Theoretical Research on Rheology
 
Rheology is a discipline that describes the flow and deformation of matter under the action of external forces from a macro level. It was founded in 1928 by Professor Bingham of Laffayette College and his colleague Reiner. Barns and others introduced the knowledge of rheology, and pointed out that rheology is a new interdisciplinary between chemistry, mechanics, physics and engineering sciences, and solids that can flow under certain conditions, such as non-Newtonian fluids, are the main ones. The nature of the object of research cannot be explained by classical viscoelastic theory. These substances cannot be expressed by a single viscosity at a certain temperature, but are affected by other factors.
 
The main research content of rheology
 
Including: rheological model, rheological measurement and the flow behavior of complex fluids, etc. After years of development, rheology has now been widely used in the fields of chemical engineering, geophysics, geotechnical engineering, pharmacy and food, forming chemical rheology and polymer rheology.
 
Main research objects of rheology
 
Including: non-Newtonian fluids and viscoelastic materials.
 
(1) Non-Newtonian fluid: refers to a fluid that does not satisfy Newton's law of viscosity. The viscosity of non-Newtonian fluids is usually not constant but changes. Non-Newtonian fluids have many special properties, such as jet swelling, pipeless siphon, shear thinning, wire drawing, turbulence drag reduction, etc. One of the more interesting ones is that some non-Newtonian fluids have elastic properties and are also called viscoelastic fluids. When the rotating rod is inserted into the viscoelastic fluid, the fluid will climb onto the rod, making the liquid surface convex.
 
In our life, production and nature, non-Newtonian fluids, such as toothpaste, coal water slurry, mud, oil, paint, etc., are widely present. For non-Newtonian fluids, the relationship between the shear stress τ and the shear rate γ can be expressed as τ=f(γ). The ratio of shear stress to shear rate is called apparent viscosity, usually expressed in μ or η.
 
(2) Viscoelastic materials: refer to materials that are both viscous and elastic at the same time. Viscoelastic materials are objects that have both elastic deformation and viscous flow. "Elastic deformation" refers to a short-term deformation that can return to its original shape. "Viscous flow" refers to a continuous deformation that cannot be restored to its original state, also known as "rheology". In the past, when talking about solids, they generally meant objects that only had elastic deformation; when talking about fluids, they generally meant fluids that only flowed viscously. In fact, there are many objects that have these two properties at the same time.
 
Rheology research methods
 
Regardless of whether it is a solid or a liquid, the main research methods of rheology are as follows: one is to study the fluid as a continuous medium, and use the mathematical method of continuum mechanics to study it. This has become the most important research method in rheology. One of the important methods is called continuum rheology. Because this method does not take into account the internal microstructure of the fluid, this research method of rheology is also called macrorheology.
 
Another method is to consider the internal structure of the material by studying the relationship between the macro-rheological properties of the fluid and the micro- and sub-micro internal structure of the fluid. This method is called structural rheology or micro-rheology. The method of continuum mechanics is used to deal with fluid rheological problems, which can simplify the treatment process to a certain extent.
 
Powder rheology research
 
Some scholars try to extend the traditional rheological theory describing Newtonian fluids and non-Newtonian fluids to the research of powders. Barois-Cazenave and Marchal used an improved cross-shaped rotor rheometer and used rheological methods to study the flow behavior of powder under different conditions. This type of rheometer is mainly composed of a cylindrical container that holds the sample and a cross-shaped rotating rotor. The advantage of this geometric structure is that the wall-powder friction is replaced by the friction between the powder, which avoids the occurrence of internal slippage of the sample. The bottom of the sample container is replaced by a vibrating membrane that can provide longitudinal movement. The effect of axial vibration, first of all, enables a better redistribution of space between particles, which can prevent the formation of voids and improve the repeatability of the experiment; on the other hand, vibration creates a macroscopic Brownian motion.
 
Powder rheological model
 
The loose powder can flow under slight external force. During the pressing process, not only elastic and plastic deformation occurs immediately, but also viscous deformation that gradually changes with time, showing strain delay, pressing creep, stress relaxation, elastic aftereffect and powder Rheological properties such as internal friction. However, the classical plastic theory regards powder as an elastoplastic body, and only considers elastic deformation and plastic yield, ignoring its rheological properties.
 
In recent decades, in the research of loose materials such as powders, rocks, soils, minerals, and polymers, people have discovered that there is a universal time effect, so rheological theories have emerged. The rheological method is to treat the loose medium as a rheological body, and use rheological theory to analyze the flow and deformation behavior in powder compaction. The rheological model can qualitatively and quantitatively explain the rheological behavior of the powder, such as stress relaxation and strain delay, and the influence of the pressing process on the density, and further reveal the physical nature of powder forming, which has obvious theoretical advantages.
 
The method of establishing rheological model is flexible. There are empirical methods to give the relationship between stress, strain and time through experimental data, molecular theory processing method using statistical mechanics model, and strict deductive processing method. Among them, it is a more commonly used method to establish a non-linear rheological model of powder through the series-parallel combination of basic components such as nonlinear elastic body, linear elastic body, nonlinear viscous body, linear viscous body, and Bingham body.
 
Chen Zhenhua et al. put the nonlinear elastic body and the nonlinear viscous component in parallel, considering the characteristics of powder relaxation and large strain, and proposed a nonlinear viscoelastic model. Guo Biao established the high temperature rheological constitutive model of powder forging and sintering Fe-0.5C-2Cu alloy for the first time and embedded it in DEFORM software to realize the optimization of powder forging simulation.
 
The rheological theory takes the time-related viscous behavior into account to construct the constitutive model of the powder, and at the same time reflects the solid and fluid properties of the powder. Based on the elasto-viscoplastic body hypothesis, the viscoelastic-plastic constitutive model constructed by fusing the elasticity, plasticity and viscosity of the material can more comprehensively and truly reflect the mechanical properties of the powder. However, the viscosity of the powder is not obvious during cold pressing, and the use of rheological theory will complicate the modeling. Therefore, the theory is more suitable for powder warm pressing, hot isostatic pressing, high-speed pressing and other situations involving high temperature and dynamic pressure.
 
Although the types and design ideas of the current rheological models are flexible, the mathematical form of the mechanical equations considering nonlinear rheological factors is complicated, the numerical solution is difficult, and the quantitative prediction ability after the solution is limited. Therefore, rheological models and numerical algorithms suitable for the powder compaction process still need to be developed and improved.