Ashby Model Research Articles

Fabrication, pore structure and compressive behavior of anisotropic porous titanium for human trabecular bone implant applications

Porous titanium with average pore size of 100–650μm and porosity of 30–70% was fabricated by diffusion bonding of titanium meshes. Pore structure was characterized by Micro-CT scan and SEM. Compressive behavior of porous titanium in the out-of-plane direction was studied. The effect of porosity and pore size on the compressive properties was also discussed based on the deformation mode. The results reveal that the fabrication process can control the porosity precisely. The average pore size of porous titanium can be tailored by adjusting the pore size of titanium meshes. The fabricated porous titanium possesses an anisotropic structure with square pores in the in-plane direction and elongated pores in the out-of-plane direction. The compressive Young׳s modulus and yield stress are in the range of 1–7.5GPa and 10–110MPa, respectively. The dominant compressive deformation mode is buckling of mesh wires, but some uncoordinated buckling is present in porous titanium with lower porosity. Relationship between compressive properties and porosity conforms well to the Gibson–Ashby model. The effect of pore size on compressive properties is fundamentally ascribed to the aspect ratio of titanium meshes. Porous titanium with 60–70% porosity has potential for trabecular bone implant applications.

Microstructure evolution and mechanical properties of a submerged friction-stir-processed AZ91 magnesium alloy

AZ91 casting alloy is subjected to friction stir processing (FSP) in air (NFSP) and under water (SFSP). The thermal histories of the two FSP procedures are measured, and their effects on microstructure evolution and mechanical properties of the experimental materials are investigated. Compared with NFSP, the peak temperature during SFSP is about 150 °C lower and a much higher cooling rate of 13 °C/s is gained. Both NFSP and SFSP produce uniform recrystallized microstructures with dominant high-angle grain boundaries. The average grain size of the NFSP specimen is 7.8 μm, and SFSP results in further grain refinement with a grain size of 1.2 μm. The observed grain sizes of the two FSP specimens match well with the predicted values calculated by the Derby–Ashby model. TEM observation, temperature data, and model criterion indicate that the grain refinement mechanism during NFSP is attributed to continuous dynamic recrystallization (DRX), while continuous DRX and discontinuous DRX affect during SFSP. The mechanical properties of the SFSP alloy are much higher due to finer microstructure.

Microstructure and mechanical properties of aluminium alloy cellular lattice structures manufactured by direct metal laser sintering

This study thoroughly investigated the microstructure and mechanical properties of AlSi10Mg periodic cellular lattice structures with a wide range of volume fractions (5–20%) and unit cell sizes (3–7mm) fabricated via direct metal laser sintering (DMLS). It was found that the arc-shaped melt pools are overlapping with each other and comprising near fully dense struts (relative densities≥99%) of the as-built lattice structures. The melt pools of the struts are characterized with very fine cellular-dendritic microstructure. Two distinctive zones in the melt pool can be distinguished: the boundary of melt pool possesses the coarse cellular/dendritic microstructure with the cell size or dendrite arm spacing ranging of 2–4µm, while the interior of melt pool exhibits the much finer cellular microstructure consisting of the 400–700nm cells mainly filled with the α-Al matrix and some embedded rod-type Si-phases, and the network boundaries predominantly generated by the aggregates of approximately 20nm Si particles. Both compression strength and microhardness decrease with the increase in the unit cell size when the volume fraction is fixed. This is mainly because the thinner struts of the smaller unit cell size lattice structures were cooled faster by their surroundings and then exhibit a higher cooling rate, leading to finer microstructure. The compression strength increases with increasing the volume fraction, and an equation based on the Gibson–Ashby model is established to estimate the compression strength of DMLS-produced AlSi10Mg gyroid cellular lattice structures with the 3mm unit cell size.

The effect of sago as binder in the fabrication of alumina foam through the polymeric sponge replication technique

Influence of various binders to alumina foam substrate was investigated. The substrate was prepared by the polymeric sponge replication technique using different solid loading ratios and binder agents. The slurries used showed a shear thinning behavior. During replication, a sponge template was coated in alumina slurry, whilst excess slurry was removed manually. The resulting substrate have been studied via the Archimedes method, morphological and phase analysis, and compression test. The total porosities varied between each binder rose from 79.2% to 90.4% depending on their solid loading. The samples with natural binders had a bulky struts and fine surface, contrary to the PVA added samples. Upon compression test, PVA added samples destroyed in fragments whilst natural binders modified samples had a collapsed microstructure but still preserved its structural integrity. Comparison of experimental data and prediction value of Gibson and Ashby model show a quiet big gap between both values.

Compressive behavior of Zn–22Al closed-cell foams under uniaxial quasi-static loading

Zn–22Al alloy closed-cell foams were fabricated by melt foaming process using hydride foaming agent. The compressive properties were investigated under quasi-static condition. The structure of the foamed material was analyzed during compression test to reveal the relationship between morphology and compressive behavior. The results show that the stress–strain behavior is typical of closed-cell metal foams and mostly of brittle type. Governing deformation mechanism at plateau stage is identified to be brittle crushing. A substantial increase in compressive strength of Zn–22Al foams was obtained. The agreement between compressive properties and Gibson–Ashby model was also detected.

Production of high porosity Zn foams by powder metallurgy method

Open-cell Zn foams with 74–92% porosity were fabricated by space holder technique, including compacting spherical carbamide granules coated with Zn powders followed by leaching the space holder and sintering. The role of compaction and sintering parameters on pore structure, cell wall integrity and compressive properties of foams was investigated. The results show that compressive yield strength and modulus of elasticity decrease with porosity and a good compatibility with Gibson–Ashby model of cellular solids is discovered. The optimum structure and mechanical properties of Zn foams are achieved by compaction at 300 MPa and sintering for 2 h at 410°C.

Mechanical properties and thermal conductivity of porous alumina ceramics obtained from particle stabilized foams

In this work, foams were obtained by direct foaming of aqueous alumina suspensions containing butyric acid. Butyric acid is incorporated in the suspensions in order to hydrophobize alumina particles, leading to their adsorption at the air/water interface. After setting and drying, wet foams were sintered at 1585°C for 2h. The resulting porous samples were characterized in terms of microstructure, mechanical properties and thermal conductivity. Microstructures of sintered alumina foams reveal closed pores surrounded by a thin alumina layer. The microstructure of these macroporous ceramics is related to (i) the composition of the initial suspension (alumina and butyric acid contents) and (ii) the stirring velocity during the foaming process. Macroporous ceramics with pore sizes (d50) ranging from 20µm to 140µm and porosities between 25% and 89% were obtained. Three-point bending tests were performed on foams with porosities between 65% and 89%. The results of mechanical tests were analyzed with Weibull statistic. The bending strength values are between 5MPa and 42MPa. The Young’s modulus, obtained from 3-point bending tests, decreases with the porosity level according to Gibson–Ashby model. Thermal diffusivity measurements were made with the laser flash technique in order to determine the effective thermal conductivity. Experimental values are significantly higher than the predictions with Landauer’s relation and almost close to Maxwell/Hashin–Shtrikman upper bound.

Anisotropic porous titanium with superior mechanical compatibility in the range of physiological strain rate for trabecular bone implant applications

Porous titanium for biomedical application was fabricated by diffusion bonding of titanium meshes. Compressive mechanical compatibility and strain rate sensitivity were studied in the range of physiological strain rate under quasi-static and dynamic conditions. The results show that porous titanium presents anisotropic pore structure suited for bone ingrowth. Quasi-static compressive Young׳s modulus and yield stress are in the range of 0.4–6.5GPa and 5–105MPa, respectively, for porous titanium with 30–70% relative density. Based on the Gibson–Ashby model, quasi-static compressive properties can be quantitatively designed and tailored with respect to relative density to match those of human trabecular bone. Porous titanium with 30–40% relative density compressed in the out-of-plane direction shows excellent mechanical compatibility in strain rate sensitivity, and has huge potential for application in human trabecular bone implants.

Preparation of porous PLLA/PCL blend by a combination of PEO phase and NaCl particulate leaching in PLLA/PCL/PEO/NaCl blend

In this study, the ternary blends containing microporosity based on poly(l-lactic acid) (PLLA), poly(e-caprolactone) (PCL) and polyethylene oxide (PEO) were prepared using an internal mixer via a polymer leaching technique. The particulate leaching is the most widely used technique to create porosity. To introduce macroporosity besides micropores, NaCl particulates were incorporated into the ternary blends at 40–80 wt % and macropores were formed by particulate leaching. Samples porosity were evaluated by calculating the ratio of porous scaffold density (ρ*) to the non-porous material density (ρ s). The results showed that with an increase in NaCl particulate content, the amount of porosity increased and the distribution of pore size was gradually transformed from monomodal into bimodal form. The porosity plays a key role in governing the compression properties. Mechanical properties are presented by Gibson–Ashby model. Compressive modulus decreased with an increase in NaCl particulate concentration due to the increase in porosity and thinning of pore wall that caused rupture at these weaker spots. Blending and forming of the bio-scaffold can be made using conventional polymer processing equipment. This process seems promising for a large-scale production of porous bio-scaffold of many sizes through an economic method.

Micro Structural Investigations and Mechanical Properties of Macro Porous Ceramic Materials from Capillary Suspensions

Recently, we have introduced a novel, material‐independent processing method for producing macro porous ceramics with capillary suspensions as a stable precursor. A capillary suspension is a three‐phase system where a small amount of an immiscible secondary liquid is added to a suspension resulting in the formation of a sample spanning particle network. This technology provides open porosities well above 50% and pore sizes ranging from 0.5–100 μm. Here we focus on microstructure formation in the capillary suspensions and its impact on mechanical strength of the corresponding sintered parts. Based on the rheological data and SEM‐images, three regimes (I, II, III) are identified with distinctly different flow properties of the wet suspension and characteristic structural features of the sintered ceramic parts depending on the amount of added secondary liquid phase. The average pore size increases and the pore size distribution changes from monomodal (I) to bimodal (II) and broad multimodal (III) with increasing amount of secondary liquid phase. A clear correlation between the yield stress of the wet suspension and the porosity and pore size is observed for regime (I) and (II). Compressive and flexural strength as well as the Young's modulus monotonically decrease with increasing amount of the secondary liquid phase. Absolute values are mainly determined by the porosity and are well predicted by the Gibson & Ashby model for samples corresponding to regime (I) and (II). The broad pore size distribution in regime (III) results in a significantly lower mechanical strength.

Mechanical and dielectric properties of microcellular polycarbonate foams with unimodal or bimodal cell-size distributions

This article reports on the compressive, dynamic mechanical and dielectric properties of microcellular polycarbonate foams with unimodal or bimodal cell-size distributions fabricated using the environment-friendly supercritical carbon dioxide. The effects of cell morphologies such as relative density, cell-size distribution and porosity on the compressive strength, Young’s modulus, storage modulus, loss modulus, dielectric constant and loss tangent of the microcellular polycarbonate foams are investigated quantitatively. Experimental values of the compressive strength and Young’s modulus fit very well with the theoretical values calculated from the Gibson–Ashby model at low relative densities. The higher relative density leads to higher storage modulus and loss modulus. The bimodal foams significantly improve the compressive and dynamic mechanical properties compared to the unimodal foams with the same relative density. The dielectric properties of microcellular foams depend only on the total porosity, but not on the cell-size distribution or microstructure of the foams. With increasing porosity, the dielectric constant of the microcellular foams gradually decreases, and agrees very well with the curve calculated from the Maxwell-Garnett-spheres model.

Influence of cell shape on mechanical properties of Ti–6Al–4V meshes fabricated by electron beam melting method

Ti–6Al–4V reticulated meshes with different elements (cubic, G7 and rhombic dodecahedron) in Materialise software were fabricated by additive manufacturing using the electron beam melting (EBM) method, and the effects of cell shape on the mechanical properties of these samples were studied. The results showed that these cellular structures with porosities of 88–58% had compressive strength and elastic modulus in the range 10–300MPa and 0.5–15GPa, respectively. The compressive strength and deformation behavior of these meshes were determined by the coupling of the buckling and bending deformation of struts. Meshes that were dominated by buckling deformation showed relatively high collapse strength and were prone to exhibit brittle characteristics in their stress–strain curves. For meshes dominated by bending deformation, the elastic deformation corresponded well to the Gibson–Ashby model. By enhancing the effect of bending deformation, the stress–strain curve characteristics can change from brittle to ductile (the smooth plateau area). Therefore, Ti–6Al–4V cellular solids with high strength, low modulus and desirable deformation behavior could be fabricated through the cell shape design using the EBM technique.

Analysis of the Mechanical Behavior of Ceramic Filters of the Systems Al<sub>2</sub>O<sub>3</sub>-LZSA and Al<sub>2</sub>O<sub>3</sub>-SiC

Ceramic filters processed by the replica method have been the subject of increasing research during the late years. In this research, ceramic filters of both 10 and 20 ppi of the systems Al2O3-LZSA and Al2O3-SiC, obtained by the replica method, have been mechanically evaluated using the compression test. The results of mechanical strength have been compared to Gibson and Ashby model. This paper proposes an adaptation of this model to explain the results.

Advanced lightweight 316L stainless steel cellular lattice structures fabricated via selective laser melting

This paper investigates the manufacturability and performance of advanced and lightweight stainless steel cellular lattice structures fabricated via selective laser melting (SLM). A unique cell type called gyroid is designed to construct periodic lattice structures and utilise its curved cell surface as a self-supported feature which avoids the building of support structures and reduces material waste and production time. The gyroid cellular lattice structures with a wide range of volume fraction were made at different orientations, showing it can reduce the constraints in design for the SLM and provide flexibility in selecting optimal manufacturing parameters. The lattice structures with different volume fraction were well manufactured by the SLM process to exhibit a good geometric agreement with the original CAD models. The strut of the SLM-manufactured lattice structures represents a rough surface and its size is slightly higher than the designed value. When the lattice structure was positioned with half of its struts at an angle of 0° with respect to the building plane, which is considered as the worst building orientation for SLM, it was manufactured with well-defined struts and no defects or broken cells. The compression strength and modulus of the lattice structures increase with the increase in the volume fraction, and two equations based on Gibson–Ashby model have been established to predict their compression properties.

Effects of porosity and crack density on the compressive strength of rocks

We analyzed a compilation of previously published and new data on the uniaxial compressive strength (UCS) of various rock types using the pore-emanated crack and the wing crack models. While previous empirical studies have highlighted the strong control of porosity over the strength, the comparison with the pore-emanated crack model demonstrates that the pore size can be another microstructural parameter that exerts strong influence on the UCS of a rock that contains significant equant pores. We proposed an analytical simplification of the Ashby and Sammis wing crack model for uniaxial compression. Our model explicitly shows the relation between the UCS and the initial level of damage and/or the crack density in a rock. Our analysis also reveals that the normalized fracture toughness for ultimate failure is always significantly larger than the normalized fracture toughness for wing crack initiation. It is therefore more appropriate to consider two different parameters for the toughness in the micromechanical analysis. To gain insights into the physics of the Coulomb criterion, we derived analytic approximations for the empirical failure parameters with reference to the sliding wing crack model. The internal friction coefficient can be approximated as related linearly to the friction coefficient of the sliding crack, and the difference between the two coefficients has a logarithmic dependence on the square root of the crack density.

Effect of pore structure on the compressive property of porous Ti produced by powder metallurgy technique

Porous Ti with an average macro-pore size of 200–400μm and porosity in the range of 10–65% has been manufactured using polymethyl methacrylate (PMMA) powders as spacer particles. The compressive strength and elastic modulus of resultant porous Ti are observed in the range of 32–530MPa and 0.7–23.3GPa, respectively. With the increasing of the porosity and macro-pore size, the compressive strength and modulus decrease as described by Gibson–Ashby model. The failure due to cracking (complete fracture) of the struts on porous Ti is controlled primarily by macro-pores. Fractography shows evidence of the brittle cleavage fracture mainly, but containing a few fine shallow dimples and a small amount of transcrystalline fracture of similarly oriented laths. The failure mechanism has been discussed by taking the intrinsic microstructural features into consideration.

Compressive property and energy absorption characteristic of 3D open-cell Ni–Cr–Fe alloy foams under quasi-static conditions

Reticulated open-cell Ni–Cr–Fe foams were manufactured by gas-phase codeposition of Cr and Fe onto the struts of pure Ni foam at 1050 °C, and then the samples were homogenization treated at 1200 °C in a vacuum atmosphere. The quasi-static compressive behavior and energy absorption characteristics of the Ni–Cr–Fe alloy foams with different Cr and Fe contents were discussed. The mechanical properties of these open-cell Ni–Cr–Fe alloy foams were also comparable with the pure Ni foams or the hypothetical Ni–Cr–Fe foam model. The results show that although the alloy foam struts show the similar hardness, the compressive strengths and energy absorption properties of the open-cell Ni–Cr–Fe alloy foams increase with increasing the Cr and Fe contents. The stress–strain behaviours of the Ni–Cr–Fe alloy foams are as smooth as those of nickel foams, indicating that the Ni–Cr–Fe alloy foams are the characteristic of typical ductile metallic foam. The energy absorption capabilities of the Ni–Cr–Fe alloy foams exhibit 22 times higher than that of the pure Ni foams. Simultaneously, the compressive strength of the Ni–Cr–Fe alloy foams at ambient temperature is in agreement with theoretical prediction by Gibson–Ashby model.

Compression deformation behavior of Ti–6Al–4V alloy with cellular structures fabricated by electron beam melting

Ti–6Al–4V alloy with two kinds of open cellular structures of stochastic foam and reticulated mesh was fabricated by additive manufacturing (AM) using electron beam melting (EBM), and microstructure and mechanical properties of these samples with high porosity in the range of 62%∼92% were investigated. Optical observations found that the cell struts and ligaments consist of primary α′ martensite. These cellular structures have comparable compressive strength (4∼113MPa) and elastic modulus (0.2∼6.3GPa) to those of trabecular and cortical bone. The regular mesh structures exhibit higher specific strength than other reported metallic foams under the condition of identical specific stiffness. During the compression, these EBM samples have a brittle response and undergo catastrophic failure after forming crush band at their peak loading. These bands have identical angle of ∼45° with compression axis for the regular reticulated meshes and such failure phenomenon was explained by considering the cell structure. Relative strength and density follow a linear relation as described by the well-known Gibson–Ashby model but its exponential factor is ∼2.2, which is relative higher than the idea value of 1.5 derived from the model.

High damping capacity in porous NiTi alloy with bimodal pore architecture

Porous NiTi exhibits pseudoelasticity, shape memory and low modulus, and thus shows application potential as high damping and bio-materials. Here Ni50.5Ti49.5 foam with bimodal pore structure was prepared by elemental powder sintering and high damping capacity demonstrated. NaCl particles of 500–600μm and 75–90μm diameters were adopted as space holder to create large and small pores with porosity of 40%. Incomplete densification of NiTi alloy created even smaller pores of 10–50μm and contributed another 21.47% porosity. This NiTi foam containing bimodal pores has a compressive modulus of 1.83GPa, smaller than that of foam with single pores or estimation by Gibson–Ashby model. This low modulus is attributed to the stress-induced martensite transformation under compressive load. The foam exhibits high damping capacities during phase transformation and at austenite region because of deformation, dislocation motion in thin nodes/walls and stress-induced martensite formation.

Rate-controlling mechanisms of hot deformation in a medium carbon vanadium microalloy steel

Isothermal compression tests were carried out on a medium carbon vanadium microalloy steel (roughly Fe-0.33C-1.5Mn-0.1V, wt%) by using a Gleeble-1500 simulator. Based on constitutive analysis including an Arrhenius term, activation energy for hot working was calculated and used to evaluate the rate-controlling mechanism of hot deformation. At low strain rates (0.1–1s−1), the activation energy for hot working (287.4kJ/mol) is very close to the austenite lattice self-diffusion activation energy, indicating that the rate-controlling mechanism is dislocation climb. While at high strain rates (10–30s−1), the activation energy becomes very high (500.6kJ/mol), and activation volume is better used under such conditions. Then, activation volume analysis based on both Schöck model and Kocks–Argon–Ashby model demonstrates that the rate-controlling mechanism at high strain rates is cross slip. That is, the rate-controlling mechanisms of hot deformation for the medium carbon vanadium microalloy steel at high and low strain rates are intrinsically different. Inspired by the findings above, processing map analysis based on dynamic materials model was further preceded and different peak domains of power dissipation efficiency in high and low strain rate regimes were found.