Lotus-type porous metals with aligned long cylindrical pores are fabricated by unidirectional solidification from the melt with a dissolved gas such as hydrogen, nitrogen, or oxygen. The gas atoms can be dissolved into the melt via a pressurized gas atmosphere or thermal decomposition of gaseous compounds. Three types of solidification techniques have been developed: mold casting, continuous zone melting, and continuous casting techniques. The last method is superior from the viewpoint of mass production of lotus metals. The observed anisotropic behaviors of the mechanical properties, sound absorption, and thermal conductivity are inherent to the anisotropic porous structure. In particular, the remarkable anisotropy in the mechanical strength is attributed to the stress concentration around the pores aligned perpendicular to the loading direction. Heat sinks are a promising application of lotus metals due to the high cooling performance with a large heat transfer.
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The formation of elongated gas pores during solidification has been investigated since the study of porous ice by Chalmers. 7 ) Air contained in water is rejected by water during the freezing process, and this air accumulates in the advancing interface until its concentration is sufficient for bubbles to nucleate. Once a bubble forms, it grows in the solidification direction to evolve a long cylindrical pore. Additionally, Knacke et al., 8 ) Svensson and Fredriksson, 9 ) and Imabayashi et al. 10 ) have studied the formation of directional pores in metals from the viewpoint of casting defects, while Shapovalov et al. have investigated the applicability of metals fabricated by high-pressure hydrogen as functional materials. 3 ) Nakajima et al. have further fabricated various directional porous metals using solidification techniques in a pressurized gas atmosphere 4 ) and by thermal decomposition of gaseous compounds. 5 ) Herein because the morphology of directional porous metals resembles a lotus root, we refer to these materials as lotus-type porous metals.
Porous and foamed metals exhibit various characteristics that differ from bulk metals, including possessing a low density and large surface area. These metals are expected to be used as lightweight materials, catalyst carriers, electrodes, vibration and acoustic energy damping materials, impact energy absorption materials, etc. 1 ) However, porous and foamed metals all suffer from deteriorating mechanical properties such as strength, stiffness, and fatigue due to the inhomogeneous pore number density distribution and pore size. Many methods, including powder metallurgy and the melt route, have been used to develop porous materials. 2 ) Among these materials, lotus-type porous metals have attracted much attention because their long cylindrical pores align in one direction. These metals are fabricated by a unidirectional solidification process using gas from a pressurized gas atmosphere such as hydrogen (Gasar methods) 3 , 4 ) or thermal decomposition of gas compounds such as hydrides. 5 ) The pores evolve from the insoluble gas when the molten metal dissolving the gas is solidified. Compared to conventional porous metals, which have nearly spherical and isotropic pores, these metals exhibit superior mechanical properties. 6 )
Table 1 is a compilation of the decomposition reactions of the three compounds in an aluminum melt. Calcium hydroxide or sodium bicarbonate decomposes into compounds (CaO, Na 2 CO 3 ), carbon dioxide, and vapor, and the latter further decomposes into metallic oxide and hydrogen. These reactions produce small pores with a homogeneous distribution. On the other hand, titanium hydride decomposes directly into titanium and hydrogen, resulting in large pores with an inhomogeneous distribution. Although the reasons for this difference are currently unclear, the evolution of small pores with a homogeneous distribution may be attributed to the existence of oxide particles, which may serve as pore nucleation sites. To investigate the content of pore gas, gas analysis has been conducted; hydrogen is the pore formation source for titanium hydride, calcium hydroxide, and sodium bicarbonate.
Optical micrographs of lotus aluminum fabricated via the thermal decomposition method using different compounds by the mold casting technique in vacuum at K. Upper and lower micrographs are the cross sections perpendicular and parallel to the solidification direction, respectively.
For lotus aluminum fabricated via TDM, 0.2 g of a gas compound such as calcium hydroxide, sodium bicarbonate, or titanium hydride has been added to 100 g molten aluminum in a vacuum and solidified unidirectionally. Figure 10 shows the microstructure of lotus aluminum on cross sections parallel and perpendicular to the solidification direction. 23 ) Pores with an average size of 400, 268, and µm are evolved using calcium hydroxide, sodium bicarbonate, and titanium hydride, respectively. The porosity is as high as 20%, regardless of the gas compound. Although the pore size is small, as little as 400 µm, its distribution is homogeneous in lotus aluminum when employing calcium hydroxide and sodium bicarbonate. In contrast, the pore size is as large as µm and its distribution is not uniform when employing titanium hydride.
The porosity has been investigated as a function of the mass of titanium hydride. Adding 0.10 g of the hydride abruptly increases the porosity, but the addition of more titanium hydride causes the porosity to become constant near 55%. When 0.10 g of titanium hydride is added to 200 g in the melt of copper, the concentration of hydrogen is 0.128 at.%, which is comparable to the maximum solubility of hydrogen in liquid copper near the melting point. 22 ) Therefore, even if more than 0.10 g of the hydride is added, the supersaturated hydrogen may generate gas bubbles, which are then liberated from the melt into the atmosphere.
Optical micrographs of cross-sectional views of lotus copper (upper views) perpendicular and (lower views) parallel to the solidification direction. Mass of titanium hydride added to the melt of 200 g copper is (a) 0.075 g, (b) 0.10 g, (c) 0.125 g, and (d) 0.25 g. Melting and subsequent solidification are carried out in 0.1 MPa argon atmosphere.
Schematic drawing of the principle to fabricate lotus metals using the thermal decomposition method and a gas compound via the mold casting technique. Pellets of titanium hydride are set in the mold. Molten copper poured from the crucible into the mold reacts with the hydride, and hydrogen dissolves in the melt simultaneously. When the melt solidifies in the upward direction, insoluble hydrogen evolves directional pores.
A high-pressure chamber is unnecessary in TDM because gas compounds such as hydride and nitride are used as the dissolving gas source. Typically the atmosphere during melting and solidification is argon or a vacuum to prevent oxidation and impurity inclusions. To fabricate lotus copper via TDM in 0.1 MPa argon, a few pellets of titanium hydride are placed on the bottom plate of the cooled mold. Molten copper, which is melted by radio-frequency induction heating in a graphite crucible, is poured into the mold (Fig. 8 ). During the unidirectional solidification, the hydride decomposes into titanium and hydrogen. The insoluble hydrogen in the solidified phase evolves into pores, while the titanium may form titanium oxide, which serves as nucleation sites for the gas pores. Figure 9 shows optical micrographs of the cross-sectional views of lotus copper parallel and perpendicular to the solidification direction. The pore growth direction is coincident to the direction of the unidirectional solidification, which is consistent with the conventional high-pressure gas method (PGM). This result reveals that TDM and PGM have similar principal mechanisms for pore evolution.
However, the production of lotus metals with an anisotropic cylindrical pore structure had not been investigated prior to the work of Nakajima and Ide. Nakajima and Ide 5 ) studied the fabrication of lotus copper using titanium hydride in an argon atmosphere instead of pressurized hydrogen atmosphere. This method is called the 'thermal decomposition method' (TDM). Because the solubility of hydrogen in aluminum is low, the porosity of lotus aluminum is inevitably low, on the level of 10%. Increasing the hydrogen pressure does not effectively increase the porosity, but it shrink the pores in accordance to Boyle's law. At a lower atmospheric pressure, the porosity increases as the hydrogen pressure decreases. The advantage of TDM under a lower pressure atmosphere is that the hydrogen source can be supplied in the melt by the decomposition of compounds containing gas elements even in a vacuum, the lowest pressure.
The fabrication process of lotus metals with unidirectional elongated pores requires the use of pressurized gas such as hydrogen, nitrogen, or oxygen. Although hydrogen gas is the most useful, it is explosive and inflammable when mixed with a small amount of oxygen. Thus, it is inconvenient for mass production in industrial applications, and lotus metal fabrication requires a safety procedure. However, an alternate technique that does not employ hydrogen gas would alleviate such difficulty. Makaya and Fredriksson 21 ) have produced porous Fe-base materials by dissolving a CrN compound into a metallic melt of Fe-base alloy in an argon atmosphere. The decomposition of the compound leads to the dissolution of a gas into the melt, and pores are subsequently formed during solidification by the solubility gap between the liquid and solid phases. Porous metals with an isotropic pore structure are solidified from the melt in the crucible.
Figure 7 plots the average pore diameter and porosity against the transfer velocity. The average pore diameter decreases as the transfer velocity increases, whereas the porosity is independent of the velocity. The amount of hydrogen diffusing from the liquid to the pores increases as the transfer velocity decreases. Thus, pores formed at a lower velocity are larger than those formed at a higher velocity. Unlike the pore size, the number density of the pores increases as the transfer velocity increases. Increasing the transfer velocity causes the hydrogen supersaturation of the solid'liquid interface to increase; thus, the number density of the pores increases and the pore size decreases. Therefore, the transfer velocity can control the pore size, while the hydrogen pressure can adjust the porosity.
(a) Photograph of lotus copper fabricated using the continuous casting technique, and (b) cross-sections parallel and perpendicular to the transfer direction of lotus copper fabricated in a mixture gas of hydrogen 0.25 MPa and argon 0.15 MPa by the continuous casting technique with a transfer velocity of 100 mm min '1 .
Schematic drawing of the fabrication apparatus of lotus metals by the continuous casting technique. Large crucible and induction heating coil are located in the upper part of the pressure vessel to melt the metal and dissolve the gas into the melt, whereas the mold with the cooling part and transfer mechanism of the solidified metal slab with pinch rolls are installed in the lower part of the vessel to solidify the melt and continuously transfer the slab downward.
When lotus metals are practically employed, mass production is indispensable. Because the aforementioned methods are not suitable due to the limitation of ingot size, we have developed a new 'continuous casting technique', which can be used to fabricate a long slab or rod (Fig. 5 ). 20 ) The metal is melted in a crucible by radio-frequency induction heating in a high-pressure mixture gas. Then the molten metal is pulled down and solidified simultaneously through the cooled mold at a given transfer velocity. Figure 6 shows the cross sections parallel and perpendicular to the transfer direction of lotus copper fabricated in a mixture gas of hydrogen 0.25 MPa and argon 0.15 MPa with a transfer velocity of 100 mm min '1 . The pore size and porosity are almost homogeneous throughout the solidified specimen slab, which is more than 700 mm long.
(a) Schematic drawings of the melting portion of the continuous zone melting technique. (b) Sectional views of lotus stainless steels fabricated by the continuous zone melting technique in 2.0 MPa hydrogen atmosphere. Transfer velocity of the rod is 330 µm s '1 . Nearly homogeneous pore size (320 µm) and porosity (40%) are obtained throughout the ingot.
To overcome this shortcoming, Ikeda et al. 19 ) have developed a continuous zone melting technique, which is depicted in Fig. 4 (a) . While part of the specimen rod is melted by induction heating, the hydrogen (or nitrogen) gas is absorbed into the melt up to the gas equilibrium solubility in the pressurized gas atmosphere according to Sieverts' law. Concurrently, the specimen rod is moved downward at a given velocity. In the lower part of the melt zone, solidification occurs simultaneously. Then directionally elongated pores evolve by precipitation of the insoluble gas in the solidified specimen rod. If the transfer velocity is kept constant, the solidification velocity becomes constant, which should yield a constant pore size. On the other hand, the mold casting technique cannot control the solidification velocity because the velocity is uniquely determined by its own inherent thermal conductivity. Figure 4 (b) shows a sectional view of a lotus stainless steel rod (SUS304L). The pore size and porosity are almost homogeneous throughout the solidified specimen rod.
Comparison of pore evolution in lotus metals fabricated by the mold casting technique in a mixture gas of hydrogen and argon. Above are schematic drawings for pore evolution during unidirectional solidification. Below are optical micrographs of sectional views parallel to the solidification direction. Left is lotus copper fabricated in a mixture gas of 0.3 MPa hydrogen and 0.7 MPa argon. Right is lotus stainless steel (SUS304L) fabricated in a mixture gas of 1.0 MPa hydrogen and 1.0 MPa argon. (a) Homogeneous pore size and porosity are observed in copper and magnesium with a high thermal conductivity, and (b) inhomogeneous pore size and porosity are found in stainless steel with a low thermal conductivity. Magnitude of the thermal conductivity affects the solidification velocity of the melt, resulting in the different pore morphologies.
Figures 3 (a) and (b) show attempts to use the mold casting technique to produce lotus copper and stainless steel, respectively. Although lotus copper has a uniform distribution of cylindrical pores, stainless steel does not. The difference is attributed to the thermal conductivities of the metals. For metals and alloys with low thermal conductivities, although the heat from the melt is easily dissipated to the water-cooled plate during the solidification process, cooling becomes slower at the upper part of the solidified ingot because the ingot is far from the cooling part, leading to coarser pores. Consequently, only porous metals and alloys with non-uniform pore sizes and porosities can be produced as illustrated in Fig. 3 (b). 18 )
Because hydrogen is inflammable and explosive when oxygen is present, its use is inconvenient from the viewpoint of safety. Thus, employing a gas other than hydrogen is desirable. Nitrogen is an important, common alloying element to improve corrosion resistance and mechanical properties of steels. 13 ) Iron exhibits a large nitrogen solubility difference between the solid and liquid at its melting temperature, 14 ' 16 ) which is similar to that of hydrogen. Utilizing the nitrogen solubility difference between the liquid and solid, lotus iron can be fabricated by above technique. 17 )
Typical examples of optical micrographs on the cross-section of lotus copper fabricated by the mold casting technique in a hydrogen atmosphere at different pressures. Above are cross-sections perpendicular to the solidification direction and below are cross-sections parallel to the solidification direction. (a) 0.4 MPa hydrogen, porosity 44.9%, and (b) 0.8 MPa hydrogen, porosity 36.6%.
The morphology of lotus metals can be characterized by the porosity, pore diameter, pore length, pore distribution, etc. Variables used to control the pore morphology are the melt temperature, solidification rate, type of dissolving gas, gas pressure, etc. Hydrogen gas is most commonly used to fabricate various lotus metals and alloys: iron, nickel, aluminum, copper, magnesium, cobalt, tungsten, manganese, chromium, beryllium and their alloys, while nitrogen is used for iron, and oxygen is for silver. 12 ) Fortunately, most base metals for commercially available, practical alloys can be made porous. Figure 2 shows typical examples of optical micrographs on the cross sections (above) and longitudinal sections (below) of lotus-type porous copper.
Figure 1 schematically depicts the mold casting technique used to fabricate lotus metals; a metal inside a crucible is melted by an induction heating in a high-pressure gas atmosphere. The gas is dissolved up to the equilibrium gas concentration into the molten metal under a given gas pressure according to Sieverts' law. 11 ) The melt, which is saturated with gas, is poured into the mold. When part of the mold is cooled by a chiller or circulated water, the melt is solidified unidirectionally in the vicinity of the cooling part. The elongated pores can evolve and grow due to the influence of the unidirectional solidification. Moving the location of the cooling part can control the pore growth direction.
Lotus metals can be fabricated by unidirectional solidification of the melt dissolving gas. The following three solidification techniques have been developed.
Conventional porous metals, including foamed metals, cellular metals, and sintered metals, possess almost nearly spherical pores and exhibit isotropic mechanical properties. Moreover, the shape of the pores is not always circular and can be distorted, leading the stress to easily concentrate, which deteriorates the strength. In addition, the non-uniform distribution of pore size and porosity causes to the stress to concentrate, further degrading the strength. These behaviors lead to inferior mechanical properties.
Unlike conventional porous metals, lotus metals have elongated cylindrical pores aligned in one direction. Additionally, their various mechanical properties remarkably differ from those of isotropic porous materials, and exhibit significant anisotropic behavior. Several topics regarding the mechanical and physical properties are described below.
Lotus metals macroscopically exhibit hexagonal (transverse-isotropy) elastic symmetry with the c-axis parallel to the pore direction.24,25) In this case, there are five independent elastic constants, c11, c33, c13, c44, and c66 = (c11 ' c12)/2. To determine all of them, resonant ultrasound spectroscopy (RUS)26,27) and mode-selective electromagnetic acoustic resonance (EMAR)28) techniques have been used. The elastic constants are determined through iterative calculations from the resonant spectrum obtained by this RUS'EMAR combination technique.
Figure 11 shows the porosity dependence of Young's moduli E' and E// and the elastic stiffness c11, c33, c13, c44, and c66 of lotus iron with hydrogen or nitrogen pores where E// and E' indicate Young's moduli parallel and perpendicular to the pore direction, respectively. Besides the porosity dependence of lotus copper,24) E// decreases linearly, whereas E' drops steeply in the small porosity region. After extensive research on the effective physical properties (e.g., the electrical conductivity, yield stress, and elastic modulus) of porous materials, their porosity dependencies have been experimentally found to follow the power-law formula29'33)
(1)where M and M0 are the physical properties of the porous and nonporous materials, respectively, and m is the coefficient empirically determined. The solid and broken lines in Fig. 11 indicate the fit of Eq. [1] to the measured data. Thus, it is concluded that Eq. [1] holds for the effective elastic constants of anisotropic porous metals.
Porosity dependence of (a) two Young's moduli, E// in the direction parallel to the x3-axis and E' in the direction perpendicular to the x3-axis, and the elastic stiffness coefficients, (b) c11, c33, c13, (c) c44, and c66 of lotus iron. Transverse isotropy condition c66 = (c11 ' c12)/2 holds. Each line is obtained by fitting Eq. [1] to the measurements.
Little data is available on the mechanical properties of this type of porous metal. Wolla and Provenzano34) and Simone and Gibson35) have measured the tensile strength of porous copper with the pore orientation parallel to the tensile direction. However, their data is largely scattered, which may be attributed to microstructural variations within each specimen as well as in between the specimens. Furthermore, an investigation on the anisotropy of the mechanical properties of lotus metals with elongated cylindrical pores has yet to be conducted. Hyun et al.6) have measured the ultimate tensile strength and the yield strength of lotus copper, and elucidated the uniaxial tensile behavior of lotus copper with the pore orientation parallel and perpendicular to the tensile direction. Moreover, the fracture surfaces of selected tensile test specimens have been investigated to obtain information about the fracture mode of these materials.
Figure 12 plots the ultimate tensile strength of specimens with cylindrical pore orientation parallel to the tensile direction against porosity. The data points for the ultimate tensile strengths lie on a straight line passing through the point of 0 MPa at a porosity of 100%, indicating that the presence of pores does not change the specific ultimate tensile strength. This fact indicates that the pores with axes aligned parallel to the tensile direction do not cause the stress to concentrate in tensile specimens. Thus, the simple rule of a mixture of the empty pores and the solid body can be applied to these specimens. Figure 12 also plots the ultimate strengths of specimens with cylindrical pores perpendicular to the tensile direction versus porosity. The ultimate tensile strength of the specimen with pores perpendicular to the tensile direction is much lower than that of specimen with pores parallel to the tensile direction at a given porosity.
Porosity dependence of the ultimate tensile strength of lotus copper parallel and perpendicular to the pore axis.
Boccaccini et al.36) have suggested an empirical relation in the form of
(2)to describe the variation in the strength with porosity p, where K is a constant that depends on the materials and fabrication method. K is related to the stress concentration around the pores in the porous materials. This formula is identical to Eq. [1].
For a specimen with cylindrical pores aligned parallel to the tensile direction, the value of K approaches unity; stress does not concentrate. Thus, Eq. [2] can be simply rewritten as
(3)However, for a specimen with cylindrical pores oriented perpendicular to the tensile direction, the value of K approaches 3. Then the stress concentration can be expressed as
(4)Figure 12 shows the ultimate tensile strength evaluated from Eqs. [3] and [4]. The experimental results agree well with the dotted lines estimated from Eqs. [3] and [4]. Thus, the tensile strength for lotus copper with cylindrical pores parallel to the tensile direction is higher than that perpendicular to the tensile direction. Hence, the anisotropy of the strength is attributed to the stress concentration around the pores. Because such anisotropy has been observed in lotus magnesium, iron and its alloys, anisotropy is a characteristic of lotus metals.
Here, we have to remark on the abnormal tensile properties of lotus iron fabricated by nitrogen. Hyun et al.37) fabricated lotus iron, not only using hydrogen gas but also by nitrogen gas. They found lotus iron exhibits a superior mechanical strength. The tensile strength of lotus iron with cylindrical pores parallel to the tensile direction, which was fabricated in hydrogen, obeys the line fitted to the constant specific strength; the strength of 100 MPa in about 50% porosity. However, the tensile strength of lotus iron fabricated in nitrogen is twice the predicted value. The high strength is ascribed to solid solution strengthening due to the solute nitrogen atoms, which contains 0. mass%.
The anisotropic tensile deformation of lotus copper has been recently investigated with an emphasis on crack formation during deformation.38) The microscopic deformation was analyzed by an acoustic emission (AE) method, which can detect crack formation. A broadband AE sensor is placed on the specimen during tensile tests to generate an AE signal by deformation. Figure 13 shows the amplitudes of the burst AE signals detected during the deformation of lotus copper and the corresponding stress'strain curves for (a) parallel loading and (b) perpendicular loading. The elongation and peak stress (ultimate tensile strength) for perpendicular loading are much smaller than those for parallel loading, which is consistent with the aforementioned result for tensile strength. It is significant that many burst AE signals are detected after yielding to a fracture, regardless of the loading direction. Unlike lotus copper, burst AE signals are not detected in nonporous copper, as shown in Fig. 13(c). Thus, the burst AE signals associated with lotus copper can be attributed to pore-related crack formation. The cumulative AE counts per unit of nominal strain for perpendicular loading are larger than those for parallel loading; the cracks are formed more easily under perpendicular loading.
Amplitude of the burst AE signals detected during deformation and the corresponding stress'strain curves for lotus copper under (a) parallel and (b) perpendicular loadings. (c) Amplitudes of the burst AE signals detected loadings parallel and perpendicular to the solidification direction are applied to nonporous copper.
The changes in the cross-section, ΔS, during parallel and perpendicular tensile loading for lotus copper and nonporous copper have also been measured. The value of ΔS for perpendicular loading is smaller than that for parallel loading, and the values of ΔS in lotus copper are much smaller than those in nonporous copper. These observations imply that under perpendicular loading, lotus copper macroscopically behaves as a semi-brittle material, although nonporous copper is ductile, whereas under parallel loading, lotus copper behaves in an intermediate manner between deformation under perpendicular loading and that of nonporous copper. These deformation behaviors of lotus copper are qualitatively consistent with that of a ductile metal, which tends to deform as a brittle material under high stress triaxiality.39)
Sound absorption materials with advanced performances to noises are required for car mufflers, air-conditioner parts, pump chambers, elevated roads, etc. Currently glass wool and foamed aluminum with closed pores are the most commonly marketed sound absorbing materials. In most cases, these materials have a low strength, but a good sound absorption capacity. The development of a sound absorbing material with comprehensive characteristics such as high strength, lightweight, and good sound absorption capacity is desirable. To investigate whether lotus metals exhibit significant sound absorption characteristics, Xie et al.40'42) have measured the sound absorption coefficients of lotus magnesium and copper plates by a standing-wave method; the details are provided in JIS A- standards.43) The absorption coefficient depends on the angle between the material surface and the incident sound wave. In their experiments, the specimen surface was perpendicular to the incident sound wave, and the specimen was set on a rigid wall in the sound tube. A pure sound with a single frequency was generated from a speaker installed at the other end. The standing-wave is caused by the interference between the incidence and reflection waves in the tube.
The absorption coefficients for lotus copper α0 have been measured as functions of pore diameter, porosity, and specimen thickness in the frequency range from 125 Hz to 4 kHz. The results can be summarized by:
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'
α0 increases as the pore diameter decreases from 660 µm to 460 µm.
'
α0 increases as porosity increases from 43% to 62%.
'
α0 increases as thickness increases.
A similar tendency has been observed for lotus magnesium.41,42) Figure 14 compares the absorption coefficients of lotus copper, foam aluminum, and glass wool with the same thickness specimen and frequency region. Similar to commercially available glass wool and foam aluminum, lotus metals exhibit a superior sound absorbing capacity. The foam aluminum is composed of numerous independent closed pores. For a high sound absorption, continuous pores are necessary so that minute cracks are introduced by rolling to connect the pores of the foam aluminum.44)
Comparison of the sound absorption coefficients for various materials with thickness of 20 mm.
It is thought that the viscosity resistance of air in the pores plays an important role in absorbing sound for a porous material. Sound is absorbed by the resistance in the fiber and the thin space of the pores when it enters into the open pores in porous materials.45) Additionally, sound is absorbed by the disturbance of the movement of air. The absorption of sound in a porous material is mainly due to the consumption of sound energy by the viscosity and thermal conduction when sound is propagating into the thin tube.
To use lotus copper effectively as heat sinks, which is discussed below, it is important to know its effective thermal conductivity and to consider the pore effect on heat flow. There are two typical methods to measure effective thermal conductivity keff of materials: an unsteady-state method (e.g., laser-flash method) and a steady-state method. In the former, the time change of the temperatures on the front and reverse sides of the specimen irradiated by a laser-flash is measured to determine keff. This method is suitable to measure keff of homogeneous and isotropic solid materials.46) On the other hand, in the latter method, a constant temperature on the front and reverse sides of the specimen is maintained to measure the steady-state heat flow through the specimen. This method is suitable to measure keff of inhomogeneous and anisotropic materials.47) Thus, the steady-state method has been adopted to measure keff of lotus metals.48) In measurements using the steady-state method, the specimen settles between a heater block and cooling block, and the temperatures at each block and the specimen are detected by thermocouples and the temperature gradient is measured.
The effective thermal conductivity of lotus copper keff is defined by
(5)where q is the heat flux from heat flow Q divided by the heat flowing through cross-sectional area A in lotus copper and T is the temperature in lotus copper. The tensor keff is orthorhombic and is expressed as
(6)Because keff of lotus copper is anisotropic, the parallel and perpendicular effective thermal conductivities, keff// and keff', of lotus copper are defined as the thermal conductivities for the heat flow parallel and perpendicular to the pore axis, respectively. Because the heat flow cross-sectional areas parallel to the pore axis in lotus copper are proportional to (1 ' p), keff// is expressed as
(7)where ks is the thermal conductivity of nonporous copper. Behrens49) has derived keff of composite materials with orthorhombic symmetry. By applying his equation to the thermal conductivity of lotus copper, keff' can be expressed as
(8)where β (= kp/ks) is the conductivity ratio; that is, it is the pore conductivity kp divided by material conductivity ks of lotus copper. Because the thermal conductivity of the hydrogen gas or air in the pores of lotus copper is negligible compared to that of the lotus material, the effective thermal conductivity of lotus copper is derived by the following equation where β = 0 in the above equation
(9)Han and Cosner50) have performed a numerical study on keff of fibrous composites using a unit-cell approach under a uniform fiber diameter condition. Because the diameter of lotus copper is distributed around a certain range, the numerical simulation for the thermal conductivity perpendicular to the pores under a nonuniform pore diameter condition was conducted to verify the applicability of Eq. [9] to lotus copper.
Figure 15 compares the experimental data and the results evaluated by the analytical equation in Eq. [7] for thermal conductivity parallel to the pores. The experimental data for keff// agrees well with the analytical results derived from the assumption that the heat flow through the cross-sectional area parallel to the pore axis is proportional to (1 ' p). A value of 335 W/(m K) for thermal conductivity ks of the lotus copper material is used for comparison. Figure 15 compares the experimental data and Eq. [9] where effective thermal conductivity keff' perpendicular to the pores is lower than that of the parallel ones (keff//), and is 40% of lotus copper material ks with a porosity of 40%. The analytical values evaluated by Eq. [9] is consistent with the experimental data, indicating that Eq. [9] can be used to predict the effective thermal conductivity perpendicular to the pores of lotus copper within an experimental accuracy of ±10%. The results show that lotus copper displays anisotropy of the effective thermal conductivity. The effective thermal conductivity keff' perpendicular to the pores is lower than that of parallel ones (keff//).
Comparison of the experimental data of the effective thermal conductivity of lotus copper parallel and perpendicular to the pore axis with the analytical data.
The Answer is just like the words: Porous Metal, porous metal materials is a kind of metals with a large number of directional or random pores distributed diffusely inside, have a diameter of about 2 um to 3 mm. due to the different design requirements of the pores, the pores can be of foam type, coupled type, honeycomb type, etc.
Porous metal materials can also be divided into two major categories according to the morphology of their pores: free-standing pores and continuous pores.
The independent type of material has a small specific gravity, rigidity, good specific strength, good vibration absorption, sound absorption performance, etc.;
the continuous type of material has the above characteristics but also has the characteristics of permeability, good ventilation, etc.
Because porous metal materials have the characteristics of structural materials and functional materials, they are widely used in aerospace, transportation, construction, mechanical engineering, electrochemical engineering, environmental protection engineering, and other fields.
Powder sintered metal porous material is a porous metal with a rigid structure made by forming and high-temperature sintering using metal or alloy powder as raw material. Characterized by a large number of internal connected or semi-connected pores, the pore structure consists of a stack of regular and irregular powder particles, the size and distribution of pores and the size of the porosity depend on the powder particle size composition and preparation process.
Common materials of sintered metal powder porous materials are bronze, stainless steel, iron, nickel, titanium, tungsten, molybdenum, and refractory metal compounds.
Sintered stainless steel filter have excellent corrosion resistance, oxidation resistance, wear resistance, and mechanical properties (ductility and impact strength, etc.). Sintered stainless steel porous materials can be used in the fields of sound dissipation, filtration, and separation, fluid distribution, flow restriction, capillary cores, etc.
Sintered titanium and titanium alloy porous materials not only have the properties of ordinary metal porous materials but also have the unique excellent properties of titanium metal such as low density, high specific strength, good corrosion resistance, and good biocompatibility, etc. They are widely used in food and beverage, environmental protection and energy, fine chemical, medical and pharmaceutical, electrolytic gas production and other industries for precision filtration, gas distribution, decarbonization, electrolytic gas production, and for making biological implants.
Sintered powder nickel-based porous materials have the advantages of corrosion resistance, wear resistance, high mechanical strength at high and low temperatures, thermal expansion, good electrical and magnetic conductivity, etc., and can be applied to high-temperature precision filtration and electrodes for rechargeable batteries. Among them, the porous materials of Monel alloy can be used to make filter elements in seamless water pipes and steam pipes in power plants, filter elements in seawater exchangers and evaporators, filter elements for sulfuric and hydrochloric acid environments, filter elements for crude oil distillation, filter equipment used in seawater, filter equipment used in the nuclear industry for manufacturing uranium refining and isotope separation, filter elements in equipment for manufacturing hydrochloric acid, filter elements in alkylation plants in oil refineries, and filter elements in low-temperature areas of hydrofluoric acid systems in refineries. filter elements in the low-temperature area of hydrofluoric acid systems in oil refineries.
Sintered powder copper alloy porous material has the advantages of high filtration precision, good permeability, and high mechanical strength, and is widely used in compressed air degreasing and purification, crude oil desanding and filtration, nitrogen and hydrogen filtration, pure oxygen filtration, bubble generator, fluidized bed gas distribution, and other fields in pneumatic components, chemical industry, and environmental protection industry.
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Sintered powder intermetallic compound porous materials are more researched and applied in TiAl, NiAl, Fe3Al, and TiNi, etc., which integrate the functional characteristics of porous materials and intermetallic compounds. Fe3Al porous materials can be applied in the fields of direct purification and dust removal of dust-containing gases at high temperatures, such as energy (clean combustion combined cycle power generation process and pressurized fluidized bed coal-fired power generation technology), petrochemical, TiNi porous material has special quasi-elasticity and overall memory effect, which makes it ideal for human bone implant material.
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