Materials Science and Engineering A 386 (2004) 390–395 lot al s i Ok 8-1 Mih ed form Abstract Lotus-typ pores w dissolving h tion c open pores, to 4 kH frequency. T specim diameter. In tus-ty attenuation c © 2004 Else Keywords: Po iamete 1. Introduction Recentl performanc conditioner glass wool most frequ present. In though they opment of characteris sound abso Boiko e vestigated t gated pores hydrogen a direction a ubility betw gate wheth good sound ∗ Correspo E-mail a In a recent experiment [14], we investigated sound ab- sorption characteristics of lotus-type porous magnesium and 0921-5093/$ doi:10.1016/j y, sound absorbing materials with an advanced e to noises are required for mufflers of cars, air- parts, pump chambers, elevated roads, etc. The and foamed aluminum with closed pores are used ently as marketed sound absorbing materials at most cases, these materials have low strength have good sound absorption capacity. The devel- the sound absorbing material with comprehensive tics such as high strength, lightweight and good rption capacity is desirable. t al. [1] and, Nakajima and co-workers [2–13] in- he fabrication of various porous metals with elon- by unidirectional solidification under pressurized nd argon. Many gas pores that are aligned in one re evolved due to the difference of hydrogen sol- een liquid and solid. It is interesting to investi- er such porous metals with elongated pores exhibit absorption capability. nding author. Tel.: +81 6 6879 8437; fax: +81 6 6879 8439. ddress:
[email protected] (Z.K. Xie). found a good absorption capability. It is interesting to inves- tigate the sound absorption characteristics of other materials such as lotus-type porous copper. Since the lotus-type porous copper fabricated by unidirectional solidification has uniform pore size and since it is easy to fabricate than other lotus-type porous metals, we have decided to examine its sound absorp- tion capability. In addition, the sound absorption mechanism is discussed according to the model of absorbing sound of the porous material. 2. Experimental procedure The fabrication apparatus of the porous metal consists of a graphite crucible (110 mm in outer diameter, 90 mm in inner diameter and 175 mm in height) surrounded by an induction- heating coil and a mould. These are installed in a high- pressure chamber [7]. Copper (purity: 99.99%) was melted in the crucible in a vacuum, and then high-pressure mixture gas of hydrogen and argon was introduced into the chamber. The temperature of the melt in the crucible was monitored by – see front matter © 2004 Elsevier B.V. All rights reserved. .msea.2004.07.058 Sound absorption characteristics of fabricated by unidirection Zhenkai Xie∗, Teruyuki Ikeda, Yosiyuk The Institute of Scientific and Industrial Research, Osaka University, Received 9 March 2004; received in revis e porous copper with large number of unidirectional cylindrical ydrogen in a pressurized hydrogen atmosphere. The sound absorp was measured by standing-wave method in the frequency range up he absorption coefficient increases with increasing porosity and addition, it was understood that the absorption coefficient of lo onstant. vier B.V. All rights reserved. rous metals; Attenuation constant; Absorption coefficient; Porosity; Pore d us-type porous copper olidification uda, Hideo Nakajima ogaoka, Ibaraki, Osaka 567-0047, Japan 15 July 2004 as fabricated by unidirectional solidification of melt oefficient of the porous copper plate, which has many z. The absorption coefficient increases with increasing en thickness, while it decreases with increasing pore pe porous materials could be evaluated by using the r Z. Xie et al. / Materials Science and Engineering A 386 (2004) 390–395 391 a W-5%Re/W-26%Re thermocouple and was controlled to be 1500 K. After 20 min to make hydrogen dissolve into the molten copper, by pulling the stopper of graphite upward, the molten copper was poured into the mould whose bottom plate was cooled with water circulated through a chiller. The lateral side of the mould was made of alumina-coated stainless steel plate of 0.1 mm thickness, which is suitable for heat insula- tion because of its small heat capacity; solidification occurs in one direction from the bottom to the top. The ingots thus obtained were 100 mm in diameter and 130 mm in maximum height and contained various levels of porosity, which were controlled by the total and partial pressures of hydrogen and argon. Typical cross-sections of the porous copper are shown in Fig. 1. The specimens for the absorption coefficient mea- surement with a gauge diameter of 85 and 30 mm were cut out from the ingots by using a spark–erosion wire cutting machine (Model A320D, Sodick Co.). The porosity ε of the specimen was calculated from the weight of specimens and their apparent volume using the equation Fig. 1. Optica fabricated und lidification di Fig. 2. Schem ε(%) = ( 1 where ρ is t of ordinary The sou measured b the absorpt material su work, the s cident soun measureme men was se with a sing stalled at th interferenc in the tube each one-q the sound p B are the a respectivel en as | inim ax in = |A+ B||A− B| = n (2) ound reflectivity of the specimen is written as∣∣∣∣BA ∣∣∣∣ = n− 1n+ 1 (3) bsorption coefficient, α0, is given by 1− ∣∣rp∣∣2 = 4 n+ (1/n)+ 2 (4) x and |p|min are measured by moving the microphone tube to determine the value of n. Then the absorption cient can be calculated using Eq. (4). This measuring od is called a standing-wave method, which is one of the l micrographs of lotus-type porous copper with 44% porosity er hydrogen of 0.4 MPa (a) a section perpendicular to the so- rection and (b) a section parallel to the solidification direction. writt and m |p|m |p|m The s ∣∣rp∣∣ = The a α0 = |p|ma in the coeffi meth atic drawing for measurement of sound absorption coefficient. − ρ ρs ) × 100 (1) he density of the porous copper and ρs the density solid copper. nd absorption coefficient of the specimen was y a standing-wave method [15]. It is known that ion coefficient depends on the angle between the rface and the incident sound wave. In the present pecimen surface was set perpendicular to the in- d wave. Fig. 2 shows the schematic drawing for nt of the sound absorption coefficient. The speci- t on the rigid wall in the sound tube. A pure sound le frequency was generated from the speaker in- e other end. The standing-wave is caused by the e between an incidence wave and a reflection wave . The sound pressure becomes the maximum at uarter of the wavelength. The maximum value of ressure is written as |p|max = |A + B|, where A and mplitude of incidence wave and reflection wave, y. The minimum value of the sound pressure is p|min = |A − B|. The ratio between the maximum um of the sound pressure, n, is given by 392 Z. Xie et al. / Materials Science and Engineering A 386 (2004) 390–395 Fig. 3. tube metho standards [ In the p resistance tance of th as the vent such as clo the absorpt of absorbin resistance o by Rf = �p u , where u is through the and �p is A pump is pressure be a U manom u = Q S , where S an respectivel 3. Results In the p lotus-type 30 mm wer to 4 kHz. T the measur while those than 1000 H functions o thickness t The abs of pore diam ness and th increases w in the who porosity de Effect of pore diameter d on sound absorption coefficient α0 of lotus- orous copper. . Effect copper. pore diameter 380�m and constant specimen thickness m. The absorption coefficient increases with increasing sity from 43 to 62%. There is some data scattering, which ributed to co-existence of non-permeable and permeable . g. 6 shows the dependence of the absorption coefficient ecimen thickness when the pore diameter and porosity onstant. The absorption coefficient increases with in- ing thickness. Especially, the absorption coefficient in- es significantly in high frequency range. The maximum was observed at 3.1 kHz in the specimen of 20-mm , while such maximum value was not found until 4 kHz Schematic drawing for measurement of flow resistance. ds, and the details are provided in JISA 1405–1963 15]. resent work, it is necessary to measure the flow of the lotus-type porous copper. The flow resis- e sound absorbing material is basically the same ilation resistance, used to show the ventilations th and paper [16]. Both the flow resistance and ion coefficient show amounts of the performance g sound in the porous material. Unit area flow f the porous sound absorbing material is defined (5) the flow ratio when the constant air is passed vertical direction on the surface of the material, difference in pressures at both sides of material. operated as shown in Fig. 3, and the differential tween both sides of the specimen is measured with eter. The flow ratio u is written as (6) d Q are area of specimen and flow volume of air, y. resent work, the absorption coefficients for the porous copper with various thickness 10, 20 and e measured in the frequency range from 125 Hz he specimens of 15 mm in radius were used for ements in the frequency range less than 1000 Hz, Fig. 4. type p Fig. 5 orous stant 10 m poro is att pores Fi on sp are c creas creas of α0 thick of 42.5 mm in radius were used in the range more z. The absorption coefficient α0was measured as f the pore diameter d, the porosity ε and specimen of the lotus-type porous copper. orption coefficient α0was measured as a function eter under the condition that the specimen thick- e porosity were constant. As shown in Fig. 4, α0 ith decrease in pore diameter from 660 to 460�m le frequency range up to 4 kHz. Fig. 5 shows the pendence of the absorption coefficient for con- Fig. 6. Effect tion coefficien of porosity ε on sound absorption coefficient of lotus-type of specimen thickness t with 10 and 20 mm on sound absorp- t α of lotus-type porous copper. Z. Xie et al. / Materials Science and Engineering A 386 (2004) 390–395 393 Table 1 Results of porosity, pore diameter, flow resistance and absorption coefficient α0 lotus-type porous copper Thickness (mm) Porosity (%) Pore diameter (�m) Flow resistance (Ns/m3) Absorption coefficient (%) Penetration ratio 1 kHz 10 61 460 8.4 9 59 550 2.8 7 58 660 1.7 7 10 62 413 0.18 8 55 404 0.15 7 43 425 0.07 6 20 51 680 1.04 35 52 510 0.56 41 47 270 1.45 43 20 43 602 4.6 49 47 609 0.6 – 54 613 4.9 32 30 18 18 – Lotus-type po ores an S1 to area of p 2. in the speci served for t been report In the p a function in Table 1. The gla ing sound terial. The copper, the same thick pared as sh a standing aluminum foam alum pores. Con absorption duced by minum. Fig. 7. C iscuss Mecha is tho an im rial. T hin sp in po sturba d in p onsum erma in tub 30 867 1.9 38 847 1.8 50 850 3.7 rous metals fabricated by unidirectional solidification include permeable p ore on surface S2 is called the penetration ratio, which is described as S1/S men of 10-mm thick. A similar tendency was ob- he lotus-type porous magnesium that had already ed [14]. resent work, the flow resistance was measured as of specimen thickness, whose result is compiled ss wool has a peculiar mechanism of absorb- and is used widely as the sound absorbing ma- absorption coefficients of the lotus-type porous foam aluminum and the glass wool with the ness, in the same frequency region were com- own in Fig. 7. All of them were measured by -wave method. The glass wool [17] and foam [18] exhibit superior absorption capacity. The 4. D 4.1. It plays mate and t pores by di soun the c the th the th inum is composed of many independent closed tinuous pores are necessary to have high sound capability [17] so that minute cracks are intro- rolling to connect the pores of the foam alu- omparison of absorption coefficient of various materials. pores in th shape. 4.2. Attenu The lotu sembly of analysis, fi tube. When of a sound ation in a s than the att attenuation β = 0.010 cr where c an spectively. when the in 2 kHz 3 kHz 4 kHz 30 76 81 High 22 66 75 High 17 31 70 High 27 43 90 High 20 39 93 High 14 30 79 High 72 52 49 Medium 73 61 57 Medium 84 52 59 Medium 36 44 68 Medium – – – Medium 44 43 49 Medium 62 71 65 Low 68 78 69 Low – – – Low d non-permeable pores. The rates of area of permeable pores ion nism of sound absorption ught that the viscosity resistance of air in pores portant role in absorbing the sound for the porous he sound is absorbed by the resistance in the fiber ace of pores, when the sound enters into the open rous materials [19]. The sound is also absorbed nce of the movement of air. The absorption of the orous material is considered to be mainly due to ption of the sound energy by the viscosity and l conduction when the sound is propagating into e. It is difficult to analyze this strictly because the e porous material are arranged to have complex ation of sound in thin tube s-type porous metal can be considered as an as- many parallel thin tubes. In order to simplify the rst consider how a sound propagates in only one a sound propagates in a thin tube, the attenuation depends on the material of the tube. The attenu- mooth metal tube has been reported to be larger enuation in air [20]. According to Igarasi [21], the constant β is expressed as 2 f 1/2 (7) d r are speed of sound and radius of tube, re- The attenuation of sound can often be disregarded ner diameter exceeds several centimetres because 394 Z. Xie et al. / Materials Science and Engineering A 386 (2004) 390–395 attenuation is reversely proportional to the inner diameter in Eq. (7). On the other hand, since the radius of pores of the lotus-type porous copper is from 200�m to 1 mm, the atten- uation incr copper. Th βN = β N = The relatio written as N = r 2 1ε r2 where r1 is From Eq type porou βN = 0.01 cεr The abs is consider changing th ing sound i sound ener of pores. S ence betwe waves and However, u [22]. In the sorbing sou lotus-type ence since some abso permeable necessary t The thicker to be perme ited in the the pores a more in thi the absorpt was increas The atte per is cons ergy into th From this v porous cop diameter, t Fig. 8 show the attenua found that ation const the thickne because pe The the vertical to t . A relation between absorption coefficient and attenuation constant s-type porous copper with 10 mm thickness. A relat s-type porous copper. anism in lotus-type porous materials. More corrections e theory have been made [23]. e absorption coefficient for thickness 30 mm may be rent from that of thickness 20 mm and falls into disor- hough that of thickness 10 mm increases with increasing resistance in Table 1. Fig. 9 shows the relation between ow resistance and the absorption coefficient of speci- with thickness 10 and 20 mm. The penetration ratio de- es with increasing specimen thickness from 10 to 30 mm g. 10. The flow resistance of the 30-mm-thick specimen ot be measured because of being hardly permeable. 0. A relation between penetration ratio and specimen thickness of ype porous copper. eases when the sound enters the lotus-type porous e attenuation constants of N pores are given by 0.0102 crN f 1/2 (8) n between the pore number and the porosity is (9) a radius of the specimen. s. (8) and (9), the attenuation constant in the lotus- s copper is given by 02 2 1 f 1/2. (10) orption coefficient of the lotus-type porous copper ed to be changed by dead ends of the pores or by e shape of the pores. It is considered that absorb- n porous materials is caused by a viscous loss of gy due to the friction between air and inner surface trictly, the absorbing sound is caused by interfer- en surface reflection waves and the back reflection thermal conduction through vibration of fiber, etc. sually, the influence is small and often disregarded present work, it is thought that the reason of ab- nd is mainly due to viscous friction of air in the porous copper. It is possible to disregard its influ- it is very small though non-permeable pores have rption coefficient. The absorption effect by only pores is taken into consideration. Therefore, it is o measure the porosity of only permeable pores. the specimen is, the more pores become difficult able because the length of elongated pores is lim- lotus-type porous copper. It has been known that re hardly permeable in the specimen of 20 mm or ckness. Therefore, some differences were seen in ion coefficient–frequency curve when the porosity ed from 43 to 62% in Fig. 5. nuation mechanism of the lotus-type porous cop- idered to be the change of absorption sound en- ermal energy by the viscous friction in the pores. iewpoint, the attenuation constant in the lotus-type per is related to the radius, the porosity, the pore he thickness of the specimen and the frequency. s the relation of the absorption coefficient and tion constant by calculating from Eq. (10). It is the absorption coefficient is related to the attenu- ant of the specimen of 10 mm in thickness. When ss is 10 mm or more, a similar trend was not seen netration was not enough. ory that is modelled as a set of a capillary tube he surface is basic for the analysis of the absorbing Fig. 8 of lotu Fig. 9. of lotu mech on th Th diffe der, t flow the fl mens creas in Fi cann Fig. 1 lotus-t ion between absorption coefficient and flow resistance at 2 kHz Z. Xie et al. / Materials Science and Engineering A 386 (2004) 390–395 395 For the foam aluminum, the absorption mechanism is not only the change of sound wave into thermal energy by fric- tion on the film side of the cell structure but also interference by diffused reflection of bubbles on the film side. The ab- sorption coefficient increases by interfering with the surface reflection wave and the back reflection wave according to the attenuation characteristics in the urethane foam of 20 mm in thickness [24]. 5. Conclusions The absorption coefficient of lotus-type porous copper was measured by the standing-wave method. (1) The absorption coefficient increases with increasing fre- quency. (2) The ab which decrea (3) The ab which increas (4) The ab rather u the thic (5) It has b tion co come d from 1 (6) The ab per can Acknowled The aut Hyun, Mr. tal assistan in-Aid for of Educatio Grant-in-A between U References [1] L.V. Boiko, V.I. Shapovalov, E.A. Chernykh, Metallurgiya 346 (1991) 78. [2] H. Nakajima, Func. Mater. 20 (2000) 27. [3] H. Nakjima, Bull. Iron Steel Inst. Jpn. 6 (2001) 701. [4] S.K. Hyun, H. Nakajima, in: J. Banhart, M.F. Ashby, N.A. Fleck (Eds.), Cellular Metals and Metal Foaming Technology, MIT-Verlag, 2001, p. 181. [5] S. Yamamura, H. Shiota, K. Murakami, H. Nakajima, Mater. Sci. Eng. A 318 (2001) 137. [6] H. Nakajima, S.K. Hyun, K. Murakami, Adv. Tech. Mater. 4 (2002) 13. [7] S.K. Hyun, H. Nakajima, Mater. Trans. 43 (2002) 526. [8] H. Nakajima, T. Ikeda, S.K. Hyun, in: J. Banhart, N.A. Fleck, A. Mortensen (Eds.), Cellular Metals: Manufacture, Properties Applica- tion, MIT-Verlag, 2003, p. 191. [9] H. Nakajima, S.K. Hyun, K. Ohashi, K. Ota, K. Murakami, Colloids Surf. A: Physicochem. Eng. Aspects 179 (2001) 209. .K. Hyun, K. Murakami, H. Nakajima, Mater. Sci. Eng. A 299 2001) 2 . Yama ng. A .K. Hy tsuka, erence nstitute . Naka eedings eptemb .K. Xie 2003) 7 . Kimu ublishin . Masa apanese . Okud . Akiya eport o . Nisim o., Ltd .L. Ber . Igaras apan, 1 . Koya apanese . Koya apanese . Akiya yushu– sorption coefficient of the 10-mm-thick specimen, has rather uniform porosity of 58%, increases with sing pore diameter from 660 to 460�m. sorption coefficient of the 10-mm-thick specimen, has rather uniform pore diameter, increases with e in porosity from 43 to 62%. sorption coefficient of specimens, which have niform pore diameter and porosity, increases with kness changed from 10 to 20 mm. een understood that the measurement of absorp- efficient becomes difficult because the pores be- ifficult to penetrate with the thickness increased 0 to 20 mm sorption coefficient of the lotus-type porous cop- be evaluated by using the attenuation constant. gments hors gratefully thank Dr. K. Murakami, Dr. S.K. T. Nakahata and Mr H.Hosiyama for experimen- ts. The present research was supported by Grant- the 21st Century COE Research of the Ministry n, Culture, Sports, Science and Technology and id for Development of Innovative Collaboration niversity and Industry. [10] S ( [11] S E [12] S O f I [13] H c S [14] Z ( [15] S P [16] K J [17] Y [18] S R [19] S C [20] L [21] J J [22] M J [23] M J [24] S K 41. mura, H. Shiota, K. Murakami, H. Nakajima, Mater. Sci. 318 (2001) 137. un, Y. Shiota, K. Murakami, H. Nakajima, in: M. Koiwa, K. T. Miyazaki (Eds.), Proceedings of the International Con- on Solid–Solid Phase Transformations’99 (JIMIC-3), Japan of Metals, Kyoto, 1999, p. 341. jima, S.K. Hyun, K. Ohashi, K. Ota, K. Murakami, Pro- of the third Inc. High Pressure School, Warsaw, Poland, er 13–16, 1999, p. 37. , T. Ikeda, Y. Okuda, H. Nakajima, J. Jpn. Inst. Met. 67 08 (in Japanese). ra, Architectural Sound and Anti-Noise Plan, Shokokusha g Co., Ltd., Tokyo, Japan, 1977, p. 142 (in Japanese). ru, Architectural Acoustics Noise Control 71 (1990) 25 (in ). a, Proc. J. Acoustic Soc. Jpn. (1990) 581 (in Japanese). ma, M. Itoh, E. Ishii, National Industrial Research Institute f Kyushu, 1991, p. 2928 (in Japanese). aki, Electro-Acoustics and Vibration, Corona Publishing ., Tokyo, Japan, 1971, p. 79 (in Japanese). anek, Acoustic Measurement, Wiley, 1950. i, Sound and Vibration, Kyoritsu Shuppan Co., Ltd., Tokyo, 970, p. 37 (in Japanese). su, Architectual Acoustics Noise Control 13 (1984) 19 (in ). su, Architectual Acoustics Noise Control 19 (1990) 5 (in ). ma, Research Lecture between University and Industry of Okinawa Region, 2001, p. 17 (in Japanese). Sound absorption characteristics of lotus-type porous copper fabricated by unidirectional solidification Introduction Experimental procedure Results Discussion Mechanism of sound absorption Attenuation of sound in thin tube Conclusions Acknowledgments References