Internal friction. Viscosity or internal friction. Viscous friction force

Internal friction in solids can be caused by several different mechanisms, and although they all ultimately result in the conversion of mechanical energy to heat, these

the mechanisms involve two different dissipative processes. These two processes are, roughly speaking, analogues of viscous losses and losses by thermal conduction during the propagation of sound waves in liquids.

The first type of process depends directly on the inelastic behavior of the body. If the stress-strain curve for a single vibration cycle has the form of a hysteresis loop, then the area contained within this loop represents the mechanical energy that is lost in the form of heat. When a sample undergoes a closed stress cycle "statically", a certain amount of energy is dissipated and these losses represent part of the specific dissipation due to vibration of the sample. As Jemant and Jackson showed, even in the case when the hysteresis loop is so narrow that it cannot be measured statically, it has a significant effect on the damping of oscillations, since in an oscillation experiment the sample can perform a large number of closed hysteresis cycles. The energy loss per cycle is constant, so the specific dissipation and, therefore, the logarithmic decrement does not depend on frequency. Jemant and Jackson found that for many materials the logarithmic decrement is indeed constant over a fairly wide frequency range, and concluded that the main cause of internal friction in these cases may simply be due to the "static" nonlinearity of the stress-strain relationship of the material. Similar results were obtained by Wegel and Walter at high frequencies.

In addition to static hysteresis, many materials exhibit losses associated with changes in velocity that occur during vibration, and the forces generating these losses can be considered to be of a viscous nature. As we have seen, the presence of such forces means that the mechanical behavior depends on the strain rate; this effect is observed, in particular, in organic polymers with long molecular chains. The subject of rheology is mainly this kind of time dependence.

It is possible to distinguish two types of viscous losses in solids, which qualitatively corresponds to the behavior of the Maxwell and Vocht models described in the previous paragraphs. Thus, when the load is held constant, it can lead to irreversible deformation, as in the Maxwell model, or the deformation can asymptotically tend to some constant value over time and slowly disappear when the load is removed, as occurs in the Vocht model. The latter type of viscosity is sometimes called internal viscosity, and the mechanical behavior of such bodies is referred to as retarded elasticity.

The interpretation of the effects of viscosity in solids at the molecular scale is not entirely clear, mainly because the types of microscopic processes that lead to mechanical dissipation

energy in the form of heat are still largely in the realm of guesswork. Tobolsky, Powell and Ehring and Alfrey studied viscoelastic behavior using rate process theory. This approach makes the assumption that each molecule (or each link in a molecular chain in the case of polymers with long molecular chains) undergoes thermal vibrations in an “energy well” formed by its neighbors. As a result of thermal fluctuations, from time to time there appears sufficient energy for a molecule to escape from the well, and in the presence of external forces, diffusion takes place, equal in all directions. The rate of diffusion depends on the probability of the molecule receiving sufficient energy to escape the well, and therefore on the absolute temperature of the body. If hydrostatic pressure is applied to a body, the height of the energy well changes, the rate of diffusion becomes different, but remains the same in all directions. Under uniaxial tension, the height of the well in the direction of the tensile stress becomes lower than in the direction perpendicular to it. Therefore, molecules are more likely to propagate parallel to the tensile stress than in the direction perpendicular to it. This flow leads to the transformation of the elastic energy accumulated by the body into random thermal motion, which on a macroscopic scale is perceived as internal friction. Where the molecules move as a whole, the flow will be irreversible and the behavior will be similar to the Maxwell model, whereas where the molecular links are entangled, the material behaves like the Vocht model and exhibits delayed elasticity.

If certain assumptions are made regarding the shape of the well of potential energy and the nature of the molecular groups that vibrate in it, it can be shown (Tobolsky, Powell, Ehring, p. 125) that the theory leads to mechanical behavior of the body similar to that described by spring-models. shock absorber discussed earlier in this chapter. This interpretation of the issue emphasizes the dependence of viscoelastic properties on temperature; Thermodynamic relationships can be derived from this dependence. The main disadvantage in applying the theory to real bodies in a quantitative sense is that the nature of the potential well for the bodies is largely a matter of conjecture and that often several different processes can occur simultaneously. However, this is still almost the only serious approach to a molecular explanation of the observed effects, and it provides a reliable basis for future development.

Losses occur in homogeneous non-metallic bodies largely in the same manner as described above, and internal friction is related to the inelastic behavior of the material rather than to its macroscopic thermal properties. In metals, however, there are

losses of a thermal nature, which are generally more significant, and Zener considered several different thermal mechanisms leading to the dissipation of mechanical energy in the form of heat.

Changes in body volume must be accompanied by changes in temperature; Thus, when a body contracts, its temperature increases, and when it expands, its temperature decreases. For simplicity, we will consider the bending vibrations of the cantilever plate (tongue). Each time the tongue is bent, the inside heats up and the outside cools, so that there is a continuous flow of heat back and forth across the tongue as it oscillates. If the movement is very slow, then the heat transfer is isothermal and therefore reversible, and therefore no losses should occur at very low oscillation frequencies. If the oscillations occur so quickly that the heat does not have time to flow across the tongue, then the conditions become adiabatic and still no losses occur. During bending vibrations, the periods of which are comparable to the time required for heat to flow across the tongue, an irreversible conversion of mechanical energy into heat occurs, observed in the form of internal friction. Zener showed that for a vibrating reed the specific scattering is given by

And - adiabatic and isothermal values ​​of the Young's modulus of the material, - vibration frequency, - relaxation frequency, which for a tongue of rectangular cross section has the expression

here K is thermal conductivity, specific heat at constant pressure, density, thickness of the reed in the plane of vibration.

Bennewitz and Rötger measured the internal friction in German silver tongues during transverse vibrations. The results of their experiments are shown in Fig. 29 along with the theoretical curve obtained using equation (5.60). No arbitrary parameters were used in constructing this curve, and the agreement between theory and experiment is remarkably good. It is clear that in the frequency region around (approximately 10 Hz) thermal conduction in the reed is the main cause of internal friction. It can also be seen that at frequencies far from the experimental values ​​of internal friction are higher than those predicted by theory, and this indicates that other influences become relatively more important here. The longitudinal stress will be

produce similar effects, since part of the sample is compressed while the other is stretched, in which case the heat flow is parallel to the direction of propagation. Since the distance between the areas of compression and rarefaction in this case is equal to half the wavelength, the losses caused by this reason will be small at ordinary frequencies.

Fig. 29. Comparisons of internal friction values ​​for German silver plates during transverse vibrations, measured by Bennewitz and Roetger and obtained from the theoretical Zener relations.

The described type of heat loss occurs regardless of whether the body is homogeneous or not. If the material is heterogeneous, there are additional mechanisms leading to heat losses. Thus, in a polycrystalline material, neighboring grains can have different crystallographic directions with respect to the direction of deformation and, as a result, receive stresses of different magnitudes when the sample is deformed. Therefore, the temperature will vary from crystallite to crystallite, as a result of which minute heat flows will occur across the grain boundaries. As with the losses due to conduction during cantilever oscillations, there is a lower frequency limit when the deformations occur so slowly that the volume changes occur isothermally without any loss of energy, and there is also an upper frequency limit when the deformations occur adiabatically, so again no losses occur. The greatest losses occur when the applied frequency hits

between these two limits; the value of this frequency depends on the size of the crystal grain and on the thermal conductivity of the medium. Zener derived an expression for the frequency at which losses of this kind are maximum. This equation is similar to (5.61) and has the form

where a is the average linear grain size.

Randall, Rose, and Zener measured internal friction in brass specimens of various grain sizes and found that, at the frequencies used, maximum damping occurred when the grain size was very close to that given by equation (5.62). The amount of internal friction caused by these microscopic heat flows depends on the type of crystal structure as well as on the grain size, and increases with increasing elastic anisotropy of individual crystallites. Zener (, pp. 89-90) proposed that at very high frequencies, heat flow is almost entirely limited to the immediate vicinity of the grain boundary; this leads to a relationship according to which the specific scattering is proportional to the square root of the oscillation frequency. This result was confirmed experimentally for brass by Randal, Rose and Zener. At very low frequencies, on the other hand, heat flow occurs throughout the material; hence the relation is obtained according to which internal friction is proportional to the first power of frequency. The experimental results of Zener and Randal are in agreement with this conclusion.

There are two other types of heat loss that need to be mentioned. The first is associated with heat dissipation into the surrounding air; the rate of loss for this reason, however, is so small that it affects only at very low oscillation frequencies. Another type of loss may arise from a lack of thermal equilibrium between the normal Debye modes; these losses are similar to the damping of ultrasound in gases, caused by the finite time required for thermal energy to be redistributed between the various degrees of freedom of gas molecules. However, in solids the equilibrium between the different modes of vibration is established so quickly that internal friction caused by such a cause would be expected to be noticeable only at frequencies of the order of 1000 MHz. The theory of the phenomenon described above was considered by Landau and Rumer and later by Gurevich.

For polycrystalline metals, he studied internal friction caused by “viscous slip” at crystal boundaries. He conducted experiments on the damping of torsional vibrations in pure aluminum and showed that internal friction in this case

can be accurately calculated under the assumption that the metal at the crystal boundaries behaves in a viscous manner.

There are two other processes that occur in crystalline bodies during their deformations, which could lead to internal friction. The first of these is the movement of regions of disorder in crystals, which are called dislocations. The second process is the ordering of dissolved atoms when a voltage is applied; the latter occurs in cases where there are impurities dissolved in the crystal lattice. The role of dislocations in the plastic deformation of crystals was first considered by Oroven, Palaney and Taylor, and although it seems likely that the movement of these dislocations may often be a significant cause of internal friction especially at large strains, the exact mechanism by which elastic energy is dissipated is currently unclear (see Bradfield). The influence of impurities dissolved in the crystal lattice on internal friction was first considered by Gorsky and later by Snoek. The reason that the presence of such dissolved atoms leads to internal friction is that their equilibrium distribution in a stressed crystal differs from the equilibrium distribution when the crystal is unstressed. When stress is applied, the establishment of a new equilibrium takes time, so that the deformation lags behind the stress. This introduces a relaxation process, which plays an important role for oscillating stresses, the period of which is comparable to the relaxation time. The rate at which equilibrium is established depends very markedly on temperature, so this type of internal friction must be very sensitive to temperature.

A special case of internal friction has been discovered in ferromagnetic materials. Becker and Döring gave a comprehensive review of experimental and theoretical studies for materials of this type on the important application problem of the magnetostrictive effect in ultrasound excitation. It has been found that internal friction in ferromagnetic materials is much greater than in other metals, and it increases when they are magnetized; it also increases rapidly with temperature when reaching the Curie point.

A mechanism that weakens stress waves in solids, but which is not strictly speaking internal friction, is dissipation. This phenomenon occurs in polycrystalline metals when the wavelength becomes comparable to the grain size; Meson and McSkimin measured the scattering effect in aluminum rods and showed that when the wavelength is comparable to the grain size, the attenuation is inversely proportional to the fourth power of the wavelength. This dependence coincides with the one given by Rayleigh (Vol. II, p. 194) for the scattering of sound in gases.

Viscosity coefficient .

Viscosity is one of the most important phenomena observed during the movement of a real fluid.

All real liquids (and gases) exhibit viscosity or internal friction to one degree or another. When a real fluid flows between its layers, friction forces arise. These forces are called forces of internal friction or viscosity.

Viscosity is the friction between layers of liquid (or gas) moving relative to each other.

The forces of viscosity (internal friction) are directed tangentially to the contacting layers of liquid and counteract the movement of these layers relative to each other. They decelerate the faster layer and speed up the slower layer. There are two main reasons for viscosity:

Firstly, interaction forces between molecules of adjacent layers moving at different speeds;

Secondly, the transition of molecules from layer to layer, and the associated momentum transfer.

Due to these reasons, the layers interact with each other, the slow layer accelerates, the fast layer slows down. In liquids the first reason is more clearly expressed, in gases the second.

To clarify the patterns that govern the forces of internal friction, consider the following experiment. Let's take two horizontal plates with a layer of liquid between them (Fig. 9). We set the upper plate in motion at a constant speed . To do this, force must be applied to the plate
to overcome friction force
, acting on the plate as it moves in the liquid. The layer of liquid adjacent directly to the top plate, due to wetting, adheres to the plate and moves with it. The layer of liquid adhering to the bottom plate is held at rest with it,
. The intermediate layers move in such a way that each upper one has a speed greater than the one lying underneath it. The arrows in Fig. 9 show the “velocity profile” of the flow. Along the axis perpendicular to the vector , the speed increases. Speed ​​measurement is characterized by the value .

Magnitude shows what measurement of speed is per unit length along the direction of change of speed, i.e. determines the rate of change in speed and direction perpendicular to the speed itself. The friction between the layers depends on this value. Magnitude measured in
.

Newton discovered that the frictional force between two layers of liquid is directly proportional to the area of ​​contact between the layers and size :

. (13)

Formula (13) is called Newton's formula for viscous friction. Proportionality factor called the viscosity coefficient (internal friction). From (13) it is clear that

In system
The unit of measure for the viscosity coefficient is

(pascal - second),

in the SGS system, the viscosity coefficient is measured in
(poises), and

Liquids for which Newton’s formula (13) is satisfied are called Newtonian. For such liquids, the viscosity coefficient depends only on temperature. Among biological fluids, Newtonian fluids include blood plasma and lymph. For many real liquids, relation (13) is not strictly satisfied. Such liquids are called non-Newtonian. For them the viscosity coefficient depends on temperature, pressure and a number of other quantities. These fluids include fluids with large, complex molecules, such as whole blood.

Blood viscosity of a healthy person
, with pathology fluctuates, which affects the erythrocyte sedimentation rate. The viscosity of venous blood is greater than that of arterial blood.

Viscosity (internal friction) - This is the property of real liquids to resist the movement of one part of the liquid relative to another. When some layers of a real liquid move relative to others, internal friction forces arise, directed tangentially to the surface of the layers. The action of these forces is manifested in the fact that an accelerating force acts on the side of the faster-moving layer on the slower-moving layer. From the side of the layer moving more slowly, a braking force acts on the layer moving faster.

Internal friction force F the greater the larger the considered surface area of ​​the layer S (Fig. 52), and depends on how quickly the fluid flow speed changes when moving from layer to layer.

The figure shows two layers, spaced from each other at a distance x and moving at speeds v 1 and v 2. In this case, v 1 -v 2 = v. The direction in which the distance between layers is measured is perpendicular layer flow rates. The value v/x shows how quickly the speed changes when moving from layer to layer in the direction X, perpendicular to the direction of movement of the layers, and is called speed gradient. Thus, the module of the internal friction force

where is the proportionality coefficient  , depending on the nature of the liquid is called dynamic viscosity(or simply viscosity).

The unit of viscosity is pascal second (Pa s): 1 Pa s is equal to the dynamic viscosity of the medium in which, under laminar flow and a velocity gradient with a module equal to 1 m/s per 1 m, an internal friction force of 1 N per 1 m2 of surface occurs touching the layers (1 Pa s = 1 N s/m 2).

The higher the viscosity, the more the liquid differs from the ideal, the greater the forces of internal friction that arise in it. Viscosity depends on temperature, and the nature of this dependence is different for liquids and gases (for liquids, m] decreases with increasing temperature, for gases, on the contrary, it increases), which indicates the difference in them

mechanisms of internal friction. The viscosity of oils depends especially strongly on temperature. For example, the viscosity of castor oil is in the range 18-40 ° WITH drops fourfold. Soviet physicist P. L. Kapitsa (1894-1984; Nobel Prize 1978) discovered that at a temperature of 2.17 K, liquid helium goes into a superfluid state, in which its viscosity is zero.

There are two modes of fluid flow. The current is called laminar (layered), if along the flow each selected thin layer slides relative to its neighbors without mixing with them, and turbulent (vortex), if intense vortex formation and mixing of the liquid (gas) occurs along the flow.

Laminar flow of liquid is observed at low speeds of its movement. The outer layer of liquid adjacent to the surface of the pipe in which it flows adheres to it due to molecular adhesion forces and remains motionless. The greater the distance from the subsequent layers to the pipe surface, the greater the speed of subsequent layers, and the layer moving along the pipe axis has the highest speed.

In turbulent flow, fluid particles acquire velocity components perpendicular to the flow, so they can move from one layer to another. The velocity of liquid particles increases rapidly as they move away from the pipe surface, then changes quite slightly. Since liquid particles move from one layer to another, their speeds in different layers differ little. Due to the large gradient

velocities, vortices usually form near the pipe surface.

The average velocity profile for turbulent flow in pipes (Fig. 53) differs from the parabolic profile for laminar flow by a more rapid increase in speed near the pipe walls and less curvature in the central part of the flow.

The English scientist O. Reynolds (1842-1912) in 1883 established that the nature of the flow depends on a dimensionless quantity called Reynolds number:

where v = / - kinematic viscosity;

 - liquid density; (v) is the average fluid velocity over the pipe cross-section; d- a characteristic linear dimension, for example the diameter of a pipe.

At low values ​​of the Reynolds number (Re1000), laminar flow is observed, the transition from laminar flow to turbulent flow occurs in the region of 1000:Re2000, and at Re = 2300 (for smooth pipes) the flow is turbulent. If the Reynolds number is the same, then the flow regime of various liquids (gases) in pipes of different sections is the same.

) mechanical energy imparted to a body during its deformation. Internal friction manifests itself, for example, in the damping of free vibrations. In liquids and gases, a similar process is usually called viscosity. Internal friction in solids is associated with two different groups of phenomena - inelasticity and plastic deformation.

Inelasticity is a deviation from the properties of elasticity when a body is deformed under conditions where there is practically no residual deformation. When deforming at a finite rate, a deviation from thermal equilibrium occurs in the body. For example, when bending a uniformly heated thin plate, the material of which expands when heated, the stretched fibers will cool, the compressed fibers will heat up, resulting in a transverse temperature difference, that is, elastic deformation will cause a violation of thermal equilibrium. Subsequent temperature equalization by thermal conduction is a process accompanied by the irreversible transition of part of the elastic energy into thermal energy. This explains the experimentally observed damping of free bending vibrations of the plate - the so-called thermoelastic effect. This process of restoring disturbed balance is called relaxation.

During elastic deformation of an alloy with a uniform distribution of atoms of various components, a redistribution of atoms in the substance may occur due to the difference in their sizes. The restoration of the equilibrium distribution of atoms by diffusion is also a relaxation process. Manifestations of inelastic, or relaxation, properties are also elastic aftereffects in pure metals and alloys, elastic hysteresis.

The deformation that occurs in an elastic body depends not only on the external mechanical forces applied to it, but also on the temperature of the body, its chemical composition, external magnetic and electric fields (magnetostriction and electrostriction), and grain size. This leads to a variety of relaxation phenomena, each of which makes its own contribution to internal friction. If several relaxation processes occur simultaneously in the body, each of which can be characterized by its own relaxation time, then the totality of all relaxation times of individual relaxation processes forms the so-called relaxation spectrum of a given material; Each structural change in the sample changes the relaxation spectrum.

The following methods are used for measuring internal friction: studying the damping of free vibrations (longitudinal, transverse, torsional, bending); study of the resonance curve for forced oscillations; relative dissipation of elastic energy during one period of oscillation. The study of internal friction of solids is a field of solid state physics and is a source of information about the processes that occur in solids, in particular in pure metals and alloys subjected to mechanical and thermal treatments.
If the forces acting on a solid body exceed the elastic limit and plastic flow occurs, then we can talk about quasi-viscous resistance to flow (by analogy with a viscous fluid). The mechanism of internal friction during plastic deformation differs significantly from the mechanism of internal friction during inelasticity. The difference in energy dissipation mechanisms determines the difference in viscosity values, which differ by 5-7 orders of magnitude. As the amplitude of elastic vibrations increases, plastic shears begin to play a large role in the damping of these vibrations, and the viscosity value increases, approaching the values ​​of plastic viscosity.

An ideal liquid, i.e. a fluid moving without friction is an abstract concept. All real liquids and gases exhibit viscosity or internal friction to a greater or lesser extent. Viscosity (internal friction), along with diffusion and thermal conductivity, is a transport phenomenon and is observed only in moving liquids and gases. Viscosity is manifested in the fact that the movement that occurs in a liquid or gas, after the cessation of the causes that caused it, gradually ceases.

Viscosity(internal friction) is one of the transfer phenomena, the property of fluid bodies (liquids and gases) to resist the movement of one part of them relative to another. As a result, the energy spent on this movement is dissipated in the form of heat.

The mechanism of internal friction in liquids and gases is that chaotically moving molecules carry impulse from one layer to another, which leads to equalization of velocities - this is described by the introduction of a friction force. The viscosity of solids has a number of specific features and is usually considered separately.

In liquids, where the distances between molecules are much smaller than in gases, viscosity is primarily due to intermolecular interactions, which limit the mobility of molecules. In a liquid, a molecule can penetrate into an adjacent layer only if a cavity is formed in it, sufficient for the molecule to jump there. The so-called activation energy of viscous flow is consumed to form a cavity (to “loose” the liquid). The activation energy decreases with increasing temperature and decreasing pressure. This is one of the reasons for the sharp decrease in the viscosity of liquids with increasing temperature and its increase at high pressures. When the pressure increases to several thousand atmospheres, the viscosity increases tens and hundreds of times. A rigorous theory of the viscosity of liquids, due to the insufficient development of the theory of the liquid state, has not yet been created.

The viscosity of individual classes of liquids and solutions depends on temperature, pressure and chemical composition.

The viscosity of liquids depends on the chemical structure of their molecules. In a series of similar chemical compounds (saturated hydrocarbons, alcohols, organic acids, etc.), viscosity changes naturally - it increases with increasing molecular weight. The high viscosity of lubricating oils is explained by the presence of cycles in their molecules. Two liquids of different viscosities that do not react with each other when mixed have an average viscosity in the mixture. If a chemical compound is formed during mixing, then the viscosity of the mixture can be tens of times greater than the viscosity of the original liquids.

The appearance in liquids (dispersed systems or polymer solutions) of spatial structures formed by the adhesion of particles or macromolecules causes a sharp increase in viscosity. When a “structured” fluid flows, the work of an external force is spent not only on overcoming viscosity, but also on destroying the structure.

In gases, the distances between molecules are significantly greater than the radius of action of molecular forces, therefore the viscosity of gases is determined mainly by molecular motion. Between the layers of gas moving relative to each other, there is a constant exchange of molecules due to their continuous chaotic (thermal) movement. The transition of molecules from one layer to the adjacent one, moving at a different speed, leads to the transfer of a certain momentum from layer to layer. As a result, the slow layers speed up and the faster layers slow down. Work done by external force F, which balances the viscous resistance and maintains a steady flow, is completely converted into heat. The viscosity of a gas does not depend on its density (pressure), since when the gas is compressed, the total number of molecules moving from layer to layer increases, but each molecule penetrates less deeply into the adjacent layer and transfers less momentum (Maxwell’s law).

Viscosity is an important physical and chemical characteristic of substances. The viscosity value must be taken into account when pumping liquids and gases through pipes (oil pipelines, gas pipelines). The viscosity of molten slag is very significant in blast furnace and open-hearth processes. The viscosity of molten glass determines the process of its production. In many cases, viscosity is used to judge the readiness or quality of products or semi-products of production, since viscosity is closely related to the structure of the substance and reflects the physical and chemical changes in the material that occur during technological processes. The viscosity of oils is of great importance for calculating the lubrication of machines and mechanisms, etc.

The device for measuring viscosity is called viscometer.