing fabrication of intricate designs which were not feasible or possible under traditional methods. This design freedom has enabled the fabrication of specifically architected cellular structures, such as lattices or triply periodic minimal surfaces (TPMS). These cellular structures have many potential applications including lightweighting and/or creating a tuneable response to mechanical loading. This thesis contributes to the body of knowledge on additively manufactured cellular structures in three key areas related to the design and additive manufacturing of TPMS-like cellular structures.
... In recent years, the focus of cellular materials research has shifted toward the study of metallic foams due to their properties and multi-functionality. Metal foams have been widely investigated due to their properties (low specific weight, excellent thermal conductivity, and high energy absorption) and their wider application areas (thermal insulation, heat sink for electronic devices, clean air technology, catalytic converter substrates, lightweight structural sandwich panels, vibration-damping devices, and energy-absorbing systems) [1]- [7]. Metal foams can geometrically be presented as a stochastic or regular configuration according to their pore distribution or based on their topology as closed-cell or open-cell foams. ...
... Therefore, it is possible to achieve a stable design of the required structures to control the performance of the final foams [31]- [46]. The manufacturing method for the production of open-cell aluminum foams with uniformly sized pores used in this study will be presented in section 3. 1 The mechanical behavior of aluminum foams can be summarized using the three stages of its compressive stress-strain response: (i) a linear elastic regime characterized by the elastic deformation of a single strut (i.e. dominated cell wall bending); (ii) a plastic flow with a roughly constant stress plateau or a practically linear increase in stress (i.e. ...
... affected by plastic hinges); and (iii) an exponential increase in the stress taking place due to the densification and the mutual contact of the struts [47]- [50]. These mechanical properties of aluminum foam depend upon several factors, such as geometrical parameters (cell topology, cell size, cell shape, cell distribution), process defects (non-uniform cell size and its distribution, cell-wall thickness, curved and wrinkled cell walls, cell wall misalignment, broken cell walls, missing cells, variations in density, microstructures, etc.) and the applied loading complexity and its rate [1], [5], [39], [51]- [63]. ...
This experimental work aimed to understand the effect of a biaxial combined compression-torsion loading complexity on the mechanical properties of two types of aluminum foams having porosities of 85% and 80% and nominal relative densities of 15% and 20%, respectively. In this investigation, open-cell aluminum foam of highly uniform architecture with a spherical porosity was designed and used to investigate the biaxial plastic response. These foams were tested under different quasi-static complex loading paths using a patented rig, called ACTP with different torsional component rates. The key responses to be examined were yield stress, stress plateau, energy absorption capacity, densification strain, micro-hardness, and microstructure. It was revealed that the greater the density of the foam with the higher the loading complexity, the greater the yield strength, the energy absorption capacity, and the micro-hardness. The highest foam strength was thus recorded under the most complicated loading path (i.e., biaxial 60°) for the densest foam (i.e., 80% porosity). This was due to the variation in the cell wall thickness. In addition, the effect of the loading complexity on the microstructure was studied using SEM. The loading complexity of biaxial-45° provides higher particle segregation at the grain boundary and a larger densification strain for the 85% porosity foams.
... Hence, to translate the measured microhardness values to mechanical yield strength, we considered the macroscopic yield strength to be equal to the measured hardness, viz., M Y = H V [14]. Further, for the nanoporous materials, the ligament yield strength L Y is related to the macroscopic yield strength M Y (= H V ) by the well-known density scaling equation [38], ...
... It appears that, the mechanical property measurement techniques discussed here monitor the deformation activity in the constrained ligament networks under the external load. Thus, the mechanical strengthening behavior in nanoporous metallic assembly depends highly on the ligament dimensions, and in such a constrained skeletal assembly, the plasticity hinges mostly at the ligament interconnections [38,44]. Based on the literature reports, the present results suggest that the microhardness data of nanoporous metallic materials obtained from the Vicker's microhardness tester relates to the yield strength values of nanoporous materials obtained from the nanoindentation and uniaxial compression experiments. ...
We report in this article, the Dysprosium doping effects on microstructure and mechanical properties of nanoporous metallic gold, synthesized by electrochemical dealloying of Ag70Au30 and Ag70Au29Dy1 alloys. It is shown that these dealloyed nanoporous metallic materials exhibit the mean ligament diameter in a length scale of 5–10 nm. The variation of ligament diameter in pure and Dysprosium doped nanoporous Au with annealing temperature influences their mechanical properties. Higher microhardness value has been obtained around 10 nm ligament diameter on both pure and Dysprosium doped nanoporous gold. The maximum values of Vickers hardness HV obtained from the analysis of indentation diagonals with applied load are close to the HV value reported for bulk gold. Since the nanoporous metallic materials behave in a way like compressible sponge materials, we used the well-known density scaling equation for the determination of ligament yield strength of pure and Dysprosium doped nanoporous gold with ligament diameter. The results obtained have been finally compared with literature reports.
... In particular, only few numbers of oscillations are visible in the stress plateau of relatively ductile Al1Mg0.6Si foam, implying cell collapse by elastic buckling and yielding of deformation bands [1,22]. This agrees with faster hardening rate of Al1Mg0.6Si ...
... Mechanical performance of the studied foams is reasonably represented in line with approach [22]. In this way relative compressive strength, pl/s, is usually brought into the use against relative density, /s, as displayed in Figure 3. open cell foams when their relative density becomes less than /s < 0.14 (porosity content >86%). ...
The study presents mechanical performance metrics, especially, energy absorption, of aluminium foams fabricated by melt processing with CaCO 3 blowing agent without Ca additive. Relatively ductile Al1Mg0.6Si alloy and high strength Al6Zn2.3Mg alloy comprising brittle eutectic domains were employed for the foams manufacture and then examined in conditions of uniaxial quasi-static compression. It was recognized that mechanical response of the foams and energy absorption is radically defined by the mechanism of cell collapse which, in turn, depends on the nature of structural constituents of the cell wall material. In particular, the presence of brittle eutectic domains in the cell wall material of foam based on Al6Zn2.3Mg alloy results in reducing the compressive strength and energy absorption compared to those of foam processed with Al1Mg0.6Si alloy, both deviate markedly from the theoretical predictions. In spite of this experimental verification of foams cell collapse is considered to be strongly required before their engineering application.
... Foams are also included within advanced materials as they can achieve lightweight without compromising on the stiffness and strength [18,19]. Nevertheless, like composites, their modelling and manufacturing is a more complicated process compared to the traditional materials [18]. ...
... The first thing is to check if the foams are effectively isotropic or anisotropic by investigating the engineering constants in different directions. The engineering constants calculated by using the Mori-Tanaka mean-field homogenisation and the FE approaches given in Tables 1 and 2 are in very good agreement with each other and they strengthen the idea that the material's mechanical properties are quasiisotropic alongside the reported cases in the literature [19,21,[42][43][44]. The engineering constants indicate isotropy by 11 ≊ 22 ≊ 33 , 12 ≊ 23 ≊ 13 and 12 ≊ 21 ≊ 23 ≊ 332 ≊ 13 ≊ 31 for the same volume fraction values of voids. ...
In the aerospace industry, the structures are subjected to significant loads and extreme conditions whilst being required to be lightweight and resilient. Metallic foams seem to meet these criteria. However, their usage in the aerospace applications are not as common as one would expect. To explore a potential application of foams, this study evaluates the performance of the foams of Ti-6Al-4V, a conventional material/alloy for aircraft engine fan blade applications performing numerical simulations. First, the mechanical properties of the Ti-6Al-4V alloy are calculated using the Mori–Tanaka mean-field homogenisation and finite element (FE) methods employing representative volume elements (RVE). Using those calculated material properties and the computer-aided design (CAD) model of a representative aircraft engine fan blade, the FE models are built. In these numerical models, the material properties and the rotational speed with the static aero-loads are selected as variables, whilst boundary conditions remain consistent to ensure a systematic investigation. Stress analysis and the prestressed modal analyses of the blades are performed, and the results are presented to discuss the impact of the void volume fraction of the alloy foams. This study reveals the complex nature of the mechanics of fan blades when made of foams.
... Commercially exploited and preferred for several applications due to their low density, excellent ductility, good thermal conductivity, and reasonable cost, they attract great interest [1][2][3][4][5][6][7]. ...
... Once again, this seems to be due to the additional hardening induced by the reverse torsional component. (1) where W is Energy per unit volume, is axial stress, and is axial strain. For FP85 foam, Figure 9a,b revealed that the absorbed energy as a function of strain evolves in a nonlinear manner for a uniaxial loading condition. ...
As a main goal of this work, a novel generation of cellular materials has been developed and manufactured by the kelvin cell model to be offered for different multifunctional applications. These Open-Cell Aluminum Foams (OCAF) have 85% porosities of spherical-shaped pores with a diameter of 11 mm. Several foamed square-section specimens were used. This work investigated the impact of different new quasi-static biaxial loading complexities on the mechanical behavior of such foams. Thus, new S-profiled rigs were already designed for examining the behavior of tested foams under biaxial loading conditions with different reverse torsional components named ACTP-S. After testing, their high specific strength and high energy absorption abilities have been characterized. Thus, in addition to the reference uniaxial test, all other tests were conducted at a speed of 5 mm/min. Thus, the mechanical responses of this foam are affected by loading complexities which are simple uniaxial, intermediate-biaxial (Bi-45 •), and sever-biaxial (Bi-60 •). These results were compared to the classical Absorption using Compression-Torsion Plastique (ACTP) responses. It was concluded that the highest dissipated energy increases with the increase in loading path complexity. Note that the energy absorption of the foam is essentially governed by its collapse mode.
... Because of their exceptional buckling and impact resistance, these materials are used as sound absorbers and building materials and also in different transport structures [1][2][3]. However, the properties of metal foams are controlled by manufacturing conditions and have paved the path for scientists to partially make their structures by controlling the cell shape in the structure, because cell morphology affects mechanical properties [4][5][6]. Lightweight aluminum and its alloy are not currently being used with steel in the same way as any other metal, so its production continues to grow. Its physical character makes it an ideal candidate for a variety of applications in industries such as packaging, transportation, construction and aerospace [6]. ...
... At this equilibrium condition, gas bubbles were reduced in size by a combination of metallostatic, atmospheric, and surface tension forces (P st ) [24]. P in = P m + P a + P st (4) The cell size of Al-Si12CuFe alloy foams is obtained by ...
Lightweight aluminum composite is a class of foam material that finds many applications. These properties make it suitable for many industries, such as the transportation, aerospace and sports industries. In the present work, closed-cell foams of an Al-Si12CuFe alloy and its composite are developed by a stir casting process. The optimization of the foaming temperature for the alloy and composite foams was conducted in terms of the ligament and node size of the alloy and also the volatility of the zircon with the melt, to provide strength to the cell walls. CaCO 3 as a blowing agent was homogeneously distributed in the molten metal without adding any thickener to develop the metal foam. The decomposition rate of CaCO 3 is temperature-dependent, which is attributed to the formation of gas bubbles in the molten alloy. Cell structure, such as cell size and cell wall thickness, is controlled by manufacturing process parameters, and both the physical and mechanical properties are dependent on the foam cell structure, with cell size being the major variable. The results show that the increase in cell wall thickness with higher temperature leads to a decrease in cell size. By adding the zircon to the melt, the cell size of the composite foam first increases, and then the thickening of the wall occurs as the temperature is increased. The uniform distribution of the blowing agent in molten metal helps in the formation of a uniform cell structure. In this work, a comparative structural study of alloy foam and composite foam is presented regarding cell size, cell shape and foam stability at different temperatures.
... The technology needed to observe aluminum foam by X-ray computed tomography (CT) has been developed [6][7][8][9][10][11][12], and there is a possibility that it can be used for the nondestructive quality assurance method for aluminum foam. Currently, aluminum foam properties are generally estimated on the basis of density (porosity, which is the ratio of pore volume to total sample volume) [2,4,13]. However, some studies have shown that even when porosity is the same, differences in pore structural characteristics, such as pore size and shape, and their distribution result in different properties [4,[14][15][16][17][18][19]. ...
... Finally, a densification region appears in which σ increases rapidly. This trend is similar to those of other aluminum foam specimens[13]. ...
Owing to its lightweight and excellent shock-absorbing properties, aluminum foam is used in automotive parts and construction materials. If a nondestructive quality assurance method can be established, the application of aluminum foam will be further expanded. In this study, we attempted to estimate the plateau stress of aluminum foam via machine learning (deep learning) using X-ray computed tomography (CT) images of aluminum foam. The plateau stresses estimated by machine learning and those actually obtained using the compression test were almost identical. Consequently, it was shown that plateau stress can be estimated by training using the two-dimensional cross-sectional images obtained nondestructively via X-ray CT imaging.
... For the core of sandwich panel, metallic foam is an idea choice because of the advantages of light weight, energy absorption and sound insulation [10][11][12]. Among the metallic foam material the gradient metallic foam has been the widespread attention, because it is a gradient pore structure from one surface of the material to the other resulting in varying material properties [13][14][15]. ...
... Then Eqs. (7), (11), (12) and (14) are substituted into Eq. (6), the total potential energy is rewritten as ...
AN improved predictive method is presented to predict the local indentation of the sandwich panel with two types of gradient foam core under a spherical indenter, which are called positive gradient foam core and negative gradient foam core, respectively. Especially for the negative foam core, a gradient influence function is defined which is proposed to describe the effects of gradient change of foam cores on local deformational behavior of sandwich panels. The analytic solutions for the plastic deformation profile of upper face sheet and the indentation force of spherical indenter are obtained, which are validated using the existing theoretical model and finite element code ABAQUS®. Subsequently, the influences of the gradient change on indentation response and energy absorption of sandwich panels with gradient metallic foam core are also investigated.
... The compression deformation of the two structures is shown in Figure 11, and it can be found that the FBCXYZ structure has a 45 • inclined fracture, while the BCCXYZ structure is collapsed layer by layer. Gibson [40] proves that the above equations estimate the mechanical prop similar structures. Figure 12 shows the ratio of relative Young's modulus ( ⁄ , the elastic modulus of 2% strain), relative compressive strength ( ⁄ ), and rela sity ( ⁄ ) of different structures. ...
... where C and n are constants, and the s subscript represents the properties of the base material. Gibson [40] proves that the above equations estimate the mechanical properties of similar structures. Figure 12 shows the ratio of relative Young's modulus (E/E S , where is the elastic modulus of 2% strain), relative compressive strength (σ/σ S ), and relative density (ρ/ρ S ) of different structures. ...
Laser powder bed fusion (L-PBF) additive manufacturing technology is suitable for the direct 3D printing of geometrically complex periodic micro-rod-lattices. However, controlling the geometric and performance consistency remains challenging due to manufacturability limitations, non-negligible process defects, and surface roughness, which is inconvenient to measure, affecting the mechanical properties and deformation behavior of the lattice structures. To improve the forming quality of the rod lattices and the consistency of repetitive 3D printing, we theoretically analyzed the causes of the defects and the effects of the L-PBF parameters on the process defects of CoCrFeNiMn high-entropy alloy micro-rods. The forming quality of the micro-rods was evaluated and classified with control experiments, and the surface roughness was measured and analyzed. Randomly protruding metal particles on the surface were mainly caused by the diffusion of laser energy, the incomplete melting of some metal powders, and/or “balling” process-induced defects caused by laser remelting. The tensile mechanical properties of typical L-PBF-printed micro-rods with different geometric characteristics were compared and evaluated. The influence of the geometric characteristics of the defects on the mechanical properties is discussed. The mechanical properties of the L-PBF-printed rod lattices were evaluated by compression experiments. It was found that the properties of different rod lattices have a positive relationship with the relative density.
... Their research has offered a formulation required for the performance analysis of cellular structures, as well as the effect of varying strut cross-section on optimizing the overall strength of the structure using the shape factor. Many researchers have investigated the hollow-walled structures and their benefits [8][9][10][11][12], with Gibson and colleagues demonstrating that with decreased relative density, the hollow-walled lattice structures do not degrade mechanical properties. This has supplied the required direction and conceptual underpinning for furthering study in this sector. ...
Lattice structures are bio-inspired designs made up of repeated unit cells consisting of beams, surfaces, or plates that fit together in an ordered or stochastic fashion. These unit cells are configured according to their size and shape in three dimensions. Simple lattices can be created using standard manufacturing techniques such as computer numerical control machining, welding, and casting. Additive manufacturing enables customers to make complex structures with small features at a reasonable cost. In the present work, using octagon, hexagrid, and rhombic dodecahedron lattice topologies, characterized by unit cell size from 3 × 3 × 3 to 7 × 7 × 7 mm and strut thickness from 0.5 to 1.5 mm, the structural behavior of a solid cylindrical model made of polylactic acid material under compression is analyzed. Finite element analysis (FEA) through Autodesk® Netfabb® solvers was used to assess lattice structure mechanical and structural properties. The results were validated by physical compression testing on additively manufactured samples. Cellular designs with 3 × 3 × 3 mm unit cells and 1.5 mm strut thickness displayed the lowest Von Mises stress and deformation. For different topologies, lowest results were rhombic dodecahedron (stress through FEA as 61.3108 MPa and stress through physical test as 61.05 MPa, deformation through FEA as 0.49921 mm and deformation through physical test as 0.48 mm), octagon (stress through FEA as 77.4147 MPa and stress through physical test as 76.92 MPa, deformation through FEA as 0.53316 mm and deformation through physical test as 0.51 mm), and for hexagrid (stress through FEA as 62.2911 MPa, stress through physical test as 62.15 MPa, deformation through FEA as 0.81997 mm and deformation through physical test as 0.81 mm). The percentage error between the stress through FEA and stress through physical test for octagon, hexagrid, and rhombic dodecahedron lattice topology was found out to be 0.63, 0.22, and 0.43%, respectively. Corresponding percentage deformation error between deformation through FEA and deformation through physical test was also found out to be 4.343, 2.435, and 3.848%, respectively. In addition, the impacts of volume reduction, surface area of the lattice, and relative density were explored pertaining to the structural behavior of the lattice. As a result of the examination into mechanical qualities based on these criteria, rhombic dodecahedron lattice topology with 3 × 3 × 3 mm unit cell size and strut thickness of 1.5 mm was found to be a better choice than octagon and hexagrid lattice topologies for 3D printing components that were loaded under axially compressive loads.
... After the elastic limit, the 10Hf sample remains at a constant stress plateau where sequential local failures occur and the scaffold structure slowly collapses, which is typical of buckling-dominated behavior [37]. The difference in mechanical behavior between closed-cell and open-cell foams is reported in literature by Gibson [38]. The 10Hf sample behaves like an open-cell foam and shows a homogenous deformation until the plateau stress is reached, which is consistent with our microstructural observations. ...
... What is more, SMA foams have been attractive for potential applications in numerous engineering fields, e.g., sensors, actuators, dampers and biomedical devices, where appropriate porosity and pore size are crucial [30]. High-porosity SMA foams have various structural characteristics of pores/struts/nodes at different levels (e.g., macro-, meso-and microlevels), which can impart excellent properties, such as large and stable magnetic field-induced strain (Ni-Mn-Ga foams with 64-76% porosity can be used for millions of thermomechanical cycles) [31,32], damping capacity (NiT foams with 69% porosity) [33], superelasticity (Cu-Al-Mn foams with 66-81%) [34] and biocompatibility (NiTi foams with 30-90% porosity for long-term implantation) [35]. ...
Solid-state refrigeration based on elastocaloric materials (eCMs) requires reversibility and repeatability. However, the intrinsic intergranular brittleness of ferromagnetic shape memory alloys (FMSMAs) limits fatigue life and, thus, is the crucial bottleneck for its industrial applications. Significant cyclic stability of elastocaloric effects (eCE) via 53% porosity in Ni-Fe-Ga FMSMA has already been proven. Here, Ni-Fe-Ga foams (single-/hierarchical pores) with high porosity of 64% and 73% via tailoring the material’s architecture to optimize the eCE performances are studied. A completely reversible superelastic behavior at room temperature (297 K) is demonstrated in high porosity (64–73%) Ni-Fe-Ga foams with small stress hysteresis, which is greatly conducive to durable fatigue life. Consequentially, hierarchical pore foam with 64% porosity exhibits a maximum reversible ∆Tad of 2.0 K at much lower stress of 45 MPa with a large COPmat of 34. Moreover, it shows stable elastocaloric behavior (ΔTad = 2.0 K) over >300 superelastic cycles with no significant deterioration. The enhanced eCE cyclability can be attributed to the pore hierarchies, which remarkably reduce the grain boundary constraints and/or limit the propagation of cracks to induce multiple stress-induced martensitic transformations (MTs). Therefore, this work paves the way for designing durable fatigue life FMSMAs as promising eCMs by manipulating the material architectures.
... Aluminum foam is a lightweight material that floats on water and has excellent shock-absorbing, sound insulation, thermal insulation, and vibration damping properties [1][2][3]. Therefore, it is expected to be used for automotive and train parts for the shockabsorbing properties, construction materials for the sound and thermal insulation properties, and milling machines to improve the vibration-damping properties [4][5][6][7][8][9][10]. Aluminum foam has been attempted to be fabricated from various aluminum alloys, such as pure aluminum [11][12][13][14][15][16][17][18], Al-Cu aluminum alloy [19,20], Al-Si aluminum alloy [21][22][23][24][25], Al-Mg aluminum alloy [26][27][28][29], Al-Mg-Si aluminum alloy [23,[30][31][32][33][34], Al-Zn-Mg Aluminum alloy [19,35,36], etc., and various properties can be obtained by changing the base aluminum alloy. ...
Aluminum foam is a lightweight material and has excellent shock-absorbing properties. Various properties of aluminum foam can be obtained by changing the base aluminum alloy. Multi-layer aluminum foam can be fabricated by varying the alloy type of the base aluminum alloy, but with different foaming temperatures, within a single aluminum foam to achieve multiple properties. In this study, we attempted to fabricate a two-layer aluminum foam with the upper layer of a commercially pure aluminum A1050 foam and the lower layer of an Al-Si-Cu aluminum alloy ADC12 foam by using an optical heating device that can heat from both the upper and lower sides. Two types of heating methods were investigated. One is to directly stack the A1050 precursor coated with black toner on top of the ADC12 precursor and to foam it from the top and bottom by optical heating. The other is to place a wire mesh between the ADC12 precursor and the A1050 precursor and place the A1050 precursor on the wire mesh, thereby creating a space between the precursors, which is then foamed by optical heating from the top and bottom. It was shown that both precursors can be foamed and joined, and a two-layer A1050/ADC12 foam can be fabricated for both types of heating methods. In the method in which two precursors were stacked and foamed, even if the light intensity of the halogen lamps on the top and bottom were adjusted, heat conduction occurred between the stacked precursors, and the foaming of each precursor could not be controlled, resulting in tilting of the joining interface. In the method of foaming using a wire mesh with a gap between two precursors, it was found that by adjusting the light intensity, the two precursors can be foamed almost simultaneously and achieve similar pore structures. The joining interface can also be maintained horizontally.
... Foams are a type of cellular solid that have low density and excellent properties in terms of mechanics, thermodynamics, acoustics, and chemistry, which make them unique among natural and artificial materials (Ashby et al., 2000;Lefebvre et al., 2008). Metal foams are a subclass of foams that have special characteristics for absorbing energy, which can replace conventional materials in various applications (Gibson, 2000;Kiratisaevee and Cantwell, 2005). In recent years, there has been a lot of scientific and industrial interest in developing good methods for producing and characterizing metal foams, especially for energy absorption purposes (Banhart, 2001;Li et al., 2012). ...
This study examined the behavior and energy absorption of open-cell aluminum foam under different loading conditions. The foam was made by infiltration, a low-cost method that produced a uniform pore distribution. The foam was compressed using two machines with varying impact velocities and weights. The stress-strain and energy absorption curves of the foam were measured and analyzed. The results showed that the strain rate and the impact weight affected the compressive properties and energy absorption of the foam. The strain rate up to 264 s À1 with constant mass did not affect the plateau stress, which was the constant stress in the plastic region. However, at 264 s À1 , increasing the impact weight increased the plateau stress and the energy absorption of the foam, which showed that the strain rate sensitivity depended on the impact inertia. The study revealed the dynamic characteristics of open-cell aluminum foam made by infiltration and provided insights for its use in impact protection. The study also showed that infiltration was a reliable and consistent method for making open-cell aluminum foam. The study highlighted the important roles of plateau stress and hardening effect in influencing the energy absorption of the foam under dynamic loading. The study suggested that future studies should consider the impact inertia as a parameter that affects the strain rate sensitivity of the foam.
... Porous metals (or metallic "foams") are often described by a stress-strain curve comprised of a small elastic region followed by a protracted plateau in the stress during pore collapse and compaction, which then culminates in a steep rise in the stress once the material reaches full density [40,41]. This "typical" stress-strain curve is most accurate in low-density, open-cell metals. ...
Powder metallurgy (PM) processes for porous copper and alloys have seen some commercial successes, but PM methods have the disadvantage of relatively low porosity or strength that is compromised by stress-concentrating interparticle bonds. To increase porosity without compromising scalability, a Cu-CuO metal matrix composite powder was utilized to produce additional microscale porosity within the particles by oxide reduction. These Cu-CuO powders were pressed at 1, 2, or 3 GPa, and made porous at 600, 800, or 1000 °C to investigate the effects of pressing and sintering parameters on the overall strength and density. It was found that the formation of porosity is weakly dependent on compaction pressure (maximum 6% difference from 1 GPa to 3 GPa), while the final porosity varied by ~16% overall (~40% for 1 GPa and 600 °C to 24% for 3 GPa and 1000 °C). The strength of the porous Cu was highest after being reduced at 600 °C but also exhibited some flaking at the edges at high strain. The 1 GPa, 600 °C samples have a higher specific strength than wrought Cu annealed at the same temperature, as was demonstrated under uniaxial quasi-static compression as well as split Hopkinson pressure bar impact.
... High-performance metal foam (MF) materials have drawn much interest because of their excellent properties, including lightweight, highstrength, high-energy absorption, and robust sound dampening. Recently, energy efficiency has encouraged the development and use of new lightweight materials in transportation [1][2][3][4][5]. Among the lightweight materials, MFs with high porosity exhibit unique mechanical characteristics, for instance, a high ratio of strength to weight. ...
Closed-cell aluminum foam (CCAF) is mainly employed as a load-bearing and energy-absorbing structural material due to its superior mechanical properties. However, besides the effect of microstructural and material parameters, the influence of strain rate (SR) and relative density (RD) on metallic foams (MF) on their mechanical behaviors is not fully understood. In this study, micro-computed tomography (micro-CT) imaging and finite element (FE) analysis were used to investigate the static and dynamic yield strength, energy absorption, and the effect of SR and RD on CCAFs. Micro-CT imaging was used to visualize the foam microstructure and measure its overall cell wall thickness and other structural parameters, which were then incorporated into the FE model. The results of the FE simulations were compared to experimental data to validate the constitutive relation. The findings of this study provide new insights into the mechanical behaviors of CCAFs and can be used to optimize its design and structural applications.
... [19][20][21][22] Metal foam, a type of porous metal material with inherent filtering properties, serves as an ideal carrier for the external electric field and can be reused after cleaning, making it an excellent pollutant collector within the plasma air purification system. 23,24 Therefore, the integration of low-temperature plasma technology and metal foam materials in this new air purification system allows for effective prevention of the spread of pathogenic microorganisms via aerosols while controlling costs. ...
Pathogenic microbial aerosols (PMA), the typical environmental pollutants, are among the major threats to human health. Here, we developed a new plasma air purification system (PAPS) that simultaneously filters PMA and kills micro-organisms within. The large area needle corona discharge array was developed to fully cover the airflow channel. The proprietary modular design allows the easy cleaning and reuse of the PAPS components for long-term, low-cost operation. Artificial neural network was integrated with genetic algorithm to optimize the working parameters of PAPS. The numerical model was developed to study the purification mechanism of the PAPS and verify its key working parameters. Experiments designed under optimal working parameters proved that PAPS can effectively intercept and inactivate bacteria in PMAs.
... Due to their porosity, they exhibit enhanced stiffness and toughness-toweight ratios under quasi-static and dynamic loadings compared to non-porous materials [1][2][3][4][5][6][7]. They serve as excellent shielding materi-als, armors, and mechanical dampers [8,9]; porous-based damping composites [10]; and radiation-tolerant materials [11]. However, on the atomistic scale, bi-continuous metallic nanofoams have received comparatively little attention. ...
Compared to their non-porous counterparts, metallic foams are known to exhibit improved functionality (e.g., damping capacity) when subjected to high-speed impact loading. Here, we report the results of a molecular dynamics study of bicontinuous nanoporous gold (NPG) subjected to impact loading. Additionally, we investigate the effects of a heterogeneous impact zone on the fate of a witness specimen initially protected by an NPG target. A cube-shaped flyer object (L_0= 408.6 Å) composed of full-density f.c.c. gold (FDG) strikes with impact speed U_flyer= 1.0 km s-1 an initially stationary equal-sized NPG target, which subsequently transmits a dispersed shock wave into a protected FDG witness specimen located at the downstream end of the target. The NPG target is stochastic, with porosity ϕ= 0.5 and mean ligament diameter D ̅_L= 64 ± 6 Å. A corresponding simulation for an FDG target serves as a baseline case. As anticipated, the sharp, planar shock imparted by the FDG flyer rapidly becomes highly curved and broadened along the shock direction in the NPG target. Intense plastic and convective flows (ejecta and jetting) lead to spatially heterogeneous mass flow and energy localization, which persist across the entire length of the NPG target studied. Whereas the shock transmitted by the FDG target leaves the witness specimen intact and essentially undamaged, the heterogeneous stress and flow fields imparted by the NPG target results in destruction of the witness. Independent simulations for the same cube-shaped NPG target shocked on the three statistically equivalent {100} target faces reveal modest run-to-run variability in the target and witness responses. The difference in the effects of the NPG and FDG targets on the witness response motivates additional study of the failure evolution inside the witness. It appears from the preliminary results that the porous-nonporous interface might induce a failure pattern that, in some aspects, resembles failure waves observed in brittle solids.
... Historically, many studies have focused on metallic foams which have very good mechanical properties [22,23]. But in the last three decades the use of polymeric foams has increased significantly due to the improved strength of the materials coupled with their intrinsic low density. ...
... The engineering literature on porous structures such as metal foams, Gibson (2000), Gibson and Ashby (1982), Roberts and Garboczi (2001), aerogels, Chandrasekaran et al. (2017), Leventis et al. (2002) or bones, Rice et al. (1988), often introduces the concept of ''density dependent Young modulus''. For example, the Young modulus E is being considered in the power-law form ...
The experimental as well as theoretical engineering literature on porous structures such as metal foams, aerogels or bones often relies on the standard linearised elasticity theory, and, simultaneously, it frequently introduces the concept of “density dependent Young modulus”. We interpret the concept of “density dependent Young modulus” literally, that is we consider the linearised elasticity theory with the generalised Young modulus being a function of the current density, and we briefly summarise the existing literature on theoretical justification of such models. Subsequently we numerically study the response of elastic materials with the “density dependent Young modulus” in several complex geometrical settings.
In particular, we study the extension of a right circular cylinder, the deflection of a thin plate, the bending of a beam, and the compression of a cube subject to a surface load, and we quantify the impact of the density dependent Young modulus on the mechanical response in the given setting. In some geometrical settings the impact is almost nonexisting—the results based on the classical theory with the constant Young modulus are nearly identical to the results obtained for the density dependent Young modulus. However, in some cases such as the deflection of a thin plate, the results obtained with constant/density dependent Young modulus differ considerably despite the fact that in both cases the infinitesimal strain condition is well satisfied.
... However, metal foam has gained more attention in various engineering applications, such as lightweight construction sandwich panels, energy absorbers, and heat sinks. Also, it has strength similar to that of wood and can be freely deformed [18]. Furthermore, the plastic Poisson ratio of the metal foam is approximately zero [19,20], which means that when a local force is applied to the metal foam, the region where the force is applied only deforms. ...
The incremental sheet metal forming (ISF) process has the flexibility to manufacture components without a specific die-set. In detail, a small incremental deformation by the forming tool movement is accumulated to form a target geometry. However, the formed part's geometrical accuracy is often observed to be lower due to no external die support. This research work is aimed to replace the commonly used dies with a nickel-metal foam that acts as flexible die support in the ISF process for improving the geometrical accuracy. The pure nickel metal foam was employed with various densities such as 20, 50, and 80 pores per inch (PPI) to identify the proper flexible support configuration. The current research work is summarized in three fields: (i) at first, the indentation tests were conducted to investigate the material deformation characteristics of the nickel-metal foam. The numerical results revealed that the high-density nickel-metal foam showed good geometric accuracy compared to other configurations. (ii) according to the indentation results, the ISF experiments were carried out with a nickel-metal foam, and the shape error was estimated for the formed parts. The findings showed that the shape accuracy was improved with the use of flexible die support compared to the conventional ISF process, and (iii) to save material costs, the nickel-metal foam was reused for manufacturing new parts and confirmed the reusability. Thus, the results show that employing proper density compressed nickel-metal foam influences geometric accuracy positively and can be devised for manufacturing complex geometries in the ISF process.
... Metallic foams have found a wide variety of engineering applications due to the attractive combination of merits, such as lightweight, high specific strength, excellent capability for impact energy absorption, and outstanding insulation performance to sound and heat [1,2]. To meet the need for service performance and manufacturing cost, optimal design of metallic foams is one of the key issues, which requires a deep understanding of the relation between the internal structure and overall mechanical response. ...
3D image-based finite element (FE) modelling provides the feasibility to explore how the subtle structural features inside metallic foams affect their complex deformation and mechanical responses. But the modelling currently includes frequent manual modifications, which makes it a time and labor consuming task. The quality of generated model depends heavily on experienced creator. This paper demonstrates an automatic procedure to extract structure information from 3D images and generate reliable geometric models for meshing. With self-adaptive algorithms that fit local features of grayscale distribution and internal structure, high-fidelity FE models can be established efficiently without interference from subjective judgments. The generated FE models well reproduce the stress-strain relation and inhomogeneous deformation of aluminium foams, compared with experimental results. Using the simulation with a high-fidelity FE model as “ground truth”, the accuracy of digital volume correlation (DVC) in the deformation measurement of complex cellular materials is for the first time evaluated quantitatively and precisely, based on the definition of an equivalent displacement vector bridging the results obtained by FE simulation and by DVC.
Estimating the mechanical properties of metal foams is becoming important in developing new materials and advancing new manufacturing processes. Among various mechanical properties, effective Young’s modulus as one of the key properties may be evaluated through several measurement methods, but because of some limitations, merely a few techniques can be used in each application. Metal foam as a novel conventional material is one of the significant materials with limited methods for effective Young’s modulus measurement. Recently, several empirical relationships have been developed between effective Young’s modulus and metal foam’s porosity to estimate its elasticity based on the material’s relative density. The present study uses the finite element method to examine a cuboid-shaped sample with various porosities to develop a better model for the relationship between resonance frequencies and elasticity. In addition to the relationship between elasticity and porosity, an empirical correlation between resonance frequencies and elasticity is proposed. The results of this research allow the researchers to estimate the porosity and effective Young’s modulus of metal foams based on the resonance frequencies.
Fabricating porous active metals through chemical dealloying poses challenges due to their reactivity and vulnerability to oxidation in aqueous solutions. The objective of this study was to create micron-sized porous Ti alloy by utilizing the Ti–Mo system as a precursor alloy for chemical dealloying. The impact of phase composition and initial microstructure of the precursor alloys (Tix at% Mo100 − x at%, x = 60 ~ 70) on the morphology of the resulting porous Ti alloy was systematically investigated. To improve the mechanical strength and minimize oxidized phases during the dealloying process, a molten salt electrolysis (MSE) method was employed. The strengthening mechanism of MSE on porous Ti alloys encompassed three key aspects. Firstly, it effectively reduced the presence of oxidized phases, thereby eliminating surface defects. Secondly, MSE facilitated grain growth and eliminated voids and cracks at the grain boundaries, leading to enhanced mechanical properties. Thirdly, the involvement of a secondary phase contributed to the overall strengthening mechanism. Following MSE treatment, the oxygen content in the porous Ti alloy decreased from over 13 to 5 at%, and needle-like nanocrystalline β-Ti precipitates formed within the ligament structure. The accumulation and aggregation of compression-induced dislocations at the grain boundaries of the precipitated phase further improved the mechanical properties. In summary, this work presents an innovative approach to fabricating porous Ti alloy with low oxygen content, high strength, and adjustable microstructure. It elucidates the strength enhancement mechanism by MSE, providing insights for future materials development and applications.Graphic abstract
Collapse mechanisms of sandwich panels with Miura-ori cores are analysed and classification of the deformation regimes under three-point bending is proposed. It is revealed that the homogenisation approach to the core material properties is not applicable to the deformation of panels with relatively strong origami cores due to the immediate simultaneous local deformations of the core and face sheets. To describe this deformation regime, an analytical model based on the development of new stationary hinge lines in Miura-ori cells and rigid motion rotation of the adjacent planes is proposed. The model pertains to a single degree-of-freedom model governed by the global bending angle of the panel. On the other hand, the homogenisation approach to the core material properties proved to be applicable to bending analysis of panels with relatively soft Miura-ori cores. This approach is used to analytically obtain the collapse load related to several deformation modes. Parametric FE analysis is conducted to further explore the deformation regimes of panels with different face sheet thicknesses.
Experiments were conducted to validate the finite element studies and analytical models. A good agreement between the analytically predicted collapse forces and those obtained by the FE simulations is shown. Deformation mode maps are constructed based on the analytical and FE analyses in terms of the face sheet thicknesses and core strength.
A brief comparison between the bending strength of sandwich panels with Miura-ori cores and panels with PVC and honeycomb cores is presented, demonstrating the superiority of the honeycomb cores loaded in the out-of-plane direction. On the other hand, the possibility of the development of high shear strains in metallic Miura-ori cores without damage gives them advantages compared to three-point bending of panels with low density PVC foam cores.
Aluminium honeycomb structure has been recognized as an exceptional lightweight energy absorber in transportation, construction and aerospace industries. An innovative fabrication method based on friction stir welding is proposed to enhance the crashworthiness property of aluminium honeycomb and address the challenges with conventional fabrication methods. Moreover, a lab-scale fixture is designed to demonstrate the feasibility of the suggested method for industrial use. Various fabricated honeycombs with different core heights and cell counts are subjected to quasi-static flatwise compression tests to investigate their crushing characteristics. The crashworthiness parameters like yield stress, average plateau stress, specific energy absorption are analysed and compared with theoretically predicted crushing strength. The failure mode of the structure is also discussed, showing the influence of non-optimal welding parameters. Experimental results indicate that average crush force and specific energy absorption do not differ significantly with cell count and core height. The specimens under flatwise compression fold with plastic hinges symmetrically positioned without any rupture of the weld. Specific compression property of the fabricated honeycomb has been compared with other aluminium honeycombs fabricated using other methods, which favours the friction stir welded honeycomb over the other conventional counterparts.
As multifunctional porous nanostructured materials (e.g., thermally/acoustically insulating), aerogels are derived from their vast porosity and their high specific surface area and may also hold exceptional specific mechanical properties under certain conditions as well. In this chapter, the mechanical characteristics of aerogels are discussed in detail. First, the mechanical characterization of traditional aerogels is summarized, and then, the mechanical behavior of polymer crosslinked silica and vanadia (X-aerogels), as well as organic aerogels, is presented. Finally, the acoustic attenuation property is briefly discussed for polyurea aerogel. In polymer crosslinked aerogels, a few-nanometer-thick conformal polymer is coating on secondary particles, while the pores is not clogging, which thus preserves the multifunctionality of the native framework and improves the mechanical strength. The mechanical properties were characterized under both quasi-static loading conditions (dynamic mechanical analysis, compression, and flexural bending testing) and high-strain-rate loading conditions using a split Hopkinson pressure bar. We evaluated the effects of strain rate, mass density, loading–unloading, moisture concentration, and low temperature on the mechanical properties of aerogels. Digital image correlation was used to analyze the surface strains through ultrahigh-speed images for calculation of properties such as dynamic Poisson’s ratio. A remarkable result is that crosslinked vanadia aerogels remain ductile even at −180 °C, indicating a property derived from interlocking and sintering-like fusion of skeletal nanoworms during compression. Due to the substantial improvement in the mechanical properties of X-aerogels with a small amount of polymeric crosslinking agent, purely polymeric aerogels with similar X-aerogel nanostructures were investigated. Therefore, in this chapter, the mechanical properties of organic aerogels including polyurea and polyurethane aerogels were also studied. Furthermore, a special attention has been carried out on the acoustic attenuation of polyurea aerogels by means of normal incidence sound transmission loss measurements. Polyurea aerogels showed unprecedented high sound transmission losses over a broad range of frequencies, a trend that clearly breaks the empirical “Mass Law” nature of the conventional acoustic materials.
Nanostructured metal foams, unlike the analogous inorganic aerogels, have a backbone that is constructed with zerovalent metal materials – instead of oxidized metal or semimetal. This chapter assesses the small but emerging field of using combustion synthesis to obtain zerovalent metal foams. We discuss how combustion synthesis employing metal complexes with energetic ligands, primarily bistetrazolamine (BTA), provides a flexible platform for preparing nanostructured, nanoporous metal foams for numerous metals and alloys. This technique, discovered in the ca. 2003, was one of the first techniques to access a wide variety of nanostructured metal foams, with some of the lowest densities and highest surface areas yet obtained for metallic materials.
Rationally engineered porous structures enable lightweight broadband electromagnetic (EM) wave absorbers for countering radar signals or mitigating EM interference between multiple components. However, the scalability of such structures has been hindered by their limited mechanical properties resulting from low density. Herein, an additively manufactured Kelvin foam‐based EM wave absorber (KF‐EMA) is reported that exhibits multifunctionality, namely EM wave absorption and light‐weighted load‐bearing structures with constant relative stiffness made possible using bending‐dominated lattice structures. Based on tuning design parameters, such as the backbone structures and constituent materials, the proposed KF‐EMA features a multilayered 3D‐printed design with geometrically optimized KF structures made of carbon black‐based backbone composites. The developed KF‐EMA demonstrated an absorbance greater than 90% at frequencies ranging from 5.8 to 18 GHz (average EM wave absorption rates of 95.89% and maximum of 99.1% at 15.8 GHz), while the low‐density structures of the absorber (≈200 kg m⁻³) still maintained a compression index between the stiffness and relative density (n = 2) under compression. The design strategy paves the way for using metamaterials as mechanically reinforced EM wave absorbers that enable multifunctionality by optimizing unit‐cell parameters through a single and low‐density structure.
In the course of service, integral-forming aluminum foam sandwich (IFAFS) needed to bear three-point bending loads in different directions, however, its deformation mechanism and failure modes were still unclear. In this work, three-point bending performances of IFAFS under flatwise and edgewise bending conditions were investigated by experiment, in-situ micro X-ray tomography and digital volume correlation (DVC) calculation. The results showed that three-point bending performance was more stable under edgewise bending condition, and with the decrease of span length IFAFS presented three different failure modes of oblique core shear, asymmetric and symmetrical surface fracture. In addition, porosity mutation was a significant reason for crack initiation, and optimizing pore homogeneity was important to improve the performance and predictability of failure location. Different strengthening effect of sandwich structure anisotropy and different internal deformation evolutions caused by internal strain vortex were two main reasons which lead to performance difference of IFAFS with different solid panel directions. Connection of pre-existing micropores with dimple-like micropores generated during deformation process leads to the failure of IFAFS. The key factors to further optimize three-point bending performance and predictability of IFAFS was to homogenize the pore distribution of IFAFS.
We report that hardness-to-strength ratio is not correlated with plastic Poisson's ratio in nanoporous gold, arguing against the Shaw–Sata relation. Instead, the hardness-to-strength ratio of nanoporous gold increases consistently with increasing rate of strain hardening. Furthermore, in samples with near-zero hardening in compression, the hardness-to-strength ratio does not deviate much from 1.0 when the plastic Poisson's ratio increases up to 0.27, echoing Miller's simulation. Current study suggests that the hardness-to-strength ratio is not a restraint factor, but an indicator of the strain hardening rate for nanoporous gold, which might apply to other porous materials with low-to-medium relative densities.
An analysis is performed in this research to obtain the natural frequencies and mode shapes of a thick sandwich beam with metal foam core. Different types of foams are considered for the sandwich beam where distribution of pores is a functionally graded patterns. The governing equations of the sandwich beam are established by means of a shear and normal deformable thick beam model. This theory considers the thickness stretching and admits the nonuniform through-the-thickness shear strain. The governing equations of the sandwich beam are established which are four in number by means of the Hamilton principle. The established equations are solved for the case of thick sandwich beams resting on elastic foundation via the Navier solution method. Results of this study are first compared with the available data in the open literature and after that novel results are given to explore the effects of different parameters on the vibration characteristics of the sandwich beam. It is shown that porosity of the core is an important factor on vibration characteristics of sandwich beam with metal foam core.
Polyurethane foam materials have broad application prospects in practical engineering as flame retardants, waterproof coatings, and grout repair materials due to advantages such as light weight, quick forming, and good durability. Due to water’s low cost and convenience, water-reactive Polyurethane foam materials are widely used in engineering. The content of the water has a significant effect on the performance of polyurethane foams after molding. Polyurethane foams with anti-seepage and reinforcement effects are used in complex water environments for long durations. This study analyzed the effects of water content on properties and the diffusion mechanism of polyurethane foam materials in water. Additionally, the effect of the water environment on the polyurethane grouting material’s properties was summarized. Finally, this study discussed the future research directions of polyurethane foam materials in a water environment.
Experimental studies show that shape memory alloys exhibit pressure-dependent deformation in the presence of porosity. In this context, a macro-scale phenomenological model is proposed for the mechanical behavior of porous SMAs using a poromechanics approach. The new phenomenological model considers the porous medium as a skeleton consisting of a solid matrix and connected porous space. The new model is built starting from a model for dense SMAs in which the porosity is included as an internal state variable. Both the pseudoelastic and plastic deformations of the skeleton are considered. The model is implemented into Abaqus through a user defined material subroutine and is validated using experimental results from the literature. The numerical results obtained by unit-cell (UC) technique are also used. The uni-axial stress–strain response is captured in a great extent with significant reduction in terms of the numerical cost when compared to the UC approach. It is shown that the proposed model can be used to study the mechanical behavior of porous SMAs. The poromechanics approach allows tracking the overall deformation of the RVE, and the porosity simultaneously.
The metal foams behavior significantly depends on the method applied for its manufacturing. Present work investigates the mechanical quasistatic three-point and compressive deformation behavior of molded die-cast open-cell Aluminum Alloy foam (OCAF). Different span lengths and loading velocities were selected for the experimentation. The deformation behavior of the OCAF was studied and the effect was correlated with different theories available for foam deformation. The plastic behavior of OCAF was also studied using a compression loading–unloading experiment at different stress and strain values. Microstructural study and phase analysis were carried out at the cell wall surfaces using fractography to establish the cause of brittle failure dominant in the foam. Further, micro-CT analysis was used to study the cell deformation in the bulk material and the role of micropores and macro-pores.
Closed-cell aluminum foam is a lightweight cellular material that can sustain considerable deformation under approximately constant stress known as plateau stress. Aluminum foam is commonly used for mitigating the effect of dynamic loadings, such as impact, through its energy absorption capability. However, the plateau stress is relatively low and thus limits energy absorption while precluding its use in structural load-bearing applications. In this investigation, aluminum foam reinforced with graphene platelets was fabricated using the liquid metallurgy route to enhance the plateau stress and energy absorption. The high strain rate response of the reinforced foam has been investigated. Graphene concentrations in the range of 0.20 to 0.62 wt.% were used. The dynamic compressive behavior of Al foam reinforced with graphene was studied under high strain rate loading from 1000 to 2200 s−1 using the split Hopkinson Pressure Bar apparatus. Among the different graphene concentrations investigated, 0.62 wt.% graphene aluminum foam showed the maximum peak stress, plateau stress and energy absorption, while 0.4 wt.% graphene exhibited the minimum plateau stress and energy absorption under the various dynamic loading conditions studied. However, the graphene-added hybrid foam always exhibited higher plateau stress and energy absorption as compared to those without graphene. Graphene-reinforced aluminum foam is a viable lightweight material for energy absorption under dynamic loading conditions. The reinforced aluminum foam displays a threefold enhancement in plateau stress and energy absorption as compared to unreinforced foam.
Topological motifs in pore architecture can profoundly influence the structural properties of that architecture, such as its mass, porosity, modulus, strength, and surface permeability. Taking the irregular cellular structure of the tri-spine horseshoe crab as a research model, we present a new approach to the quantitative description and analysis of structure–property–function relationships. We employ a robust skeletonization method to construct a curve-skeleton that relies on high-resolution 3D tomographic data. The topological motifs and mechanical properties of the long-range cellular structure were investigated using the Grasshopper plugin and uniaxial compression test to identify the variation gradient. Finite element analysis was conducted for the sub-volumes to obtain the variation in effective modulus along the three principal directions. The results show that the branch length and node distribution density varied from the tip to the base of the sharp corner. These node types formed a low-connectivity network, in which the node types 3-N and 4-N tended to follow the motifs of ideal planar triangle and tetrahedral configurations, respectively, with the highest proportion of inter-branch angles in the angle ranges of 115–120° and 105–110°. In addition, mapping the mechanical gradients to topological properties indicated that narrower profiles with a given branch length gradient, preferred branch orientation, and network connectedness degree are the main factors that affect the mechanical properties. These factors suggest significant potential for designing a controllable, irregularly cellular structure in terms of both morphology and function.
The mechanisms of compressive deformation that occur in both closed and open cell Al alloys have been established. This has been achieved by using X-ray computed tomography (CT) and surface strain mapping to determine the deformation modes and the cell morphologies that control the onset of yielding. The deformation is found to localize in narrow bands having widths of order of a cell diameter. Outside the bands, the material remains elastic. The cells within the bands that experience large permanent strains are primarily elliptical. A group of cells work collectively to allow large localized deformation. Size does not appear to be the initiator of the deformation bands. Equiaxed cells remain elastic. The implications for manufacturing materials with superior mechanical properties are discussed.
The behaviour of cellular materials under multiaxial loads was modelled in the previous companion paper. Here we present data for the failure of foams by elastic buckling and plastic yielding and compare them to the results of the models. The models describe the main features of the multiaxial behaviour of foams well.
The compressive flow behavior of Al, Al−7 pct Mg and 7075 Al alloy foams has been determined in structures whose void fraction
varies from 0.80 to 0.95 of the total volume. In all cases, a greater than linear increase in flow strength with increase
in density was exhibited, indicating that bending stresses within the foam structure are an important feature of the collapse
mode. The flow strength did not follow proportionately changes in bulk flow strength in comparisons of either alloy or of
heat-treatment conditions. Ancillary tensile and metallographic observations show that this lack of correlation arises because
the different foams collapse by different modes with localized fracture becoming dominant in the higher strength 7075 alloy.
The energy absorbing efficiency was found to be independent of foam density for all the materials. However, the efficiency
was found to be a strong function of the alloy and heat treatment increasing from about 30 pct in Al, to 43 pct in Al−7 pct
Mg and to 50 pct in the solution heat treated and aged 7075 alloy. The increase in efficiency occurs because of an increase
in the propensity to fracture in the higher strength alloys which introduces the potential for a propagating constant-stress
collapse process.
The evolution of plastic deformation in a cellular Al alloy upon axial compression is monitored through a digital image correlation procedure. Three stages in the deformation response have been identified. The first involves localized plastic straining at cell nodes. It occurs uniformly and leads to a nominal loading modulus appreciably lower than the stiffness. The second comprises discrete bands of concentrated strain containing cell membranes that experience plastic buckling, elastically constrained by surrounding cells. In this phase, as the loading increases, previously formed bands harden, giving rise to new bands in neighboring regions. The localized bands exhibit a long-range correlation with neighboring bands separated by 3–4 cells along the loading direction. This length scale characterizes the continuum limit. Thirdly, coincident with a stress peak, σo, one of the bands exhibits complete plastic collapse. As the strain increases, this process repeats, subject to small stress oscillations around σo.
Materials with a cellular structure are increasingly used in engineering. Proper design requires an understanding of the response of the materials to stress; and, in real engineering design, the stress state is often a complex one. In this paper we model the elastic buckling, plastic yield and brittle fracture of cellular solids under multiaxial stresses to develop equations describing their failure surfaces. The models are compared to data in the following, companion, paper.
The possibilities for making metallic foams or similar porous metal structures are reviewed. The various processes are classified according to the state of the starting metal - liquid, powdered, ionised. Liquid metal can be foamed directly by injecting gas, gas-releasing foaming agents or by producing supersaturated metal-gas solutions. Indirect methods include investment casting and usage of filler materials. Metal powders can also be used as starting materials for metallic foams; mixtures of such powders with foaming agents are compacted to foamable precursor materials that can be foamed in a second step. Instead of foaming agents inert gas can be directly entrapped in the precursor. Metal foams can also be made from metal powder slurries or by using polymer/powder mixtures. Finally, galvanic electro-deposition also allows to make highly porous metallic structures with open pores.
The deformation behaviour of a series of aluminium and zinc foams was investigated by uniaxial testing. Because the deformation behaviour of metal foams is expected to be anisotropic owing to the existence of a closed outer skin and with respect to the foaming direction, a series of measurements was carried out where the orientation of the outer skin and the foaming direction were varied. Stress-strain diagrams and corresponding compression strengths were determined for aluminium-and zinc-based foams. The influence of an age-hardening heat treatment was investigated. Finally, the axial deformation behaviour of aluminium tubes filled with aluminium foam was tested under uniaxial loading conditions. The results of the measurements are discussed in the context of (C) 1998 Chapman & Hall.
Geometrical shapes of interstices of two types of closest packing of uniform spheres, 1) hexagonal closest packing, 2) face centered cubic closest packing are studied, and the structures of interstices of these two types of packing are used to represent those of the actual foamed elastomers.
Equivalent elastic constants for these two structures are calculated in terms of the slenderness of a thread (which is a function of voids content) l'/A where l is the length of a thread and A its cross-sectional area, and of the elastic constants of the interstices. The calculated value of Poisson's ratio of a model containing 67 percent of the interstices of hexagonal closest packing and 33 percent those of face centered cubic packing corre lates fairly well with existing experimental data.
The elastic constants of an open-cell foam model, having tetrakaidecahedral cells on a BCC lattice, were found. The Young's modulus, shear modulus and Poisson's ratio were derived, as functions of the edge cross section and the foam density, by considering the bending, twisting and extension of the cell edges. If edge bending were the only mechanism the moduli would vary with the square of the foam density. The other deformation mechanisms are predicted to reduce the power law exponent by 3–5%, and the effect of edge torsion on the modulus level is small. The foam bulk modulus is predicted to vary linearly with its relative density, so Poisson's ratio approaches 0.5 at low densities. The lattice model is elastically isotropic, whereas other lattice models of foams are highly anisotropic.
The high strain compression of open-cell foams is analysed, using a lattice model with tetrakaidecahedral cells. The buckling of elastic cell edges, under combined bending and torsional loads, is analysed, and the deformed shapes predicted. The stress-strain relation and Poisson's ratio are predicted for strains up to 70%, for compression in the [001] and [111] directions of the BCC lattice. The prediction for [111] compression is closest to experimental stress-strain curves for polyurethane foams, especially when the cell shape anisotropy is taken into account. A plateau in the compressive stress-strain curve is not predicted, whereas one is observed for compression along the foam rise direction. Reasons for this are discussed; there is a small contribution from the polymer non-linearity, but irregular cell structures need to be analysed. The deformation, both of individual cells and of the PU foam, is compared with the theory.
A compressed closed-cell polymer foam was modelled using a BBC lattice model of tetrakaidecahedral cells, loaded in the [001] direction. The contributions of cell face tensions and edge bending were analysed, assuming that the faces act as membranes, for a linearly-elastic, or a yielding material. The moduli and tensile yield stresses of highly oriented polymer films were measured to provide data for modelling, and the amount of polymer in the foam cell faces found to be high. Tensile face strains are predicted to reach 40% of the foam compressive strain. The predicted Youngs moduli are slightly low, because compressive face stresses are ignored, but Poissons ratio is correctly predicted. The compressive foam yield stress is predicted to depend on tensile yielding of the cell faces. Predicted values are close to experimental values for polyethylene foams, but half those of polystyrene extruded foams. The latter foam may collapse in compression when face yielding commences, rather than by the collapse mechanism of the model.
The mechanical properties (the moduli and collapse strengths) of three-dimensional cellular solids or foams are related to the properties of the cell wall, and to the cell geometry. The results of the analyses give a good description of a large body of data for polymeric foams.
Foamed aluminum is a promising candidate in hydroacoustics as a possible pressure-release material. Previously, the measurement of its dynamic shear modulus has been reported for various densities and pore sizes of the material, [Proc. IEEE, 1985 Ultrasonics Symp. 2, 1052-1055 (1985)]. In an attempt to complete the characterization of the material, its Young's modulus and Poisson's ratio were measured by means of laser Doppler vibrometry. The lowest value for the ρc product found was 0.20 SI Mrayl, about 15% of the ρc product of water. Some of the samples appear to be anisotropic. An attempt was made to measure the five compliance coefficients of one foamed- aluminum type that follow from assuming uniaxial symmetry. The results did not conform to the relationships pertinent to this type of symmetry.
The measured mechanical properties of conventional lightweight metallic foams fall far short of those predicted by idealized models for closed cell foams. Their poor mechanical performance can be attributed, to a large extent, to curved and corrugated cell faces present within the foams. Idealized honeycombs and foams with idealized cell structure and curved or corrugated cell edges and faces are modeled using finite elements. The elastic modulus and plastic collapse stress of these honeycombs and foams are calculated relative to those of a comparable cellular material model with flat cell edges and faces. The results are presented in terms of the radius of curvature and the amplitude and frequency of the corrugation.
Mechanics analyses are used to derive the effective elastic moduli for low density materials. Both open cell and closed cell geometric models are employed in the case of isotropic media. The five independent effective moduli are derived for a low density transversely isotropic medium. Compressive strength, as defined by elastic stability, is also derived for open cell and closed cell isotropic materials. The theoretical results are compared with some experimental results, and also are assessed with respect to previous work.
Abstract—Honeycombs and foams, loaded at low temperatures (T < 0.3Tm), deform by the elastic deflec- tion, elastic buckling and plastic collapse of their cell walls. At more elevated temperatures, creep contrib- utes to the deformation, which becomes time-dependent. In this paper we develop expressions for the creep-bending of cell walls allowing the creep rate of honeycombs,and foams to be predicted from the cell- wall properties and relative density. The analysis follows the general approach,[1] of Gibson and Ashby (Cellular Solids, Structure and Properties. Cambridge University Press, Cambridge, 1997), extending it to time-dependent deformation. To assess the validity of the model, a set of creep experiments was carried out on an open-cell aluminum,foam. The analysis gives a good,description of the experimental,results. # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Creep; Foams; Aluminum
The tensile and compressive stress-strain behavior of closed cell aluminium alloy foams (trade name Alulight) has been measured and interpreted in terms of its microstructure. It is found that the foams are anisotropic, markedly inhomogeneous and have properties close to those expected of an open cell foam. The unloading modulus and the tensile and compressive yield strengths increase non-linearly with relative density. The deformation mechanisms were analyzed using image analysis software and a d.c. potential drop technique. The scatter in results is attributed to imperfections within the foam. These include non-uniform density, weak oxide interfaces, and cell faces containing voids and cracks.
A micromechanical analysis for the linear elastic behavior of a low-density foam with open cells is presented. The foam structure is based on the geometry of a Kelvin soap froth with flat faces: 14-sided polyhedral cells contain six squares and eight hexagons. Four struts meet at every joint in the perfectly ordered, spatially periodic, open-cell structure. All of the struts and joints have identical shape. Strut-level force-displacement relations are expressed by compliances for stretching, bending, and twisting. We consider arbitrary homogeneous deformations of the foam and present analytic results for the force, moment, and displacement at each strut midpoint and the rotation at each joint. The effective stress-strain relations for the foam, which has cubic symmetry, are represented by three elastic constants, a bulk modulus, and two shear moduli, that depend on the strut compliances. When these compliances are evaluated for specific strut geometries, the shear moduli are nearly equal and therefore the elastic response is nearly Isotropic. The variational results of Hashin and Shtrikman are used to calculate the effective Isotropic shear modulus of a polycrystal that contain grains of Kelvin foam.
In this study, mechanical properties of three types of polymeric foams (polypropylene (PP), polystyrene (PS), and polyurethane (PU) foams) are investigated. Focus has been placed on the strain rate and temperature effects on these foams under large deformations. Selected experimental results from uniaxial compression, hydrostatic compression, and simple shear tests are presented. A phenomenological hydrodynamic elastoplastic constitutive law is developed to model these polymeric foams. Numerical implementation and validation of the constitutive model are also described.
Low weight is required especially for those means of transport, in which material properties have to be evaluated with respect to their specific mass. The possibility of increasing the specific properties of recyclable light metals are described: reinforcements by ceramic particulates, by continuous ceramic or carbon fibres, or by the reduction of weight by foaming the metal. Examples of castings, extrusions and forgings of particulate reinforced (40 vol.%) of reinforcements can be produced by gas pressure infiltration of either particulate or fibre preforms. In the case of aluminium matrix, the specific strength can be increased by a factor of up to 15, and the specific stiffness by a factor of up to 7, whereas for carbon fibre reinforced magnesium the specific strength can be increased even more. The anisotropy of fibre reinforced metal matrix composites is discussed as well as the possibilities to use cross ply preforms. The technique of foaming aluminium alloys yields materials with a specific mass in the range of 0.3–1.0 g/cm3. Such structures with essentially closed pores exhibit higher specific stiffness for beams and membranes than massive metal. The measurement and definition of stiffness and strength values appropriate for aluminium foams are presented by referring to compression tests.
A theoretical model for the linear elastic properties of three-dimensional open-cell foams is developed. We consider a tetrahedral unit cell, which contains four identical half-struts that join at equal angles, to represent the essential microstructural features of a foam. The effective continuum stress is obtained for an individual tetrahedral element arbitrarily oriented with respect to the principal directions of strain. The effective elastic contants for a foam are determined under the assumption that all possible orientations of the unit cell are equally probable in a representative volume element. The elastic constants are expressed as functions of compliances for bending and stretching of a strut, whose cross section is permitted to vary with distance from the joint, so the effect of strut morphology on effective elastic properties can be determined. Strut bending is the primary distortional mechanism for low-density foams with tetrahedral microstructure.
The Low Density Core (LDC) process is a method for making metallic structures with solid surfaces covering a porous core. The development of the LDC process for making Ti-64 sheet based structures is described. Sheets ∼ 2000 × 1200 × 4 mm3 have been made with ∼ 40 vol. % core porosity levels, and several forming techniques have been demonstrated. The LDC billet breakdown and forming behavior was found to be similar to conventional Ti-64 processes, so LDC Ti-64 sheet has the advantage that it can be fabricated into structures using well-established methods.
This work contains theoretical discussions concerning the large amount of previously published experimental data related to gas eutectic transformations in metal-hydrogen systems. Theories of pore nucleation and growth in these gas-solid materials will be presented and related to observed morphologies and structures. This work is intended to be helpful to theorists that work with metal-hydrogen systems, and experimentalists engaged in manufacturing technology development of these ordered gas-solid structures.
Rigid plastic foams find application in construction mainly as core materials for loaded sandwich structures—in buildings, ground vehicles, and airplanes. This work provides an equation for the mechanical behavior of polyurethane foams as a function of foam density. Starting from a model conception and the qualitative microscopic consideration of the deformation and failure mechanism, simple relations are found for the tensile, compressive and shear strength and the elastic modulus, which sufficiently express the measured results.
A theoretical treatment is given which predicts the behavior of a foamed elastic material on the basis of a model consisting of a network of thin threads. Two cases are considered: (1) small strains, and (2) finite compressions, when the major part of the deformation of the threads is attributed to buckling. The behavior is given in terms of Young's modulus of the matrix and the density of the foam. Measurements of the load-deformation relations for small tensile strains and finite compressions are described for natural rubber foams prepared from latex. A wide range of density is covered (0.09–0.57), giving a variation of compression hardness of about 100:1. Satisfactory agreement with theory is found for both the cases considered, indicating that the basic concepts of the structure and mode of deformation are correct.
The cyclic compression of a cellular Al alloy has been evaluated. Plastic compression occurs beyond a critical number of cycles, N T . At N BN T the cumulative strains are negligible and the material has cyclic stability. At N \ N T , strain accumulates rapidly and preferentially within deformation bands, until the densification strain has been reached. The bands form preferentially from large cells in the ensemble. Such cells develop plastically buckled membranes which experience large strains upon further cycling, which lead to cracks. The cracks, once formed, result in rapid cyclic straining. This feature controls the fatigue life.
The compression properties of an aluminium foam containing a nonuniform density gradient have been examined. Specimens were taken from various locations within the foam slab, and were tested in two directions. Measured foam properties were compared to calculated values using models derived by Ashby and Gibson [1]. The effect of the density gradient on the compression properties and also the energy absorption characteristics of the foam was found to be significant.
Techniques for the preparation of metallic foams, including casting, powder metallurgy and metallic deposition, have been reviewed. Properties of metallic foams such as mechanical properties, energy absorbing characteristics, permeability, acoustical properties and conductivities are described. Finally, examples of the use of metallic foams in practice have been given to indicate the wide range of circumstances in which metallic foams are able to be utilized.
The yield behaviour of poly(methylmethacrylate) (PMMA) has been investigated in tension and compression over a range of testing temperatures and strain-rates. Both tensile and compressive yield stresses were found to increase monotonically with increasing strainrate and decreasing temperatures. Compressive yield stresses were in general found to be more dependent on strain-rate.
The results of this investigation have been correlated with previous published data for the dependence of the torsional yield stress of PMMA on hydrostatic pressure. This was done by a modification of a theory proposed by Robertson which uses the internal viscosity approach to yield in glassy polymers. The modified theory clearly explains the temperature and strain-rate dependence of the yield stress and provides a quantitative explanation of the differences in behaviour between tension and compression in terms of the dependence of yield on the hydrostatic component of the applied stress.
The tensile yield behaviour of isotropic amorphous poly(ethylene terephthalate) (PET) sheets has also been investigated over a wide range of temperatures and strain-rates. No torsion or compressive yield stresses are available because of the sheet form of the PET, but the results obtained in tension are shown to be fully consistent with the above theory, and with other published work.
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The compressive behavior of a rigid polyurethane foam reflects its geometric structure and the physical properties of the matrix polymer. Foam properties may be modified by the inclusion of silica particles in the polymer matrix. These silica particles alter the mechanical properties of the base polymer as well as the geometrical structure of the foam. The yield stress and the modulus of the foam decrease with the initial introduction of the silica filler after which the mechanical properties of the foam increase with increasing filler content. A model is presented expressing the foam yield stress and the modulus as a function of the polymer modulus and the cell parameters. These parameters are l, a cell edge length, and d, a characteristic strut thickness. This results in the expressions, E f =C<sup>″</sup>E p (d/l)<sup>4</sup> and σ y =‐E p (d/l)<sup>4</sup>. This model is applicable to either filled or unfilled foams and accommodates changes in the properties of the solid phase, through the use of E p , as well as changes induced in the cell geometry through the d/l relationship.
The mechanical response of composite foam AlSiC has been examined in compression and indentation. The foam has a closed cell structure and is made of aluminium matrix with SiC particles dispersed in it. The cell walls have a complex microstructure consisting of non-uniform distribution of particles, voids and cavities as well as micro-segregation and precipitates resulting from dendritic solidification. Consequently, the mechanical response is complex. In compression, deformation localizes in a band which extends outward with increasing strain. A similar response is observed in indentation, where localization takes place near the indenter and deformation proceeds radially outward. The mechanism of deformation in individual cell walls is identified to be a combination of processes, such as debonding at the particle/matrix interface, particle pull-out and microvoid coalescence in the ductile matrix. The growth of cracks in the cell membranes is associated with a wide damage zone, resulting in high specific energy absorption capacity.
Variational principles in the linear theory of elasticity, involving the elastic polarization tensor, have been applied to the derivation of upper and lower bounds for the effective elastic moduli of quasi-isotropic and quasi-homogeneous multiphase materials of arbitrary phase geometry. When the ratios between the different phase moduli are not too large the bounds derived are close enough to provide a good estimate for the effective moduli. Comparison of theoretical and experimental results for a two-phase alloy showed good agreement.
The stiffness of open and closed cell low density cellular solids, or solid foams, is affected by “imperfections” such as non-uniform cell size (multi-dispersity), non-uniform cell wall thickness, wavy distortions of cell walls, etc. Metal foams generally have lower relative stiffnesses than, for example, expanded PVC based polymer foams, and a comparison of the morphologies suggests that the main difference between these cellular solids is wavy distortions of the cell walls of the metal foams. The influence of wavy distortions on stiffness is modeled in this paper. The concepts are introduced through application to open cell materials, for which closed form solutions are obtained, primarily to illustrate the phenomenon. Closed cell materials are analysed subsequently, and results that are considered to be in good agreement with experimental observations are obtained.
Lightweight metallic cellular materials can be used in the construction of composite plates, shells and tubes with high structural efficiency. Previous models for the mechanical performance of cellular materials have focused on their dependence on relative density, cell geometry and the properties of the solid material of which the cell faces and edges are composed. In this study, we consider the effect of the distribution of solid between the cell faces and edges on mechanical properties using finite element analysis of idealized 2D (hexagonal honeycomb) and 3D (closed-cell tetrakaidecahedral foam) cellular materials. The effects of the distribution of the solid on the stiffness and strength of these materials are presented and discussed.
The effective elastic behavior of some models for low density cellular solids, or solid foams, are calculated using analytical and numerical techniques. The models are perfect in the sense that imperfections or irregularities as often encountered in real foams have been removed. We believe that the present models can serve as references to which more advanced models which include imperfections and irregularities can be compared. The work in this paper does not address buckling or yielding in cell walls, which play an increasingly important role as foam stresses increase.
The uniaxial compressive and tensile modulus and strength of several aluminum foams are compared with models for cellular solids. The open cell foam is well described by the model. The closed cell foams have moduli and strengths that fall well below the expected values. The reduced values are the result of defects in the cellular microstructure which cause bending rather than stretching of the cell walls. Measurement and modelling of the curvature and corrugations in the cell walls suggests that these two features account for most of the reduction in properties in closed cell foams.
The tension–tension and compression–compression cyclic properties are measured for an open cell “Duocel” foam of composition Al 6101–T6, and a closed cell “Alporas” foam of composition Al–5Ca–3Ti (wt%). The Duocel foam has a relatively uniform microstructure, and undergoes homogeneous straining in both monotonic and fatigue tests. In contrast, the Alporas foam is more irregular in microstructure, and exhibits crush-band formation at random locations under uniaxial compression; in compression–compression fatigue, a single crush band forms and broadens with additional fatigue cycles. Progressive shortening of the specimen in compression–compression fatigue, and progressive lengthening in tension–tension fatigue are due to a combination of low cycle fatigue failure and cyclic ratchetting. S–N fatigue curves are presented for the onset of progressive shortening in the compression tests, and material separation in the tension tests; it is envisaged that such curves will be of practical use in design.
The influence of each of the six different types of morphological imperfection—waviness, non-uniform cell wall thickness, cell-size variations, fractured cell walls, cell-wall misalignments, and missing cells—on the yielding of 2D cellular solids has been studied systematically for biaxial loading. Emphasis is placed on quantifying the knock-down effect of these defects on the hydrostatic yield strength and upon understanding the associated deformation mechanisms. The simulations in the present study indicate that the high hydrostatic strength, characteristic of ideal honeycombs, is reduced to a level comparable with the deviatoric strength by several types of defect. The common source of this large knock-down is a switch in deformation mode from cell wall stretching to cell wall bending under hydrostatic loading. Fractured cell edges produce the largest knock-down effect on the yield strength of 2D foams, followed in order by missing cells, wavy cell edges, cell edge misalignments, Γ Voronoi cells, δ Voronoi cells, and non-uniform wall thickness. A simple elliptical yield function with two adjustable material parameters successfully fits the numerically predicted yield surfaces for the imperfect 2D foams, and shows potential as a phenomenological constitutive law to guide the design of structural components made from metallic foams.
The results of creep tests on a closed-cell aluminum foam (Alporas) are reported. At low stresses and temperatures, the behavior is well described by existing models for foams. At high stresses and temperatures, the power law creep exponent increases from about 4 to 15 and the activation energy increases from about 100 to 450 kJ/mol. The increase in power law exponent may be related to damage; a finite element damage model of a two-dimensional honeycomb gives consistent results with the measured foam behavior.