Melting Wear

Deformations are divided into reversible (elastic) and irreversible (plastic, creep). Elastic deformations disappear after the end of the applied forces, but irreversible deformations remain. Elastic deformations are based on reversible displacements of metal atoms from the equilibrium position (in other words, the atoms do not go beyond the limits of interatomic bonds); Irreversible are based on irreversible movements of atoms to significant distances from the initial equilibrium positions (that is, going beyond the boundaries of interatomic bonds, after removing the load, reorientation to a new equilibrium position).

Plastic deformations are irreversible deformations caused by changes in stress. Creep deformations are irreversible deformations that occur over time. The ability of substances to deform plastically is called plasticity. During plastic deformation of a metal, simultaneously with a change in shape, a number of properties change - in particular, during cold deformation, strength increases.

Types of deformation

Most simple types deformations of the body as a whole:

In most practical cases, the observed deformation is a combination of several simultaneous simple deformations. Ultimately, however, any deformation can be reduced to two simplest ones: tension (or compression) and shear.

Study of deformation

The nature of plastic deformation may vary depending on temperature, duration of load or strain rate. With a constant load applied to the body, the deformation changes with time; this phenomenon is called creep. As temperature increases, the creep rate increases. Special cases of creep are relaxation and elastic aftereffect. One of the theories that explains the mechanism of plastic deformation is the theory of dislocations in crystals.

Continuity

In the theory of elasticity and plasticity, bodies are considered “solid”. Continuity (that is, the ability to fill the entire volume occupied by the material of the body, without any voids) is one of the main properties attributed to real bodies. The concept of continuity also refers to elementary volumes into which a body can be mentally divided. The change in the distance between the centers of each two adjacent infinitesimal volumes in a body that does not experience discontinuities should be small compared to the initial value of this distance.

The simplest elementary deformation

The simplest elementary deformation is the relative elongation of some element:

In practice, small deformations are more common - such that .

Strain measurement

Strain measurement is carried out either in the process of testing materials in order to determine their mechanical properties, either when studying a structure in situ or on models to judge the magnitude of stresses. Elastic deformations are very small, and their measurement requires high accuracy. The most common method for studying deformation is using strain gauges. In addition, resistance strain gauges, polarization optical stress testing, and X-ray diffraction analysis are widely used. To judge local plastic deformations, knurling a mesh on the surface of the product, covering the surface with easily cracked varnish or brittle gaskets, etc. is used.

Notes

Literature

• Rabotnov Yu. N., Strength of Materials, M., 1950;
• Kuznetsov V.D., Solid State Physics, vol. 2-4, 2nd ed., Tomsk, 1941-47;
• Sedov L.I., Introduction to continuum mechanics, M., 1962.

See also

Links

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Synonyms:

• Beta (letter)
• Bulgarian Commission for Antarctic Names

See what “Deformation” is in other dictionaries:

deformation- deformation: Distortion of the shape of a bar of soap compared to that intended technical document. Source: GOST 28546 2002: Solid toilet soap. General technical specifications original document De... Dictionary-reference book of terms of normative and technical documentation

DEFORMATION- (French) Ugliness; change in shape. Dictionary foreign words, included in the Russian language. Chudinov A.N., 1910. DEFORMATION [lat. deformatio distortion] change in the shape and size of the body under the influence of external forces. Dictionary of foreign words. Komlev... Dictionary of foreign words of the Russian language

DEFORMATION Modern encyclopedia

Deformation- – change in the shape and/or size of the body under the influence of external forces and various types of influences (changes in temperature and humidity, settlement of supports, etc.); in the strength of materials and the theory of elasticity - a quantitative measure of dimensional change... Encyclopedia of terms, definitions and explanations of building materials

Deformation- (from Latin deformation distortion), change relative position particles of matter due to any external or internal reasons. The simplest types of deformation of a solid body: tension, compression, shear, bending, torsion.... ... Illustrated Encyclopedic Dictionary

DEFORMATION- (from Latin deformatio distortion) 1) a change in the relative position of points of a solid body, in which the distance between them changes, as a result external influences. The deformation is called elastic if it disappears after the impact is removed, and... ... Big Encyclopedic Dictionary

deformation- Cm … Dictionary of synonyms

DEFORMATION- (from lat. deformatio distortion), change in the configuration of the kl. object resulting from external influences or internal strength D. may experience TV. bodies (crystal, amorphous, organic origin), liquids, gases, physical fields, living... ... Physical encyclopedia

deformation- and, f. deformation f. lat. deformatio distortion. 1. Changing the size and shape of a solid body under the influence of external forces (usually without changing its mass). BAS 1. || IN fine arts deviation from the natural one perceived by the eye... ... Historical Dictionary of Gallicisms of the Russian Language

deformation- deformation, deformed. Pronounced [deformation], [deformed] and obsolete [deformation], [deformed] ... Dictionary of difficulties of pronunciation and stress in modern Russian language

Deformation - rocks(from Latin deformatio change in shape, distortion * a. rock deformafion; n. Deformation von Gesteinen; f. deformation des roches; i. deformacion de las rocas) a change in the relative position of rock particles, causing a change ... Geological encyclopedia

Books

• Plastic deformation of metals, R. Honeycombe, For engineering and technical and scientific workers of factories and research institutes, university teachers, graduate students and senior students. Reproduced in original... Category:

DEFINITION

Deformation in physics they call a change in the size, volume and often shape of a body if an external load is applied to the body, for example, during stretching, compression and/or when its temperature changes.

Deformation occurs when different parts of the body make different movements. So, for example, if a rubber cord is pulled by the ends, then its different parts will move relative to each other, and the cord will be deformed (stretched, lengthened). During deformation, the distances between atoms or molecules of bodies change, so elastic forces appear.

Types of deformation of a solid body

Deformations can be divided into elastic and inelastic. Elasticity is a deformation that disappears when the deforming effect ceases. With this type of deformation, particles return from new equilibrium positions to crystal lattice to the old ones.

Inelastic deformations of a solid body are called plastic. During plastic deformation, an irreversible restructuring of the crystal lattice occurs.

In addition, there are the following types deformations: tension (compression); shear, torsion.

Unilateral stretching involves increasing the length of the body when exposed to a tensile force. A measure of this type of deformation is the value of relative elongation ().

All-round tensile (compression) deformation manifests itself in a change (increase or decrease) in the volume of the body. In this case, the shape of the body does not change. Tensile (compressive) forces are evenly distributed over the entire surface of the body. A characteristic of this type of deformation is the relative change in the volume of the body ().

Shear is a type of deformation in which flat layers of a solid are displaced parallel to each other. With this type of deformation, the layers do not change their shape and size. The measure of this deformation is the shear angle.

Torsional deformation consists of a relative rotation of sections parallel to each other, perpendicular to the axis of the sample.

The theory of elasticity has proven that all types of elastic deformation can be reduced to tensile or compressive deformations that occur at one point in time.

Hooke's law

Let us consider a homogeneous rod having length l and cross-sectional area S. Two forces equal in magnitude F, directed along the axis of the rod, but in opposite directions, are applied to the ends of the rod. In this case, the length of the rod changed by .

The English scientist R. Hooke empirically established that for small deformations the relative elongation () is directly proportional to the stress ():

where E is Young's modulus; - the force that acts on a unit cross-sectional area of ​​the conductor. Otherwise, Hooke's law is written as:

where k is the elasticity coefficient. For the elastic force arising in a rod, Hooke’s law has the form:

The linear relationship between and is satisfied within narrow limits, at small loads. As the load increases, the dependence becomes nonlinear, and then the elastic deformation turns into plastic deformation.

Examples of problem solving

EXAMPLE 1

Exercise	What is the potential energy of a stretched elastic rod if its absolute elongation is , and the elasticity coefficient is k? Consider that Hooke's law is fulfilled.
Solution	Potential energy() of an elastic stretched rod is equal to the work (A) performed by external forces, causing deformation: where x is the absolute elongation of the rod, which changes from 0 to . According to Hooke's law, we have: Substituting expression (1.2) into formula (1.1), we have:

DEFORMATION- a change in the size, shape and configuration of the body as a result of the action of external or internal forces (from the Latin deformatio - distortion).

Solids are capable of maintaining their shape and volume unchanged for a long time, unlike liquid and gaseous ones. This well-known statement is true only “to a first approximation” and needs clarification. Firstly, many bodies that are generally considered solid “flow” very slowly over time: there is a known case when a granite slab (part of a wall) over several hundred years, due to soil sedimentation, noticeably bent, following a new microrelief, and without cracks and kinks (Fig. 1). It was calculated that the characteristic rate of movement was 0.8 mm per year. The second clarification is that all solids change their shape and size if external loads act on them. These changes in shape and size are called deformations of a solid body, and the deformations can be large (for example, when stretching a rubber cord or bending a steel ruler) or small, invisible to the eye (for example, deformations of a granite pedestal when installing a monument).

From the point of view internal structure many solids are polycrystalline, i.e. consist of small grains, each of which is a crystal having a lattice certain type. Glassy materials and many plastics do not have a crystalline structure, but their molecules are very closely linked to each other and this ensures the preservation of the shape and size of the body.

If external forces act on a solid body (for example, a rod is stretched by two forces, Fig. 2), then the distances between the atoms of the substance increase, and with the help of instruments it is possible to detect an increase in the length of the rod. If the load is removed, the rod restores its previous length. Such deformations are called elastic; they do not exceed fractions of a percent. With increasing tensile forces, there can be two outcomes of the experiment: samples made of glass, concrete, marble, etc. are destroyed in the presence of elastic deformations (such bodies are called brittle). In samples made of steel, copper, aluminum, along with elastic deformations, plastic deformations will appear, which are associated with the slipping (shear) of some particles of the material relative to others. The magnitude of plastic deformation is usually several percent. A special place among the deformable solids occupied by elastomers - rubber-like substances that allow enormous deformations: a rubber strip can be stretched 10 times without rupture or damage, and after unloading the original size is restored almost instantly. This type of deformation is called highly elastic and is due to the fact that the material consists of very long polymer molecules, coiled in the form of spirals (“spiral staircases”) or accordions, with neighboring molecules forming an ordered system. Long, repeatedly bent molecules are able to straighten due to the flexibility of atomic chains; in this case, the distances between the atoms do not change, and small forces are sufficient to produce large deformations due to partial straightening of the molecules.

Bodies are deformed under the influence of forces applied to them, under the influence of changes in temperature, humidity, chemical reactions, neutron irradiation. The easiest way to understand deformation under the influence of forces - they are often called loads: a beam, fixed at the ends on supports and loaded in the middle, bends - bending deformation; when drilling a hole, the drill experiences torsional deformation; when the ball is inflated with air, it retains its spherical shape but increases in size. Globe deforms when a tidal wave passes over its surface layer. Even these simple examples show that the deformations of bodies can be very different. Usually the design details in normal conditions experience small deformations, during which their shape remains almost unchanged. On the contrary, during pressure processing - during stamping or rolling - large deformations occur, as a result of which the shape of the body changes significantly; for example, a glass or even a part of a very complex shape is obtained from a cylindrical workpiece (in this case, the workpiece is often heated, which facilitates the deformation process).

The easiest to understand and mathematical analysis is the deformation of the body at small deformations. As is customary in mechanics, some arbitrarily chosen point is considered M bodies.

Before the deformation process begins, a small neighborhood of this point is mentally selected, having simple form, convenient for study, for example, a ball of radius D R or cube with side D a, and so that the point M turned out to be the center of these bodies.

Even though the bodies various shapes under the influence of external loads and other reasons, very diverse deformations occur, it turns out that a small neighborhood of any point is deformed according to the same rule (law): if a small neighborhood of a point M had the shape of a ball, then after deformation it becomes an ellipsoid; similarly, the cube becomes an oblique parallelepiped (usually they say that the ball goes into an ellipsoid, and the cube into an oblique parallelepiped). It is this circumstance that is the same at all points: the ellipsoids at different points, of course, turn out to be different and differently rotated. The same applies to parallelepipeds.

If in an undeformed sphere we mentally select a radial fiber, i.e. material particles located at a certain radius, and follow this fiber in the process of deformation, it is discovered that this fiber remains straight all the time, but changes its length - it lengthens or shortens. Important information can be obtained as follows: in an undeformed sphere, two fibers stand out, the angle between which is right. After deformation, the angle, generally speaking, will become different from a straight line. Change right angle called shear deformation or shear. It is more convenient to consider the essence of this phenomenon using the example of a cubic neighborhood, when deformed, the square face transforms into a parallelogram - this explains the name shear deformation.

We can say that the deformation of the neighborhood of a point M is known completely if for any radial fiber selected before deformation, its new length can be found, and for any two such mutually perpendicular fibers, the angle between them after deformation can be found.

It follows from this that the deformation of the neighborhood is known if the elongations of all fibers and all possible displacements are known, i.e. required indefinitely large number data. In fact, the deformation of the particle occurs in a very orderly manner - after all, the ball turns into an ellipsoid (and does not fly into pieces and does not turn into a thread that is tied in knots). This ordering is expressed mathematically by a theorem, the essence of which is that the elongations of any fiber and the shift for any pair of fibers can be calculated (and quite simply) if the elongations of three mutually perpendicular fibers and the shifts - changes in the angles between them - are known. And of course, the essence of the matter does not depend at all on what shape is chosen for the particle - spherical, cubic or some other.

For a more specific and more rigorous description of the deformation pattern, a coordinate system (for example, Cartesian) is introduced. OXYZ, a certain point is selected in the body M and its surroundings in the form of a cube with the vertex at the point M, whose edges are parallel to the coordinate axes. Relative elongation of the rib parallel to the axis OX, –e xx(In this notation the index x repeated twice: this is how matrix elements are usually denoted).

If the edge of the cube in question had a length a, then after deformation its length will change by the amount of elongation D a x, while the relative elongation introduced above will be expressed as

e xx=D a x/ a

The values ​​e have a similar meaning yy and e zz.

For shifts, the following notations are accepted: change in the initially right angle between the edges of the cube parallel to the axes OX And OY, denoted as 2e xy= 2e yx(here the coefficient “2” is introduced for convenience in the future, as if the diameter of a certain circle was designated 2 r).

Thus, 6 quantities are introduced, namely three elongation strains:

e xx e yy e zz

and three shear deformations:

e yx= e xy e zy= e yz e zx= e xz

These 6 quantities are called deformation components, and this definition has the meaning that any elongation and shear deformation in the vicinity of a given point is expressed through them (often abbreviated as simply “deformation at a point”).

The strain components can be written as a symmetric matrix

This matrix is ​​called the small deformation tensor, written in the coordinate system OXYZ. In another coordinate system with the same origin, the same tensor will be expressed by another matrix, with components

The coordinate axes of the new system and the coordinate axes of the old system make up a set of angles, the cosines of which are conveniently designated as in the following table:

Then the expression of the strain tensor components in the new axes (i.e. e ´ xx ,…, e ´ xy,...) through the components of the strain tensor in the old axes, i.e. via e xx,…, e xy,…, have the form:

These formulas are essentially the definition of a tensor in the following sense: if some object is described in the system OXYZ matrix e ij, and in another system OX´ Y´ Z´ – another matrix e ij´, then it is called a tensor if the above formulas hold, which are called formulas for transforming the components of a tensor of the second rank to new system coordinates Here, for brevity, the matrix is ​​denoted by e ij, where the indices i, j match any pairwise combination of indices x, y, z; It is significant that there are always two indices. The number of indices is called the rank of the tensor (or its valence). In this sense, the vector turns out to be a rank one tensor (its components have the same index), and the scalar can be considered as a rank zero tensor that has no indices; in any coordinate system the scalar obviously has the same meaning.

The first tensor on the right side of the equality is called spherical, the second is called a deviator (from the Latin deviatio - distortion), because it is associated with distortions of right angles - shifts. The name “spherical” is due to the fact that the matrix of this tensor in analytical geometry describes a spherical surface.

Vladimir Kuznetsov

What is deformation?

Materials and finished goods when exposed to loads they deform. Deformation is a change in the shape of a material or product under the influence of loads. This process depends on the magnitude and type of load, internal structure, shape and nature of the arrangement of particles.

Deformation occurs due to changes in the structure and arrangement of molecules, their approach and distance, which is accompanied by changes in the forces of attraction and repulsion. When loads are applied to a material, they are counteracted by internal forces called elastic forces. The magnitude and nature of deformation of the material depends on the ratio of external forces and elastic forces.

Deformation is distinguished:

• - reversible;
• - irreversible;

Reversible deformation is a deformation in which the body is completely restored after the load is removed.

If the body does not return to its original position after removing the load, then this deformation is called irreversible (plastic).

Reversible deformation can be elastic or elastic. Elastic deformation is when the size and shape of a body, after removing the load, is restored instantly, at the speed of sound, i.e. it manifests itself in a short period of time. It is characterized by elastic changes in the crystal lattice.

Elastic deformation is when the size and shape of the body, after removing the load, are restored over a long period. The concept of elastic deformation is applicable mainly to high molecular weight organic compounds, which is part of the skin, rubber, consisting of these molecules with a large number links It is usually accompanied by thermal phenomena, absorption or release of heat, which is associated with the phenomena of friction between molecules and their complex. Elastic deformation is greater than elastic deformation.

Elastic deformations are important when using clothing, especially sportswear; this is associated with creasing and straightening of fabrics. Fabrics that exhibit elastic deformation are characterized by increased wear.

Irreversible deformation is accompanied by a new location elementary particles due to shears or slips, displacement of some particles.

Each type of deformation is measured after a certain time after the load is removed, for example, elastic is measured after 2 minutes, elastic after 20 minutes. etc. These values ​​will correspond to conditionally elastic, conditionally elastic and conditionally plastic deformations.

Deformation indicators.

The main indicators of deformation are: absolute and relative elongation and contraction, proportionality limit, yield strength, elastic modulus, breaking length, relaxation.

Absolute and relative elongation:

where Dl is absolute elongation (m); l and l0 - final and initial length of the body (m).

• - limit of proportionality: characterizes the strength of the material within the limits of elasticity;
• - yield strength: the property of a material to deform under constant load is called yield.

The yield point is when the yield of a material is not clearly expressed, i.e. when it receives a permanent elongation of 0.2%.

• - relaxation - a decrease in stress in a deformable body, associated with the spontaneous transition of particles to an equilibrium state.
• - breaking length - the minimum length at which the material breaks under the influence of its own weight.