Basic terms and definitions rheology, axioms rheology
Plan of the lecture:
1. Axioms of rheology
2. The kinds of deformation.
Purpose of the lecture: get acquainted with the axioms of rheology.
1. Axioms of rheology. Rheology, like any other science, relies on a set of axioms, assumptions, assumptions and other restrictions that are caused by the need to absolyutirovaniya from secondary issues.
The first axiom. Under the action of a comprehensive (isotropic) pressure all materials behave in the same manner as perfectly elastic body.
This means that comprehensively uniform pressure will have the same effect on a ball, made of steel, or a ball of meat (test). The density of both balls will increase without distortion. Changing diameters happens due to the elastic deformation, i.e. by removing the pressure diameter and density of these bodies will take initial values. Differences in rheological properties are manifested only in strain, change the shape of the body - strain variation.
The second axiom. Each product has all the rheological properties, albeit in different degrees. To the main rheological properties include elasticity, plasticity, strength and durability.
This means that one and the same material, depending on its condition and loading conditions can result in a greater or lesser extent various rheological properties. For example, such visco-plastic material, like pasta dough, with instantaneous load mostly behaves like an elastic body and plastic deformation and viscous flow are almost absent. Other conditions of loading of more importance plastic and viscous properties. Therefore, first of all, it is necessary to determine the properties of the test material under specified conditions are the main determinant.
Consider the basic physical-mechanical and mathematical concepts used in rheology.
2. The kinds of deformation. Under the application of a material of external load subjected to, which is expressed in the change of its size and shape. These changes of a material called deformation. Depending on the application, load deformation fundamentally divided into two types: first - deformation of three-dimensional (linear) tension-compression and second - shear strain. When the first volume changes only (the linear size) of the material and its shape does not undergo significant changes. When shear change the shape of the material, and its volume remains the same. Between these kinds of deformation there is a close relationship, defined by the ratio of a Punch. The ability to deform under the influence of external forces is the main property of materials of all real phone.
Warp is a form and (or) the linear dimensions of a body under the action of external forces, with the change of humidity, temperature and other, in which particles or molecules are shifted up one relative to another without discontinuities of the body. The amount and nature of deformation depends on the method of application of external forces, the material properties of the body and its forms.
As you know of course, «Resistance of materials», deformation divided into two types: a) reversible (elastic), which disappears after the termination of force; b) plastic (viscous), which does not disappear after removal of load. When elastic deformation part of the mechanical energy is converted into heat. In addition, there is another division of deformations. For example, by type of loading they can be shear (Fig. 1 (a), uniaxial (linear) (Fig. 1. b), as well as two-axle flat and volumetric. The strains are calculated by the equations:
; . (1.1)
Fig. 1. Scheme of loading of materials:
a) shift; b) stretching
If the deformation change in time t, and a transient process, take into account the speed of deformation (gradient); at the steady state process of deformation of a change of deformation in a unit of time. All this is described by the concept of «speed deformation,» [c-1], while stretching - compression and [c-1], after the shift:
; . (1.2)
If the deformation when moving under the action of finite forces increases continuously, the material begins to flow. Steady-state flow regime is characterized by the velocity gradient, which is similar in meaning deformation velocity (Fig. 1.2):
where: t is the shear stress, PA;
u - linear speed elementary layer, m/s;
y - coordinate of the layer along the normal to the velocity vector, m.
In rheology, there are two types of flow: 1. viscous flow is realized in a truly viscous Newtonian fluids under any arbitrarily small shear stresses t. This current is described by the equation of Newton:
èëè , (1.4)
where n is the coefficient of dynamic or absolute viscosity, reflecting the amount of effort that occur between two elementary liquid layers with their relative displacement, PA * s;
F - resistance force between two elementary layers, N;
A - the area of the surface resistance of these layers, m2;
2. Plastic flow - a period when the voltage value of t, equal to the yield strength τÒ.
Voltage is a measure of the internal forces of F [N]that occur in the body under the influence of external forces per unit area [m2], normal to the vector of force application:
, Pa. (1.5)
The voltage at the point Laden body:
Formally, shear or tangential stress (t), normal voltage (s), pressure, or hydrostatic pressure (p), and adhesion, or the pressure of adhesion (P0), describes the dependence of (1.5) where power and area will have a physical meaning.
The study of different kinds of deformations depending on the accompanying stress and is the subject of rheology.
To the main rheological properties of materials include : viscosity, elasticity, plasticity, strength and hardness. At one and the same material, depending on its condition and loading conditions, they appear different rheological properties. Therefore first of all it is necessary to determine the properties of the test material under given conditions of deformation are the main determinant.
Viscosity is a measure of the resistance to flow. It is a key feature for liquid bodies, as well as for plastic bodies after exceeding the limit of fluidity. For non-Newtonian fluids, the viscosity function of the shear rate, so it is called the «apparent», or as effective viscosity of the EFF [PA•s]. For non-Newtonian effective viscosity consists of two components:
1) the Newtonian viscosity ETA, which is based on internal friction and represents a physical constant of the material;
2) structural resistance, which depends on the structural condition of the disperse systems and is a function of the shear rate
Resilience - the ability of the body after deformation fully recover their initial form or amount, i.e. deformation equal to the work of restoration. Elasticity tel tensile - compressive characterized by a modulus of elasticity of the first kind (young's modulus) [PA], and shear - second kind (the shear modulus) G [PA].
Plasticity - the ability of a body under the action of external forces permanently deformed without discontinuities. In rheology in this sense with deformation there is the concept of «maximum shear stress» (PNS), which is represented θ0. This voltage, above which the material appears plastic deformation.
Durability is called the body resistance to the action of external forces that lead to the course or to their destruction. Gukovsky (elastic) tel speed of deformation does not affect the strength, so that differences in static and dynamic strength does not exist. Nehalevsky tel (which includes almost all solid food products), which have both elastic and plastic (viscous) properties, durability depends on the speed of deformation.
Hardness is a comprehensive property Nehalevsky bodies to resist the penetration of another body irreversible deformations. Hardness cannot be expressed as a physical quantity with a unique dimension. It is some technical parameter, which is expressed in relative terms, depending on the method of determination.
Other physico-mechanical properties of materials can be attributed gentleness, delicacy, adhesion and stickiness.
The shift is very important kind of deformation in rheology. Simple shear is considered as a plane strain, parallel stationary plane as a result of action on the faces of the element of tangential stresses. Simple shear is a case of a laminar flow, in which the body can be considered as consisting of infinitely thin layers. These layers are not deformed, and only slip one another (Fig. 1,a).
Gentleness is a property the opposite of hardness.
Brittle, and the property of solid bodies to achieve the destruction of minor plastic deformation. Pure gukovskii body find brittle fracture at any deformation speed. Nehalevsky tel brittle fracture occurs only at high strain rates or low temperatures, when you lose the effect of viscous properties.
Adhesion - property, which is based on the interaction of two different bodies at the phase boundary and causes grip phone At division tel need to overcome friction. Stickiness is a property of a boundary layer of viscous or plastic materials to resist the division in contact surfaces. Each material has all the complex rheological properties, albeit in different degrees. At one and the same material, depending on its condition and loading conditions, may, to a greater or lesser extent various rheological properties.
1. What are the axioms of rheology.
2. List the types of deformations.
3. I know rheological properties of food products?