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Rheological characterization of fumed silica lubricating greases Zakani, Behzad 2017

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RHEOLOGICAL CHARACTERIZATION OF FUMED SILICA LUBRICATING GREASES by  Behzad Zakani  BASc, University of Tehran, 2015  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mechanical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   December 2017  © Behzad Zakani, 2017 ii  Abstract  Lubricating greases have been widely used for rail lubrication systems. For an efficient grease pump design, it is important to study grease shear viscosity and it is also crucial to analyze grease yielding behavior to determine its consistency on rail surface. Among all rheological properties measured through experiments, yield stress is an ill-defined property, which investigation of a reproducible method for its determination can be invaluable. As the flow properties of a material will be usually influenced by the changes in environment temperature, studying the effects of temperature on the rheological properties of grease are important.  In this study, different rheological measurements and visualization techniques, previously developed to study a wide range of materials, have been performed to characterize fumed silica based lubricating greases manufactured by L.B. Foster Rail Technologies Corp. Using commercial rheometers and different approaches to determine the yield points of these materials, it was revealed that the values obtained by curve fitting on steady-state flow curves, creep, amplitude sweep crossover and stress ramp-up were roughly similar. The microstructure of this grease was analyzed using Scanning Electron Microscope (SEM) on Cryo and non-Cryo modes. Besides visualizing a new thickener microstructure, it was shown that the heterogeneous structures developed by small fumed silica agglomerates lead to the formation of greases with higher shear viscosities. Finally, thermo-rheological analysis of these samples revealed that these materials follow neither Arrhenius equation nor time-temperature superposition principle.   iii  Lay Summary  One of the most integral parts of Canada’s transportation system is rail transport, which its industry generates $10 billion per year. Transport Canada has spent roughly $14 million to improve transport safety of 810 railway crossings across the country. One of the key elements of rail transport system which can influence its safety and economy is rail lubrication process. Lubricating greases will be pumped on the surfaces of the rail to decrease the wear and friction in wheel-rail contact. It also helps to eliminate squealing in railway curves continuously. In order to manufacture the most suitable greases for this application, flow properties of these samples such as viscosity and yield stress should be analyzed. In this work, some special lubricating greases were characterized by visualization techniques and roughly equivalent values were measured for their yield stress. Effect of temperature on flow properties was also analyzed.       iv  Preface  The identification and design of this research project was performed by Dr. Dana Grecov. For all chapters, all research, experimental work and analysis were completed by me, except as specified below. In Chapters 3 and 4, all lubricating greases studied were manufactured by L.B. Foster Rail Technologies Corp. The company kindly provided these samples throughout the whole project. The studies in Chapter 3 will be submitted for publication. The studies in Chapter 4 includes my contribution to an accepted paper in Rheologica Acta in November 2017:  B. Zakani, M. Ansari, D. Grecov, Dynamic rheological properties of a fumed silica grease, accepted, Rheologica Acta, November 2017   v  Table of Contents  Abstract .......................................................................................................................................... ii Lay Summary ............................................................................................................................... iii Preface ........................................................................................................................................... iv Table of Contents ...........................................................................................................................v List of Tables .............................................................................................................................. viii List of Figures ............................................................................................................................... ix List of Symbols ............................................................................................................................ xii Acknowledgements .................................................................................................................... xiv Dedication .....................................................................................................................................xv Chapter 1: Introduction ................................................................................................................1 1.1 Motivation ....................................................................................................................... 1 1.2 Objectives ....................................................................................................................... 3 1.3 Organization .................................................................................................................... 3 Chapter 2: Background .................................................................................................................5 2.1 Lubricating greases in industry ....................................................................................... 5 2.2 Rheometry principles ...................................................................................................... 6 2.2.1 Test modes .................................................................................................................. 7 2.2.2 Measuring systems ...................................................................................................... 7 2.2.3 Parallel plates working equations ............................................................................... 9 2.2.4 Rheological tests ....................................................................................................... 13 2.3 Lubricating greases ....................................................................................................... 18 vi  2.3.1 Grease composition ................................................................................................... 18 2.3.2 Grease microstructure ............................................................................................... 21 2.3.3 Grease rheology ........................................................................................................ 23 2.4 Conclusion .................................................................................................................... 27 Chapter 3: Yield stress measurements of fumed silica greases ...............................................28 3.1 Introduction ................................................................................................................... 28 3.2 Material and methods .................................................................................................... 31 3.2.1 Material ..................................................................................................................... 31 3.2.2 Rheological characterization ..................................................................................... 31 3.2.3 Visualization techniques ........................................................................................... 32 3.3 Results and discussion .................................................................................................. 33 3.3.1 Rheological measurements ....................................................................................... 33 3.3.2 Visualization micrographs ........................................................................................ 59 3.4 Conclusion .................................................................................................................... 65 Chapter 4: Thermo-rheological analysis of fumed silica greases ............................................67 4.1 Introduction ................................................................................................................... 67 4.2 Material and methods .................................................................................................... 69 4.2.1 Material ..................................................................................................................... 69 4.2.2 Rheological characterization ..................................................................................... 69 4.3 Results and discussion .................................................................................................. 71 4.4 Conclusion .................................................................................................................... 81 Chapter 5: Conclusion .................................................................................................................83 5.1 Summary ....................................................................................................................... 83 vii  5.2 Contributions................................................................................................................. 83 5.3 Future directions ........................................................................................................... 84 Bibliography .................................................................................................................................87  viii  List of Tables   Table 3-1 Characteristics of the studied grease samples .............................................................. 31 Table 3-2 Results of using different rheological models for steady flow curve fitting ................ 38 Table 3-3 stress vs strain rate obtained by creep tests in viscous region ...................................... 41 Table 3-4 Yield stress measurements using different approaches based on strain sweep data .... 49 Table 3-5 Curve fitting parameters using HB model for two selected greases batches ............... 64 Table 4-1 Characteristics of the fumed silica grease .................................................................... 69 Table 4-2 Plateau modulus and its corresponding frequency from results in Figure 4-2 a&b ..... 80  ix  List of Figures  Figure 3-1 Reproducibility of the pre-shear sequence, illustrating that each of the selected runs on fresh samples showed the same value of shear stress at equilibrium after applying the shear rate of 0.01 (1/s) for 300 s. The working gap was 0.5 mm. ..................................................................... 34 Figure 3-2 Comparing the accuracy of applying a fixed value of shear rate (0.01 (1/s)) between two different gaps ......................................................................................................................... 35 Figure 3-3 Shear viscosity at different gaps, showing that viscometry data was not influenced by slip effect ....................................................................................................................................... 36 Figure 3-4 Illustrating viscosity bifurcation of studied grease under different applied levels of stress based on the graphs of instantaneous shear viscosity vs time (a) and instantaneous shear strain vs time (b) ........................................................................................................................... 39 Figure 3-5 Comparison between data obtained by steady viscometry table and creep measurements....................................................................................................................................................... 41 Figure 3-6 Evolution of viscoelastic moduli under amplitude sweep sequence at frequency of 2 Hz....................................................................................................................................................... 43 Figure 3-7 Evolution of complex modulus and viscosity under amplitude sweep sequence at frequency of 2 Hz.......................................................................................................................... 44 Figure 3-8 Yield stress measurements using different approaches based on data obtained by amplitude sweep sequence at frequency of 2Hz ........................................................................... 46 Figure 3-9 Yield stress measurements using elastic stress component obtained by amplitude sweep sequence at frequency of 2 Hz ...................................................................................................... 48 x  Figure 3-10 Evolution of Loss modulus in the LVER at very working low frequencies showing inaccuracy in data collection ......................................................................................................... 50 Figure 3-11 Schematic illustration of the Maxwell viscoelastic model ........................................ 51 Figure 3-12 Frequency sweep data at the strain of 0.05% illustrating the evolution of complex shear stress with frequency ........................................................................................................... 52 Figure 3-13 A comparison between the viscosities obtained from steady viscometry and that of frequency sweep (strain=0.05 %) showing a deviation from Cox-Merz principle ....................... 54 Figure 3-14 Hysteresis observed during up and down stress ramp sequences indicating the thixotropic behavior of the grease sample .................................................................................... 56 Figure 3-15  Results of increasing (a) and decreasing (b) stress ramps illustrating static and dynamic yield points respectively ................................................................................................. 57 Figure 3-16 SEM micrograph of a fumed silica grease sample at 35K magnification. ................ 60 Figure 3-17 Cryo-SEM micrograph of a fumed silica grease sample after coating by Pt at 50K magnification ................................................................................................................................ 61 Figure 3-18 Cryo-SEM micrographs of Batch1 (a) & Batch2 (b) with no coating at magnification of 35K ........................................................................................................................................... 63 Figure 3-19  A comparison between steady state shear viscosities of Batch 1 & Batch 2 ........... 63 Figure 4-1 Amplitude sweep data at frequency of 1 Hz, at different temperatures. The star indicated the data point at this value of strain and frequency in frequency sweep measurements .............. 72 Figure 4-2 The (a) storage (G’) & (b) loss (G”) moduli of lubricating grease as function of frequency at different temperatures .............................................................................................. 74 Figure 4-3 The Cole-Cole plot of lubricating grease in terms of G’ versus G” at various temperatures .................................................................................................................................. 76 xi  Figure 4-4 The (a) storage & (b) loss moduli of lubricating grease as function of inversed absolute temperature at various frequencies. There is an abnormal behavior around 0°C which is more evident in G’ ................................................................................................................................. 77 Figure 4-5 Complex modulus (G*) as a function of the inverse temperature in the transient temperature ramp experiment for lubricating grease (continuous line) and its base oil (dash-line). The heating ramp is 1°C/min. ....................................................................................................... 79 Figure 4-6 The non-monotonic behavior of plateau modulus as a function of inversed temperature....................................................................................................................................................... 81 xii  List of Symbols  𝜏     Shear stress. 𝑅     Radius of the measuring system. 𝑀    Torque. ?̇?     Shear rate. Ω    Angular speed. 𝐻    Gap between the plates. 𝜂    Shear viscosity. 𝛾    Shear strain. 𝛾°   Shear strain amplitude. 𝜔   Angular frequency.  𝜏°   Shear stress amplitude. 𝛿    Phase shift. 𝑡     Time. 𝐺∗   Complex modulus. 𝐺′   Storage modulus. 𝐺"   Loss modulus. 𝜂∗    Complex shear viscosity. 𝜃𝜊    Angular displacement amplitude.  𝑚𝑝   Consistency factor of power law model. 𝑛𝑝    Power law index of power law model. xiii  𝜏𝑦𝐻𝐵   Yield stress value predicted by Hershel-Bulky model.  𝑚𝐻𝐵   Consistency factor of Hershel-Bulky model. 𝑛𝐻𝐵    Power law index of Hershel-Bulky model. 𝜏𝑦𝐵     Yield stress value predicted by Bingham Plastic model. 𝜇𝐵      Constant viscosity predicted by Bingham Plastic model. 𝜏𝐿𝑉𝐸𝑅𝐿      Stress value at the limit of linear viscoelastic region. 𝜏𝐿𝑖𝑛−𝑅𝑒𝑔   Yield stress measured by linear regression. 𝜏𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝑠  Yield stress measured at intersection of tangents.  𝜏𝐶𝑂    Stress value at cross over of viscoelastic moduli. 𝜏𝑒𝑦    Maximum elastic stress value. 𝐺      A viscoelastic modulus. 𝐺°     A viscoelastic modulus at a reference temperature. 𝐸𝑎𝑐𝑡  Thermal activation energy. 𝑅      Universal constant. 𝑇      Absolute temperature.       xiv  Acknowledgements  First, my special thanks are owed to my parents and my sister, who have supported me throughout my years of education. I would not have had such a fulfilling life without your support and unconditional love even from far away. I would like to thank my supervisor, Dr. Dana Grecov, for her guidance and expertise throughout my degree completion. Her research experience was instrumental in my progress and achievements throughout this degree. I would like to thank Dr. Mahmoud Ansari, a postdoctoral researcher in our group, for enlarging my vision of science and providing coherent answers to my endless questions. I would like to thank all of the following individuals, without whom this research would not have been possible. Nick Yeh and Anish Maturi for their helpful discussions about my thesis formatting. Michael Chernos for his patience in training me on the Kinexus rheometer. Dr.Gethin Owen, Xin Zhang, Arian Amirkeyvan for training me with SEM, Cryo-SEM equipment, and Anton Paar rheometer respectively.  I would like to thank L.B. Foster Rail Technologies Corp. for providing the studied fumed silica greases and their base oil as well as our helpful discussions.  This project had been funded by Mitacs program and L.B. Foster Rail Technologies Corp. which are highly appreciated.  xv  Dedication  I would like to dedicate my thesis to my lovely parents and sister, whose love and unselfish support laid the foundations for discipline necessary to complete this work.  1  Chapter 1: Introduction  1.1 Motivation One of the most integral parts of Canada’s transportation systems is rail transport, which according to Transport Canada statistics, its industry generates roughly $10 billion per year. There are more than 46,000 kilometers of tracks in Canada justifying the significance of this type of transportation system economy. According to statistics, in 2011, 1023 railway accidents occurred in Canada causing 71 casualties. Transport Canada spent roughly $14 million to improve transport safety of 810 railway crossings across the country. The importance of rail transport industry demands providing appropriate conditions to run this type of transportation in a safe manner1.  One of the key elements of rail transport system which can influence its safety and economy is the rail lubrication process. Greases have been widely used for rail lubrication systems. Application of these materials on rail surface results in the reduction of wear and friction in the wheel-rail contact, elimination of generated noise in railway curves and increasing transportation safety. Thus, it is important to study grease viscosity for designing an appropriate pump which pours this material on the rail surface, and it is also crucial to analyze grease yielding behavior to determine its ability to attach to the rail surface. Yield stress is an ill-defined rheological property, which investigation of a reproducible method for its determination can be invaluable. As flow properties of a material is usually influenced by changes in environment temperature, it is important to study the effect of temperature on grease rheological properties. The flow properties of lubricating greases are probably the governing properties for qualifying the performance of grease lubricated surfaces. Grease should remain attached to the contact area to form a lubricant reservoir and act 2  like a sealant. Thus, the grease should not flow at rest or when small magnitudes of force are applied on, which is a characteristic of yielding materials. At these small deformations, grease behaves like a viscoelastic material where the ‘storage modulus’ is larger than the ‘loss modulus’. However, in the lubrication process, the grease should be able to flow easily, and therefore a low resistance or viscosity is required. In terms of rheology, lubrication mechanism results in a shear-thinning response of grease2. The grease quality and performance can strongly be influenced by its main additive called thickener which forms a 3-dimensional network trapping oil particles. At present, there is no ideal method available to characterize the physical microstructure of lubricating greases. The most common method to visualize the thickener structure is Scanning Electron Microscopy (SEM), where the base oil needs to be removed from the thickener matrix 3. An ideal technique is non-invasive, does not require pretreatment of the grease and can image low-contrast features down to nanometer level. Fumed silica, which consists of inorganic nanoparticles, has a very high thermal stability. It also has a huge surface area to absorb oil, due to its porous structure. These characteristics make it an ideal choice as a thickener for high-temperature greases 4.  The microstructure of thickeners in commercial lubricating greases such as the fibrous structure of lithium 5,6, spherical shape of calcium soap 6,7 and polyuria platelets 8 and their corresponding rheology have been widely studied. L.B. Foster Rail Technologies Corp. has developed some ultra-high-performance lubricating greases thickened by fumed silica which have exceptional physical properties such as tackiness, pumpability, worked and un-worked penetration in comparison to other commercialized lubricating greases. To our knowledge, there is no academic research related to the rheological and structural characterization of fumed silica based lubricating greases. 3  1.2 Objectives The general objective of this work is to study fumed silica based lubricating greases as a newly developed grease by L.B. Foster Rail Technologies Corp, using different rheometry and visualization techniques, which have been previously used to study a wide range of materials. The sub-objectives of this work are as follows: 1. Rheological characterization of fumed silica based lubricating greases with the main focus on yielding behavior of these samples.  2. Correlating the fumed silica based grease rheology with its microstructure revealed by different visualization techniques. 3. Thermo-rheological analysis of fumed silica based lubricating greases.  1.3 Organization Chapter 2 provides a background of lubricating grease role in the industry, basic principles of rheological measurements and previous works using different characterization techniques to evaluate grease performance.  Chapter 3 presents a study on rheological properties of fumed silica greases, with the main focus on their yielding behavior, application of SEM (both Cryo and non-Cryo) visualization technique on these samples, and correlating the results of rheometry and microscopy in a qualitative manner. Chapter 4 describes results of applying small amplitude oscillatory shear tests on the studied fumed silica grease samples at various temperatures.  4  Chapter 5 presents the overall conclusions of this thesis, as well as some recommendations for potential future work.   5  Chapter 2: Background  In this chapter, a background about the role of lubricating greases in industry, rheometry principles and presentation of previous studies on grease composition, visualization of its structure and its corresponding rheology is reviewed.   2.1  Lubricating greases in industry The main role that lubricating greases play in any types of bearings is providing the sliding elements contact area with enough lubricant material to secure the separation of the two surfaces such that the system attains a long lifespan and low coefficient of friction9. The sliding elements such as wheel and rail are able to run in the absence of lubrication, but without lubricants, service life will be significantly shortened. The first types of grease lubrication took place in the 19th century using animal fats. The addition of lye or lime to these fats produced simple greases appropriate for early machinery. Lubricating greases can be utilized in a wide range of environmental conditions. The applied temperatures on these lubricants can be as low as -70°C and as high as 300°C. The operating environments are usually humid. Corrosive agents like salt water can have an adverse effect on the machinery performance. The grease composition is a suitable variable to assist lubrication performance in different operating conditions. Greases are economical and convenient sources for lubrication10. Grease lubrication has many advantages over oil lubrication. Grease can act like a perfect sealant. It cannot easily leak out of the contact area due to its yield stress and consistency. Grease protects the systems from corrosion, when the contact area is properly covered with this lubricant9. 6  Considering the disadvantages, the main issue of grease lubrication is its limited lifetime. Applied temperatures, speed, load and even the grease type can affect grease life span11. Mechanical work and extremely high temperatures can destroy grease structure. The grease lifetime is such an important factor that in some cases, it can define the service life of the bearing. In these cases, the bearing manufacturers indicate some re-lubrication intervals in their catalogues based on the grease life which is based on the time at ‘which 1% of the population of the bearings is expected to have failed’12. One should consider three main challenges in studying lubricating grease performance. The first challenge is trying to develop a grease sample that is able to last longer under bearings and/or has the capability to be utilized under severe conditions such as extremely low and high temperatures. The next task, which is much related to the former one, is trying to design bearing systems that can increase the grease life. The third challenge which one may face is the development of tools, such as numerical models or rheological measurements to predict the grease behavior under different applied flow types and conditions. All these points require a fundamental knowledge of the lubrication mechanisms of greases. Although the attempts to do research in the field of grease lubrication has not received the attention that it deserves; the bearing industry is keen on a fundamental understanding of this particular subject 9. 2.2 Rheometry principles Rheology can be defined as the science of the deformation and flow of matter. The scope of this field includes flow behavior of many complex fluids such as foods, suspensions, emulsions, pastes, and polymers. In order to study the flow behavior of a material under external forces, one should consider three equations simultaneously which are the mass conservation equation, the momentum 7  conservation equation and a constitutive equation which relates material deformation to its stress. The accuracy of the simulations which aim to describe material flow properties in real life condition highly depends on the selection of this constitutive equation. The only way to decide on the choice of this equation is doing experimental measurements and comparing the obtained results with the ones predicted by constitutive equations13. 2.2.1 Test modes Performing rheological measurements using commercial rheometers can be achieved under controlled shear rate mode (CSR) or under controlled shear stress mode (CSS). In the former case, the rotational speed or the shear rate applied on the controlled volume is controlled and the corresponding torque or shear stress is then measured. Under CSS mode, the applied torque or shear stress is under control and the resultant shear rate or rotational speed is then recorded14. It is worth to note that the results of CSR and CSS modes measurements, performed on the same sample are not necessarily identical15.  2.2.2 Measuring systems There are different types of measuring systems, which can be used to measure material rheological properties such as concentric cylinders (known as bob and cup), cone and plate geometry, parallel plates measuring systems and vane in cup. The choice of a geometry for doing rheological measurements is based on many criteria and limits like wall slip, edge fracture and sample amount 14. Wall slip is a phenomenon which occurs when the classic well known no-slip boundary conditions of Newtonian fluid mechanics is not valid anymore and the fluid actually slips over solid surfaces of the measuring system. This would cause inaccuracy during the measurements. There are some remedies found in literature to decrease slip effect during rheological 8  measurements such as using geometries with roughened surfaces 16 and modifying the surface chemistry of the geometry for a better adhesion of the samples to the tools 17. Edge fracture is another phenomenon which causes errors during rheometry. This instability manifests itself by partial ejection of the sample from the geometry. During the measurements using vane in cup and concentric cylinders, this phenomenon is less likely to occur (depending on sample nature). Rheometry of various types of fluids18 has revealed that decreasing the cone angle in the case of cone and plate and the working gap in the case of parallel plates measuring systems, would significantly postpone edge fracture effect to higher values of shear rates. Amount of sample required to do rheometry with any of the mentioned geometries is another limit. This is very crucial especially when one works with biological samples such as synovial fluids, which a volume of only around 0.5 ml of this fluid can be aspired from a normal person knee 19. When one performs rheometry, for samples with low viscosity, measuring systems with large diameters is used to generate enough torque and for high viscosity samples, smaller geometries are more preferable. In this study, different commercial geometries were considered to finalize the choice of the measuring system. Using concentric cylinders or vane in cup measuring systems, a relatively huge amount of sample was required. Moreover, due to the limits of rheometer cooling system, it was not experimentally practical to reach to stable temperatures below -5°C. Therefore, studying the thermo-rheological behavior of the samples was not practical. Using cone and plate geometry, edge fracture occurred at very low shear rates. In addition, no sandblasted or serrated cone and plate geometry was available to reduce wall slip effect.  The measuring system in this study was parallel plates. This measuring system consists of two circular plates. When one works with this geometry, the radius and the gap between the plates need 9  to be reported. The plates with diameters of 20-25 mm were used to study grease rheology. The choice of the working gap is really important. Working with large gap dimensions may lead to edge fracture 18. On the other hand, wall slip effect is more pronounced when one works with small gaps, especially for lubricating greases 20.Therefore, a proper gap should be a somehow optimum value, reducing the adverse effects of these two phenomena as much as possible. To do this, using a gap of 0.5 mm was appropriate for the studied sample. An important feature of these geometries is their available serrated and sandblasted profiles manufactured by the rheometer companies14. As lubricating greases are known as samples which slip on the surfaces of geometries20, rheometry of the studied sample was performed using plates with rough surfaces. Using an oven connected to a tank of liquid nitrogen, thermo-rheological analysis of grease was possible even at temperatures as low as -40°C (trapping sample by the oven).  2.2.3 Parallel plates working equations As described in the previous section, the measuring system in this study was parallel plates. Thus, it is worth to review its rheological working equations under rotational and oscillatory tests. Rotational shear working equations:  The working equations under rotational shear tests using the parallel plates measuring system are as follows14:                                                      𝜏(𝑅) = (2. 𝑀)/(𝜋. 𝑅3)                                                                      (2.1)  ?̇?(𝑅) = (𝑅. Ω)/𝐻                                                                 (2.2) 𝜂(𝑅) =  𝜏 ?̇?⁄ = (2. 𝑀. 𝐻) (𝜋. 𝑅4⁄ . Ω)                                               (2.3)   10  Where  𝜏 is the shear stress  𝑅 is the radius of the measuring system  𝑀 is torque  ?̇? is the shear rate  Ω is the angular speed  𝐻 is the working gap between the plates  𝜂 is the shear viscosity  It is worth to mention that as the main disadvantage of using these measuring systems is the dependency of their applied shear rates on the radius of plates, commercial rheometers usually consider measuring the shear rates at points that are at 2/3 or 3/4 of the distance from plate edge to its center. Using this factor, a somehow averaged and more acceptable measurement that has less dependency on radius can be obtained.  Oscillatory shear working equations: Before describing the oscillatory working equations of the parallel plates measuring system, it is worth to study the main concepts of small amplitude oscillatory tests.  Let’s define 𝛾 (the applied strain) 13as a complex function of time with the magnitude of 𝛾° and frequency of 𝜔: 𝛾(𝑡) = 𝛾°𝑒𝑖𝜔𝑡                                                          (2.4) 11  Considering the strain amplitude small enough for assuming the measurements are within Linear Viscoelastic Region (LVER), the response of oscillatory shear stress can be described by one harmonic with a phase shift angle (δ):                                                                 𝜏(𝑡) = 𝜏° 𝑒𝑖(𝜔𝑡+𝛿)                                                      (2.5) For an ideal elastic behavior, this angle is 0° , for an ideal viscous material it is equal to 90° and in the case of a viscoelastic material, this angle is between these two limits.  Expanding the obtained stress function results in:                                                   𝜏(𝑡) = ( 𝜏°𝛾°cos 𝛿 + 𝑖𝜏°𝛾°sin 𝛿 ) 𝛾(𝑡)                                          (2.6) A term known as complex modulus (G*) is then defined as follows:                                                                      𝐺∗ =𝜏(𝑡)𝛾(𝑡)                                                              (2.7) This complex modulus contains real and unreal parts known as G’ (storage modulus) and G” (loss modulus) respectively. The term G’ is a measure of the deformation energy stored by the sample during the application of the oscillatory shear forces and G” describes the deformation energy lost, during this process. Therefore, the latter term represents the viscous irreversible behavior and the former one represents the elastic behavior:                                                                   𝐺∗ = 𝐺′ + 𝑖𝐺"                                                        (2.8)                                                         |𝐺∗| = (|𝐺′2| + |𝐺"2|)12⁄                                                 (2.9) Therefore, some useful equations can be derived describing these viscoelastic moduli:                                                                   𝐺′ =𝜏°𝛾°𝑐𝑜𝑠 𝛿                                                          (2.10)                                                                   𝐺" =𝜏°𝛾°sin 𝛿                                                           (2.11)                                                                   tan(𝛿) =𝐺"𝐺,                                                            (2.12) 12  Another useful viscoelastic property which has a significant meaning in characterizing material behavior is the complex viscosity defined as follows:                                                                        𝜂∗ =  𝜏?̇?                                                              (2.13)  Based on equations above this function can be derived as follows:                                                                        𝜂∗ =𝐺∗𝑖𝜔                                                             (2.14) An alternative way of expressing periodic rheological properties is to use sinusoidal functions14. The applied strain and the stress response can then be defined as follows:                                                             𝛾(𝑡) = 𝛾𝜊 sin(𝜔𝑡)                                                       (2.15)                                                              𝜏(𝑡) = 𝜏ο sin(𝜔𝑡 + 𝛿)                                                (2.16) Rheometer considers sinusoidal functions for oscillatory measurements. It should be mentioned that by using sinusoidal functions, the definitions for G’, G”, G* and δ remain the same. Considering 𝜃𝜊  as the magnitude of the applied angular displacement, for the case of parallel-plates geometry, the working equations for properties at linear viscoelastic region are as follows13:                                                                𝐺′(𝜔) =2.𝐻.𝑀.cos 𝛿𝜋.𝑅4.𝜃𝜊                                                                  (2.17)                                                                𝐺"(𝜔) =2.𝐻.𝑀.sin 𝛿𝜋.𝑅4.𝜃𝜊                                                      (2.18) Using the two equations above, all other viscoelastic functions can be defined then. Rheometer can also perform oscillatory shear tests under controlled stress and thus strain response with a phase lag will be generated and the definitions provided in above for viscoelastic moduli do not change. It should be noted that the physical meaning of the viscoelastic moduli measured by rheometers under large applied strains is completely different from the ones calculated at small strain amplitudes. As the applied strain increases in an oscillatory shear flow, material viscoelastic response may pass the LVER leading to a stress response which is no longer sinusoidal and thus 13  the linear viscoelasticity assumption will be violated21. However, the rheometer is not able to recognize this transition and thus it generates the above-mentioned moduli in the same way as those measured under low strain amplitudes22. 2.2.4 Rheological tests  Considering the sequences that one may apply on different samples, we can categorize them into two main types, known as oscillatory and rotational rheometry. In the latter, a rotational force or speed will be applied by the upper component of the geometry on the sample and the corresponding shear rate or shear stress will be then recorded. After geometry and sample set up, shear rate or shear stress can be easily manipulated by controlling rotational speed or torque under CSR and CSS modes, respectively. In the case of oscillatory sequences, the upper geometry applies an oscillatory motion on the sample which both the deformation and the frequency of this motion is of great importance. The deformation is whether under controlled stress or strain mode and the frequency of the motion can be changed manually using rheometer’s software.   There are many sequences and tests developed under rotational and oscillatory procedures. They all have their own significance and different rheological properties such as steady shear viscosity, yield stress, relaxation time, and viscoelastic moduli can be determined directly or indirectly from these measurements. Here, some of these useful experiments and their corresponding rheological properties will be addressed. All of these measurements are described in the Isothermal condition.  Single value viscometry During this rotational sequence, a constant stress or strain rate will be applied on the sample and the transient and steady state response of the material will be defined by time. In other words, the evolution of shear stress and viscosity under CSR mode or the change of shear rate and viscosity 14  under CSS mode will be recorded at a defined period of time. An ideal Newtonian fluid will reach the steady state condition at a defined shear rate or stress, after a specific amount of time. However, the scenario is more complex for many industrial and biologic materials. As an example, if one applies different levels of stress on an aqueous suspension of bentonite (4% solid concentration), an obvious viscosity bifurcation will be observed in the results of viscosity vs time. At low levels of stress, viscosity increases by time reaching to infinite, an effect called ‘ageing’. On the other hand, applying high levels of stress leads to ‘shear rejuvenation’: Viscosity decreases by time to reach to a steady state value23. Therefore, the transient behavior obtained by single value viscometry can provide valuable information about sample behavior. Table of shear viscometry This sequence is a combination of several single viscometry experiments performed on the samples consecutively. Different levels of stress or shear rate will be applied on the sample and the resultant steady state values of viscosity will then be plotted. The experiment can be performed under an ascending order or descending order of stress and shear rate.  The obtained results will be usually reported as steady stress vs steady shear rate or steady viscosity vs steady shear rate known as flow curves. The accuracy and range of the applied torque or rotational speed and their corresponding results are strongly dependent on geometry and rheometer limits. The time interval needed for reaching to steady state at each fixed value of stress or shear rate may vary. Different properties can then be measured based on curve fitting using different steady state rheological models. There are many models found in the literature, describing different types of materials and predicting their properties such as yield stress, zero shear viscosity14.   15  Stress or strain ramps  These sequences are again another type of rotational tests in which the applied strain rate or shear stress increases or decreases linearly by time at different ramp rates. This test can provide valuable information about material properties such as yield stress and thixotropic behavior. If one does stress ramp sequence on a yielding material and sketches the resulting viscosity vs the applied stress, the shear stress at which viscosity reaches to its maximum value can be referred to as yield stress. In this way, yield stress can be measured directly and the problems such as dependency on the choice of the rheological model which rise in indirect measurement method of steady flow curves will be eliminated24,25. The time needed to perform ramp sequences is much smaller than tests like creep. Thus, samples are less prone to damage under these experiments 26. Performing an up and down ramp on a sample one can reveal the time dependency of its rheological properties15.  Strain or stress amplitude sweep These oscillatory sequences will be performed under a fixed value of frequency. A controlled shear strain or stress sinusoidal function of time will be applied on the sample and as soon as the steady state value of the oscillatory properties such as G’ and G’’ are obtained, the value of the applied strain or stress increases to the next point at again the previous constant frequency. The working frequency for amplitude sweep tests is usually 10(rad/s) or 6.28(rad/s). At the end of the sequence, usually, the values of viscoelastic functions will be plotted against the strain or stress on logarithmic scales. As stated before, the regime at very low amounts of strain or stress is called linear viscoelastic (LVE) range. The term is derived due to the simultaneous existence of linear elastic behavior and linear viscous behavior showing the proportionality of the preset and 16  measured properties. In this range, the ratio of stress to strain and that of stress to strain rate are both constant representing complex modulus and complex viscosity respectively. Thus, both G’ and G’’ show constant plateaus regardless of the applied stress or strain. The material structure can be analyzed based on LVE results.  If the constant value of G’ is more than that of G’’, the material has a gel characteristic like pastes, gels, and stable dispersions. If storage modulus plateau occurs below that of loss modulus, the material has a liquid characteristic like many Newtonian liquids. If the values of G’ and G” show the same order of magnitudes, the material has reached to a state called gel point. In this case, which rarely happens for samples in industry, there is a balance between elastic and viscous behaviors defining the border between gel and liquid-like characteristics. This range is of great importance as the material deforms reversibly and beyond its limit, the sample structure will whether change irreversibly or wholly demolished. There are different approaches to determine the limit of this range. In some cases, the end of this regime will be defined as a change in the plateau values of any viscoelastic functions. It is worth to note that this limit can have frequency dependency, especially under CSR mode. For some materials, when this sequence is performed under higher working frequencies, the elastic modulus will reach to higher levels and LVE limit will be smaller due to the induced brittle behavior. The term SAOS (Small amplitude oscillatory strain) refers to the measurements done with a stress or strain below this limit and LAOS (Large amplitude oscillatory strain) to those done beyond LVE limit. Some other rheological terms such as yield point or flow point can also be determined based on amplitude sweep results 14.   17  Frequency sweep This test is another type of oscillatory sequences. The term dynamic oscillation is sometimes used as an alternative phrase or this sequence.  A sinusoidal function will be applied on the sample like that of amplitude sweep sequences. The difference is that here stress or strain is fixed and the frequency is the controlling parameter which can be manipulated. Viscoelastic functions at the end will be plotted against frequency and based on these results useful information about material structure will be obtained. Many materials perform a frequency dependent response to this sequence which can be categorized into short-term and long-term behaviors. Considering PDMS (Polydimethylsiloxane) as a good example, this material behaves like an elastic solid (G’> G”) at high frequencies (Short-term behavior) and when left at rest (low frequencies), spreads like a liquid (G’<G”) representing its long-term response. Measurements performed under SAOS condition provide useful information about material behavior. Therefore, amplitude sweep sequences must be carried out before frequency sweep sequences to determine the limit of the linear viscoelastic region. After obtaining rheological results under both steady table of shear and frequency sweep, a very useful relation called Cox/Merz rule can be derived which relates the shear viscosity to complex viscosity (|𝜂∗(𝜔)| = 𝜂(𝛾)̇) indicating that these two viscosities have the same amounts at the same values of angular frequency or shear rates. It should be noted that this relation is valid only for those samples which mechanical interactions like molecular entanglements play part in their rheological response. Any physical or chemical interactions between material particles can violate this rule. Therefore, this relation is not valid for suspensions, pastes and gels 14.  18  2.3 Lubricating greases In this section, a review of grease composition, visualization of its structure and its rheology is addressed and discussed.  2.3.1 Grease composition Lubricating grease performance is a strong function of the properties of the materials used in its composition. There are different definitions found in the literature describing the nature of lubricating greases. In general, the grease can be defined as a solid to semi-fluid colloidal suspension consisting of some dispersed particles called thickener which form a structure trapping lubricating oil as its dispersive medium27.The thickener particles (3-30% of grease composition) can be metallic soaps, organic and inorganic matters28.There are some other additives such as corrosion inhibitors and antioxidants in the grease, which all of them have their own significance in grease performance. Base oil Lubricating greases provide liquid films for reducing friction between bearing elements. Therefore base oil viscosity is of great importance and this matter should maintain its fluidity over a range of pressures and temperatures and preferably provide a full film lubrication over a wide range of speeds. There are some properties which define the effect of temperature on base oil. Thermal and oxidative stability of base oil often dictates the upper working temperature in different applications27. Pour point of lubricating oils defines the lowest temperature that base oil can still flow. Obviously, the working environment determines temperature requirements, as northern hemisphere cold winters considerably influence lubrication performance29. 19  Different mineral or synthetic oils can be used as base oils. Many of synthetic base oils are not compatible with the common metallic soap thickeners such as Calcium and Lithium. In these cases, thickening agents such as fumed silica and Teflon will be used instead. The advantage of synthetic oils over mineral ones is their ability to perform lubrication in extreme conditions. Sometimes a mixture of these mineral or synthetic oils will be used as the base oil. Mixtures of mineral oil and synthetic esters are common in lubricating greases composition 27. Mineral oil is the most common choice of base oil in many lubricants composition and it can even be used without any additives for machinery lubrication. The chemical structure of mineral oil, which is a product of crude oil distillation, can be Paraffinic, Naphthenic and Aromatic. Any of these basic categories of mineral oil have their own special properties if used as base oil. As an example, a Paraffinic mineral oil has a very nonpolar structure which limits the choice of additives. However, the existence of saturated Carbon bonds in their structure improves lubricant oxidation stability 27. The cost of mineral oil is low and it can be found in a wide range of viscosities which is determined by its controllable molecular weight. Mineral oil has the characteristics of a liquid over an acceptable range of pressures and temperatures. Its molecules are hydrophobic. Thus, mineral oil can repel water molecules and protect the metallic surfaces of machinery against rust. Unlike synthetic ones, mineral oils are compatible with a wide range of additive and thickening agents 30,31.  Thickener The grease thickener plays an important role in determining the grease properties and rheology and lubricating greases can be categorized based on thickener nature and its interactions with dispersing medium (base oil) 28. The most common thickeners are soap based. Thickeners with 20  narrow molecular weight distributions are known as simple soap based greases. Lithium, Calcium, Sodium, and Aluminum soaps are examples of these types of thickeners. Another type of soap based thickeners are complex ones which the chemical reactions behind their formation lead to their complex structures. These reactions are performed on reactants having the same previously named elements such as Lithium and Calcium.  Complex soap based greases are designed for high temperature performance. However, as their thickener concentrations are usually way higher than that of simple ones, they are not preferable for low temperature applications27. There are also some other types of thickeners such as fumed silica known as non-soap thickeners which do not show any phase change at even very high temperatures27. Fumed silica consists of inorganic spherical nanoparticles. Due to the presence of the silanol groups on the surfaces of primary particles and the possibility for hydrogen bonding, these nanoparticles form aggregates32. The aggregates then form agglomerates which this transition is reversible. Fumed silica has a high thermal stability. Thanks to its huge surface area (Surface area of primary particles33 is in the order of 100 (m2/g)), the structure can absorb a significant amount of oil 4. Moreover, it has been shown that for many applications, the addition of fumed silica to a solution can form a complex non-Newtonian system commonly accompanied by yield stress, shear thinning and thixotropic behaviors. Thus, a fumed silica based microstructure can provide a low viscosity under high shear stresses and yield point or a high viscosity at lower shear stresses, suitable for lubrication33. These characteristics show that this material can be an appropriate option for thickening role in lubricating greases used for high temperature applications 4.  A combination of each of the thickeners mentioned above and different base oils will result in a lubricating grease appropriate for specific applications27. Thus, it is always worth to work on 21  lubricating greases that whether their base oil or their additives make them a unique material not studied before by different characterization methods. Additives Additives are some chemicals added to lubricating greases to improve their performance under different environments and conditions. Using antioxidants is mandatory in the composition of those greases that are based on mineral oils to perform well at high temperatures. Aromatic secondary amines are common antioxidants used in greases. Sometimes blends of different antioxidants are preferred for an improved performance34. Viscosity improvers are another additives existing in the grease composition that are usually aliphatic compounds. Corrosion inhibitors are used to inhibit corrosion process of metallic surfaces. Barium and Calcium sulfonates are common compounds used for this purpose in grease composition27. For those operations under severe load conditions, anti-wear and extreme pressure additives may be used35.  2.3.2 Grease microstructure Considering grease properties in machinery and bearings, except the lubrication role performed by base oil, other characteristic functions are highly dependent on grease microstructure formed by thickener particles. Thus, having a knowledge about grease microstructure can provide valuable information about lubrication performance 6. Details of grease microstructure can be too small to be visualized by optical microscopy. There are many attempts done to characterize grease microstructure using high resolution visualization techniques6,7,36–39. One can categorize these microscopy methods into two main groups: The techniques in which the grease microstructure is not effectively perturbed before visualization such as AFM (Atomic Force Microscopy), ESEM (Environmental Scanning Electron Microscopy) and Cryo-SEM (Cryo-Scanning Electron 22  Microscopy) and those characterization methods which require sample preparations disturbing grease structure, such as TEM (Transmission Electron Microscopy) and SEM (Scanning Electron Microscopy). The most common visualization technique for lubricating greases is SEM. Its visualization mechanism in simple words is as follows: A focused electron beam will hit the surface of the sample resulting in the emission of secondary electrons of the specimen. The signal of those excited electrons will then be detected using specific equipment to form an image of surface topography. Conventional SEMs can be utilized under high vacuum. However, ESEM provides the opportunity to perform imaging even at low vacuum. Cryo-SEM works under very low temperatures and one can visualize the topography of the sample surface using freeze-fracture technique 40. Therefore, using conventional SEM, the base oil needs to be extracted to avoid releasing of contaminant gaseous hydrocarbons in the chamber. This will be done using a non-polar solvent such as n-Hexane. A small amount of grease sample will be immersed in this solvent for some days (5-10 days) and the solvent may also be replaced to improve oil extraction process. After that, the sample will be mounted on SEM stub and dried at room temperature. Next, samples will be coated using different elements such as Au (Gold) and Ir (Iridium) to prevent surface charging and improve secondary electron emission. The amount of coating is an important consideration during image analysis, as an excessive coating results in masking details and information. Obviously, this oil removal and the subsequent drying may lead to the formation of thickener agglomerates and collapse of the structure. However, SEM provides valuable information about thickener dimensions and in some cases, the images revealed that the structure is not perturbed considerably in comparison to that obtained by techniques like AFM 6. The fibrous 23  structure of lithium greases 6, spherical shape of calcium soap 6,7 and polyuria platelets 8 have all been revealed using this technique. Images taken by ESEM 39 as a method which does not require a highly vacuumed environment (thus, it does not perturb grease structure) has proved the existence of a highly structured and entangled structure of Lithium fibers observed by SEM6. Another useful technique as previously stated is SEM under Cryo mode. A very small amount of sample will be mounted on a specific holder. The whole stuff becomes frozen by immersing the sample holder in a liquid nitrogen bath. In vacuum condition and at very low temperature (~ -140°C) the frozen grease specimen will be then fractured and (in some cases) coated using specific equipment. Structural analysis using Cryo-SEM has been performed on Lithium greases37. 2.3.3 Grease rheology As stated before, having a knowledge about grease flow properties is crucial for evaluating grease performance. In terms of rheology, lubricating greases can be considered as complex fluids, as they can be classified as yielding 20,41–44 and shear-thinning 20,42,45 fluids. This material should have a very high viscosity at very low deformation rates to overcome motion (This is crucial as it should act like a sealant and provide lubrication reservoir) and a low viscosity when lubrication is required. Under different circumstances, the applied shear rates on lubricating greases2 can be as high as 106(1/s) and as low as 10-6 (1/s). However, it is impossible to study this shear rate region using commercial rheometers, as these conditions cause significant sample fracture or equipment damages. The explanation for justifying the shear thinning behavior in the case of Lithium lubricating greases is as follows. It has been suggested that this decline in the order of magnitude of shear viscosity is due to the alignments of fibers and/or loss of joints between their entanglements caused by the applied deformations. At very higher levels of shear rates, the fibers 24  height decreases2. For these types of greases, yield stress can then be defined as the minimum stress required to break an adequate number of joints in the entangled fibers network leading to the lubricant flow. It is then obvious that by increasing the thickener content one may be able to increase the value of yield stress. It has been shown for Lithium greases that the thickener concentration can have a power law relation with yield stress46.  There have been attempts to measure yield stress of commercial lubricating greases using different rheological sequences 43,46. However, it is worth to note that not only in the case of lubricating greases, but also for other complex materials, yield stress is a rheological property that is hard to be determined 15,43,47. Different rheological tests can give rise to very different results depending on the measuring systems (geometries) and experimental setup15,25,48. The most common technique for yield stress measurements is an indirect method which involves obtaining steady state stress vs shear rate flow curve and extrapolation of the stress to zero shear rates49. However, this method highly depends on the used rheological model and less reliable data obtained at low shear rates due to effects such as slip24,25,49.A direct yield stress measurement method such as creep and stress ramp independently determines the yield stress value. The main concern in these measurements is the time scale of the experiment. Considering creep tests, as a constant stress will be applied on the sample for an approximately long time, samples are very prone to damage50. Stress ramp results are also time sensitive and to a great extent depend on the applied ramp rate 51. It should be mentioned that the huge variation observed in the reported results of yield stress measurements should not be ascribed to the resolution power of different equipment and this issue is more related to the application of a constant yield stress concept to many yielding materials. Although this issue is well known for rheologists, engineers and researchers in the industry often ignore the existence 25  of a variable yield stress and treat this property as a material constant that is only hard to be determined15.  Lubricating greases have time dependent flow properties. An interesting rheological feature of lubricating greases is their thixotropic behavior which describes the decrease in viscosity by time when a constant stress is applied. The driving force in a system is the result of the competition between the bond breakdowns due to applied forces and bond formations due to Brownian motion and in-flow collision48. In the case of thixotropic materials, usually, the rate of destruction overcomes the rate of construction. Applying single viscometry sequences under constant imposed shear rates, revealed that if one plots stress as a function of time, at the beginning, the stress increases by time linearly on a log-log scale. Here grease microstructure is accumulating energy and only weak bonds are destroyed. A stress overshoot will then take place. At this point, enough energy is stored for the breakdown of thickener bonds. This accumulated energy will be released slowly and more bonds will be destroyed resulting in a slow decline of stress or viscosity by time. This observed evolution of stress over time for the case of Lithium greases can be justified by thixotropy concept2,52. The other time dependent rheological properties of greases which are worth to be studied are viscoelastic ones obtained by oscillatory tests. Amplitude sweep results reveal that lubricating greases have a gel structure (G’>G”) at low strains and liquid characteristics (G’<G”) at high deformations. Results of frequency sweep at LVE range on commercial greases has shown that these materials can be classified as highly entangled systems53 which has been proved by different microscopy techniques such as SEM and AFM 54. Rheometry is a powerful characterization method which can provide useful information about samples structure. There are some studies done on correlating grease microstructure to its 26  rheology. In an interesting article55, authors used SEM and studied the evolution of a Lithium grease microstructure and its corresponding rheology at different steps of this lubricant manufacturing process. Using AFM as the visualization technique, Calcium and Lithium7 based lubricating greases have shown different viscoelastic and microstructural features. Studying the effect of polymer addition at different stages of Lithium grease manufacturing56, revealed a similar structure and rheology among those stages that polymer effect was not significant. A work considering a correlation between fumed silica grease microstructure and resultant rheology is missing. Based on their applications and operating conditions, lubricating greases may be exposed to a wide temperature range. Thus, it is vital to study grease thermal service by tailoring the effect of temperature on its properties. There are some studies done, focusing on thermo-rheological of well-known commercial greases such as Lithium and Calcium thickened ones7,44,57–61. Studying temperature effect on SAOS functions of the Lithium greases7,54 has revealed that grease can retain its highly entangled structure at a wide temperature range, as G’ evolving moderately with frequency is always higher than G” which shows a minimum at certain frequencies. Studying the effect of temperature on the steady flow curves54,62, revealed a non-monotonic response of commercial greases by the occurrence of a minimum at viscometry data at relatively high temperatures. The effect of temperature on viscoelastic functions and peculiar behavior in steady flow curves data quantitatively and qualitatively depend on grease thickener and additives7.To our knowledge, there is no work done on thermo-rheological analysis of a fumed silica based grease. 27  2.4 Conclusion Following the provided information in this chapter, fumed silica based lubricating greases have not been previously studied using rheometry and electron microscopy. L.B. Foster Rail Technologies Corp. has developed a fumed silica grease with exceptional performance. As stated before, it is always worth to study lubricating greases that whether their base oil or their additives make them a unique material not characterized before using different lab equipment. Thus, this study aims to analyze fumed silica greases manufactured by L.B. Foster Rail Technologies Corp. using rheometry and electron microscopy which are well known characterization methods for analyzing a wide range of materials. 28  Chapter 3: Yield stress measurements of fumed silica greases  In this chapter, rheology and yielding behavior of fumed silica based greases developed by L.B. Foster Rail Technologies Corp, using different approaches previously developed for a wide range of materials, will be analyzed. Using SEM results, a correlation between rheology and microstructure of these greases will be investigated.  3.1 Introduction Greases are used in a great variety of situations to reduce the wear and friction between surfaces. They are highly structured suspensions consisting of a thickener dispersed in lubricating liquid and additives61 .The type of base oil used in grease production is one of the key determinants of grease performance at different temperatures. The type and amount of thickener and additives have a critical effect on grease properties. Thus, it is always important to study greases with new compositions. L.B. Foster Rail Technologies Corp. have newly developed a fumed silica grease with exceptional physical properties such as tackiness, worked and unworked penetration. As Gay and Leibler63 have quoted: “A substance appears sticky when some work is required to remove one’s finger from it. This property is known as tackiness”. Cone penetration or consistency can be described as follows. Under a standard setup, a conic metallic surface will be allowed to fall and subsequently penetrate into a grease sample at a specific amount of time and temperature. Thus, a lower penetration value means a stiffer grease. The worked penetration is another grease physical property. The measurement procedure resembles that of unworked cone penetration with one difference. Prior to measurements, grease will be sheared in a grease worker. The number of 29  strokes applied on the grease plays an important part in the evaluation of final penetration. Worked penetration values are usually more reliable than unworked values, as in the latter case, sometimes a minor shear can affect the reported penetration64. There are some attempts in literature regarding a correlation between grease rheology and its physical properties2,65–67. Lubricating greases are thermo-rheologically complex materials62. It is known that when a shear stress is applied to a lithium lubricating grease, a reorientation of thickener fibers in the microstructural network takes place, resulting in shear-thinning flow55. Lubricating greases are considered classical yielding materials 68with an apparent yield stress and a subsequent shear thinning flow region. Lubricating grease’s flow behavior is time dependent; therefore, one must always consider a complete rheological description of the material. The greases are viscoelastic and thixotropic materials. Shear bulk rheology of Lithium and Calcium lubricating greases has been already studied3,7,43,55,68.  Among all rheological properties, yield stress is of great importance for the evaluation of grease performance. The choice of an appropriate pump, as well as the time that grease will remain on rail surface, are both influenced by this property 2. There have been many attempts to measure yield stress of commercial lubricating greases using different rheological sequences 2,43,46. However, it is worth to note that not only in the case of lubricating greases, but also for other complex materials, different rheological tests can give rise to very different results depending on the measuring systems (geometries) and experimental setup 15,25,48. The most common technique for yield stress measurements is an indirect method which involves obtaining steady state stress vs shear rate flow curve and extrapolation of the stress to zero shear rates49. However, this method highly depends on the used rheological model and less reliable data obtained at low shear rates 30  due to effects such as slip 24,25,49.A direct yield stress measurement method such as stress ramp independently determines the yield stress value. Stress ramp results are also time sensitive and to a great extent, depend on the applied ramp rate 51. A study on yield stress measurements of fumed silica based lubricating greases is still missing. The grease quality and performance are strongly influenced by the thickener 3-dimensional network structure built up by fibers. At present, there is no ideal method available to characterize the physical structure of the greases. The most common method to visualize the thickener structure is SEM (Scanning Electron Microscopy) where the base oil has to be washed from the thickener matrix 6. An ideal technique is non-invasive, does not require pretreatment of the grease and can image low-contrast features down to nanometer level. There are some works done6,7 demonstrating the application of AFM (Atomic Force Microscopy) for the examination of grease microstructures. Mansot et al.69 applied the freeze-fracture technique using TEM (Transmission Electron Microscopy) for analysis of lithium hydroxystearate greases. The freeze-fracture technique is a very useful method for investigating the physical form of thickener particles in grease matrix. It can act as a perfect complementary technique to other well-known electron microscopy methods such as SEM. Probably the most important advantage of this technique over other conventional ones is the fact that specimens will be minimally affected before imaging37.To our knowledge, there is no academic research related to microstructural characterization of fumed silica grease.  This chapter presents a study, covering rheological characterization of fumed silica based greases developed by L.B. Foster Rail Technologies Corp, with the main focus on analyzing their yielding behavior. Different approaches will be used and compared to determine yield point. The chapter 31  also covers the application of SEM visualization technique to characterize grease microstructure. Finally, the results of these characterization methods will be correlated in a qualitative manner. 3.2 Material and methods 3.2.1 Material The lubricating greases studied in this chapter were provided by L.B. Foster Rail Technologies Corp. consisting of fumed silica as thickening agent and group III base oil. The basic known properties for these samples are summarized in Table 3-1. Table 3-1 Characteristics of the studied grease samples Oil Grease Thickener Oil Viscosity @100°C [cSt] Oil Viscosity @40°C [cSt] Unworked Penetration [mm/10] Group III base oil Fumed silica 8 46 285  3.2.2 Rheological characterization The rheological measurements were all performed with a Malvern Kinexus Rheometer under both controlled stress and strain modes using 20 mm serrated plate-plates measuring system to decrease slip effect. Measurements were all done at 25◦c. Before each measurement, after sample trimming, the same pre-shear procedure was applied on all samples: applying a shear rate of 0.01 (s-1) for 5 minutes followed by 20 minutes relaxation helped to secure the repeatability of the results. The reproducibility of grease state after the pre-shear sequence is shown in Figure 3-1. For preventing shear history on rheological measurements, all experiments were performed on fresh samples. Viscometry single values at different stress levels were performed to study transient behavior of grease under rotational tests. Steady-state flow curve measurements were performed in the range of 10-3-102 (s-1) at different gaps. Amplitude sweep sequences on strain controlled mode were 32  performed at different fixed values of frequency (0.1, 0.5,1,2,10 Hz) in the range of 0.01 to 100 % to characterize the LVE region and yield stress. Frequency sweep sequences were performed in LVE region in the range of 0.01-30 (Hz) at the strain of 0.05 %. Linear stress ramps were performed at the rate of 1 (Pa/s) to analyze thixotropy and yield stress of the studied greases. The results of rheometry were repeatable within 2%.  3.2.3 Visualization techniques In order to characterize the microstructure of fumed silica grease, Scanning Electron Microscopy (SEM) was performed with an FEI Helios NanoLab 650. As morphological characterization of different specimens through this system requires high Vacuum, extraction of mineral oil particles before conducting any visualization with this technique is inevitable. A small amount of grease sample was immersed in n-hexane for 10 days. The replacement of the solvent was carefully done 5 times per day to complete oil removal. The sample was dried at room temperature on the SEM stub subsequently. Afterwards, the specimen was coated using Leica EM MED 020 system equipped with Ir sputtering to prevent surface charging and improve secondary electron emission. The micrographs were taken at a magnification of 35K and accelerating voltage of 1 kV. Cryogenic scanning electron microscopy (Cryo-SEM) was performed again with FEI Helios NanoLab 650 to characterize the fumed silica grease microstructure using the freeze-fracture technique. A small amount of lubricating grease was mounted on a Cryo-SEM specific holder. The whole set was then immersed in a bath of liquid nitrogen to become frozen. In vacuum condition and at very low temperature (~ -140°C) the frozen grease specimen was fractured and coated using Quorum cryo system equipped with Pt sputtering. Visualization was then performed on the surface of the fractured area. The images were taken in a cryo chamber at accelerating voltage of 2 kV and 33  magnification of 50K. Prior to sample coating with Pt, some micrographs were also taken at a magnification of 35K. 3.3 Results and discussion 3.3.1 Rheological measurements  The examined fumed silica lubricating grease in this study showed the characteristics of a thixotropic yield stress material. For describing the yielding points of these type of samples, the term ‘apparent yield stress’ has been used which indicates that for these systems, yield point depends on the shear history of the material and its definition is thus ill-defined 15,70. In this manuscript, the term ‘yield stress’ refers to the scientific ‘apparent yield stress’ word. Here, the rheological properties of a fumed silica grease batch manufactured by L.B. Foster Rail Technologies Corp. will be explained in detail.  Steady state flow curves Rheological measurements of lubricating greases under rotational tests can always be influenced by phenomena such as sample ejection and wall slip 43. Using parallel plates measuring systems, wall slip is more pronounced working with small gaps and edge fracture instability is common when the gap is large18. 34   Figure 3-1 Reproducibility of the pre-shear sequence, illustrating that each of the selected runs on fresh samples showed the same value of shear stress at equilibrium after applying the shear rate of 0.01 (1/s) for 300 s. The working gap was 0.5 mm.  Measurements with the gap of 1 mm or higher resulted in a significant amount of sample ejection at even low values of applied shear rates ( ?̇? = 1 (1 𝑠)⁄ ). As illustrated in Figure 3-2, working with gaps as low as 0.3 mm, caused inaccuracy in applying the desired shear rate. As the gap was so small and shear rate was very low, the existence of tolerance in the constant applied shear rates was inevitable. Moreover, the time instrument needs to reach to a steady state shear rate condition decreases by increasing the gap and this time will be even less at higher values of shear rate. Therefore, considering both edge fracture instability and measurement limits, the gap should be set between 0.3 and 1mm. Steady state shear viscosities are depicted in Figure 3-3 at two different gaps of 0.5 and 0.7mm. The results confirmed that slip effect on the measurements was minimal. Rheometry results at low shear rates are more influenced by slip effect than high deformation rates43, which result in obtaining higher values of steady stress or viscosity at higher gaps.  Time (s)0 50 100 150 200 250 300 350Shear str ess, (Pa)0100200300400500Run 1Run 2Run 3 Run 4Run 535   However, in our case, using a measuring system with rough surfaces, influence of wall slip was negligible. The shear-thinning behavior of the studied lubricating grease can be verified as shear viscosity decreased by increasing shear rate. Power-law model is the simplest rheological model describing the shear-thinning (n < 1) or shear-thickening (n > 1) behavior of a material14.                                                                    𝜂 = 𝑚𝑝. ?̇?𝑛𝑝−1                                                                       (3.1) Where   𝜂  is the steady shear viscosity   ?̇?   is the steady shear rate   𝑚𝑝  is the consistency factor of power law model  𝑛𝑝  is power law index of power law model  Figure 3-2 Comparing the accuracy of applying a fixed value of shear rate (0.01 (1/s)) between two different gaps 36    Figure 3-3 Shear viscosity at different gaps, showing that viscometry data was not influenced by slip effect  If one applies this model to data shown at Figure 3-3, the obtained value for power index (np) will be 0.05. This low value of power index demonstrates the yielding behavior of the studied lubricating grease at very low deformation rates. Thus, it is worth to apply rheological models with the capability of yield stress prediction on the obtained data to provide an approximate value for this property. The simplest models describing the existence of yield stress are Hershel-Bulkley and its special case Bingham Plastic (𝑛𝐻𝐵=1) which are presented in Equations 3.2 and 3.3, respectively14,43.                                                                     𝜏 = 𝜏𝑦𝐻𝐵 + 𝑚𝐻𝐵?̇?𝑛𝐻𝐵                                               (3.2)                                                                          𝜏 = 𝜏𝑦𝐵 + 𝜇𝐵?̇?                                                          (3.3)  Steady shear rate, (1/s)10-4 10-3 10-2 10-1 100Steady shear viscosity, Pa.s)103104105106Gap= 0.7mmGap= 0.5mm37  Where   𝜏 is the steady shear stress  ?̇? is the steady shear rate  𝜏𝑦𝐻𝐵 is the yield stress value predicted by Hershel-Bulky model   𝑚𝐻𝐵 is the consistency factor of Hershel-Bulky model  𝑛𝐻𝐵 is power law index of Hershel-Bulky model  𝜏𝑦𝐵 is the yield stress value predicted by Bingham Plastic model   𝜇𝐵 is a constant viscosity predicted by Bingham Plastic model Results of curve fitting by using above mentioned models are summarized in Table 3-2. Based on 𝑅2 values shown in the table, one can conclude that Hershel-Bulkley function can describe grease rheology better than the other two models. As Bingham Plastic model is not able to predict shear thinning behavior and power law function lacks including yield point, choice of Hershel-Bulkley which provides inclusion of both properties simultaneously, results in the highest reported value of 𝑅2. However, it should be noted that the all of the fittings results reported in Table 3-2 were based on the whole range of steady flow curve data points. If one applies Hershel-Bulkley model on different ranges of data points, the 𝑅2 value can change within 0.9975-0.9981, resulting in a variable yield stress in the range of 218.6-291.8 (Pa). Thus, the main drawbacks of using this indirect technique of yield stress measurement are the dependency of the obtained yield points on the choice of rheological model 24,49 and of course the range of data chosen for doing curve fitting studied here. 38  Therefore, using Hershel-Bulkley model, one can report 255±37 (Pa), as the yield point of the studied fumed silica lubricating grease. This means that based on this model prediction, our sample does not flow unless it is subjected to a shear load in the range of 255±37 (Pa).   Table 3-2 Results of using different rheological models for steady flow curve fitting   𝑚𝑝 (𝑃𝑎. 𝑠𝑛𝑝)    𝑛𝑝   ( )  𝑚𝐻𝐵 (𝑃𝑎. 𝑠𝑛𝐻𝐵)  𝑛𝐻𝐵   ( )  𝜏𝑦𝐻𝐵 (𝑃𝑎)  𝜇𝐵 (𝑃𝑎. 𝑠)  𝜏𝑦𝐵 (𝑃𝑎)  𝑅2      ( ) Power-law 386.2 0.05      0.99403 Hershel-Bulkley   191.2 0.18 218.6   0.99814 Bingham Plastic      623.5 291.8 0.88124  Creep: Based on the results from Figure 3-3, at very low shear rate region (<2×10-3(1/s)), steady shear viscosity is not stable; suggesting that in order to have a better understanding of the material, behavior at these low deformation rates, one should record transient response of the material using creep tests46. Applying different levels of constant shear stress on the fresh samples and recording their transient viscosity can provide useful information about structural changes especially in the case of thixotropic yield stress materials15,23. Figure 3-4 a&b depict transient viscosity and instantaneous strain vs time at different levels all stress, all performed on fresh samples. Model Parameters 39     Figure 3-4 Illustrating viscosity bifurcation of studied grease under different applied levels of stress based on the graphs of instantaneous shear viscosity vs time (a) and instantaneous shear strain vs time (b)  Based on Figure 3-4 a, as the applied stress level increases, lower values of the viscosity are obtained due to the shear-thinning behavior of the grease. The results illustrated a clear viscosity bifurcation phenomena typical of thixotropic yield stress materials 23,71,72. In these materials, yield 40  stress concept is related to a microstructure showing resistance to rearrangements 23. When the applied stress is small (Here: 𝜏 < 280 𝑃𝑎 ), the resulting shear rate is so low that the rate of construction overcomes the rate of destruction and the viscosity of the grease increases by time and no steady state value can be obtained. Therefore, one cannot observe the reported steady zero shear viscosity of Calcium and Lithium43,2,46 lubricating greases for the case of fumed silica thickened one. For those commercial greases, authors have reported a clear viscosity plateau at very low shear rates. In order to have a better understanding of the difference between the concept of yield stress and zero shear viscosity one can consider inserting a rod into two distinct fluids in terms of rheological behavior, both showing a high resistance to flow under low deformation rates. The rod remains standing in the fluid which has a yielding behavior and moves very slowly in the case that zero shear viscosity exists14. Figure 3-4 b illustrates that grease performs an elastic behavior in this region. The recorded strain of the grease is constant over a considerable time scale showing a solid-like behavior.  On the other hand, when a sufficiently high shear force is applied on the sample (Here:𝜏 >280 𝑃𝑎 ), destruction of the microstructure wins over its buildup, resulting in a decrease in viscosity by time reaching to a steady state condition which is known as shear rejuvenation 15,23. It should be noted that, for the case of applying stress of 500 Pa, a small amount of grease was ejected from the measuring system due to applying a high level of stress for a prolonged time. The effect of this sample fracture on rheometry data is observable in Figure 3-4 a. Again, considering the material response, Figure 3-4 b depicts a viscous behavior under high values of applied stress: Instantaneous strain increases linearly by time showing a constant strain rate value typical of a 41  liquid –like behavior. This constant slope is measured in the last 200 seconds of applying the constant stress and reported in Table 3-3. Table 3-3 stress vs strain rate obtained by creep tests in viscous region Stress (Pa) 287.5 300 400 500 Shear rate (1/s) 0.0087 0.0254 2.46 14.91  The results of Table 3-3 and steady state flow curve are presented in Figure 3-5 and a good overlap of data using both methods can be observed. This can confirm a similarity between the results obtained by two different sequences under controlled stress and strain modes.        Figure 3-5 Comparison between data obtained by steady viscometry table and creep measurements Thus, one can conclude that by increasing the level of stress, a transition from a solid-like behavior to a liquid-like behavior takes place. Considering the observed viscosity bifurcation in the results, a yield stress value of 283±3 Pa can be obtained. It is worth to mention that this method measured a value for yield point directly and effects of errors such as inaccuracy of data obtained at low Shear rate, (1/s)10-3 10-2 10-1 100 101 102 103Shear  stress, Pa)102103Steady viscometry resultsCreep results 42  shear rates or the choice of rheological model which rise in an indirect method such as steady flow curves24,49, are therefore negligible. However, creep tests are more time consuming than steady viscometry tests. Applying several values of constant stress, all on fresh samples for an approximately long time is not preferable to the indirect method when one needs to have a rough estimation of yield stress value for an industrial application. Moreover, as stated before, samples are very prone to damage under creep tests. Oscillatory tests:  The application of oscillatory tests for determining the rheology of lubricating greases is very popular. The main advantage of these experiments over rotational ones is that samples are much less susceptible to be fractured2. Furthermore, gap and roughness dependencies of oscillatory results for the case of lubricating greases43,73 are shown to be negligible.  Figure 3-6 illustrates amplitude sweep results obtained at a frequency of 2 Hz. Results show the evolution of G’ (Storage modulus) and G” (Loss modulus) by the applied strain at different viscoelastic regions. At very low amplitudes of strain (Here below 0.1 %), in the so-called linear viscoelastic range (LVER), both G’ and G” functions perform constant plateau values at different magnitudes. The term SAOS (Small amplitude oscillatory strain) function refers to viscoelastic properties in this range and the term LAOS (Large amplitude oscillatory strain) describes these properties in the non-linear region14. 43        Figure 3-6 Evolution of viscoelastic moduli under amplitude sweep sequence at frequency of 2 Hz  The term linear describes that in this range, the proportionality of the stress and strain and that of stress and strain rate are both satisfied in a way that these two ratios are equal to two constant values. In other words, Hooke’s elasticity law (𝜏 𝛾⁄ = 𝐺∗ = 𝑐𝑜𝑛𝑠𝑡) and Newton’s law of viscosity ( 𝜏 ?̇?⁄ = 𝜂∗ = 𝑐𝑜𝑛𝑠𝑡)  are both valid in this range. Figure 3-7, illustrates the evolution of G* and 𝜂∗, confirming the described linear term at low strain values.      Strain amplitude , (%)10-3 10-2 10-1 100 101 102 103Storage and loss Moduli, G' &G"Pa)101102103104105G'G''44             Figure 3-7 Evolution of complex modulus and viscosity under amplitude sweep sequence at frequency of 2 Hz  Based on Figure 3-6, at very low strain values, the elastic response of grease dominates its viscous one. The material exhibits a certain rigidity and acts like a solid (G’>> G”) which has been observed for the case of Lithium and Calcium greases43.  In this region, the applied strain is so small that the integrity of the microstructure formed by thickener particles does not change. The viscoelastic response of the material is completely reversible14. Just after this critical strain value, the viscoelastic behavior of material becomes irreversible and the ability of the thickener particles to recover elastically decreases showing a decline in G’ function. On the other hand, the loss modulus (G”) increases slightly showing a maximum that has been observed for some complex fluids22,74. The initial increase in G” can be due to the buildup of weak complex structures 22 which have been formed temporarily and their formation is highly energy dissipative. Further breakdown of these structures at higher values of applied strains result in the decrease of G”. This maximum has been previously observed for fumed silica suspensions75,76 and using the explanations above the increase in G” was attributed to the breakdown of agglomerates into many smaller units Strain amplitude , (%)10-3 10-2 10-1 100 101 102 103Complex Modulus, G*( Pa) & viscosity, *(Pa.s)101102103104105G**45  followed by the further destruction of these structures at higher strains leading into G” decline76 .After the occurrence of a maximum for loss modulus, the decrease in oscillatory functions continues until a crossover happens and viscous effects dominate (G”>G’) the irreversible response of non-linear viscoelastic region. The applied shear is so high that the structural integrity will be lost and viscous shear contributes to the resultant shear force much more than the thickener particle elastic interactions43. Amplitude sweep results and their corresponding explanations can provide some approaches to define a yield point. In order to cover these techniques, the complex stress is illustrated along with the viscoelastic moduli as functions of the amplitude in Figure 3-8. The first method considers the reversibility of the viscoelastic properties14 and yield point will be determined based on the LVE limit. This value is shown in Figure 3-8 as 𝜏𝐿𝑉𝐸𝑅𝐿 and for this sample at frequency of 2 Hz it was 11.57 (Pa). It is worth to note that here, the criterion for determining the limits of LVER was based on the selection of the smallest deformation required for deviation of any viscoelastic functions from their plateau values on Figure 3-6 & 3-7.  46   Figure 3-8 Yield stress measurements using different approaches based on data obtained by amplitude sweep sequence at frequency of 2Hz  As loss modulus was the first function which started to deviate from its constant value, the strain chosen to describe the limits of LVE was 0.1%. However, if one considers this limit as the stress or strain that the linear relation between complex stress and complex strain is not valid anymore, this strain increases up to 1.78%. Although, by applying amplitudes above 0.1%, G’ decreases, the initial increase of G” contributes to the value of G* keeping it constant. This plateau region of G* continues until the strain of 1.78% keeping the stress-strain linear relation valid. Applying the linear –regression on stress-strain data and defining the yield stress at the point that this curve fitting is not valid anymore, lead to obtaining a yield point in the order of 100 (Pa) shown in Figure 3-8 as 𝜏𝐿𝑖𝑛−𝑅𝑒𝑔 . However, the criterion for choosing the above described strain limit and its corresponding yield stress highly depends on the value set for R2 before curve fitting. If one considers 0.995< R2 < 0.998, the strain limit can change from 0.75 to 1.78% resulting in a variable yield stress value of 100±18 (Pa). This means that the obtained yield stress value can change up to 47  18%. In recent works considering yield stress measurements of Calcium and Lithium lubricating greases 43,44, R2 criteria was set as 0.995 and thus, authors reported a fixed value for yielding point. Another method for determining yield point based on amplitude sweep data is 77 considering the end of LVER as the intercept of two straight lines fitted to the graph of the complex shear modulus versus the applied strain data points. The first straight line lies on the constant values of the complex modulus plateau within the LVR and the second one is the tangent of the complex modulus at high deformations. This yield point is illustrated in Figure 3-8 as 𝜏𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝑠. While choosing the data points for the first fitting is clear, there is an obvious ambiguity in data selection for fitting of the second tangent which leads to a variation in determination of yield point. Considering the inaccuracy of this method, a variable yield point of 84 ± 16 (Pa) can be determined for the studied fumed silica thickened lubricating grease. Therefore, the accuracy of this technique is not that much better than that of linear-regression method. The next approach for yield point measurement based on amplitude sweep data discussed here is determining the complex stress at the cross-over78 of dynamic moduli (G’ and G”). This approach is not sensitive to data selection or the accuracy of the curve-fitting and thus it is much more robust. The obtained yield point shown on Figure 3-8 as  𝜏𝐶𝑂 was 197.8 (Pa). This value is the closest amount to that of obtained by rotational techniques described earlier. This is due to the fact that the yield point at the cross-over describes the transition between from elastic (G’ > G”) to viscous (G’< G”) behavior similar to the studied creep method. However, there is a difference between the measured values using these two techniques which can be described by the fact that the output stress waveform during oscillatory measurements in non-linear viscoelastic region cannot be described by only one harmonic79. The stress response is no longer a sinusoidal function21 and 48  rheometer software cannot recognize this change and generates LAOS viscoelastic functions as if it produces SAOS properties22. Using this technique for the case of Lithium and Calcium commercial greases43, authors also reported cross-over yield stresses which were again different from that of obtained by rotational tests. The final approach which will be discussed here for measuring yield point is working with a stress known as elastic stress component. This method is developed by Yang and coworkers80 and it is based on replotting the amplitude sweep data as the product of the elastic modulus and absolute strain amplitude (Known as elastic stress81) versus strain amplitude. Yield stress can then be determined as the maximum of this stress component. Figure 3-9 demonstrates this data at a frequency of 2 Hz. The maximum of the elastic stress was 163 (Pa). Similar to cross-over method, this technique is not influenced by curve-fitting and data selection.   Figure 3-9 Yield stress measurements using elastic stress component obtained by amplitude sweep sequence at frequency of 2 Hz  49  The amplitude sweep data discussed above were all based on the frequency of 2 Hz. The fixed working frequency in the isothermal amplitude sweep measurements is a variable which can generate different oscillatory results causing a frequency dependency of the discussed yield points. Table 3-4 demonstrates yield stress measurements using strain amplitude data at different frequencies. The value of yield point using described elastic stress component technique is referred to as 𝜏𝑒𝑦. Table 3-4 Yield stress measurements using different approaches based on strain sweep data   𝜏𝐿𝑉𝐸𝑅𝐿   𝜏𝐿𝑖𝑛−𝑅𝑒𝑔    𝜏𝑇𝑎𝑛𝑔𝑒𝑛𝑡𝑠   𝜏𝐶𝑂   𝜏𝑒𝑦 1 12.51 75 ± 25 81 ± 14 174.2 140 2 11.57 100 ± 18 84 ± 16 197.8 163 10 11.38 103 ± 35 85 ± 17 222.6 164  The working frequencies shown here were 1, 2 and 10 Hz. While trying to obtain last points of amplitude sweep curve after cross over point, the grease sample showed signs of the onset of fracture at a frequency of 10 Hz. Moreover, frequencies as high as 10 Hz will increase the risk of damaging the equipment in amplitude sweep sequences at high deformations. Therefore, 10 Hz was chosen as the maximum working frequency for this study. On the other hand, amplitude sweep data at frequencies below 1 Hz contained a significant amount of noise as shown in Figure 3-10. At frequencies of 0.1 and 0.5 Hz, rheometer was not able to generate reliable results and G” plateau Frequency       (Hz) Yield Stress      (Pa) 50  region was not obtained suggesting that the rheometer was reaching to its lower applied strain and torque generation limits. Thus, the lowest working fixed frequency shown in Table 3-4, was 1 Hz.  Figure 3-10 Evolution of Loss modulus in the LVER at very working low frequencies showing inaccuracy in data collection  Results shown in Table 3-4 illustrated that an increase in frequency leads to an increase in the value of yield points obtained by methods which focused on measurements after the deviation of G” from its plateau region. This increase in yield point values by increasing the frequency has been previously observed for the case of Lithium and Calcium43 lubricating greases and has been described using a viscoelastic constitutive equation based on Maxwell model shown in Figure 3-11. At very low frequencies, dashpot is very soft and a large portion of energy will be dissipated by this component of Maxwell model, while at higher frequencies or fast motions dashpot will be very rigid and the role of spring is more effective.  51   Figure 3-11 Schematic illustration of the Maxwell viscoelastic model  This model can at least qualitatively describe the increase in yield stress values by increasing the frequency. Based on the discussion above, the yield stress of the lubricating grease studied here is not only a function of applied stress and strains but also a function of the time scale of the experiment. The interesting point observed in Table 3-4 is the fact that as frequency increases from 2 to 10 Hz, the increase in the value of yield point is moderate. The most comparable yield stress obtained using amplitude sweep data with that measured by rotational tests was the cross over stress method at a frequency of 10 Hz. As stated before, the most accurate curve-fitting done by HB model provided a yield stress value of 218.6 (Pa) and at a frequency of 10 Hz, the yield at crossover was 222.6 (Pa). Unfortunately, as stated before, it was not practical to collect strain sweep data at higher frequencies to check the possibility of measuring a yield point with a magnitude comparable with that obtained by creep method.  52  Another point observed in Table 3-4 was that the yield stress obtained at the limit of LVER based on G” deviation from its plateau, decreased with the applied frequency. As the value of stress was so small and its frequency dependency was not significant, this behavior can be due to the imperfect sample loading or errors that rise from other steps of the experimental protocol. In order to verify this assumption, a frequency sweep sequence was performed at the strain of 0.05% to ensure that only SAOS properties were collected. The resultant complex shear stress is shown as a function of applied frequency in Figure 3-12.   Figure 3-12 Frequency sweep data at the strain of 0.05% illustrating the evolution of complex shear stress with frequency  As can be observed, the amplitude of complex stress in a fixed value of strain amplitude was almost constant, confirming the predominance of elastic response of grease within the LVER.  The value of stress plateau was measured and divided by the magnitude of applied strain. The obtained value for an averaged complex modulus is 9660 (Pa) shown in Figure 3-12, which is very close to the magnitude of this modulus in Figure 3-7 (~104 (Pa)). It is worth to note that if one performs this 53  stress averaging within a shorter range of frequency from 1-10 Hz (To cover the selected frequencies shown in Table 3-4), the value obtained for complex modulus will be 10220 (Pa) which is much closer to that of obtained by amplitude sweep. These comparable values of complex moduli confirm that if one does several frequency sweep tests at different levels of applied strain which all are within the LVER limit defined by G” deviation (strains below 0.1%), the complex stress will reach to a plateau when plotted against frequency.  Therefore, the observed frequency dependency of the method which determines the yield stress at the point which transition from linear to non-linear viscoelastic behavior occurs does not have any significant meaning and this decrease in yield stress by increasing frequency is just an experimental artifact. Another advantage of applying frequency sweep sequence in LVER is providing a correlation between oscillatory and rotational tests known as Cox-Merz rule 82. Using this validation, doing many sequences of rheological measurements will not be necessary anymore. Based on this principle, the complex viscosity (complex modulus) obtained from frequency sweep within LVER is equivalent to steady shear viscosity (stress) where the angular frequency and shear rates have the same order of magnitude:                                                               𝜂∗(𝜔) =  𝜂(𝛾)̇                                                           (3.4) Therefore, if one validates this principle for a system, G*(𝜔), can be then used83 instead of steady shear stress 𝜏(𝛾)̇. Figure 3-13, illustrated that the rheological behavior of the studied lubricating grease sample deviated from this principle. It should be noted that for correlations using oscillatory components14, frequency should always be considered with the unit of (rad/s).  54           Figure 3-13 A comparison between the viscosities obtained from steady viscometry and that of frequency sweep (strain=0.05 %) showing a deviation from Cox-Merz principle  Although this useful principle has been proved to be valid for materials such as polymeric melts 84,85, it should be taken into account that any kind of physical and/or chemical interactions are leading to a certain deviation from the Cox/Merz relation and therefore this relation is not useful for materials like pastes, gels, solids and colloidal suspensions 14,86,87. In many of these systems, the shear rate dependency of the hydrodynamic interactions and the particle-particle forces are not the same. However, in dynamic shear flow, the frequency dependency of all forces is almost the same87. This can be the reason for the failure of this rule here. The influence of soap concentration and oil viscosity on this deviation has been illustrated for the case of Lithium greases39 and results showed a significant thickener concentration dependency of this principle breakdown.    Angular frequency, Shear rate, (1/s)10-1 100 101 102 103Steady viscosity, Complex viscosity *Pa.s)100101102103104105Complex  viscositySteady shear visocosity55  Stress ramp The final rheological experiment studied here was linear stress ramp. This sequence is a method which can provide valuable information about material rheological properties. Considering this sequence as a method to determine the yield stress, one can directly measure the stress at yield point. The procedure is simple. The stress will increase from zero to a level well above yield stress at a constant rate. The resultant deformation and shear viscosity can then be plotted vs the applied stress. The peak of this instantaneous shear viscosity vs shear stress or the point at which the slope of deformation versus shear stress changes rapidly (solid like to viscous like behavior) can then be used as an estimation of the yielding point. For non-thixotropic materials, decreasing ramps are preferable. This is due to the fact that short-term transients which are the consequences of a transition from viscoelastic solid to mobile liquid will be considerably avoided70.In comparison, an indirect method to determine yield stress like extrapolation of flow curve data (obtained from rheometers) to zero shear rate, highly depends on the variety of utilized rheological models and the ambiguity in the accuracy of measurements at low shear rates due to slip phenomena and nature of the sample 24,25.Another advantage of these sequences is that the time needed to perform a stress ramp sequence in comparison to methods like creep is much smaller. Thus, the chance of damaging the sample is much less 26. Stress ramp experiments take into account the time evolution of material properties. Thus, it can also be used as a tool to differentiate between thixotropic and non-thixotropic behavior in a yielding material 15.Figure 3-14 depicts results of performing an up and down stress ramp on the studied fumed silica grease. Performing up-and-down stress sweep sequences, the corresponding results are not identical upon going up and down. Data obtained from increasing ramp was higher than that of obtained from the decreasing sequence showing a drop in viscosity by time and confirming the thixotropic behavior of the sample.  56   Figure 3-14 Hysteresis observed during up and down stress ramp sequences indicating the thixotropic behavior of the grease sample  This important hysteresis effect has been previously reported for various types of materials like foams, granular materials, emulsions 72 and concentrated suspensions 88 suggesting that grease can be classified as a thixotropic yielding material. For a simple (Non-thixotropic) yield stress material, the increasing and decreasing shear stress ramp data should coincide, while in the case of thixotropic yielding fluids the flow will have notably liquefied the material at high stresses and the result of the decreasing ramp sequence are way lower than the increasing one 15. As stated before, stress ramp data can also provide useful information about yielding process of the material. By performing an up and down stress sweep, two yield points known as static and dynamic yield stress can then be defined. The static yield stress which can be determined by the increasing ramp sequence is the stress above which material behavior changes from a solid state to a liquid one and the dynamic yield stress which can be determined by decreasing ramp sequence is the stress below which material liquid-like behavior turns into a solid one and thus flow stops15,70. In order to study 57  these yield points, Figure 3-15 a&b illustrates the instantaneous viscosity versus the applied stress for both increasing and decreasing ramp sequences.    Figure 3-15  Results of increasing (a) and decreasing (b) stress ramps illustrating static and dynamic yield points respectively  58  The result shown on Figure 3-15a which demonstrate the change of viscosity by shear stress in the increasing stress ramp has been observed for the case of fumed silica suspensions75 and authors considered the yield stress at the point that viscosity performs a significant drop. Considering the arrow shown in Figure 3-15 a, the estimated static yield stress was around 271.5 (Pa). At very low values of stress, one can observe a considerable noise in the collected data of the rheometer and it seems that the obtained viscosity is oscillating around a plateau value. This interesting behavior can be justified by results of Figure 3-4 a, the observed viscosity bifurcation. The amount of yield stress obtained by creep method was very close to the static yield stress indicating that the observed unreliable data at low shear stress region of Figure 3-15 a, were due to an elastic response of the lubricating grease. Based on creep data at Figure 3-4a, at very low values of stress (Below 280 (Pa)), the difference between instantaneous viscosities is minimal indicating that regardless of the applied stress, the value of instantaneous viscosity remains almost the same. On the other hand, these instantaneous viscosities increase by time. These similar viscosities and the time dependency of their values suggest that a constant viscosity can be obtained at very low values of applied stress and this plateau value can reach to higher viscosity levels as time increases. This explanation can fairly justify the observed oscillation in Figure 3-15 a.  Figure 3-15 b, illustrates the results of decreasing stress ramp sequence. The value of stress decreases till it reaches to a stress that flow stops and viscosity reaches infinite. This suggests that a yield point known as dynamic yield stress exists and its estimated value is 246.5 (Pa). In recent works 89,90, it has been shown that for non-thixotropic simple yield stress materials, the static and dynamic yields are the same, and the difference between these two stress levels is observable only for thixotropic yield ones. The concept of thixotropy indicates that the static yield stress is higher than that of dynamic one 89,91 which is observable in Figures 3-15 a&b. It should be noted that the 59  above discussed ramp rate can affect the measured yield stress values 70,92.Working on low concentrated carbopol and highly concentrated TiO2 suspensions 93 authors have observed that below a limiting ramp rate,  a less dependency of static yield stress exists. The difference between static yield stress measured by increasing ramp sequence and that of obtained from creep can be due to the difference between the timescales of these two techniques.  3.3.2 Visualization micrographs In previous discussions of this thesis, rheology of fumed silica greases has been studied. Here, the main focus is on visualization of fumed silica greases manufactured by L.B. Foster Rail Technologies Corp. and at the end, a comparison between shear viscosities data at low shear rates and the corresponding microstructures for two grease batches will be done.  SEM micrographs Figure 3-16 depicts the microstructure of fumed silica as the thickener agent after oil removal. Fumed silica structure is composed of roughly spherical nanoparticles that form swarms: aggregates of the mentioned spherical nanoparticles and agglomerates of these aggregates. This interesting material does not exist in the form of individual nanoparticles, and the characteristic length roughly increases by 10 times from each structure level to another (Nanoparticles to aggregates and aggregates to agglomerates)94.      60           In comparison to the well-known fibrous structure of lithium 5,6, spherical shape of calcium soap 6,7 and polyuria platelets 8, chain-like form of fumed silica nanoparticles introduces a new thickener microstructure. The compactness of the structure observed in Figure 3-16, made it difficult to estimate the real size of aggregates and agglomerates. This can be due to the dissolution of grease in Hexane, oil extraction, and subsequent air drying prior to imaging. Since smallest fumed silica particles play an important role in partial dissolution and larger particles dominate heat transfer 95 rearrangement of the agglomerates of aggregates after the above mentioned procedure is inevitable. Moreover, due to the same reason, no conclusion about differences between the samples could be made. However, as stated before, SEM micrographs, revealed the chain-like nature of fumed silica as a new thickening agent and it helped to get a rough idea about the size of nanoparticles. The size of nano-spheres seen in Figure3-16 was estimated in the range of 7-10 nm.    Figure 3-16 SEM micrograph of a fumed silica grease sample at 35K magnification. 61  Cryo-SEM micrographs Figure 3-17 illustrates grease microstructure using freeze fracture technique. The main difference between the structure observed using conventional SEM and one taken by Cryo-SEM is the compactness of the structure in Figure 3-16. The benefit of using cryogenic method is to avoid any crystallization process or structural disturbance 37. This is due to the rapid bulk freezing thanks to the very low applied temperature (~ -140°C) and the small size of the material.   Figure 3-17 Cryo-SEM micrograph of a fumed silica grease sample after coating by Pt at 50K magnification  A particulate structure consisting of agglomerates of aggregates with an averaged diameter of 0.1 µm can be seen in this micrograph which is different from the revealed commercial soap thickened lubricating greases possessing fibrous structures 37,39.Thus, the round-shaped small structures seen in Figures 3-17 are aggregates of about 10 fumed silica nanoparticles which their size was revealed in Figure 3-16 using conventional SEM. It should be noted that the elongated lines seen in Figure 3-17 are just some simple cracks in the dispersing oil due to the brittle nature of Freeze-Fracture 62  technique that are then coated by a thin layer of Platinum. It should be noted that due to the high temperature of the electron beam that bombards the surface of the frozen area, imaging using this technique is very time sensitive. If the electron beam hits the fractured area for an approximately long time (Here about 30 seconds), the frozen surface melts. Therefore, cryo-SEM visualization of a certain point needs to be performed as fast as possible.  Figure 3-18 a&b reveals Cryo-SEM micrographs of two fumed silica batches which were not coated by Pt. As can be observed the agglomerates of first Batch 1 are bigger than that those in Batch2. There are many void areas in Batch 2 that do not contain thickener particles. Thus, fumed silica nanoparticles have formed bigger agglomerates and a denser structure than Batch 2.   63    Figure 3-18 Cryo-SEM micrographs of Batch1 (a) & Batch2 (b) with no coating at magnification of 35K  Figure 3-19, depicts steady shear viscosity data of these two batches. Shear viscosity of Batch 2 was higher than that of Batch1 at these low shear rate rates region suggesting that Batch 2 may have a higher value of yield stress.            Figure 3-19  A comparison between steady state shear viscosities of Batch 1 & Batch 2  Steady shear rate, (1/s)10-3 10-2 10-1 100 101Steady shear  viscoisity, Pa.s)01000020000300004000050000Batch 1Batch 2 64   Table 3-5 provides the parameters obtained from curve-fittings using Hershel-Bulkley model on steady stress-steady shear rate data of Batch 1 and Batch 2. The yield stress of Batch 2 was higher than that of Batch 1. On the other hand, flow index of Batch 1 was slightly bigger than that of Batch 2. It is worth to mention that during lubrication process, the applied shear rates on grease samples may be much higher than the range shown in Figure 3-19. Shear viscosities of these two grease batches were studied in a wider range of shear rates and results confirmed that Batch 1 had a lower shear viscosity and higher flow index in the whole shear rate range. However, as rheological measurements during the application of high shear rates were influenced a bit by a small amount of grease fracture, data shown in Table 3-5 was based on low shear rates region. Thus, one can conclude that during lubrication process, Batch 1 is more preferred, whereas Batch 2 can provide a better lubricant reservoir. Table 3-5 Curve fitting parameters using HB model for two selected greases batches   𝑚𝐻𝐵 (𝑃𝑎. 𝑠𝑛𝐻𝐵)  𝑛𝐻𝐵           ( )  𝜏𝑦𝐻𝐵 (𝑃𝑎) Batch 1 109.7 0.3623 337.3 Batch 2 120.8 0.3364 429.7  Using data provided in Table 3-5 and Cryo-SEM micrographs observed in Figure 3-18 a&b, one can conclude that Batch 2 has a higher shear viscosity value and yield stress which can be due to the existence of small fumed silica agglomerates and an ununiformed microstructure developed by them in grease structure.  Model Parameters 65  3.4 Conclusion In this chapter, an experimental rheological study on a fumed silica lubricating grease was performed with the main focus on its yielding behavior. Steady flow curve results illustrate that these specimens perform shear-thinning behavior and thus their viscosity decreases as the applied force or shear rate increases. Performing up and down stress ramps and the observed hysteresis in the corresponding flow curves revealed that these samples can be classified as thixotropic yield stress materials. Yield stress is a rheological property which is very hard to be determined and one may find several different approaches using different geometries in the literature for its measurements. In this thesis, using some of these methods by applying different rotational and oscillatory sequences on grease samples provided different values for yield points. Yield points obtained by Hershel-Bulkley curve fittings on steady viscometry data are highly dependent on the selected R2 criteria. However, the magnitudes of these yield stresses are comparable with that of obtained by creep method. Creep sequences on fresh samples revealed a clear viscosity bifurcation in the results typical of again thixotropic yield stress materials. The application of stresses below yield stress resulted in an elastic material response, whereas performing these measurements with stresses well above yield point leads to a dominant viscous behavior. The transition from the region that elastic response dominates to the region that viscous behavior governs can then be used as a good estimate for yield point. Using amplitude sweep data, one can choose different points as a definition for yield stress. However, a clear frequency dependency which was less effective at higher frequencies was observed. Among these yield points, the stress at which the cross-over of viscoelastic moduli occurs, has the closest value to that of obtained by creep tests. This is due to the fact that this stress again defines a transition from the predominant elastic behavior (G’ > G”) to the viscous one (G” > G’). However, there is an acceptable difference between the values 66  obtained using these two different sequences which can be due to the possible inaccuracy in data generation of the rheometer under LAOS measurements. Another approach for characterizing the yield stress of thixotropic materials is working with two yield points: static and dynamic yield stresses. The former describes a transition from solid to liquid behavior, while the latter considers the transition from liquid to a solid-like state. However, the main drawback of this method is its ramp rate dependency. Among all methods described in this study, the values of static yield stress determined by increasing stress ramp and yield points obtained by Hershel-Bulkley curve fitting, creep and viscoelastic cross-over had fairly consistent and equivalent values.  Visualization by means of SEM on its Cryo and non-Cryo modes revealed useful information about fumed silica microstructure as the thickener of these lubricating greases. The images show that fumed silica thickener does not exist in the form of individual nanoparticles, and its characteristic length roughly increases by 10 times from each structural level to another. A comparison between two grease batches illustrated that the existence of small fumed silica agglomerates and a heterogeneous microstructure developed by them leads to the formation of a grease with a higher yield stress value and lower shear-thinning index.   67  Chapter 4: Thermo-rheological analysis of fumed silica greases  In this chapter, the effect of temperature on viscoelastic functions of fumed silica greases will be discussed and analyzed.  4.1 Introduction Lubricating grease is a colloidal suspension consisting of a mineral or synthesized oil (80-95 wt%) 20,96 as suspending medium and various solid suspended ingredients including thickener, antioxidant, corrosion inhibitor, anti-wear and extreme pressure agent 97. Inclusion of all these components in a single system forms a three-dimensional network possessing various types of physical and chemical interactions 3,60. Hence, the material exhibits complex rheological properties such as thixotropy 3,20,60,98 and yield stress 41,43,44. Among all the mentioned ingredients, thickener is one of the most important parts to the extent that for many cases the greases are classified based on their thickener type 27. In the grease formulation, it is incorporated 10-20 wt% of the thickener 99 which can be either a simple/complex soap (e.g. lithium substrate) or organic (e.g. polyurea) and inorganic (e.g. clay) nonsoap substrates 100. Fumed silica which consists of inorganic nanoparticles has a very high thermal stability as well as huge surface area to absorb oil. These characteristics make it an ideal choice as a thickener for high-temperature greases 4.  Depending on its application, operating conditions, and types of equipment, the lubricant may be exposed to a wide temperature range. Therefore, it is vital to enhance the grease thermal service 68  lifespan by tailoring its structure through tuning the ingredients and/or manufacturing process. In order to evaluate grease’s physical and mechanical properties there are number of parameters which can be determined through standard methods including worked penetration, tackiness, dropping point, etc. But the results from these testing methods are not very reproducible and can be different by changing the apparatus and personnel. Moreover, most of them need quite large amount of lubricant and cannot be used for quality control of used materials. All these properties are related, directly or indirectly, to the structure of the grease. Since rheological properties are very sensitive to the material structure, it can be utilized as a reliable alternative to characterize grease’s properties. The benefits of using rheology are its high precision as well as possibility to use of very little amount of material.  There are numerous studies on the rheology of lubricating grease 3,20,42,61,101 where some of them are on its thermo-rheological behavior 7,44,57–61.Among these works, oscillatory sequences are more popular than rotational ones. This can be due to the fact that these measurement are less susceptible to phenomena such as fracture and slip which can occur in rotational ones and lead to unreliable data collection. Among these experiments, frequency sweep sequences are even less affected by the mentioned instabilities. Thermo-rheological analysis using frequency sweep has been done for the case of Lithium and Calcium lubricating greases 7,41,54,102. The main objective of chapter 4 is to address different linear viscoelastic rheological aspects of a fumed silica lubricating grease in a wide range of temperatures (-40 to 80°C). This temperature range covers the typical working temperatures of this lubricating grease.    69  4.2 Material and methods 4.2.1 Material The grease studied here was provided by L.B. Foster Rail Technologies Corp. consisting of group III base oil and fumed silica as thickener agent. This lubricating grease was manufactured in large commercial scale for wayside rail lubrication system. The basic properties of this sample are provided in Table 4-1. Table 4-1 Characteristics of the fumed silica grease Grease Thickener Oil Oil Viscosity @40°C [cSt] Oil Viscosity @100°C [cSt] Unworked Penetration [mm/10] Fumed Silica Group III base oil 46 8 285  4.2.2 Rheological characterization The rheological measurements were done using an MCR501 state-of-art rheometer made by Anton Paar. This rheometer runs under both strain and stress control conditions. Four types of experiments were performed all by using sandblasted parallel disks having a diameter of 25mm and gap of 0.5mm namely amplitude sweep, frequency sweep and temperature ramp experiments. As it is well studied, slip and edge fracture, are the two main instabilities that usually exist in grease rheometry. The slip is more accentuated in small gaps, while it is vice versa for fracture 20. Thus, the selection of a gap of 0.5mm is to mitigate both phenomena as much as possible. The amplitude sweep tests were done at a fixed frequency of 1 Hz with amplitude changing from 0.1% up to 100%. Frequency sweep experiments were also performed at constant amplitude of 70  0.1% and frequencies ranging from 0.01 to 100 Hz. The amplitude value of 0.1% is selected according to amplitude sweep results to ensure that the data are within linear viscoelastic envelope. To further study the effect of temperature a linear heating ramp of 1°C/min at a fixed frequency of 1 Hz and strain (0.1% for grease and 1% for base oil) was performed on both the fumed silica grease and its base oil.  It should be noted that for the sake of reproducibility, prior to each of described experiments above, a pre-shear of 0.5 (1/s) for 30s followed by a 30 min rest were applied on fresh samples. The rest was performed by removing the load from the sample rather than fixing the strain at zero. This would allow the sample to recover any stored stress during strain recovery. This is essential for a yielding material, since stress cannot be fully recovered in the stain-control relaxation 103. All of these experiments were carried out for a wide range of temperature from -40°C up to 80°C. The temperature in the first two types of experiments mentioned above, was controlled using an oven manufactured by Anton Paar. In this case, the temperature in the cell can be controlled by convective heat transfer mechanism resulting in a bit more reliable data than the case conductive heat transfer, performed by peltier systems, controls the temperature. This is due to the fact that using ovens leads to having a more control on temperature of both upper and lower parts of measuring system. For reaching to temperatures below 30°C, a tank of liquid Nitrogen was attached to a converter connected to the oven cell. After opening the hand valve of liquid nitrogen tank, as soon as the temperature reached to its low desired value by converter and rheometer controller, the gap of measuring system was zeroed. Then, the distance between the plates was increased, the oven was opened and after waiting for a while, the plates reached to room temperature and the condensed water on the plates was cleaned. Next, the grease sample was 71  mounted on the lower plate. The gap reached to its trimming distance, but sample was not trimmed due to the possible shrinkage that can happen at low temperatures (and possible expansion at high temperatures). After closing the oven cell, the temperature again reached to its low desired value by converter and rheometer controller. As soon as the temperature reached to equilibrium, the oven was opened and sample was then trimmed fast. Next, the oven was closed, the gap reached to its working value (0.5mm) and measurements were then started. For temperatures above 30°C, the rheometer controller was able to provide enough heat for these high temperatures in a short time period. The principles were the same, without of course any need for liquid nitrogen tank and the converter for cooling purpose. The time required for the described setup procedure was way lower for these high temperatures. This time was in the order of 1.5 hour for a temperature as low as -40°C and about 10 minutes for a temperature as high as 80°C. As the temperature of the heating ramp sequence could not be controlled by the oven, these measurements were performed using the peltier system. 4.3 Results and discussion Amplitude sweep Oscillatory experiments are useful tools for characterizing complex materials, since they provide information about the viscous and elastic properties at the same time. Although linear viscoelastic properties can be useful to assess the material structure, for practical purposes it is vital to extend measurements into the non-linear viscoelastic region as well. Strain amplitude sweeps in oscillatory motions have gained a huge interest in the past decade, since they provide not only the information in linear viscoelastic range, but also on non-linear viscoelastic properties of the material. It has also been used for the case of the lubricating grease 41,104 to correlate the physical 72  properties of these samples to their nonlinear viscoelastic characteristics. For example, Suetsugu et al 105 has found that worked penetration of some lubricating greases with different types of thickeners scales with the linear G’ and the non-linear G” in amplitude sweep experiment.  However, there are some difficulties regarding collecting reliable data due to several reasons. First of all, since the stress response beyond the LVE is no longer sinusoidal, application of classical definition for elastic and loss moduli should be given careful attention 22. The edge fracture in geometries like cone and plate and parallel disks can limit the highest applicable strain.         Figures 4-1 depicts the dynamic moduli, as functions of applied strain amplitudes at 5 different selected temperatures. The working frequency as previously mentioned is 1 Hz. There are some stars shown on this Figure indicating results of frequency sweep at strain of 0.1% and selected Figure 4-1 Amplitude sweep data at frequency of 1 Hz, at different temperatures. The star indicated the data point at this value of strain and frequency in frequency sweep measurements  73  frequency of 1 Hz. A good correlation between these two sets of measurement can be observed and as the chosen amplitude for frequency sweep is within the plateau region of amplitude weep data, the LVER assumption for these measurements has been satisfied. SAOS results will be discussed later in this manuscript. The general trend for viscoelastic moduli in Figure 4-1 at all the temperatures is more or less similar. A plateau viscoelastic region followed by a decrease in storage modulus and a maximum in G” and at the end a dominant viscous behavior after the cross-over strain, which all of these viscoelastic features have been described in details in Chapter 3. However, some features are changing with temperature such as the crossover strain, the LVE strain limit and of course the magnitudes of moduli. To further study temperature effect, frequency sweep measurements were performed.  Frequency sweep Figure 4-2 a&b illustrate the storage and loss moduli, respectively, as functions of frequency for the studied fumed silica grease at different temperatures. Since these rheological properties are very sensitive to material structure, selection of a wide range of temperature from -40°C up to 80°C enables one to track down any possible thermal effects on the grease microstructural network. As can be observed in these figures, there is a sharp drop in both SAOS functions, G’ & G” at very low temperatures up to 0°C, while above that, they are less sensitive to temperature. This suggests that the studied fumed silica grease, retains a less temperature dependent structure at these temperatures, making this grease a perfect choice for high temperatures applications. At all temperatures studied, the value of storage modulus was way higher than that of loss modulus. This suggests that grease behaves like a solid-like material in this wide range of frequency and temperatures studied. 74                 Figure 4-2 The (a) storage (G’) & (b) loss (G”) moduli of lubricating grease as function of frequency at different temperatures      75  Another feature of Figure 4-2 a&b is that regardless of the applied temperature; both G’ & G” are weak functions of frequency, where G’ has a slope of 0.02-0.18 depending on temperature and G” possesses a minimum. The same qualitative trend with different slopes has been reported previously for the case of Lithium and Calcium lubricating greases 7,41,54,102. This is also a typical feature of some colloidal suspensions 106 and different types of physical and chemical gels 107.  When one studies the effect of temperature on rheological properties of different materials, Arrhenius equation and time-temperature superposition principle (tTS) 13 are two methods which can describe the temperature dependency of flow properties 14. The former predicts that different properties obtained at the same time scale, change exponentially by inverse absolute temperature and the latter presents a superposition between time scales and temperatures by defining a temperature dependent parameter known as shift factor (aT). Here, both principles will be studied to investigate whether they have the ability to describe effect of temperature on grease viscoelastic properties. The samples such as polymer melts 14 that their flow properties can be explained using tTS ,  are known as thermo-rheologically simple materials. In order to check the applicability of tTS principle for this  specimen, one can plot the Cole-Cole plot 108,109 as shown in Figure 4-3 where G’ is plotted versus G” for all the temperatures studied. Since the plot is not a continuous temperature-independent curve, it can be concluded that the sample is thermo-rheologically complex and thus tTS principle is not applicable for this sample. Delgado and coworkers 54 also stated that this principle cannot describe temperature dependency of Lithium lubricating grease flow properties.  76    Figure 4-3 The Cole-Cole plot of lubricating grease in terms of G’ versus G” at various temperatures Figure 4-2 illustrated SAOS properties as functions of frequency at different temperatures. To further study the effect of temperature, Figures 4-4 a&b plot the dynamic moduli, G’ & G” respectively, at various frequencies as functions of inversed absolute temperature. SAOS functions are shown in logarithmic scale and the inverse temperature on linear scale (As 1/T has a very small value, it is magnified 1000 times for the sake of a better visibility). Thus, it is also possible to check if the results follow Arrhenius equation:                                                            𝐺 = 𝐺° exp(𝐸𝑎𝑐𝑡 𝑅𝑇)⁄                                                       (4.1) where G, T, R, Eact & G0 are modulus (G’ or G”), absolute temperature (Kelvin), a universal constant, thermal activation energy and the modulus at reference temperature, respectively. If viscoelastic moduli in Figure 4-4 a&b, at a fixed frequency and amplitude of strain, increase linearly by the inverse temperature, the applicability of Arrhenius equation will be concluded. 77    Figure 4-4 The (a) storage & (b) loss moduli of lubricating grease as function of inversed absolute temperature at various frequencies. There is an abnormal behavior around 0°C which is more evident in G’ As it was shown on Figure 4-2 a, the storage modulus is a weak increasing function of frequency and thus G’ reaches to higher levels as the fixed frequency increases in Figure 4-4 a. Figure 4-2 b, illustrated that a minimum occurs in the plot of loss modulus versus frequency. Thus, the level of 78  G” function in Figure 4-4b, does not necessarily increase as fixed frequency increases. As it is depicted in Figure 4-4 a&b, there is a significant drop in dynamic moduli by increasing temperature for very low temperatures, but it remains almost constant/very small drop at higher temperatures. This states that the Arrhenius trend is not applicable for this lubricating grease, at least for this wide range of temperature. Delgado et al 54 reported that for a lithium lubricating grease, G’ was almost constant for a temperature range of 20 to 100°C, while G” showed a weak decreasing trend. Moreover, there is an interesting non-monotonic behavior for temperatures around 0°C, which is more pronounced in storage modulus.  In order to study this peculiar temperature dependency of SAOS functions, using complex modulus (G*) enables one to track down a net temperature effect on both elastic and loss moduli simultaneously. The non-monotonic behavior observed in Figure 4-4, may be due to a physical change which needs to be studied experimentally. In order to check the validity of the assumption stated above, Figure 4-5 illustrates how the complex modulus of the grease and its base oil change with temperature in a linear heating ramp of 1°C/min at a fixed frequency of 1 Hz and strain (0.1% for grease and 1% for base oil). As viscoelastic functions were shown previously in Figure 4-4 a&b, using frequency sweeps at LVER, it is worth to have a comparison between data obtained by temperature ramp with that of obtained by SAOS measurements at frequency of 1 Hz. Thus, the solid symbols observed in Figure 4-5, represent the previous LVER results, showing an acceptable similarity. 79   Figure 4-5 Complex modulus (G*) as a function of the inverse temperature in the transient temperature ramp experiment for lubricating grease (continuous line) and its base oil (dash-line). The heating ramp is 1°C/min. It is interesting to see that in that specific temperature range, there is a significant change in the oil mechanical properties. This is close to the pour point of the oil (-12°C) reported by manufacturer. This confirms that there is a phase transition in the base oil in that regime from a semi-solid behavior to a liquid phase. However, the complex modulus of fumed silica grease performs a minimum like that of occurred for storage modulus in Figure 4-4a. The occurrence of the minimum in this regime can be explained as follows. Although, phase change of the dispersing medium (oil) from semi-solid to liquid like behavior would decrease its contribution to the dynamic moduli, the dispersing fumed silica aggregates can move easier in the low viscosity medium. Therefore, these aggregates would get access to more aggregates in their neighborhood within a wider range which leads to much stronger interactions that are mostly elastic. On the other hand, the dispersing medium (base oil) contributes more to the loss modulus.    80  This explanation would also justify the above observed minimum for the elastic modulus in Figure 4-4a and its non-existence for loss modulus in Figure 4-4 b. As the elastic modulus of the grease is higher than the viscous one in LVER, complex modulus value is more governed by elastic component resulting in the observed similarities between Figure 4-4 a and 4-5. From classical rheology, the corresponding value of G’ at the minimum of G” is defined as plateau modulus ( 𝐺𝑁° ) which is an important property representing the number of interactions (entanglement density in the case of polymers) in the system 53. Table 4-2 collects the plateau moduli and their corresponding frequencies (𝜔𝐺′𝑚𝑖𝑛) at different temperatures.  Table 4-2 Plateau modulus and its corresponding frequency from results in Figure 4-2 a&b Temperature (°C) 𝝎𝑮′𝒎𝒊𝒏 (rad/s) 𝑮𝑵°  (Pa) -40 N/A 126478 -30 2.50 50242 -20 3.96 22649 -10 1.00 12854 0 10.0 12065 10 10.0 15486 30 15.8 13903 50 10.0 11755 80 0.63 10220 81  Figure 4-6, depicts the results of plateau modulus of the studied fumed silica grease as a function of the inversed of absolute temperature. Interestingly, the above described minimum again occurred for even this viscoelastic modulus.   Figure 4-6 The non-monotonic behavior of plateau modulus as a function of inversed temperature  4.4 Conclusion We have investigated the thermo-rheological characteristics of a fumed silica lubricating grease through oscillatory rheometry. The material represented rheological characteristics of a thermo-rheologically complex fluid, not following the time-temperature superposition principle. The results confirmed that there is an abnormal temperature dependency in the range of -10 to 10°C which shows itself by a ditch-like shape in the Arrhenius plot of various types of viscoelastic moduli except loss modulus. 82  It was demonstrated that the phase transition of the base oil and elastic interaction of the thickener particles are responsible for such peculiar temperature dependent behavior in grease structure. 83  Chapter 5: Conclusion  In this chapter, an overall description about the experiments performed, the contribution of the study and some suggestions for possible future research directions will be reviewed.  5.1 Summary In this study, rheometry of fumed silica grease samples provided useful information about their yielding behavior. Visualization by means of SEM on its Cryo and non-Cryo modes contributed to analysis of the data obtained by rheometry. Thermo-rheological analysis of these greases revealed interesting information about the temperature dependency of their viscoelastic properties.  5.2 Contributions In this study, using rheometry and electron microscopy which are well known equipment to analyze a wide range of materials, fumed silica based lubricating greases developed by L.B. Foster Rail Technologies Corp. were studied. In comparison to commercialized greases, L.B. Foster stated that these samples have exceptional physical properties. The present work contributed to the current literature through yield stress measurements of fumed silica based lubricating greases, their microstructural analysis and temperature effect on their rheology, as a material which has not been previously studied using rheometry and electron microscopy.  Using several yield stress measurement approaches, it was shown that the values obtained by HB-curve fitting, creep, amplitude sweep crossover and stress ramp up had similar values. This was due to the fact that all these methods define yielding point of the material 84  as a transition from predominant elastic response to the viscous one. The slight differences between yield stresses measured by these techniques have been addressed and discussed.   Visualization by means of SEM on its Cryo and non-Cryo modes revealed useful information about fumed silica microstructure as the thickener of these lubricating greases. The images show that fumed silica thickener does not exist in the form of individual nanoparticles, and its characteristic length roughly increases by 10 times from one structural level to another. A comparison between two grease batches illustrated that the existence of small fumed silica agglomerates and a heterogeneous microstructure developed by them leads to formation of a grease with a higher yield stress value and lower shear-thinning index.   A thermo-rheological analysis on fumed silica lubricating greases was performed through oscillatory experiments. The material represented rheological characteristics of a thermo-rheologically complex fluid which did not follow the time-temperature superposition principle. The results confirmed that there is an abnormal temperature dependency in the range of -10°C to 10°C which shows itself by a ditch-like shape in the Arrhenius plot of various types of viscoelastic moduli except the loss modulus. It was demonstrated that the phase transition of the base oil and an increase in the elastic interactions between fumed silica aggregates is responsible for such peculiar temperature dependent behavior.  5.3 Future directions There are some works in literature regarding a correlation between grease rheology and its physical properties. Using rheometry and a sequence called ‘Pull off test’ 65one can describe tackiness. Another important property for qualification of lubricating greases performance is consistency or 85  cone penetration. There have been some attempts to find a correlation between grease yield stress and its consistency66,67. The effect of temperature on this correlation has also been studied2. Suetsugu et al 105 has found that worked penetration of Lithium lubricating greases scales with linear plateau of G’ and nonlinear G” at strain of 50% in amplitude sweep experiment. Therefore, in a future work, some attempts will be done to correlate the rheological properties of fumed silica grease measured in this thesis to its physical properties provided by the company.  The main rheological property studied in the Chapter 3 was yield stress. This property was measured using different approaches. Results through these different methods were compared with each other and some conclusions were made. In a future work, rotational tests such as creep, steady flow curves and stress ramps will be performed at different temperatures to study the validity of the observed difference between yield points at room temperature. For the case of Lithium and Calcium lubricating greases, Cyriac and coworkers43 studied the effect of temperature on yield stresses measured at the point, stress-strain relation deviates from linearity. As stated before, a relationship between the yield stress and the temperature can also be correlated to the grease consistency2. Using data provided in Chapter 4, this future plan can also contribute to a study about the effect of temperature on the deviation from the Cox-Merz rule.  Stress ramp sequences are rheological experiments which can provide useful information about the time dependency of material flow properties. Thus, they are strong tools for characterization of thixotropic yield stress materials. Using these sequences to perform a rheological study is very widespread. However, there are very few works done for studying the effect of the ramp rate on the measurements51,110 with no focus on lubricating greases. The timescale of these measurements can affect the obtained yield points70.Uhlherr and coworkers 93 observed that lower applied rates 86  lead to lower corresponding yield stresses. These authors mentioned that there was a limiting ramp rate below which, a less rate dependency of the yield stress was perceived. The yield stress measured through these low ramp rates was considered as yield point. In this manuscript, stress ramps were performed under the rate of 1 (Pa/s) and the observed difference between the obtained yield point and the ones measured by rotational tests was referred to the chosen ramp rate. Therefore, it is worth to study the effect of a change in the rate on yield points in a future work.  87  Bibliography 1. Canada, T. https://www.tc.gc.ca/eng/policy/anre-menu-3020.htm. doi:https://www.tc.gc.ca/eng/policy/anre-menu-3020.htm 2. Lugt, P. M. Lubricating Grease Rheology. Grease Lubr. Roll. Bear. 99–136 (2012). doi:10.1002/9781118483961.ch5 3. Paszkowski, M. & Olsztyńska-Janus, S. Grease thixotropy: evaluation of grease microstructure change due to shear and relaxation. Ind. Lubr. Tribol. 66, 223–237 (2014). 4. Abul Bari, H. A., Abid, R. T. & Mohammad, A. H. A. Fume silica base grease. J. Appl. Sci. 8, 687–691 (2008). 5. Baart, P., van der Vorst, B., Lugt, P. 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