**4. MRE rheology**

A rotational Rheometer (MCR 301, Anton Paar Companies, Germany) and a Magneto Rheolgical Device (MRD 180, Anton Paar Companies, Germany) were used to measure the MREs' mechanical properties. The Magneto Rheolgical Device is equipped with an electromagnetic kit which can generate a magnetic field perpendicular to the direction of the shear flow. Specifically, a 20mm diameter parallel-plate measuring system with 1 mm gap was used. The samples were sandwiched between a rotary disk and a base placed in parallel. In this study both a steady-state rotary shear and an oscillatory shear were applied for the experiments.

The schematic of the experimental setup is shown in Fig. 4. The stress and stain signals were output from two ports which were detected through a Data Acquisition (DAQ) board (Type: LABVIEW PCI-6221, National Instruments Corporation. U.S.A) and transferred to a computer by which the data was processed.

In this experiment the magnetic flux density of the sample of MRE (*BMRE*) in the measuring gap depends not only on the current (*I*) applied to the samples, but also on the magnetic properties of MRE materials. The relationship between *BMRE* versus *I* is found to be: *BMRE* = 220 *I*, where the units of *BMRE* and *I* are in mT and Ampere (A), respectively.

In the following test, the test current varies from 0A to 2A with the increment 0.5A, for which the intensity of magnetic field is 0 mT to 440 mT with the increment 110 mT.

**Figure 1.** Microstructure of Gr-MREs (Gr 0%) (a) anisotropic (b) isotropic

## **4.1. Steady state results**

252 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

carbonyl iron chains, which influence the magnetorheology of MREs.

Graphite weight

**4. MRE rheology** 

for the experiments.

**Table 1.** Components of Gr MRE samples

computer by which the data was processed.

Graphite based MREs

Sample No. 1 2 3 4 5 6 7 8

Carbonyl iron 10g 10g 10g 10g 10g 10g 10g 10g

Silicone oil 3g 3g 3g 3g 3g 3g 3g 3g Silicone rubber 3g 3g 3g 3g 3g 3g 3g 3g Graphite 0g 1g 2g 3g 3.5g 4g 4.5g 5g

fraction (Gr %) 0% 5.88% 11.11% 15.79% 17.95% 20% 21.95% 23.81%

A rotational Rheometer (MCR 301, Anton Paar Companies, Germany) and a Magneto Rheolgical Device (MRD 180, Anton Paar Companies, Germany) were used to measure the MREs' mechanical properties. The Magneto Rheolgical Device is equipped with an electromagnetic kit which can generate a magnetic field perpendicular to the direction of the shear flow. Specifically, a 20mm diameter parallel-plate measuring system with 1 mm gap was used. The samples were sandwiched between a rotary disk and a base placed in parallel. In this study both a steady-state rotary shear and an oscillatory shear were applied

The schematic of the experimental setup is shown in Fig. 4. The stress and stain signals were output from two ports which were detected through a Data Acquisition (DAQ) board (Type: LABVIEW PCI-6221, National Instruments Corporation. U.S.A) and transferred to a

In this experiment the magnetic flux density of the sample of MRE (*BMRE*) in the measuring gap depends not only on the current (*I*) applied to the samples, but also on the magnetic properties of MRE materials. The relationship between *BMRE* versus *I* is found to be: *BMRE* =

In the following test, the test current varies from 0A to 2A with the increment 0.5A, for

220 *I*, where the units of *BMRE* and *I* are in mT and Ampere (A), respectively.

which the intensity of magnetic field is 0 mT to 440 mT with the increment 110 mT.

By comparing Fig. 1 (a), Fig. 2 (a) and Fig. 3 (ba), we can see that the carbonyl iron chains in the sample without graphite have the best alignment performance. Further, the carbonyl iron chains in Fig. 2 (a) are aligned better than those in Fig. 3 (a). The reason is that when the mixture of carbonyl iron, silicone rubber, silicone oil and graphite is curing under the magnetic field, the graphite powders in Gr-MREs affect the carbonyl iron particles' movement. The more graphite in the mixture, the more effects are applied on to the

> Under rotary shear the shear stress and shear strain of MREs under fields varying from 0~440mT were measured. The MR effect was evaluated by measuring the shear strain-stress curve of the sample with and without a magnetic field applied.

> Figures 5 and 6 show the strain-stress curve of different samples at 5 different magnetic field intensities ranging from 0 to 440mT.

The slope of the strain-stress curve is the shear modulus of the material. As can be seen in the figures, all the samples' shear modulus show an increasing trend with magnetic field before they reach magnetic saturation at high field strength, which proves that all the MRE samples exhibit obvious MR effects.

**Figure 2.** Microstructure of Gr-MREs (Gr 11.11%) (a) anisotropic (b) isotropic

From Figures 5 and 6, the shear stress shows a linear relationship with the shear strain when the strain is within a range. This means the MRE acts with linear viscoelastic properties when the strain is below a certain limit. For conventional MREs, the limitation is around 50% shear strain. When the graphite weight fraction increases from 0 to 15.79%, the range of linearity decreases from 50% to around 10%. For the samples with higher graphite weight fraction alike 23.81%, the linearity ranges are only 6% and 4% for isotropic and anisotropic samples, respectively. When the strain is above the limitation, the shear modulus reaches a saturation (maximum value) and decrease steadily. This could be due to sliding effect. The higher magnetic field intensity leads to higher steady shear stress. Fig. 7 shows the linear ranges of different samples at various magnetic field intensities.

254 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

**Figure 2.** Microstructure of Gr-MREs (Gr 11.11%) (a) anisotropic (b) isotropic

From Figures 5 and 6, the shear stress shows a linear relationship with the shear strain when the strain is within a range. This means the MRE acts with linear viscoelastic properties when the strain is below a certain limit. For conventional MREs, the limitation is around

samples exhibit obvious MR effects.

The slope of the strain-stress curve is the shear modulus of the material. As can be seen in the figures, all the samples' shear modulus show an increasing trend with magnetic field before they reach magnetic saturation at high field strength, which proves that all the MRE

**Figure 3.** Microstructure of Gr-MREs (Gr 20%) (a) anisotropic (b) isotropic

**Figure 4.** A diagram of the experimental setup

For the isotropic and anisotropic samples with same compositions, the isotropic samples always have the bigger linearity ranges and steady shear stress than chose of anisotropic samples.

For each curve, the slope equals the ratio between peak shear stress and relevant shear strain. By analyzing the slope of these curves, it is easy to see that the more graphite in the material, the smaller increment in slopes occurs when the magnetic field increase from 0 to 440mT. This is due to the contributions of graphite powders to the stiffness of the samples. The graphite increases the initial stiffness of Gr-MREs, thus the stiffness change induced by the MR effect can not be comparable to that conventional MREs. Fig. 8 shows the peak stresses of different samples for a magnetic field intensity equalling 220mT, 330mT and 440mT, respectively.

The relative MR effect (ΔGmax/G0) of several samples is shown in Fig. 9. G*<sup>0</sup>* denotes the MRE samples' zero-field modulus, ΔGmax denotes the saturated field-induced modulus, and ΔGmax/G0 denotes the relative MR effect.

It can be seen from Fig. 9 that *G0* is enhanced with the increase in graphite powders content. This result indicates that graphite powders can modify particle properties and, consequently, influenced the MR effect. From the abovementioned results, the exhibited MR effects correspond well with the microstructures of Gr-MREs.

### **4.2. Dynamic tests result**

The dynamic mechanical behavior of MREs was studied by using the strain amplitude sweep tests. Five sets of data were collected for different amplitudes of oscillation, according to various magnetic fields applied to the samples of MREs. Similar to the steady state tests, five different magnetic field intensities, 0, 110, 220, 330 and 440mT, were used in this experiment. A constant frequency of 5Hz was selected for the strain amplitude sweep tests.

256 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

**DAQ board**

For the isotropic and anisotropic samples with same compositions, the isotropic samples always have the bigger linearity ranges and steady shear stress than chose of anisotropic

For each curve, the slope equals the ratio between peak shear stress and relevant shear strain. By analyzing the slope of these curves, it is easy to see that the more graphite in the material, the smaller increment in slopes occurs when the magnetic field increase from 0 to 440mT. This is due to the contributions of graphite powders to the stiffness of the samples. The graphite increases the initial stiffness of Gr-MREs, thus the stiffness change induced by the MR effect can not be comparable to that conventional MREs. Fig. 8 shows the peak stresses of different samples for a magnetic field intensity equalling 220mT, 330mT and

The relative MR effect (ΔGmax/G0) of several samples is shown in Fig. 9. G*<sup>0</sup>* denotes the MRE samples' zero-field modulus, ΔGmax denotes the saturated field-induced modulus, and

It can be seen from Fig. 9 that *G0* is enhanced with the increase in graphite powders content. This result indicates that graphite powders can modify particle properties and, consequently, influenced the MR effect. From the abovementioned results, the exhibited MR

The dynamic mechanical behavior of MREs was studied by using the strain amplitude sweep tests. Five sets of data were collected for different amplitudes of oscillation, according

**Rheometer**

**Computer**

samples.

440mT, respectively.

**4.2. Dynamic tests result** 

**Figure 4.** A diagram of the experimental setup

ΔGmax/G0 denotes the relative MR effect.

effects correspond well with the microstructures of Gr-MREs.

**Figure 5.** Strain-stress curve versus magnetic field (isotropic MRE) (a) Gr 0% (b) 15.79% (c) Gr 23.81%)

**Figure 6.** Strain-stress curve versus magnetic field (anisotropic MRE) (a) Gr 0% (b) 15.79% (c) Gr 23.81%)

0mT 110mT 220mT 330mT 440mT

**Shear stress (Pa)**

**Shear stress (Pa)**

**Shear stress (Pa)**

0 20 40 60 80 100 **Shear strain (%)**

> 0mT 110mT 220mT 330mT 440mT

0 10 20 30 40 **Shear strain (%)**

> 0mT 110mT 220mT 330mT 440mT

0 5 10 15 20 25 30 **Shear strain (%)**

(c)

(b)

(a)

**Figure 6.** Strain-stress curve versus magnetic field (anisotropic MRE) (a) Gr 0% (b) 15.79% (c) Gr

23.81%)

**Figure 7.** Linear ranges versus different samples (a) isotropic samples (b) anisotropic samples

**Figure 8.** Peaks stresses versus different samples (a) isotropic samples (b) anisotropic samples

**Figure 9.** Relative MR effects versus different samples (a) isotropic samples (b) anisotropic samples

In the strain sweep test, the storage and loss moduli were measured by varying strain from 0.01% to 100% at different magnetic fields. Figs. 10-13 show the variation of storage and loss moduli with the strain amplitude sweep.

As shown in Figures from 10 to 13, the overall trend of storage modulus is decreasing with strain amplitude. The storage modulus goes down smoothly until 10% shear strain and begins to drop significantly beyond 10% shear strain. Except for isotropic MREs without graphite, the Loss modulus has almost the same trend as the storage modulus. This means that at the higher shear strains, the storage and loss moduli are much smaller than those at lower shear strains.

Figures 14 and 15 show the storage modulus of different samples at 0mT, 220mT and 440mT magnetic field. The data are collected at 10% and 87.5% shear strain, respectively.

As can be seen from Fig. 14, the storage modulus of all samples shows an increasing trend with graphite weight fraction at 10% shear strain which is in the linear range for most of the samples. In Fig. 15, it turns to a diminishing trend with graphite weight fraction at 87.5% shear strain which is out of the linear range. This means that in the linear range of shear strain, the samples with higher graphite weight faction have the bigger storage modulus.

Figures 16 and 17 show the storage modulus vs. magnetic field at 0.1% and 10% shear strain, respectively. The two shear strains are the beginning and the end of the linear range. From these figures we can see that the storage modulus shows an increasing trend with the intensity of magnetic field. The ratio of storage modulus at 440mT to that at 0mT is indicative of the MR effect. The MR effect of isotropic MREs with 0% graphite is around 4.5,

when the graphite weight fraction increases to 15.79% and 23.81%, the MR effect decreases down to around 2.8 and 2.8, respectively. For anisotropic samples, the MR effects of 0%, 20% and 23.81% Gr-MREs are 4.8, 3.2 and 2.2, respectively. This proves again that with the increase of graphite weight fraction, the MR effect decreases.

260 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

220mT 330mT 440mT

Gr 0% Gr 15.79% Gr 23.81% **Isotropic samples**

moduli with the strain amplitude sweep.

lower shear strains.

0

10

20

30

**Relative MR effect (**

**∆G/G0)**

40

50

60

70

80

**Figure 9.** Relative MR effects versus different samples (a) isotropic samples (b) anisotropic samples

In the strain sweep test, the storage and loss moduli were measured by varying strain from 0.01% to 100% at different magnetic fields. Figs. 10-13 show the variation of storage and loss

(a) (b)

0

Gr 0% Gr 15.79% Gr 23.81% **Anisotropic samples**

220mT 330mT 440mT

5

10

**Relative MR effect (**

**∆G/G0)**

15

20

25

As shown in Figures from 10 to 13, the overall trend of storage modulus is decreasing with strain amplitude. The storage modulus goes down smoothly until 10% shear strain and begins to drop significantly beyond 10% shear strain. Except for isotropic MREs without graphite, the Loss modulus has almost the same trend as the storage modulus. This means that at the higher shear strains, the storage and loss moduli are much smaller than those at

Figures 14 and 15 show the storage modulus of different samples at 0mT, 220mT and 440mT

As can be seen from Fig. 14, the storage modulus of all samples shows an increasing trend with graphite weight fraction at 10% shear strain which is in the linear range for most of the samples. In Fig. 15, it turns to a diminishing trend with graphite weight fraction at 87.5% shear strain which is out of the linear range. This means that in the linear range of shear strain, the samples with higher graphite weight faction have the bigger storage modulus.

Figures 16 and 17 show the storage modulus vs. magnetic field at 0.1% and 10% shear strain, respectively. The two shear strains are the beginning and the end of the linear range. From these figures we can see that the storage modulus shows an increasing trend with the intensity of magnetic field. The ratio of storage modulus at 440mT to that at 0mT is indicative of the MR effect. The MR effect of isotropic MREs with 0% graphite is around 4.5,

magnetic field. The data are collected at 10% and 87.5% shear strain, respectively.

**Figure 10.** Storage and Loss Modulus versus strain amplitude sweep (isotropic MRE Gr 0%) (a) Storage modulus vs. shear strain (b) Loss modulus vs. shear strain

**Figure 11.** Storage and Loss Modulus versus strain amplitude sweep (isotropic MRE Gr 20%) (a) Storage modulus vs. shear strain (b) Loss modulus vs. shear strain

1.00E+04

1.00E+06

1.00E+04

1.00E+05

**Loss Modulus (Pa)**

1.00E+05

**Storage Modulus (Pa)**

1.00E+06

1.00E+07

**Figure 11.** Storage and Loss Modulus versus strain amplitude sweep (isotropic MRE Gr 20%) (a)

0mT 110mT 220mT 330mT 440mT

0.01 0.1 1 10 100 **Shear strain (%)**

0.01 0.1 1 10 100 **Shear strain (%)**

(b)

(a)

0mT 110mT 220mT 330mT 440mT

Storage modulus vs. shear strain (b) Loss modulus vs. shear strain

**Figure 12.** Storage and Loss Modulus versus strain amplitude sweep (anisotropic MRE Gr 0%) (a) Storage modulus vs. shear strain (b) Loss modulus vs. shear strain

**Figure 13.** Storage and Loss Modulus versus strain amplitude sweep (anisotropic MRE Gr 20%) (a) Storage modulus vs. shear strain (b) Loss modulus vs. shear strain

1.00E+03

1.00E+06

1.00E+04

1.00E+05

**Loss Modulus (Pa)**

1.00E+04

**Storage Modulus (Pa)**

1.00E+05

1.00E+06

**Figure 13.** Storage and Loss Modulus versus strain amplitude sweep (anisotropic MRE Gr 20%) (a)

0.01 0.1 1 10 100 **Shear strain (%)**

0.01 0.1 1 10 100 **Shear strain (%)**

(b)

(a)

0mT 110mT 220mT 330mT 440mT 0mT 110mT 220mT 330mT 440mT

Storage modulus vs. shear strain (b) Loss modulus vs. shear strain

**Figure 14.** Storage Modulus of different samples at 10% shear strain (a) isotropic samples (b) anisotropic samples

**Figure 15.** Storage Modulus of different samples at 87.5% shear strain (a) isotropic samples (b) anisotropic samples

**Figure 16.** Storage Modulus versus magnetic field at 0.1% shear strain (a) isotropic samples (b) anisotropic samples

isotropic Gr 0% isotropic Gr 15.79% isotropic Gr 23.81%

0

0

**Storage Modulus(Pa)**

200000

400000

600000

800000

**Storage Modulus(Pa)**

1000000

1200000

1400000

**Figure 16.** Storage Modulus versus magnetic field at 0.1% shear strain (a) isotropic samples (b)

0 100 200 300 400 500 **Intensity of magnetic field (mT)**

0 100 200 300 400 500 **Intensity of magnetic field (mT)**

(b)

(a)

anisotropic Gr 0% anisotropic Gr 15.79% anisotropic Gr 23.81%

anisotropic samples

**Figure 17.** Storage Modulus versus magnetic field at 10% shear strain (a) isotropic samples (b) anisotropic samples
