Normal force of lithium-based magnetorheological grease under quasi-static shear with large deformation

An experimental study was conducted to explore the normal force of lithium-based magnetorheological (MR) grease under quasi-static shear. Firstly, MR grease with various carbonyl iron (CI) particles content was prepared. Then the influence of magnetic field strength, CI particles content, shear rate and temperature on the normal force–strain curves for MR grease under a quasi-static monotonic shear condition were investigated. The results exhibit that the normal force of MR grease under quasi-static monotonic shear decreases first and then maintains constant along with the increase of shear strain, and the critical strain is affected by the magnetic field strength and CI particles content. Finally, the normal force versus shear strain curves under different magnetic fields and shear strains were obtained by using quasi-static cyclic shear. It was found that the normal force of MRG-70 under quasi-static monotonic shear exhibits peak phenomenon at the beginning of the unloading stage, and the peak value increases with the enlargement of shear strain. Furthermore, when the strain amplitude is higher than 40%, normal force exhibits an abrupt change during the transition from the loading stage to the unloading stage.


Introduction
MR grease is a member of the family of MR intelligent materials with tunable rheological properties under the inuence of an external magnetic eld. Due to the semi-solid state of the grease matrix, MR grease has good sedimentation stability in the absence of magnetic eld strength. Meanwhile, when an external magnetic eld is applied, the CI particles in MR grease can form a chain or cluster structure, causing a change in the yield stress of MR grease. The above rheological properties of MR grease endow it with outstanding prospects in the application of MR damper, 1-4 clutch 5-7 and actuator. [8][9][10] Until now, in order to promote the practical application of MR grease, researchers have carried out a series of studies on the rheological properties of MR grease, i.e. viscosity, yield stress, storage modulus and loss modulus. [11][12][13][14][15][16] The normal force of the MR materials is the force induced by the forming of chain or cluster structure along the direction of the magnetic eld which is perpendicular to the shear stress. This normal force has signicant impacts on the mechanical performance of MR materials-based devices and is suggested to be considered in the design stage of MR devices. 17 Vicente et al. studied the relationship between normal force and yield behavior of MR uid by using steady and oscillatory shear test, and they found that the maximum normal force of MR uid appeared at the position of the suspension began to ow. 18 See et al. conducted an experiment to study the normal force of MR uid under ow conditions, the results showed that the normal force of MR uid is correlated with the shear rate. The higher shear rate leads to the smaller shear stress. 19 Jiang et al. tested the inuence of shear rate and magnetic eld on normal stress of MR uid under steady shear. The normal stress showed an increasing trend with the increase of magnetic eld and shear rate but decrease suddenly at the beginning of shear thickening in MR uid. 20 Pang et al. investigated the normal stress of MR polymer under large amplitude oscillatory shear, and revealed that the change in normal stress of MR polymer is drastically affected by factors: the Poynting effect and the particle structure. 21 Ju et al. studied the normal force of MR gel under steady and dynamic shear test. It demonstrated that the normal force of MR gel is heavily affected by the external magnetic eld. However, with the presence of magnetic eld, the dependence of normal force on time, shear rate and frequency are not obvious. 22 The normal force of MR elastomer in compression condition was analyzed by Liao et al. experimentally and theoretically. They found that, with the enhancement of external magnetic eld and precompression force, the normal force of MR elastomer shows an increasing trend. 17 In the eld of engineering application of MR devices, the external loading condition that applied to MR device are mainly classied into three types, i.e. static load, quasi-static load and dynamic load, which are oen differentiate by loading rate (shear rate). The shear rate of the dynamic load is oen higher than 10 À1 s À1 , while the shear rate boundary of quasi-static load varies from 10 À4 s À1 to 10 À1 s À1 . 23,24 To date, the investigations into the normal force of MR materials are only carried out under limited loading conditions, i.e., static (shear rate< 10 À4 s À1 ) and dynamic (shear rate> 10 À1 /s) loadings. 16,17,21 Researches addressing the normal force of MR grease under quasi-static shear (10 À4 s À1 < shear rate < 10 À1 s À1 ) were rarely reported. For real-life engineering applications of MR grease dampers to civil infrastructures, i.e., building and bridge, MR grease is oen subjected to the combination of large deformation and quasi-static shear loadings. To ensure the effective vibration isolation performance of such adaptive devices, the study on the normal force of MR grease under quasi-static shear is of great signicance.
In this paper, the normal force of MR grease under different quasi-static shear modes, i.e. quasi-static monotonic shear and cyclic shear, with large deformation will be discussed. Firstly, MR grease with various weight fraction of CI particles were prepared. Then the inuence of the shear rate and temperature on the magnetic-induced normal force of MR grease with different CI particles content under quasi-static monotonic shear were tested and analyzed. Finally, the shear strain dependence magnetic-induced normal force under quasi-static cyclic shear were investigated in detail.

Sample preparation
MR grease used in this paper consist of carbonyl iron (CI) particles dispersed in a commercial lithium-based grease. CI particles with polycrystalline structure are purchased from BASF (Germany) Ltd. The type of the CI particles is CN, and its Fe content is as high as 99.5%. In addition, the average diameter of CI particles is 6 mm. The commercial lithium-based grease are obtained from the Shell (China) Ltd, whose properties are shown in Table 1. The process of the preparation of MR grease is as follows: rst, a specied amount lithium-based grease with NLGI 0 was heated to 80 C and stirred at 500 rpm for 10 minutes. Then CI particles with different weight fractions were mixed with the stirred grease at 800 rpm until fully mixed. MR grease with CI particles weight fraction of 30%, 50% and 70% were prepared separately, as shown in Table 2. Fig. 1 shows the macroscopic behavior of MR grease with and without magnetic eld. Fig. 1(a) is the photograph of the MR grease with CI particles weight fraction of 70%, which shows a semi-solid state in the zero-eld condition. The behavior of MRG-70 with a magnetic eld strength of 740 kA m À1 is shown in Fig. 1(b), it is found that many sheet structures are formed along the direction of magnetic eld. In gure (c) and (d), when we touch these sheet-like structures with our hands, we feel very hard and the structures are not broken. Fig. 1(e) shows that the sheet-like structures can be maintained aer removing the magnetic eld, which is very different from the disappearance of the MR uid microstructures. 25,26 . In gure (f), (g) and (h), in the absence of the magnetic eld, when we touched the sheet structures again with our hands, we found that the retained structures were destroyed instantly, which indicates that the retained structures of MR grease are very fragile.

Experimental setup
The magnetic properties of CI particles used in this paper is measured by using the Vibrating Sample Magnetometer (VSM, Lakeshore, 7404 Series) at room temperature. The normal force of MR grease under quasi-static shear was tested using a parallel-plate rheometer (type MCR 302, Anton Paar Co., Austria) equipped with magnetorheological module (Type MRD180, Anton Paar Co., Austria) and temperature-control accessory (Type F25, Julabo Technology Co, Germany). Fig. 2(a) shows the main conguration of MCR 302 rheometer, the diameter of the parallel-plate under the test head is 20 mm. A 0.318 ml sample of MR grease was placed on the base plate and the gap between the plate was set as 1 mm. The magnitude of the magnetic eld strength passing through the gab can be controlled by the coil current. Fig. 2(b) shows the schematic diagram of the magneto-induced normal force in the testing system. CI particles distributed in MR grease are arranged in the direction of external magnetic eld to form a chain structure, which make the test head subjected to a upward force (normal force). The maximum normal force measurement range of MCR 302 rheometer is 50 N.
In this paper, there are two modes, i.e. monotonic and cyclic shear, were used to test the normal force of MR grease with different CI particles content under various magnetic eld. Fig. 3(a) shows the test principle of the quasi-static monotonic shear. In this mode, the shear strain that applied to the sample through the rheometer using displacement control was linearly increase from initial 0% to maximun 100% in different time such as 10 s, 20 s, 30 s, 50 s and 200 s. The corresponding quasistatic shear rate can be obtained by dividing the maximum shear strain by the time, which is 0.1 s À1 , 0.05 s À1 , 0.033 s À1 , 0.02 s À1 and 0.005 s À1 respectively. For the quasi-static monotonic shear of MRG-70 under different magnetic eld strength, four different magnetic eld, i.e. 0 kA m À1 , 96 kA m À1 , 194 kA   Fig. 3(b) shows the test principle of the quasi-static cyclic shear. In this mode, shear strain applied to the sample changes in the form of a triangular wave. For the quasi-static cyclic shear test of MRG-70 under different magnetic eld, two types of magnetic eld strength, i.e., 0 kA m À1 and 96 kA m À1 , were used and tested at a shear strain, 100%, and shear rate, 0.05 s À1 . For the quasi-static cyclic shear test of MRG-70 under different shear strain, ve different shear strain, i.e. 20%, 40%, 60%, 80%

Magnetic properties of the CI particles
The magnetization curve of the CI particles used in this paper is shown in Fig. 4. In the initial stage, the magnetization of the CI particles shows a linear increase with the increase of magnetic eld strength. When the external magnetic eld is higher than 400 kA m À1 , the magnetization curve tends to saturate. The highest magnetization of CI particles used in this paper display is around 206 emu g À1 . under different magnetic led. When an external magnetic eld was not applied, normal force of MRG-70 remains constant along with the shear strain. In the presence of magnetic eld strength, there is a critical strain amplitude, g c , that divide the relationship between the normal force and shear strain into two stages. When the shear strain is smaller than g c , normal force presents a rapid decrease trend. However, normal force remains almost constant at the shear strain higher than g c . This phenomenon is consistent with the research of See et al. on MR uid. 19 A possible reason for the phenomenon can be attributed to the microstructure change of MR grease under the shear and magnetic eld. Under the external magnetic eld strength, CI particles distributed in MR grease aggregate and form chains or clusters structure along the direction of magnetic eld strength, when the shear strain increase from 0 to g c , the chains or clusters structure gradually rupture, causing the normal force to decrease. As the shear strain increases above g c , the rupturing and rebuilding of the chains or clusters microstructure reach a dynamic equilibrium under the action of the external shear and magnetic eld, the microscoptic performance is that normal stress remains constant.
3.2.2 Quasi-static monotonic shear for MR grease with different CI particles content. Fig. 6 shows the normal force     Table  3. From Table 3, when the magnetic eld strength increase from 96 kA m À1 to 391 kA m À1 , the magneto-induced increase of critical strain amplitude of MRG-30, MRG-50 and MRG-70 are 4.8%, 8.2% and 12.1%, respectively. In addition, the particles content-induced increase of the critical strain amplitude of MR grease presented an increasing trend with the enlargement of the external magnetic eld, i.e. 10.3%, 12% and 17.6% for 96 kA m À1 , 194 kA m À1 and 391 kA m À1 . The above phenomenon indicate that the critical strain amplitude of MR grease increase with the increase of the CI particles content and magnetic eld strength, which is attributed to the stronger chains or cluster structures are formed at higher magnetic led and CI particles content.    Fig. 7. It is observed from Fig. 7 that, under a given shear strain, normal force exhibits a decreasing trend with the increase of shear rate, and this change regularity is affected by the external magnetic eld. The above phenomenon is opposite to the relationship that shear stress of MR plastomer increases with the shear rate. 27 Moreover, from Fig. 7(a), in the absence of magnetic eld strength, the normal force of MRG-70 under different shear rate keeps constant along with the shear strain. From Fig. 7(b), (c) and (d), under the application of the magnetic eld strength, the normal force of MRG-70 under different shear rate are all demonstrate a decrease at the beginning stage of the shear strain, and as the magnetic eld increases, the rate of decrease becomes slower. Another interesting phenomenon from Fig. 7 is that, under the small magnetic eld strength such as 96 kA m À1 , the critical strain amplitude of normal force-strain curves, g c, is increasing with the shear rate, and this increasing trend is not obvious with the increase of the magnetic eld.

3.2.4
Quasi-static monotonic shear for MRG-70 under different temperature. Fig. 8 shows the change of normal force of MRG-70 with shear strain under different temperature and magnetic eld strength. As the increase of the shear strain, normal force of MRG-70 under different temperature remains constant in the absence of magnetic eld, but decreases rst and then tends to unchanged at the applied magnetic eld. On the other hand, it also can be seen from Fig. 8(b), (c) and (d) that, when the shear strain is smaller than a critical value, temperature has no effect on normal force and the corresponding critical value decrease with the increase of magnetic eld, i.e. 3.2%, 2.4% and 0.9% for 96 kA m À1 , 194 kA m À1 and 391 kA m À1 . With the increase of strain amplitude, the normal force of MRG-70 demonstrates an increasing tendency along with the temperature, and this increasing tendency is correlated with the magnetic eld strength. The reason for this is that, the solid-like grease matrix has an effect on the chain formation of CI particles, as the temperature increase, the viscosity of the grease matrix decreases which benets the chain formation of CI particles distributed in the matrix. Meanwhile, the magnetic force between the CI particles also enhanced by the increase of magnetic eld strength. Therefore, the normal force of MR grease can be enhanced at high temperature and magnetic eld strength.

Normal force of MR grease under quasi-static cyclic shear
3.3.1 Quasi-static cyclic shear for MRG-70 under different magnetic eld. To investigated the normal force behavior of MR grease under quasi-static cyclic shear, the shear strain linearly increased from 0 to 100%(I: loading stage) and then decreased to 0(II: unloading stage). Aer that, shear strain reversely loaded to À100% (III: reverse loading stage) and then restored to 0 (IV: reverse loading stage). The time that used for every stage is 20 s, and the corresponding quasi-static shear rates is 0.05 s À1 . To ensure the stability of the material properties in each case, at least 5 cycles were measured for each cycle loading. Fig. 9 shows the normal force versus shear strain curves of MRG-70 at the quasi static shear rate of 0.05 s À1 under different magnetic eld strength. We only discuss the loading stage I and unloading stage II of the cyclic curve here due to the symmetry of the cyclic normal force versus shear strain curve. When the external magnetic eld was not applied, the normal force of MRG-70 in stage I, II, III and IV are the same and tend to 0. Under the magnetic eld strength of 96 kA m À1 , the normal force at different stages presents a big difference. At the loading stage I, the normal force of MRG-70 nearly maintains constant with the increase of shear strain, but in the unloading stage II, the normal force of MRG-70 exhibit peak phenomenon at the beginning of unloading stage. This is because of that, under the action of magnetic eld and shear, the chain structures reconstruct and rupture of MR grease in loading stage I has reached an equilibrium state aer multiple shear loading cycles. At the beginning of shear strain decrease from 100% to 0, the internal broken chain structures are gradually reconstructing, which is benecial to the increase of normal force. As the further decrease of shear strain, the continuous reconstruction of the particle chain is squeezed by the parallel-plate, which in turn causes the chain structure to rupture. The coupled inuence leads to the peak phenomenon of normal force for MR grease in unloading stage II. In addition, the normal force behavior of MR grease in reverse loading stages III and reverse unloading stage IV is similar to loading stage I and unloading stage II, respectively.
3.3.2 Quasi-static cyclic shear for MRG-70 under different shear strain. Fig. 10 shows the cyclic normal force versus strain curves for MRG-70 under ve different shear strain. It can be seen from Fig. 10(a) that, as the applied shear strain increased, the peak normal force of the cyclic curves demonstrates an increase trend, with the applied shear strain higher than 80%,  the peak normal force of the cyclic curves nearly maintains constant, i.e. 1.12 N, 1.24 N, 1.32 N, 1.36 N and 1.36 N for 20%, 40%, 60%, 80% and 100%, respectively. From Fig. 10(b)-(d), at the applied shear strain of 20%, the cyclic normal force versus strain curve displays a buttery-like shape, as the increase of the applied shear strain, the intersection point of the cyclic normal force versus strain curve gradually shis downward, causing the buttery-like shape of cyclic curve to disappear. In addition, the area enclosed by the cyclic normal force versus strain curves increases with the increase of applied strain, which can be attributed to the phase difference between the applied shear strain and structural strain. 21 Another interesting phenomenon we can nd from the cyclic normal force-strain curves marked by the green dotted line in Fig. 10(b)-(f) is that, when the shear strain is higher than 40%, normal force exhibits an abrupt change during the transition from loading stage I to unloading stage II (or reverse loading stages III to reverse unloading stage IV), and the abrupt change rate increase along with the increase of shear strain, i.e. 163%, 242%, 303% and 308% for 40% 60%, 80% and 100%, respectively. This has never been reported in MR uid or MR polymer. The possible reason may be induced by the special viscoplastic properties of grease matrix of MR grease.

Conclusion
In this paper, three types of MR grease were prepared by dispersing different weight fraction of CI particles into lithiumbased grease. The normal force versus strain curves of these three MR samples under different test conditions, i.e. shear rate, temperature and magnetic eld strength, were obtained by using quasi-static monotonic and cyclic shear test. In the quasi-static monotonic shear test, the results demonstrate that, a critical strain amplitude, g c , divides the relationship between the normal force and shear strain into two stages. When the shear strain is smaller than g c , normal force presents a rapid decrease trend with the increase of shear strain. However, normal force remains almost constant at the shear strain higher than g c , and the critical strain is affected by the magnetic eld strength, CI particles content and shear rate. Moreover, when the shear strain is smaller than a critical value, temperature has no effect on normal force. With the increase of strain amplitude, the normal force of MRG-70 demonstrates an increasing tendency along with the temperature, and this increasing tendency is correlated with the magnetic eld strength. For the quasi-static cyclic shear test, the results indicate that, at the unloading stage II, the normal force of MRG-70 exhibit peak phenomenon at the beginning of the unloading stage. As the applied shear strain increased, the peak normal force of the cyclic curves demonstrates an increasing trend, with the applied shear strain higher than 80%, the peak normal force of the cyclic curves nearly maintains constant. In addition, when the shear strain is higher than 40%, normal force exhibits an abrupt change during the transition from loading stage I to unloading stage II(or reverse loading stages III to reverse unloading stage IV).

Conflicts of interest
There are no conict to declare.