Damping in some cellular metallic materials

Journal of Alloys and Compounds 355 (2003) 2–9

L

www.elsevier.com / locate / jallcom

Damping in some cellular metallic materials ,1

I.S. Golovin* , H.-R. Sinning ¨ Werkstoffe, Technische Universitat ¨ Braunschweig, Langer Kamp 8, D-38106 Braunschweig, Germany Institut f ur

Abstract The ability to absorb energy of mechanical vibrations by different cellular metallic materials with porosities from 14 to 96% (metallic foams, metallic sponges and sintered metals) is discussed. Different mechanisms of internal losses (thermoelastic and microeddy currents, magnetic domains, dislocations, microcracks) are considered in respect of low weight, peculiarities of structure and applicability for damping of mechanical vibrations.  2003 Elsevier Science B.V. All rights reserved. Keywords: Metals; Surfaces and interfaces; Dislocations; Strain

1. Introduction Cellular metallic materials (CMM) [1]: metallic foams, metallic sponges and porous (specially sintered) metals are a relatively new and uncommon group of engineering materials. From the commercial viewpoint, Al foams have already found their application for sound and energy absorption (when crashed) if weight minimisation is demanded [2]. Very limited information is available as yet about mechanical damping and mechanisms of internal friction (IF) in any type of these cellular metals. It is notable that most of IF mechanisms, acting in dense metals, contribute to damping in CMM [3]. The density of CMM might be 1 / 10 or even lower than that of the metals used for the CMM carcass [1–5]: then the damping in relation to weight is a promising parameter in the case of CMM. Taking into account that strength (and some other engineering properties) is not always in conflict with the capacity to absorb energy of mechanical vibrations, the advantages and limitations of different mechanisms of energy dissipation in CMM are discussed in this paper. 2. Materials characterisation The main engineering parameter of porous materials, porosity, is defined as P 5 1 2 r * /rs , where r * is the

density of the porous material and rs is that of the solid of which it is made. Fe- and Ti-based sintered metals (P 5 14–78%), Al- and Zn-based foams (P 5 75–90%), and also Ni-, Cu-, and Al-based sponges (P 5 90–96%) are studied in this paper. Some of them have closed cell structures, some have open or partially open cells; the corresponding macro- and microstructures are presented in Ref. [3]. In this paper we choose only one representative for each subgroup to illustrate quantitatively their behaviour when vibrating and different mechanisms controlling damping. The main structural parameters of these representatives— Al foams with trade name Alporas  (Shinko Wire, Japan), sintered PM 316L steels (GKN Sinter Metals GmbH, Germany), and Ni-based sponges (NPO ‘Inorganic Materials’, Perm, Russia)—are given in Table 1. It should be noted that dense Al ( rs 52.7) and FeNiCr 316L type steel ( rs ¯8.0) are known as materials with very ordinary damping properties, and only Ni ( rs ¯8.9) exhibits high damping due to the magneto-elastic effect. Mechanical tests were carried out using a Zwick universal testing machine; damping was tested, using free-decay vibrations of free-clamped specimens at bending or torsion, as logarithmic decrement d 5 ln A 1 /A n11 from two successive vibrations with amplitudes A n and A n11 . 3. Results and discussion

*Corresponding author: Tel.: 149-531-391-3066; fax: 149-531-3913058. E-mail address: [email protected] (I.S. Golovin). 1 On leave from the Russian State Technology University (MATI), Moscow, Russia.

3.1. Elasto-plastic behaviour of foams, critical amplitudes of deformation When a compressive force increases, foams exhibit

0925-8388 / 03 / $ – see front matter  2003 Elsevier Science B.V. All rights reserved. doi:10.1016 / S0925-8388(03)00241-X

I.S. Golovin, H.-R. Sinning / Journal of Alloys and Compounds 355 (2003) 2–9

3

Table 1 Studied materials a Material

Denoted as

Porosity P, %

Density r *, Mg m 213

Average size of (in mm): Pores

Particles

Walls / struts thickness

,0.002 0.004 0.010 0.032 0.065

,0.05 0.075 0.150 0.250 0.600

– – – – –

Sintered 316L steels

RCJ-14 b GKN-21 GKN-32 GKN-44 GKN-51

14 21 32 44 51

6.85 6.26 5.40 4.48 3.86

Al-based foams

Alp-85 Alp-90

85 90

0.40 0.26

4 4

– –

Ni-based sponges

Ni[95 Ni[96 c

95 96

0.376 0.371

5 0.5

– –

0.12 0.4 #0.1

a

We are grateful to Dr. T. Miyoshi (foams), Dr. M. Bram (sintered steels) and Dr. V. Kruzhanov (sponges) for these materials. ¨ RCJ—Research Center, Julich (Dr. M. Bram). c Ni [ 96 sponge contains ¯2% Fe. b

elasticity, elasto-plasticity, plateau-plasticity and densification (Fig. 1a). In case of tension, a softening takes place instead of the plateau. Energy absorption due to compression is an advanced characteristic of cellular materials and, in particular, Al foams [1,5]: energy is absorbed as the cell walls bend plastically, or buckle, or fracture, while the stress is limited by the long, flat s – ´ plateau. The higher the porosity, the lower the plateau stress is. Foams show linear elasticity at very low compressive stresses below the beginning of microplasticity (´mpd ); both intervals are better seen in log s vs. log ´ scales (insert in Fig. 1a), followed by the formation of plastic hinges in the elastoplastic range (below ´pl ), and then a long collapse plateau * ) associated with collapse of under the plateau stress (s pl the cells by the formation of plastic hinges and cell wall buckling, finally truncated by a regime of densification (above ´D ) in which the stress rises steeply. The energy absorbed per unit volume (W ), up to the densification strain, is: ´D

W5

E s(´) d´ 1E ( p 2 p ) d´, o

0

Fig. 1. Stress–strain behaviour of Alp-85 (see Table 1): (a) compression test with distinction of deformation ranges: 1—linear elasticity, 2— elasto-plastic transition, 3—plateau plasticity, 4—densification; ´mpd, ´pl and ´D are the critical transition amplitudes between these ranges (insert: enlargement of the low-´ range in logarithmic scales); (b) cyclic tension– compression tests; 1, 2, and 2700 cycles, deformation rate 0.2 mm min 21 .

´D

0

where the first term is due to deformation of the material, the second one due to air pressure ( p) changes in the cells. In most cases (open cells, close cells with small voids, not high strain rate) the second term for CMM is negligible. When the plateau is flat, the value of energy absorbed per unit volume is about Wv 5 s *pl ´D . Often, minimum weight is the goal: the value of energy absorbed per unit weight is then Ww 5 (s *pl 3 ´D ) /r *, with ´D ¯ 0.8– 1.75( r * /rs ) [6]. For the ‘Alp-85’ specimen used (Table 1, Fig. 1a): ´D ¯ 55% and Ww ¯ 4.5 MJ m 23 . If foams or other CMM are applied for damping of mechanical vibrations, the energy losses in the first (elastic) and in the second (elasto-plastic) ranges of deformation are the most important. The cyclic tension–compression

I.S. Golovin, H.-R. Sinning / Journal of Alloys and Compounds 355 (2003) 2–9

4

tests of Alp-85 Al foam (Fig. 1b) with an amplitude of ´o ¯ 66 3 10 24 show an influence of the number of vibrations (N) on the energy (DW ) dissipated per cycle (i.e. the area enclosed between the loading and unloading curves), on the modulus of elasticity (E), and on the residual microplastic deformation (´r ). The DW value increases with applied stress s and number N of vibrations both, but is practically independent on the deformation rate within the range between 10 27 and 10 24 s 21 . An increase in N from 2 2 to 2700 leads to a decrease in averaged Young’s modulus (from 1.66 to 1.53 GPa), determined as the slope of the middle line of a tension–compression cycle, and to an increase in residual microplastic deformation (from ¯1.8 to 2.05 in 10 24 ). In addition, the curves shift to the compression side (D´ ¯ 1.5 ? 10 24 ) due to accumulation of deformation in the compression part of the tension–compression tests. Similar dependencies are observed in free-clamped damping tests (Fig. 2): the damping d increases both with the amplitude (´) and number (N) of vibrations (Fig. 2a); an increase in N also leads to a decrease in the apparent elastic modulus E, and to a growth of maximal vibration amplitude ´o belonging to a certain, constant excitation strength of the vibrating-reed apparatus (Fig. 2b). In addition, a decrease in r * of foams leads to an increase in d, and to a decrease in E and ´mpd [3,9]. Annealing at 200 8C decreases damping of the Alp-85 specimen.

3.2. Sound absorption and aerodynamic losses Interaction between CMM and the surrounding atmosphere, in case of vibration of either air (sound) or of the CMM itself, leads to effects of sound absorption and aerodynamic losses, correspondingly. Up to now there is no analytical solution of these problems in respect to CMM in the literature. The same also concerns experimental results. High values of the sound absorption coefficient a ¯ 90% are reported even for closed-cell foams [2,6], values between 20 and 80% are given in Ref. [7], while ˇ et al. [8] point out that close-cell metallic foams Kovacik are too stiff to convert sound energy into heat by vibration of their cell walls, so that the sound is entirely reflected (a ¯ 20%). Much better sound absorbing performance is observed for ACCESS  -sponge metals with open-cell structure (mainly by viscous losses as the sound pressure wave pumps air in and out of the interconnected pores) [8]. In all cases a depends on frequency. The sound absorption performance of metallic foams can be improved by opening of close-cell structures [8], in this case the foams can serve as multiple cavity resonator. The variability of the pore size will provide a wider frequency range of good sound absorption than typical resonators. 2

Asymmetric deformation occurs by hardening within the first cycle; from the 2nd cycle the hysteresis loop is nearly symmetric.

Fig. 2. Results of vibrating-reed tests of Alp-85: (a) amplitude dependent internal friction (ADIF) after different number of cycles N at maximal amplitude ´o (solid points—as received, open points—after annealing at 200 8C), solid line—dense Al; (b) the change of Young’s modulus E (from resonance frequency) and ´o as a function of N; (c) macrostructure of Alp-85 foam.

If the foam itself is vibrating in an atmosphere, the energy of mechanical vibrations is partly transferred to aerodynamic losses. These depend on the width of the vibrating beam and on the frequency. At low amplitude when the intrinsic losses in the material are relatively low, the aerodynamic losses are a powerful source of damping, which depends on the CMM structure (open or closed cells) and increases with frequency due to a pump effect. Since the structure of CMM (the surface of the beam) is different not only from one material to another but also from one individual specimen to another, only empirical equations are suggested in Refs. [9,10] on the basis of the experimental data. The aerodynamic losses can increase twice the intrinsic damping of a beam made from Al foam (at low amplitude of deformation ´ ¯ 10 25 ) when the air pressure increases from 10 26 to 1000 mbar (from 10 24 to 10 5 Pa). At higher vibration amplitude the intrinsic losses in CMM are more important [3], which makes the relative contribution of the aerodynamic losses much smaller, and sometimes, negligibly small.

I.S. Golovin, H.-R. Sinning / Journal of Alloys and Compounds 355 (2003) 2–9

3.3. Thermo-elastic amplitude independent damping Mechanical losses caused by transverse thermo-elastic currents (TTEC) are amplitude independent and can be described by a Debye peak of the form [11]: f ? fo 2 dte 5 D]] ; D 5 pa Eu T /Cs ; f 2 1 f o2 2

fo 5 pl / 2d Cs ,

5

From a practical viewpoint it should be noted that damping in foams even at amplitudes ¯10 25 is not absolutely amplitude independent, which means that damping caused by the TTEC can be sometimes overlapped with amplitude dependent mechanisms and can depend on several external and internal factors.

3.4. Magneto-elastic damping (1)

where fo is the peak frequency, DT is the relaxation strength, d, l, Cs ( 5 r Cp ), a, Eu are the thickness, thermal conductivity, specific heat, thermal expansion coefficient, and unrelaxed elastic modulus of the dense specimen, respectively, T is the temperature. The effect can be important for those CMM which exhibit high values of the quantity a 2 Eu /Cs (i.e. of the relaxation strength D), like Al- or Zn-based foams [3,9,10]. The main peculiarity of damping caused by TTEC in foams to be compared with dense material is the distribution of ‘d’ value: contrary to dense metals, where the meaning of ‘d’ is the thickness of the specimen, there is no well-defined structural scale in CMM for the TTEC. The maximum distance for TTEC is the thickness of the sample, the minimum distance is the thickness of the cell walls; thermal currents on the scale of the cell size are also not excluded (Fig. 2c). Finally, there is a corresponding broad distribution in the peak frequency fo ( fo | d 22 ). This results in lowering of the maximum thermoelastic damping in Al foam to be compared with dense Al at peak conditions (d ¯ 0.0072 [11]); at the same time the range of frequency where the TTEC contribute to damping is obviously much broader [9,10].

If one looks at damping from the viewpoint of step-bystep increasing of the vibration amplitude, then next to amplitude independent damping due to TTEC can be hysteretic magneto-elastic damping (MED) caused by irreversible displacements (the stress-induced Barkhausen jumps) of non-1808 walls of magnetic domains. The effect of MED is observed on Ni-based sponges (Fig. 3). In general, this effect in Ni [ 96 sponge keeps the main features of damping in dense Ni, i.e. there is a peak in the amplitude dependent internal friction (ADIF) curve at an amplitude about (244)310 24 due to energy dissipation by a motion of magnetic domain walls under applied cyclic stress. This contribution to damping is enhanced by annealing, but suppressed by an external magnetic field (in saturation, Fig. 3b,—only the dislocation-related damping is remaining). To be compared with dense Ni (the data for Ni [12] are scaled on the right Y axis in Fig. 3a), this effect in sponge is lower in magnitude but broader from the viewpoint of amplitude range. Since the maximal value of hysteretic MED (dh.max ) is inversely proportional to the average level of internal stress field si , the aforementioned result means a broader stress distribution in sponge with a higher average value of stress. The quantitative values

Fig. 3. Damping behaviour of Ni-based sponges (see Table 1): (a) ADIF of Ni [ 96 sponge: effect of annealing (i—as received, ii—600 and iii—1000 8C, 1 h, bending, H 5 0) and of magnetic field (1–0, 2–1.6, 3–4, 4–8, 5–16 and 6–32 kA m 21 , specimen annealed at 950 8C, 1 h, torsion) compared to dense Ni (right scale) [12], (b) magnetic field dependence of damping at constant torsion amplitude g 5 3.3 3 10 25 [12] (above: macrostructure of Ni [ 96 sponge, height of picture 1.5 mm), (c) influence of number of vibrations N at ´ ¯ 10 23 on ADIF: (I) Ni [ 96 sponge (a—first measurement, b—after N 5 5 3 10 6 ), (II) Ni [ 95 sponge (c—first measurements, d—after N 5 2.3 3 10 7 ); (d) fatigue fracture of Ni [ 96 sponge: striation lines (picture width 18 mm) and brittle fracture of strut (picture width 180 mm).

6

I.S. Golovin, H.-R. Sinning / Journal of Alloys and Compounds 355 (2003) 2–9

given in Fig. 3 are still very preliminary, because they relate mostly to an individual specimen used. If the sponge vibrates at a higher amplitude, where microplastic deformation takes place, the effect of MED can be overlapped with microplastic or fatigue-related damping (see §§3.6 and 3.7). At this stage it is not yet clear if the cycling (Fig. 3c) helps Ni-based sponges to develop the typical magneto-elastic peak in ADIF curve at about ´h.max ¯ 2 3 10 4 , or if it is the effect of cracks (Fig. 3d) discussed below. It was shown earlier for ‘dense’ Fe–Cr alloys that pre-testing can either increase (for pretesting at ´ # ´h.max ) or decrease (for pre-testing at ´ 4 ´h.max ) hysteretic MED [13]. The results presented in Fig. 3c do not fit to this scheme, which gives some indirect argument in favour of the idea of a crack-related contribution. We should also mention a possible contribution of amplitude independent damping due to macro- and microeddy currents, caused by local changes of the magnetization arising from stress-induced domain wall displacement. The contribution of microeddy currents is described analogous to Eq. (1) with the difference that the quantities D and fo are now functions of magnetic properties and the size (D) of magnetic domains ( fo | D 22 ), while the contribution of macroeddy currents is inversely proportional to the specimen thickness [11]. Since the average thickness of struts in the Ni-based sponges studied (0.1–0.5 mm) is rather close to the average magnetic domain size (¯0.5 mm in dense Ni [11]), one can expect that the contributions of eddy currents to damping (in the high kHz range) are different in sponges and in dense Ni. This is still to be studied in future, taking into account real parameters of magnetic domains and stress–strain distribution in CMM.

3.5. Reversible dislocation motion Amplitude dependent damping due to dislocation motion is, probably, the most common mechanism of damping not only in dense but also in cellular metallic materials. The main difference in this case is a higher stress–strain localisation in CMM. This makes it important to distinguish between the ranges of reversible and irreversible (including generation of new dislocations) dislocation motion under applied stress. For the critical amplitude ´mpd between these ranges, the following values were determined using effects of both zero point drift and opening of the loading–unloading hysteretic loops in ADIF: ´mpd # 4 3 10 24 for Alp-85 (bending), and for 316L GKN PM steels (torsion): 1.8310 24 (GKN-52), 5.4310 24 (GKN24 24 52), 8.3310 (GKN-52), 10310 (GKN-52). 24 In case of relatively low amplitudes (´ # 10 ), mostly reversible dislocation motion in Al foams takes place, and the experimental data [14–19] show a reasonable fit to the ¨ well known Granato–Lucke string model. From the other

side, a high IF background (Alp-85 in Fig. 2a, sintered 316L steels in Fig. 4a) is remarkable, and a contribution to damping from other defects, e.g. weakly connected grains, is also possible. The absolute values of damping in this amplitude range have been scaled in case of foams with respect to porosity (P), pore size (d) and frequency ( f ) as [17]: d | P/ [d(1 2 P)] ? 1 /f. Experimental data for Al foams reasonably fit to this equation in the range of kHz frequency [17], but stronger deviations with respect to pore size and, especially, frequency occur in the Hz range for Al foams [18] and other CMM [3]. This, in our opinion, is the result of the fact that the damping mechanism is not restricted to reversible dislocation motion only. A similar idea about different contributions of frequency to dilatation and distortion of pores is discussed in Ref. [19]; effects from TTEC and grain sliding are also possible.

3.6. Damping caused by microplasticity If the critical amplitude ´mpd is exceeded, micro-structural changes in CMM become irreversible and microplastic deformation takes place (Fig. 1a and 4b). In this range, most of related changes in damping—either as a function of ´ (Figs. 2a and 4a) or with increasing N (Figs. 2a, 3c and 4c)—result from the accumulation of these microstructural changes like generation of new dislocations [15,16] or crack nucleation and propagation [14,20]. When microyielding takes place the resulting damping can be calculated, knowing the applied stress, the porosity of CMM and the mechanical properties of the carcass material, with the help of statistical theory of mechanical behaviour of inhomogeneous media. This has been applied to one-level porous GKN steels (produced by direct sintering of particles of different size, Table 1) [15], and to a two-level porous steel (produced with the help of space holder elements, 14–78%) [16]. The experimental results reasonably fit to the equations: g

d

(i ) mpd

5

1E

2

(i ) C mpd (g ) dg /G i*g 2 , where

gmpd

) C (impd 512f

Sœ

DD

]] t (iy.s) 12P ]]i 3 ] 2 1 Pi t

S

(2)

) where d (impd means the damping due to microplastic deformation for each type of porosity P (i ) (with i 5 1 for one-level or i 5 1, 2 for two-level porosity), Cmpd is the (i ) concentration of zones with microplastic deformation, t y.s is the yield stress of the dense (i 5 1) or porous (i 5 2) metallic carcass. The resulting damping dmpd is equal to 1) (1) (2) d (mpd in case of one-level porosity or to d mpd 1 d mpd in case of two-level porosity. Experimental results and simulations of microplastic damping on the basis of Eq. (2) as a function of amplitude and porosity for a fixed amplitude are reported in Refs. [15,16].

I.S. Golovin, H.-R. Sinning / Journal of Alloys and Compounds 355 (2003) 2–9

7

Fig. 4. The FeNiCr 316L steels with different porosity: (a) amplitude dependent damping, (b) bending tests, (c) change of ADIF curves with number of vibrations (for ´ ¯ 10 23 ) and microstructure of GKN-33 specimen, (d) modulus defect as a function of number of vibration (for ´ ¯ 10 23 ).

3.7. Fatigue-related damping As a result of accumulation of microplastic deformation in the range ´ . ´mpl , a fatigue-related instability of damping and a decrease in elastic modulus (Figs. 1b, 2b and 4d) take place. Often, this effect leads to an increase in damping at relatively low amplitudes (Fig. 4c). Structural studies [3] and simulations [20] have shown that this effect is connected with microcracks. The observed difference between fatigue-induced damping in Alp-85 Al foam (Fig. 2b) and porous 316L steels (Fig. 4c) shows two different ways of stress relaxation: by microplasticity (Alporas  foams) and by microcracks (sintered 316L steel). A crackrelated contribution to damping can also not be excluded in case of Ni sponges (Fig. 3c,d). One should keep in mind that crack-related damping is a result of fatigue which

leads to failure, and can not be considered as a source for long-term high damping applications.

3.8. Influence of porosity, complex damping–strength– stiffness criteria As a rule-of-thumb, an increase in porosity of CMM leads to an increase in damping (e.g. Fig. 4a). The advantage of CMM is not in absolute values of damping only, but mostly in a combination of intrinsic damping with other mechanical, thermal and electrical etc. properties. Different parameters are used to characterise materials for such a purpose. Sugimoto [21] suggested a combination of the specific damping capacity (C01 5 DW/W ) at a stress level of 0.1sB with the tensile strength (sB ) as a 5 C01 3 sB . This parameter was later modified in Ref.

I.S. Golovin, H.-R. Sinning / Journal of Alloys and Compounds 355 (2003) 2–9

8

[22] to the normalised intrinsic damping (logarithmic decrement of free decay vibrations d01 ((1 / 2C01 ), measured at a strain level ´ 5 0.1s0.2 /E) multiplied with the yield stress (s0.2 ) as a 9 5 d01 3 s02 . Experimental values of d01 , E and s0.2 as well as values of modified Sugimoto parameter a 9 and its ratio to density (a 9 /r ) are collected in Table 2. Another complex structural parameter, z 5 d 3 E n /r, where n 5 1, 1 / 2 or 1 / 3 for columns, beams and panels, correspondingly [2,6], is used to characterise a combination of damping, stiffness and density (Table 2). Although this parameter was originally introduced without specification of stress or strain, we calculated it by using the same d01 value as for the a 9 parameter. The goal is to maximize the parameters a 9, a 9 /r and z to optimise the structure. The increase in a 9, a 9 /r and z parameters in CMM to be compared with solids they are made from is obvious and demonstrates their advantages when a combination of damping with stiffness and strength is desirable.

3.9. Unsolved questions and outlook Many aspects of damping mechanisms in CMM are still not clear. First among others are the questions of microstructure of CMM to be compared with corresponding dense materials (dislocation structure, nature of pinning points (e.g. Ti in Al remaining from the foaming process, which results in Al 3 Ti particle formation), weaker connectivity between grains in foams to be compared with dense materials, etc.), distribution laws of pore size and shape and corresponding stress–strain and microplasticity distributions, influence of heat treatment when applicable (see examples in Figs. 2a and 3a), and peculiarities of crack propagation in discontinuous media. The use of materials in which damping and strength are controlled by different mechanisms (e.g. better thermo- or magneto-elastic damping characteristics, or materials with a thermoelastic martensitic transformation (Mn–Cu, NiTi, Cu–Al–Ni)) can be

also promising. Scattering from specimen to specimen caused by high heterogeneity of CMM materials demands statistical averaging of the results over at least five tests in the case of damping measurements, which was not always done in this paper.

4. Conclusions Mechanical damping in CMM has been studied in a wide range of deformation amplitude. It can sometimes be comparable with dense high damping metals, while their density is much lower. The applicability of studied CMM for damping of mechanical vibrations, when estimated by complex parameters (a 9, a 9 /r and z, which also consider strength, stiffness and weight), demonstrates some advantages of CMM compared to the dense materials they are made from. Density, pore size and other structural parameters, chemical composition, pre-deformation, time of vibration, and air pressure inside the cells can influence the damping capacity via different structural mechanisms. At least three ranges of internal friction in respect to vibration amplitude are distinguished by dominating internal friction mechanisms, namely: • amplitude independent IF (background damping, thermoelastic currents in case of Al and Zn foams, possibly micro-eddy currents in ferromagnetic CMM, etc.), • 1st amplitude dependent IF range—reversible effects (string-like dislocation motion, magneto-elastic hysteresis, possibly stress-induced martensitic transformation, etc.), • 2nd amplitude dependent IF range—irreversible phenomena (generation of new dislocations, nucleation and propagation of cracks); this range should, however, be avoided for long-term damping application because of fatigue problems.

Table 2 Intrinsic damping capacity with respect to other mechanical properties Material

FeNiCr RCJ-14 GKN-21 GKN-32 GKN-44 GKN-51 Al Alp-85

s0.2 MPa

E GPa

d01 310 3

a9 5 d01 3 s0.2

a 9 /r

400 – 160 110 48 22 25 2.5

210 145 89 55 25.4 9.7 69 2.2

1.0 7.0 10 23 38 87 1.1 40

0.40 – 1.60 2.53 1.82 1.91 0.028 0.10

0.05 – 0.26 0.47 0.41 0.50 0.01 0.25

Bending tests for 316L steels and tensile tests for Al and Alp-85. a 23 E is in GPa and r in Mg m by analogy with Ref. [6].

z 5 d01 3 E n /r

(a)

n 5 1 column

n 5 1 / 2 beam

n 5 1 / 3 panel

0.026 0.147 0.142 0.234 0.214 0.219 0.028 0.220

0.002 0.012 0.015 0.032 0.043 0.070 0.003 0.148

0.001 0.005 0.007 0.016 0.025 0.048 0.002 0.130

I.S. Golovin, H.-R. Sinning / Journal of Alloys and Compounds 355 (2003) 2–9

Acknowledgements The support of this work by DFG (SPP ‘Zellulare metallische Werkstoffe’) is gratefully acknowledged. We thank Prof. W. Riehemann for permission to use his vibrating reed apparatus for some of our experiments and fruitful discussions.

[11] [12] [13] [14]

[15]

References [1] J. Banhart, Progr. Mater. Sci. 46 (2001) 559–632. [2] L.G. Gibson, M.F. Ashby (Eds.), Cellular Solids, Cambrige University Press, 1997, p. 510. [3] I.S. Golovin, H.-R. Sinning, Invited talk at ICIFUAS-13 (Bilbao, July 2002, http: / / icifuas.ehu.es), Mater. Sci. Eng. A, in press. ¨ [4] C. Korner, R.F. Singer, J. Adv. Eng. Mater. 2 (4) (2000) 159. [5] J. Banhart, M. Ashby, N. Fleck (Eds.), Cellular Metals and Metal Foaming Technology, Verlag MIT Publishing, 2001. [6] M.F. Ashby, A. Evans, N.A. Fleck et al., Metal Foams: A Design Guide, Butterworth–Heinemann, 2000. [7] F. Han, Z. Zhu, C. Liu, Acta Acustica 84 (1998) 573. ˇ [8] J. Kovacik, F. Simancik, in: H.P. Degischer, B. Kriszt (Eds.), Handbook of Cellular Metals, Production, Processing, Applications, Chapter 5.3, Vol. XXIV, Wiley–VCH, Weinheim, March 2002. [9] I.S. Golovin, H.-R. Sinning, J. Mater. Sci. and Heat Treatment of Metals (MiTOM) (5) (2002) 26–33 (in Russian). [10] I.S. Golovin, H.-R. Sinning, Solid State Phenomena 89 (2003)

[16]

[17] [18] [19]

[20]

[21] [22]

9

261–266 (Proceedings of the 2nd Int. School on Mechanical Spectroscopy, Poland, 3–8 December, 2003). A.S. Nowick, B.S. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, New York, 1972. In collaboration with N.Ya. Rokhmanov. I.S. Golovin, I.U. Kanunnikova, J. Mater. Sci. and Heat Treatment of Metals (MiTOM), (7) (1993) 35–38. ¨ I.S. Golovin, H.-R. Sinning, J. Goken, W. Riehemann, In: J. Banhart, M. Ashby, N. Fleck (Eds)., Cellular Metals and Metal Foaming Technology, Verlag MIT Publishing, 2001, pp. 323–328. N. Kirillova, I.K. Arhipov, S.A. Golovin, I.S. Golovin, H.-R. Sinning, M. Bram, In: J. Banhart, M. Ashby, N. Fleck (Eds.), Cellular Metals and Metal Foaming Technology, Verlag MIT Publishing, 2001 pp. 409–414 I.S. Golovin, H.-R. Sinning, I.K. Arhipov, S.A. Golovin, M. Bram, Report at ICIFUAS-13 (Bilbao, July 2002, http: / / icifuas.ehu.es / ), Mater. Sci. Eng. A, in press. C.S. Liu, Z.G. Zhu, F.S. Han, J. Banhart, Philos. Mag. A. 78 (6) (1998) 1329. C.S. Liu, Z.G. Zhu, F.S. Han, J. Banhart, J. Mater. Sci. 33 (1998) 1769. C.S. Liu, Z.G. Zhu, Solid State Phenomena. 89 (2003) 273–278 (Proceedings of the 2nd Int. School on Mechanical Spectroscopy, Poland, 3–8 December, 2003). ¨ I.S. Golovin, H.-R. Sinning, J. Goken, W. Riehemann, Report at ICIFUAS-13 (Bilbao, July 2002, http: / / icifuas.ehu.es / ), Mater. Sci. Eng. A, in press. K. Sugimoto, Nihon Kinzoku Gakkai Kaiho 14 (7) (1975) 491. I.S. Golovin, S.A. Golovin, High Damping Materials, Review, in: Bulleten NTI, Chermet Informacia, 1989, No. 5 (1081), pp. 7–30 (in Russian).