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The tensile and compressive deformation in porous Mg with unidirectionally oriented cylindrical pores and a unique fiber texture in which the normal direction of the {1 0 1 ¯ 3} plane was preferentially oriented was studied. Porous Mg specimens with unidirectional pores and texture were prepared by unidirectional solidification in a hydrogen atmosphere using a continuous-casting technique and their quasi-static tensile deformation and quasi-static and dynamic compressions were investigated. In tensile loading parallel to the orientation direction of the pores (the “pore direction”), the porous Mg exhibited a large tensile elongation of ∼60% strain despite the presence of ∼42% porosity, whereas it showed high energy absorption of ∼30 kJ kg−1 along the same direction. To clarify these superior mechanical properties, the underlying operative deformation modes and rotation of crystallographic orientation during loadings were analyzed by X-ray pole figures, optical microscopy and crystal plasticity finite-element modeling. The analyses revealed that in the initial stage of both the compression and tensile loadings along the pore direction, basal slip mainly operated. Importantly, the activity of basal slip was enhanced during the tensile loading by rotation of the crystallographic orientation, which resulted in high tensile elongation. On the other hand, the activation of basal slip was initially suppressed by the crystal rotation during compression. However, the localization of basal slip originating from the elongated grains with the unique texture subsequently enhanced the activity of basal slip, which suppressed the steep increase in the flow stress. This unique localized deformation gave rise to the superior impact energy absorption.

Porous Ti–xAl–8Nb (x = 45, 48, and 49 at%) alloys (i.e., intermetallic TiAl–Nb compounds) with cylindrical pores oriented along a single direction were prepared via unidirectional solidification in a hydrogen and helium gas atmosphere, while making use of the differences in the hydrogen solubilities of the liquid and solid phases of the alloys. The microstructures and pore morphologies of the alloys revealed that pore formation in the alloys was closely related to their solidification processes. In the case of the alloy with x = 45 at%, a primary solidified β (bcc) phase with high hydrogen solubility suppressed the formation of pores during solidification. On the other hand, in the case of the alloy with x = 49 at%, the formation of the primary β phase was suppressed, leading to the formation of elongated pores along the solidification direction. After being heat treated, the porous TiAl–Nb alloys exhibited a fully lamellar structure composed of α2-Ti3Al and γ-TiAl phases. These porous TiAl–Nb alloys with lamellar structures and directional pores exhibited superior compressive properties parallel to the direction of the pores.

Lotus-type porous materials exhibit some unique anisotropic mechanical and thermal properties which are very useful for a number of industrial applications. This paper evaluates several computational models for determining the compressive engineering elastic modulus and engineering yield stress of lotus-type iron in transversal and longitudinal direction in regard to pore orientation with parametric nonlinear finite element computational simulations for porosities ranging from 0 to 0.65. The considered pore topologies of evaluated computational models are either regular (indirectly reconstructed) or irregular (directly reconstructed). Comparison of computational results, experimental tests and analytical estimations shows good correlation of some evaluated computational models. The simplified porous model with π/4 rotated aligned regular pores can be recommended for fast computational estimation of lotus-type material behaviour under mechanical loading, when some material parameters for homogenised lotus-type material modelling have to be determined.

Dynamic and quasi-static compressive deformation of as-cast and normalized porous S15CK carbon steels with cylindrical pores oriented in one direction was investigated at 298 and 77 K, using the split Hopkinson pressure bar method and a universal testing machine, combined with an acoustic emission measurement system, to clarify the formation mechanism of a plateau stress region where deformation proceeds with almost no stress increase. Dynamic and quasi-static compressions perpendicular to the orientation of the pores at 298 and 77 K do not produce a plateau stress region in the as-cast and normalized porous S15CK, because the localized crack formation and slip deformation that originate from the large concentration of stress around pores promotes densification in the early stage of the stress–strain curves. When the samples undergo dynamic compression parallel to the pore direction at 77 K, the matrix becomes brittle, and cracks are easily formed. However, the pores do not easily collapse, because they are oriented along the compressive direction. Therefore, densification occurs at a higher strain level. In addition, the formation of small cracks in the matrix decreases the work hardening rate. As a result, a plateau stress region with high stress amplitude and wide strain range appears, which is independent of the microstructure. This mechanism for the formation of the plateau stress region is completely different from that of metal foams with isotropic pores, which is based on sequential inhomogeneous deformation. As a result, energy absorption 10 times that of commercial aluminum foams is achieved.

Lotus-type porous aluminum with cylindrical pores oriented in one direction was deformed by Equal Channel Angular Extrusion (ECAE) through a 150° die with sequential 180° rotations, and the pore morphology and Vickers hardness after the extrusion were investigated. The Vickers hardness increases with increasing number of passes in the extrusions both parallel and perpendicular to the pore direction, accompanied by the decrease of porosity. The densification occurs more easily in the perpendicular extrusions than in the parallel extrusions, and the large deformation by the densification gives rise to the large increase in the Vickers hardness for the perpendicular extrusions.

Numerical calculations for porous magnesium with cylindrical oriented pores showed significant influences of active deformation modes in magnesium (Mg) on distinctive "two-stage deformation behavior" during compression. Calculated results also imply that larger grain aspect ratio results in better energy absorption efficiency.

Al foams whose matrix contains dispersed AlN particles (Al/AlN composite foams) were prepared by a melt foaming method, and the effect of foaming temperature on the pore morphology of the prepared foams was investigated. First, Al/AlN composites were prepared by non-compressive infiltration of Al powder compacts with molten Al alloy in nitrogen atmosphere. Next, the prepared composites were melted by induction heating and foamed at various temperatures using TiH2 powders as blowing agents. The porosity of prepared Al/AlN composite foams slightly decreases with increasing foaming temperature, and the pore morphology of the foam becomes homogeneous simultaneously. When the foaming temperature is 1123 K, homogeneous pores are formed in all over the ingot. This pore homogeneity is probably achieved by the stabilization of the foaming behavior due to the formation of Al3Ti particles in the melt and dispersion of AlN particles.

Al-3.7 pct Si-0.18 pct Mg foams strengthened by AlN particle dispersion were prepared by a melt foaming method, and the effect of foaming temperature on the foaming behavior was investigated. Al-3.7 pct Si-0.18 pct Mg alloy containing AlN particles was prepared by noncompressive infiltration of Al powder compacts with molten Al alloy in nitrogen atmosphere, and it was foamed at different foaming temperatures ranging from 1023 to 1173 K. The porosity of prepared foam decreases and the pore structure becomes homogeneous with increasing foaming temperature. When the foaming temperature is higher than 1123 K, homogeneous pores are formed in the prepared ingot without using oxide particles and metallic calcium granules, which are usually used for stabilizing a foaming process. This stabilization of the foaming at high temperatures is possibly caused by Al3Ti intermetallic compounds formed at high temperature and AlN particles. Compression tests for the prepared foams revealed that the absorbed energy per unit mass of prepared Al-3.7 pct Si-0.18 pct Mg foam is higher than those of aluminum foams strengthened by alloying or dispersion of reinforcements. It is remarkable that the oscillation in stress, which usually appears in strengthened aluminum foams, does not appear in the plateau stress region of the present Al-3.7 pct Si-0.18 pct Mg foam. The homogeneity in cell walls and pore morphology due to the stabilization of pore formation and growth by AlN and Al3Ti particles is a possible cause of this smooth plateau stress region.

Porous Al-5 mass%Ti alloy was fabricated by unidirectional solidification in hydrogen atmosphere, using a continuous casting technique. The porous Al-Ti alloy was prepared at different transfer (solidification) velocities, and the effect of transfer velocity on the pore morphology was investigated. It was found that the pore shape changes with increasing transfer velocity, while the porosity does not change with increasing transfer velocity. In the case of a low transfer velocity (0.5 mm·min -1 ), elongated pores surrounded by the columnar microstructure are formed, which indicates that the pores grow along the solidification direction together with the solid phase. In the case of a middle transfer velocity (5.0 mm·min -1 ), elongated pores surrounded by the columnar microstructure and needle or plate-like Al 3 Ti alloys are formed. In the case of a high transfer velocity (10.0mm·min -1 ), spherical pores surrounded by the equiaxed microstructure are formed, because the primary crystals formed in the solidification front prevent the growth of elongated pores. It is suggested that the pore morphology is closely related with the solidification rate.

Lotus-type porous aluminum with cylindrical pores oriented in one direction was fabricated by a casting method utilizing the decomposition of moisture in a vacuum. Hydrogen decomposed from moisture is utilized for cylindrical pores to grow during unidirectional solidification. However, pores are not formed in the case of a casting in hydrogen or argon atmosphere, because hydrogen or argon gas pressure suppresses the pore growth. The porosity of lotus aluminum does not depend on the moisture amount, which indicates that the moisture amount is almost saturated within the amount used in this study. The average pore diameter does not depend on the moisture amount, because the pore diameter depends mainly on ambient pressure and solidification rate. The distribution of pores becomes homogeneous by decreasing melting temperature, because the rate of the reaction of moisture possibly becomes low (more suitable for pore growth) by decreasing the melting temperature.

Porous magnesium with directional cylindrical pores (or “lotus-type” porous magnesium) was fabricated through the use of hydrogen decomposed from MgH2 powders during unidirectional solidification. Liquid magnesium was cast into a mold in which MgH2 powders were placed and was unidirectionally solidified, which achieved growth of pores elongated along the direction of solidification. The effect of the amount of the MgH2 powders on the pore structure (porosity, diameter, and number density of pores) and the change in the pore structure along the pore growth direction were clarified. The porosity and number density of pores increase with increasing amount of MgH2 powder, and the average diameter of pores decreases with increasing amount of MgH2 powder. The pore structure changes with the growth of pores along the solidification direction.

We studied the effects of anisotropic pores and fiber texture on the fatigue strength and fracture surface of lotus-type porous magnesium fabricated through unidirectional solidification in pressurized hydrogen and argon atmospheres. The fatigue strength in the direction parallel to the longitudinal axis of pores is higher than that in the perpendicular direction. Not only anisotropic pores but also fiber texture grown along the pore direction contributes to the anisotropy in the fatigue strength. The fatigue strength at finite life of lotus magnesium is closely related to the ultimate tensile strength; the fatigue strength is proportional to the ultimate tensile strength for both loadings parallel and perpendicular to the pore direction. The fracture surface of lotus magnesium is not flat, which originates from porous structure. For parallel loading, fiber texture in lotus magnesium also contributes to the irregular surface, i.e., a combination of texture and pore structure affects fracture surfaces.

We studied the fatigue strength of lotus-type porous magnesium with cylindrical pores aligned unidirectionally, which was fabricated through unidirectional solidification in pressurized hydrogen atmospheres. The fatigue strength shows anisotropy; the fatigue strength in the direction parallel to the longitudinal axis of pores is higher than that in the perpendicular direction. Not only anisotropic pores but also fiber texture grown along the pore direction contributes to the anisotropy in the fatigue strength.

We investigated the pore morphology in lotus-type porous copper fabricated by continuous casting technique as a function of transference velocity range from 1 to 100 mm･min-1 under hydrogen gas pressure of 1.0 MPa. Lotus-type porous copper with long cylindrical pores aligned in one direction parallel to the transference direction was fabricated, which posses a sufficient uniformity of the porosity and pore size. The pores formed at transference velocity of 1 mm･min-1 were larger than other condition. Necks were observed in these pores, whose formation may be attributed to bubbling in the melt. The pore size decreased with increasing transference velocity, while the porosity was not varied much by transference velocity.

Lotus-type porous NiAl and Ni3Al intermetallic compounds, possessing cylindrical pores aligned in the direction parallel to the solidification direction, were fabricated by using a unidirectional solidification technique in a pressurized hydrogen atmosphere of 2.5MPa. The porosity of lotus NiAl is 24.2 %, and the porosity of lotus Ni3Al is 3.2%; the porosity of the porous NiAl is larger than that of Ni3Al. This is because the solubility gap of hydrogen between liquid and solid phases of NiAl is larger than that of Ni3Al.

We studied the effect of anisotropic pore morphology on the fatigue behavior and fracture surface of lotus-type porous copper, which was fabricated through unidirectional solidification in pressurized hydrogen and argon atmospheres. The fatigue strength at finite life is closely related to the pore morphology. The fatigue strength decreases with increasing porosity, and the strength depends on applied-stress direction. The fatigue life is the longest in the direction parallel to the longitudinal axis of cylindrical pores. The fatigue strength at finite life is proportional to the ultimate tensile strength and can be expressed by a simple power-law formula. Anisotropic pores affect the fracture surface of lotus copper; crack-initiation site depends on applied-stress direction, and the anisotropic shape pores affect the direction of crack propagation and final fracture surface.

Lotus-type porous metals with low thermal conductivity are fabricated by continuous zone melting technique, which possess directional elongated pores. The porous metals have been able to be fabricated through the conventional casting method by utilizing the solubility gap between solid and liquid in pressurized gas atmosphere. However, there is a shortcoming that the pores are coarsened in the part farther from the chill plate in the ingot. In order to overcome such a shortcoming, we developed the continuous zone melting technique and successfully produced the lotus-type porous metals with even low thermal conductivity such as stainless steel and superalloys. Furthermore, from the viewpoint of mass production with low cost, we invented novel ”continuous casting technique”. The molten metals dissolving gas are solidified continuously by passing through the mold cooled with chiller and thus, lotus-type porous metal plate as long as one meter was produced for short time. Sufficient uniformity of the porosity and pore size was obtained in such long porous ingots. This technique is prospective method for commercial mass production.

We extend Qiu and Weng’s mean-field approach for predicting yield behaviors of porous metals [J. Appl. Mech.-Trans. ASME 59, 261–268, 1992] in a more rigorous mathematical form. This extended method can explicitly take account of the pore morphology and the elastic and plastic anisotropies of metal matrix. The validity of our method is first demonstrated by applying to the lotus-type porous iron that exhibits the anisotropic yield behavior experimentally. We next consider the porous materials possessing elastically and plastically anisotropies, and carry out the calculations of their macroscopic yield behaviors. The calculations revealed that the yield stress is virtually independent of the elastic anisotropy of the matrix, but strongly depends on the plastic anisotropy and also on the pore morphology.

The geometrical effective thermal conductivity of different porous materials is investigated based on two different approaches: the finite element method as a representative for numerical approximation methods and the mean-field method as a representative for analytical methods. Different pore geometries, i.e., cylindrical and spherical, and different arrangements of these pores, namely in different periodic ways and random distribution are considered. It is found that the relative conductivity is practically independent of the specific pore arrangement. Only the morphology (spherical or cylindrical) of the structure influences the conductivity.

Lotus-type porous iron and stainless steel (SUS304L) whose long cylindrical pores are aligned in one direction were fabricated by unidirectional solidification in a pressurized hydrogen or nitrogen gas atmosphere. Pores are formed as a result of precipitation from the supersaturated gases when the liquid metal dissolved with gas atoms is solidified. The ultimate tensile and yield strengths of the porous iron produced in nitrogen atmosphere are about two times higher than in a hydrogen atmosphere. Such superior strength is attributed to solid-solution hardening due to solute nitrogen atoms in iron matrix.

Lotus-type porous materials whose long cylindrical pores are aligned in one direction were fabricated by unidirectional solidification from the melt dissolving gas. The pores were evolved by supersaturation of gas atoms when the liquid was solidified. Although such porous metals with high thermal conductivity were produced by casting process, the process could not produce porous metals with low thermal conductivity, which possess uniform pore size and porosity. In order to obtain uniform pore size and porosity in metals with low thermal conductivity, we invented a new “continuous zone melting technique”. Using this technique various metals, alloys, intermetallic compounds and semiconductors were fabricated. Mechanical properties of tensile strength on lotus-type porous metals are described; lotus-type porous iron fabricated using a pressurized nitrogen gas instead of hydrogen exhibits superior strength. The lotus materials can be applied to various functional materials. Some examples are also shown in this paper.

Tension and compression fatigue property was investigated for lotus-type porous copper possessing cylindrical pores aligned in one direction. The cyclic stress was applied in the direction parallel and perpendicular to the longitudinal axis of the pores. It was found that the fatigue strength at finite life of lotus-type porous copper is lower than that of nonporous copper, and the strength in the direction parallel to the longitudinal axis of the pores is higher than that in the perpendicular direction.

Lotus-type porous magnesium with a large number of unidirectional cylindrical pores was fabricated by unidirectional solidification of melt dissolving hydrogen in a pressurized hydrogen atmosphere. The vibration-damping capacity of the lotus-type porous magnesium plate which has many open pores was measured in this work. The attenuation coefficients of the free vibration of lotus-type porous magnesium were measured by hammering-vibration-damping test, which revealed that the attenuation coefficients increase with increase in porosity; the damping capacity of lotus magnesium is higher than that of non-porous magnesium. The mechanism for high damping capacity was analyzed on the basis of the Fourier transform technique, which indicates that various vibration modes of high frequency are observed. The excited vibrations of high frequency enhance the damping capacity of lotus-type porous magnesium.

The effective-mean-field (EMF) theory, consisting of Mori–Tanaka’s mean-field theory and Bruggeman’s effective medium approximation, was extended in order to calculate the coefficients of thermal expansion (CTE) of composite materials. The effective elastic constants and CTE of lotus-type porous metals, possessing cylindrical pores aligned unidirectionally, were evaluated with the EMF theory.

Lotus-type porous magnesium with cylindrical pores aligned unidirectionally was fabricated by the unidirectional solidification of molten magnesium under pressurized hydrogen atmosphere. The apparent attenuation coefficient of the free vibration of lotus-type porous magnesium was measured by hammering–vibration–damping tests, which revealed that the apparent attenuation coefficient increases with increase in porosity, i.e., the damping capacity of lotus magnesium is higher than that of non-porous magnesium. The mechanism of high damping capacity was analyzed by using the Fourier transform technique, which revealed that various vibration modes of high frequency are excited by a hammering. The excited vibrations of high frequency enhance the damping capacity of lotus-type porous magnesium.

Lotus-type porous copper with long cylindrical pores aligned in one direction parallel to the solidification direction was fabricated by unidirectional solidification of the melt in a mixed gas of hydrogen and argon. Compression tests were performed in the direction parallel to the cylindrical pores in order to investigate the relationship between the specimen size and compressive yield strength. The compressive yield strengths and the standard deviation decrease with an increase in specimen size. Increments of the standard deviation are caused by the standard deviation of porosity occurred by inhomogeneous pore diameter and irregular pore arrangement.

Ni3Al with and without boron was melted and unidirectionally solidified in pressurized hydrogen atmosphere by using a continuous zone melting method. For Ni3Al without boron, cylindrical pores elongated in the direction parallel to the solidification direction, are formed in Ni3Al matrix. On the other hand, no pore is formed in Ni3Al with 0.23 mol% B solidified under the same condition. This result suggests that the solubility gap of hydrogen between liquid and solid Ni3Al with boron is extremaly small.

Effects of specimen thickness on the tensile strength of lotus-type porous copper were investigated. The ultimate tensile strength in the direction perpendicular to the longitudinal axis of pores hardly depends on the thickness of a specimen when the width of the specimen is large enough compared with the pore diameter, while the ultimate tensile strength increases with an increase in the thickness when the width is not large enough compared with the pore diameter. The 0.2% offset strength in the direction and strain at the peak stress depend on the thickness of specimens; the 0.2% offset strength decreases with an increase in the thickness, and the strain at peak stress increases with the increase in the thickness.

We studied the plastic behavior of lotus-type porous iron with unidirectional long cylindrical pores. Lotus-type porous iron with different porosities was fabricated by the continuous zone melting method in a pressurized hydrogen and helium atmosphere. To calculate the stress-strain curves for lotus iron, we applied a modified Qiu-Weng’s micromechanical mean-field theory that has recently been proposed by the present authors [J. Mater. Res., in press], and compared the results with those of compression tests. We experimentally found that the deformation resistance and work hardening rate depend on the sample porosity and loading direction. They decrease with an increase in porosity, and their values in the loading along the direction perpendicular to the longitudinal axis of pores are smaller than those in the parallel-direction loading. Our micromechanical calculations reproduce well the stress-strain curves experimentally obtained and express the experimental trends successfully.

Anisotropic yield behavior of lotus-type porous iron fabricated using the continuous-zone-melting method in a pressurized nitrogen and hydrogen atmosphere has been investigated. The 0.2% offset strength (compressive yield stress) in the loading direction parallel to the longitudinal axis of pores decreases linearly with increasing porosity, while the perpendicular strength decreases steeply. The strength versus porosity curves can be expressed using a well-known power law formula. In addition, the 0.2% offset strength of lotus iron prepared in a nitrogen and hydrogen atmosphere is found to be larger than that of lotus iron prepared in a hydrogen and helium atmosphere, which is attributed to the solid solution hardening by the solute nitrogen. Furthermore, we compare the experimental results to calculations obtained by means of the extended Qiu-Weng’s mean-field method, and the comparison suggests that local stresses deviated from the average stress are dominant in the macroscopic yield behavior of lotus metals.

We studied the elastic properties of lotus-type porous iron experimentally and theoretically. First we determined the elastic constants of lotus iron fabricated by the continuous zone-melting method by using the acoustic resonance techniques. All the elastic moduli are found to follow the well-known power-law formula. Next, we extended the effective-mean-field (EMF) theory so as to consider effects of the pore orientation on the effective elastic constants. The model calculations proved that the extended EMF theory is capable of calculating satisfactorily the elastic properties of lotus metals.

Lotus-type porous (LTP) metals possess a markedly anisotropic porous structure, in which long straight pores are homogeneously aligned unidirectionally. In this paper, we first describe a procedure for the determination of reliable elastic constants of LTP metals with high porosity, and next apply the technique to LTP magnesium, and finally compare the measurement results with those from the effective-mean-field (EMF) theory that has been recently proposed by Tane and Ichitsubo [Appl. Phys. Lett. 85, 197 (2004)]. Young’s modulus in the direction parallel to the longitudinal axis of pores decreases virtually linearly with porosity p, i.e., E‖≈45.3(1−p)1.33, whereas the normal Young’s modulus E⊥, falls rapidly, i.e., E⊥≈45.3(1−p)2.64. The Mori-Tanaka mean-field theory yields values that are close to the measured elastic constants in a wide porosity range, but cannot explain this power-law behavior. In contrast, the EMF theory gives more accurate values in the high-porosity range, and can reproduce the power...

We studied temperature dependence of anisotropic elastic constants of lotus-type porous copper that consists of unidirectionally aligned pores and the matrix of oriented crystallites. All the independent elastic constants were measured from room temperature to 400 °C using an electromagnetic acoustic resonance method. All the elastic constants decrease with increase of temperature. The porosity and oriented crystallites have the influence on the temperature dependence of the elastic constants. Micromechanics theory allows calculation of the temperature dependence of the elastic constants of lotus copper from those of monocrystal copper and shows agreement with the measurements. It is concluded that micromechanics model is then valid to predict the temperature dependence of the elastic constants of the lotus-type porous metals.

We studied the elastic constants of a lotus-type porous copper, regarding it as a composite material showing hexagonal elastic symmetry with the c-axis along the longitudinal direction of the pores. We used the combination of resonance ultrasound spectroscopy and electromagnetic acoustic resonance methods to determine the elastic constants of the composite. The resulting Young’s modulus E∥ decreases linearly and c33 does slowly with porosity, while E⊥ and c11 drop rapidly and then slowly. Micromechanics calculations considering the elastic anisotropy of the copper matrix can reproduce the measured anisotropic elastic constants. This indicates that the elastic properties of various types of porous metals can be predicted and designed with the present approach using micromechanics modeling.

We propose an evaluation method for macroscopic elastic constants of composites, which is called the effective-mean-field method. The method is based on Mori–Tanaka’s mean-field (MTMF), and the effective-medium approximation methods, in which complex elastic fields disturbed by many inclusions are replaced by the average fields of a virtually homogenized composite, and the MTMF formulae are utilized in the entire fraction range of inclusion. It is demonstrated for porous samples that the proposed method can reproduce power-law behavior with regard to porosity.

The mechanical properties of lotus metals were experimentally investigated and the effect of the anisotropic pores on the mechanical properties was clarified. The mechanical strength in the direction parallel to the pore direction linearly decreases with increasing porosity, while that perpendicular to the pore direction drastically decreases. This is caused by the anisotropy of stress concentration. The porosity dependence of the mechanical strength obeys a power-law formula.

Lotus-type porous magnesium was fabricated through thermal decomposition of MgH2 powders as a source of hydrogen. Liquid magnesium was cast into a mold in which MgH2 powders were placed and solidified unidirectionally in the mold, which achieved the growth of unidirectional elongated pores in magnesium matrix. The fabrication method is safer than a conventional method using pressurized hydrogen atmosphere, because the risk of explosion can be avoidable. The effect of the amount of MgH2 powders and the distance from the bottom of the ingot on the porous structure was investigated, which clarified that the two factors have the large influence on the pore growth.