ARTICLE IN PRESS
POTE3374_proof 6 September 2008 1/5
Polymer Testing xxx (2008) 1–5
Contents lists available at ScienceDirect
Polymer Testing
journal homepage: www.elsevier.com/locate/polytest
Material Performance
Paris R. von Lockette a, *, Samuel E. Lofland a, Jeong-Hoi Koo b,
Jennifer Kadlowec a, Matt Dermond a
b
Rowan University, Mechanical Engineering, Rowan Hall, 201 Mullica Hill Road, Glassboro, NJ 08028, United States
Miami University, 501 East High Street, Oxford, OH 45056, United States
RO
a
OF
Dynamic characterization of bimodal particle mixtures in silicone rubber
magnetorheological materials
a b s t r a c t
Article history:
Received 13 June 2008
Accepted 4 August 2008
Available online xxxx
Samples of a magnetorheological composite comprised of a silicone elastomer containing
varying mixtures of 40- and 10-mm iron particles were tested in dynamic shearing
experiments. These bimodal mixtures were used in order to determine whether such
particle combinations might influence the composite’s behavior as evidenced by changes
in the relative magnetorheological (MR) effect, DG. Field-dependent results are consistent
with DG f M2, M being the magnetization, and allow one to extrapolate a maximum
relative MR effect. The extrapolated maximal DG values were effectively independent of
particle-size ratio for fixed 30% [v/v%] Fe, suggesting that volume fraction was the
important parameter and that particle positions were disordered. However, for 1% [v/v%] of
the 10-mm particles to 30% [v/v%] 40-mm particles, there was enhanced response, perhaps
due to the smaller particles sitting in beneficial interstitial positions. Further addition of
10-mm particles resulted in decreased performance.
Ó 2008 Elsevier Ltd. All rights reserved.
EC
TE
DP
a r t i c l e i n f o
1. Introduction
CO
RR
Magnetorheological elastomers (MREs) are a reemerging class of smart materials comprised of magnetic
particles embedded in an elastomer matrix. The materials
are technologically important due to their ability to change
stiffness under the influence of a magnetic field H, the socalled magnetorheological (MR) effect [1–4]. This capability
makes them ideal materials for the development of variable
stiffness (tuned) vibration absorbers and other vibration
attenuation devices [5–10].
The relative MR effect in shear DG can be defined as the
relative change in the shear modulus G with H,
DG ¼
GðHÞ GðH ¼ 0Þ
GðH ¼ 0Þ
UN
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
(1)
* Corresponding author. Tel.: þ1 856 256 5341; fax: þ1 856 256 5241.
E-mail address: [email protected] (P.R. von Lockette).
Renewed interest was spurred by the recent development of materials having approximately 30% iron content
by volume exhibiting a maximal DG of 60% [2,11]. This
result has led to interest into research into the impact that
various particle shapes, sizes, and orientations have on the
MR effect of the material. However, this work begins to
examine the role of particle-size distribution on the overall
MR effect by employing bimodal distributions of 40- and
10-mm iron particles.
2. Background
The focus on particle size, shape, and orientation has led
to several important results. Several researchers have
found that using lenticular particles (particles having
distinct major and minor geometric axes) improves the MR
effect for a fixed volume content [1]. Other researchers
have found that curing the particles in a magnetic field also
produces an enhancement to the MR effect over similar
composites not cured in a magnetic field [9,10]. Good
0142-9418/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.polymertesting.2008.08.007
Please cite this article in press as: Paris R. von Lockette et al., Dynamic characterization of bimodal particle mixtures in silicone
rubber magnetorheological materials, Polymer Testing (2008), doi:10.1016/j.polymertesting.2008.08.007
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
ARTICLE IN PRESS
ð36pÞ
6
!
C 1=3 1 Rz 1:612C 1=3 2 R
(2)
CO
RR
For the case of 40-mm particles with the critical volume
particle concentration chosen at 30%, Eq. (2) yields
2d ¼ 16 mm. From the values, and from the scale of the
figure, it can be seen that the major dimension of the nonmagnetic volume becomes large with respect to the cell.
The central aim of this work is to begin investigating the
efficacy of inserting particles into this excluded volume
with a bimodal size distribution.
2δ
2δ
a
RO
OF
The materials used in this work were all cast from Dow
Corning HS II RTV silicone elastomer compound as the matrix
material. The compound was preheated in an oven to 60 C
before mixing to decrease viscosity. Once heated, the desired
amount of iron particles were added and mixed thoroughly.
The catalyst was added in a 15:1 compound:catalyst ratio by
weight in the final step. Specimens were cast in rectangular
prism molds 19.05 12.7 12.7 mm3 for dynamic shearing
tests. The molds were coated with a release agent for easy
removal. The samples were not cured in a magnetic field to
avoid the added complexity of particle aggregation due to
differential action of the magnetic field on particles of varying
sizes (which is clearly an area for future work).
To investigate the role of particle distributions, a series
of samples containing 40- and 10-mm iron particles with
a fixed total iron content of 30% [v/v%] was made in steps of
5% [v/v%] (see Table 1). In addition, to investigate the
behavior of adding secondary particles to an MRE composition, a second set was made with 30% [v/v%] of 40-mm
particles with additional 10-mm particles (see Table 2).
Dynamic tests were conducted with a one-degree-offreedom shearing apparatus designed for these experiments (Fig. 2). The shearing device allows the hanging mass
(an accelerometer) to respond to the forced motion of the
base, driven by an MTS 831.10 servo-hydraulic frame, suspended by MRE springs. The apparatus includes integrated
induction coils (300 turns/coil) capable of producing
a maximal magnetic field H ¼ 1.2 105 A/m across the gap
where the samples were suspended.
For the experiments, the servo-hydraulic frame was
driven with a white noise input having 10–200 Hz
frequency content and a maximal amplitude of 0.38 cm. An
accelerometer mounted on the base of the device (not
shown) measured the input to the system while the
hanging mass accelerometer measured the output response
dictated by the behavior of the MRE material in shear. The
dynamic response of the two accelerometers was collected
with a Bruel and Kaer PULSE data acquisition system with
acquisition rate of 10 kHz. Three measurements were made
per sample with 6 samples for each composition.
Magnetization measurements were done with either
a Quantum Design PPMS vibrating sample magnetometer
(VSM) or a Lakeshore 7300 VSM.
EC
1=3
2d ¼ 2
3. Methods
TE
results have been obtained on particles ranging from 100–
400-mm coarse iron filings down to 5–10-nm particles of
carbonyl iron [1,12].
In all work so far, however, a critical particle volume
concentration (CPVC) of roughly 30% has been either
proposed or determined experimentally [1,9,13]. A CVPC of
26% was calculated analytically using equations governing
the stiffness enhancement caused by adding filler particles
to a rubbery matrix [14]. In this work we begin by examining the elastomer matrix which comprises, ideally,
roughly 70% of the MRE. This volume is critically important
since it is the bulk of the material, and though the elastomer does not contribute to its magnetic behavior, its
elastic softness is central to the MR effect.
For the sake of argument, one could assume an ordered
arrangement of iron particles, as shown in Fig. 1. In the
figure, the particle spacings are repetitions of a unit cell
arrangement of perfect spheres of radius R resembling
a simple cubic cell (SCC) with an interstitial position with
a sphere of radius r. An important difference is the inclusion
of a gap d between the primary particles. The volume
within a cubic cell defined in-plane by the dotted line is
Vcell ¼ 8(R þ d)3 which is greater than the volume of the
particles contained inside the cell Vpart ¼ 4/3p(R3 þ r3). For
d ¼ 0, the packing factor, PF ¼ Vpart/Vcell for the SCC
arrangement with no interstices is approximately 52%,
yielding 48% open space within the cell which is nonmagnetic.
The CVPC would limit the effective amount of particles
further. Assuming a CVPC of C, the unit cell case without
interstices would require PF ¼ C which would define
a constraint for 2d, namely
UN
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
P.R. von Lockette et al. / Polymer Testing xxx (2008) 1–5
DP
2
POTE3374_proof 6 September 2008 2/5
4. Results and discussion
After testing, the samples were cut into vertical slices
and the magnetization was measured at 1.5 106 A/m,
r
R
b
Fig. 1. Schematic of simple cubic unit cell arrangement in-plane. (a) Spatial
arrangement and (b) close-up with interstitial spacing.
Table 1
Samples prepared for 30% [v/v%] Fe content
40 mm Content [V/V%]
10 mm Content [V/V%]
0
5
10
15
20
25
30
30
25
20
15
10
5
0
Please cite this article in press as: Paris R. von Lockette et al., Dynamic characterization of bimodal particle mixtures in silicone
rubber magnetorheological materials, Polymer Testing (2008), doi:10.1016/j.polymertesting.2008.08.007
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
ARTICLE IN PRESS
POTE3374_proof 6 September 2008 3/5
0
1
2
4
more than sufficient to reach magnetic saturation (see
below). The results indicated showed that the total iron
volume fractions throughout each batch were constant
within w1% [v/v%] since the measured saturation magnetization Ms w 520 kA/m ¼ 0.30 MFe, MFe being the magnetization of Fe (MFe ¼ 1.75 106 A/m). This suggests
uniformity and that little sedimentation took place during
curing. Fig. 3 shows the field dependence of the magnetization M for the two end members. Ignoring the small
hysteresis, the S-shaped curves can be described by
2
H
MðHÞ ¼ Ms arctan
p
H0
0
-5105
-5105
0
5105
Magnetic Field (A/m)
b
5105
0
(3)
CO
RR
EC
TE
DP
where H0 is a characteristic field. Note that the H0 values
are different for the two curves in Fig. 2, which is taken to
be an effect of sample demagnetization (extrinsic) since
both types of particles are soft iron.
Fig. 4 shows a representative frequency response of the
system (base excitation to hanging mass) to a white noise
input with frequency content from 10 to 200 Hz. There was
a sizable shift in the resonance frequency as the field was
RO
10 mm Content [V/V%]
30
30
30
30
5105
Magnetization (A/m)
40 mm Content [V/V%]
a
3
OF
Table 2
Samples prepared by adding 10 mm particles to the 30% – 40 mm base
UN
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
Magnetization (A/m)
P.R. von Lockette et al. / Polymer Testing xxx (2008) 1–5
0
5105
Magnetic Field (A/m)
Fig. 3. Field-dependent magnetization of MRE samples with (a) 30% [v/v%]
10-mm Fe particles and (b) 30% [v/v%] 40-mm Fe particles. The full line is a fit
to Eq. (3). The saturation magnetization values correspond to w520 kA/m, as
expected for 30% [v/v%] Fe.
increased from 0 to 1.2 105 A/m. Ideally, the resonance
frequency un is governed by the well known relationship
un ¼ (k/m)1/2 where k is the spring-like stiffness of the
material and m is the mass of the hanger. From that relationship, the MR effect with respect to the spring-like
stiffness Dk can be found experimentally from
DkðHÞ ¼
u2n ðHs0Þ u2n ðH ¼ 0Þ
u2n ðH ¼ 0Þ
(4)
For the shearing case, F ¼ k$Dh where Dh is the shearing
deflection,
k ¼
Fig. 2. Schematic showing (a) dynamic shear testing device including MRE
material and (b) deflection, Dh and width w of MRE sample. Base excitation
causes the hanging mass to accelerate which shears the MRE material.
-5105 5
-510
G,A
w
(5)
with F being the vertical force accelerating the hanging
mass, A the cross sectional area of the MRE sample normal
to the field and w the width of the specimen parallel to the
field (see Fig. 2b). Since A and w are constant geometric
Please cite this article in press as: Paris R. von Lockette et al., Dynamic characterization of bimodal particle mixtures in silicone
rubber magnetorheological materials, Polymer Testing (2008), doi:10.1016/j.polymertesting.2008.08.007
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
ARTICLE IN PRESS
40 kA/m
10
0
5
0
120 kA/m
20
40
60
80
100
120
140
160
180
200
Frequency (Hz)
Fig. 4. Representative frequency response function (FRF) of base excitation
to hanging mass for field strengths shown. Peaks in the FRF denote un which
shifts with field strength.
properties, it is clear that DG f Dk. By measuring the
resonant frequency as a function of magnetic field, one can
calculate the relative MR effect via Eqs. (4) and (5). In each
case, un shifted higher as the magnetic field strength was
increased.
Fig. 5 shows DG as a function of H for samples with 30%
[v/v%] total iron content. The mean of the standard deviations of the data collected for all composition-field-strength
points is 5%. To understand this behavior, one can make
a simple argument based on energy considerations. The
demagnetizing energy is proportional to M2 while the linear
elastic shear strain energy is proportional to G. Therefore, it
seems reasonable to suggest that
OF
15
DG. At high field strength, M saturates and consequently so
does DG, which leads to the observed sigmoidal dependence.
Fig. 6a shows DGmax for each composition. Within the
scatter, the fitted values are effectively independent of the
particle-size ratio, suggesting that volume fraction is the
important parameter and that disorder must play a role.
Note that the H0 values (Fig. 6b) are also effectively
constant, as might be expected since the samples all
contain the same volume fraction of soft iron.
To investigate disorder in particle arrangement, we
studied the MR effect for samples where additional
amounts of 10-mm particles were added to a 30% [v/v%] 40mm composition. Samples were tested at the maximal field
of 1.2 105 A/m, and the error is about 3% (Fig. 7). The
graph shows a clear maximum in the MR effect when 1% [v/
v%] 10-mm iron particles were added to the base composition. In fact, that particular composition showed the highest measured DG (49%) of all samples tested. The MR effect
decreases with the inclusion of more 10-mm iron. This
suggests that while disorder dominates at large mixing
a
0.8
RO
80 kA/m
0.7
0.6
0.5
DGðHÞfM2
(6)
TE
Consequently, the full line in Fig. 5 is a fit to
4
H
0.4
0.3
(7)
0.2
EC
DG ¼ DGmax 2 arctan2
p
H0
Gmax
Amplitude (dB)
20
where DGmax is the asymptotic value of DG as H / N. At
small fields, M f H, giving a quadratic field dependence to
RR
1.2
0.1
0
0
5
10
1
0.6
0.2
0
UN
0.4
40 μm
0
2104
4104
6104
8104
1105
b
20
25
30
5 104
4 104
H0 (A/m)
CO
0.8
15
Vol % 40 µm Fe
10 μm
G
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
P.R. von Lockette et al. / Polymer Testing xxx (2008) 1–5
DP
4
POTE3374_proof 6 September 2008 4/5
3 104
2 104
1 104
1.2105
Magnetic Field (A/m)
Fig. 5. Field dependence of the relative change in shear modulus for various
mixtures of 10- and 40-mm Fe particles comprising 30% [v/v%] of the MRE in
steps of 5%. The curves are shifted vertically arbitrarily for clarity; DG for
a particular sample follows from Eq. (1). The full lines represent fits to Eq. (7).
0
0
5
10
15
20
25
30
Vol % 40 µm Fe
Fig. 6. Composition dependence of (a) DGmax and (b) H0 determined from
the fits in Fig. 5. Both are effectively constant.
Please cite this article in press as: Paris R. von Lockette et al., Dynamic characterization of bimodal particle mixtures in silicone
rubber magnetorheological materials, Polymer Testing (2008), doi:10.1016/j.polymertesting.2008.08.007
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
ARTICLE IN PRESS
POTE3374_proof 6 September 2008 5/5
P.R. von Lockette et al. / Polymer Testing xxx (2008) 1–5
50
relative MR effect being proportional to the square of the
magnetization. Within the scatter of the data, the extrapolated maximum relative MR effect was effectively independent of particle-size ratio, suggesting that volume
fraction was the important parameter and that disorder
plays a role. However, there were indications that small
mixing ratios lead to arrangements which yield an
enhanced relative MR effect.
40
30
G
20
References
1
2
3
4
5
vol% 10-µm Fe
Fig. 7. MR effect at 1.2 105 A/m for MRE samples with various amounts of
10-mm Fe particles added to 30% [v/v%] 40 mm Fe.
ratios, there may well be some arrangements of the particles that are important at small values.
5. Conclusions
CO
RR
EC
TE
Samples of magnetorheological elastomers comprised
of a silicone elastomer containing varying mixtures of 40and 10-mm iron particles were fabricated and tested in
dynamic shearing experiments. Results from field-dependent dynamic shearing experiments were consistent, the
RO
0
DP
0
[1] L. Lanotte, G. Ausiano, C. Hison, V. Iannotti, C. Luponio, C. Luponio Jr.,
J. Opt. Adv. Mater. 6 (2) (2004) 523–532.
[2] G.Y. Zhou, Smart Mater. Struct. 12 (1) (2003) 139–146.
[3] G.Y. Zhou, Q. Wang, in: Proceedings of SPIE – The International
Society for Optical Engineering Smart Structures and Materials 2005
– Damping and Isolation 5760, 2005, pp. 226–237.
[4] G.Y. Zhou, Q. Wang, in: Proceedings of SPIE – The International
Society for Optical Engineering Smart Structures and Materials 2005
– Smart Structures and Integrated Systems 5764, 2005, pp. 411–420.
[5] T. Shiga, A. Okada, T. Kurauchi, J. Appl. Polym. Sci. 58 (1995) 787–792.
[6] M.E. Nichols, J.M. Ginder, J.L. Tardiff, L.D. Elie. The dynamic
mechanical behaviour of magnetorheological elastomers, in: 156th
ACS Rubber Division Meeting, Orlando, Florida, 1999.
[7] J.M. Ginder, M.E. Nichols, L.D. Elie, J.L. Tardiff, in: Proceedings of SPIE –
The International Society for Optical Engineering Smart Structures
and Materials: Smart Materials Technologies 3675, 1999, pp.131–138.
[8] J.M. Ginder, W.F. Schlotter, M.E. Nichols, in: Proceedings of SPIE –
The International Society for Optical and Engineering Smart Structures and Materials: Damping and Isolation 4331, 2001, pp. 103–110.
[9] M. Kallio, S. Aalto, Lindroos, T.E. Jarvinen, T. Karna, T. Meinander,
AMAS Workshop on Smart Materials and Structures, SMART’03,
Jadwisin, September 2–5, 2003, pp. 353–360.
[10] H. Deng, X. Gong, L. Wang, Smart Mater. Struct. 15 (2006) 111–116.
[11] M. Lokander, B. Stenberg, Polymer Test. 22 (2003) 677–680.
[12] D. Szabó, M. Zrı́nyi, Int. J. Mod. Phys. B 16 (2002) 2616–2621.
[13] M. Lokander, B. Stenberg, Polymer Test. 22 (2003) 245–251.
[14] L.C. Davis, J. Appl. Phys. 85 (6) (1999) 3348–3351.
OF
10
UN
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
5
Please cite this article in press as: Paris R. von Lockette et al., Dynamic characterization of bimodal particle mixtures in silicone
rubber magnetorheological materials, Polymer Testing (2008), doi:10.1016/j.polymertesting.2008.08.007
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529