What is called the proportional limit. Indicators of the elastic and plastic state of metals. Limits of proportionality, elasticity and fluidity. Influence of radioactive irradiation on the change in mechanical properties

PROPORTIONAL LIMIT

mechanical character of materials: stress, at which the deviation from the linear relationship between stresses and deformations reaches a certain definition. value set by technical. conditions (for example, an increase in the tangent of an angle, images, tangent to the deformation curve with the stress axis, by 10, 25, 50% of its original value). It is denoted by bp. P. p. Limits the scope of justice Hooke's law. With practical. strength calculations P. p. is taken equal to yield point. See fig.

Back to articles Proportionality limit, Tensile strength, Yield strength, Elastic limit. The diagram of the conditional stresses obtained by stretching a specimen from a ductile metal: b - stress; e - relative elongation; b pts - proportionality limit; (Tu - elastic limit; (Тт - yield point; О, - ultimate strength (tensile strength)

Big Encyclopedic Polytechnic Dictionary. 2004 .

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Proportionality limit s pts- The stress at which the deviation from the linear relationship between the force and the elongation reaches such a value that the tangent of the angle of inclination formed by the tangent to the curve "elongation force" at the point Ppc with the axis of forces increases by 50% of ... ...

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Tensile properties, as in other static tests, can be divided into three main groups: strength, plastic and viscosity characteristics. Strength properties are the characteristics of the resistance of the sample material to deformation or fracture. Most of the standard strength characteristics are calculated from the position of certain points on the tensile diagram, in the form of conditional tensile stresses. Section 2.3 analyzed diagrams in coordinates true stress - true strain, which most accurately characterize strain hardening. In practice, the mechanical properties are usually determined from the primary tensile curves in the coordinates load - absolute elongation, which are automatically recorded on the chart tape of the testing machine. For polycrystals of various metals and alloys, the whole variety of these curves at low temperatures can be reduced in the first approximation to three types (Fig. 2.44).

Figure 2.44- Types of primary stretch curves

The tension diagram of type I is typical for specimens that fail without noticeable plastic deformation. Type II diagram is obtained when specimens are stretched uniformly deforming until fracture. Finally, a Type III diagram is characteristic of specimens that collapse after necking as a result of focused deformation. Such a diagram can also be obtained when tensile specimens fail without necking (high-temperature stretching); plot bk here it can be strongly stretched and is almost parallel to the deformation axis. The increase in the load until the moment of destruction (see Fig. 2.44, II) or to the maximum (see fig. 2.44, III) can be either smooth (solid lines) or discontinuous. In the latter case, a tooth and a yield plate may appear on the tension diagram (dotted line in Fig. 2.44, III, III).

Depending on the type of diagram, the set of characteristics that can be calculated from it, as well as their physical meaning, changes. In fig. 2.44 (type III diagram) characteristic points are plotted, along the ordinates of which the strength characteristics are calculated

(σ i = P i / F 0).

As you can see, in the diagrams of the other two types (see Fig. 2.44, I,II) not all of these points may be plotted.

Proportional limit. The first keypoint in the stretch diagram is a point p(see fig. 2.45). Force P nu determines the value proportionality limit - the stress that the sample material can withstand without deviating from Hooke's law.

An approximate value of P nu can be determined by the point where the divergence of the tension curve and the continuation of the straight section begins (Fig. 2.46).

Figure 2.46- Graphic methods for determining the proportional limit.

In order to unify the technique and improve the accuracy of calculating the proportionality limit, it is estimated as the conditional stress (σ nu), at which the deviation from the linear relationship between load and elongation reaches a certain value. Usually, the tolerance in determining σ nu is set by the decrease in the tangent of the slope angle formed by the tangent to the tension curve at the point p with the axis of deformations, compared with the tangent at the initial elastic section. The standard tolerance is 50%, but 10% and 25% tolerances are also possible. Its value should be indicated in the designation of the proportionality limit - σ nu 50, σ nu 25, σ nu 10.

With a sufficiently large scale of the primary stretching diagram, the value of the proportional limit can be determined graphically directly on this diagram (see Fig. 2.46). First of all, the straight section is continued until the intersection with the deformation axis at the point 0, which is taken as a new origin of coordinates, thus excluding the initial section of the diagram distorted due to insufficient rigidity of the machine. Then you can use it in two ways. According to the first of them, at an arbitrary height within the elastic region, the perpendicular is restored AB to the load axis (see Fig. 2.46, a), lay along it the segment BC =½ AB and draw the line OS. Moreover, tan α ′ = tan α / 1.5. If you now draw the tangent to the stretch curve parallel OS, then the touch point R will determine the required load P nu.

In the second method, a perpendicular is lowered from an arbitrary point of the straight section of the diagram KU(see fig. 2.46, b) on the abscissa axis and divide it into three equal parts. Through point C and the origin of coordinates is drawn with a straight line, and parallel to it, a tangent to the tension curve. Touch point p corresponds to the effort P nu (tan α ′ = tan α / 1.5).

It is possible to more accurately determine the proportionality limit using tensometers - special devices for measuring small deformations.

Elastic limit... The next characteristic point on the primary tension diagram (see Fig. 2.45) is the point e... It corresponds to the load for which the conditional elastic limit - the stress at which the residual elongation reaches a given value, usually 0.05%, sometimes less - up to 0.005%. The tolerance used in the calculation is indicated in the designation of the conditional elastic limit σ 0.05, σ 0.01, etc.

The elastic limit characterizes the stress at which the first signs of macroplastic deformation appear. Due to the small tolerance for residual elongation, even σ 0.05 is difficult to determine with sufficient accuracy from the primary tensile diagram. Therefore, in cases where high accuracy is not required, the elastic limit is taken equal to the proportionality limit. If you need an accurate quantitative assessmentσ 0.05, then tensometers are used. The method for determining σ 0.05 is in many respects similar to that described for σ nu, but there is one fundamental difference. Since, when determining the elastic limit, the tolerance is set in terms of the residual deformation, after each loading step it is necessary to unload the sample to the initial stress σ 0 ≤ 10% of the expected σ 0.05 and then only measure the elongation using a tensometer.

If the scale for recording the tensile diagram along the elongation axis is 50: 1 or more, and along the load axis is ≤10MPa per 1 mm, a graphical definition of σ 0.05 is allowed. To do this, a segment is laid along the axis of elongations from the origin of coordinates OK= 0,05 l 0/100 and through point TO draw a straight line parallel to the rectilinear section of the diagram (Fig. 2.47). Point ordinate e will correspond to the size of the load R 0.05, which determines the conditional elastic limit σ 0.05 = P 0.05 / F 0.

Yield point. In the absence of the tooth tension and the yield area on the diagram, calculate conditional yield stress - the stress at which the residual elongation reaches a given value, usually 0.2%. Accordingly, the conventional yield stress is denoted by σ 0.2. As you can see, this characteristic differs from the conditional elastic limit only in the size of the tolerance. Limit

Yield characterizes the stress at which a more complete transition to plastic deformation occurs.

The most accurate estimate of the value of σ 0.2 can be made using strain gauges. Since the elongation tolerance for calculating the conventional yield strength is relatively large, it is often determined graphically from the tensile diagram, if the latter is written on a sufficiently large scale (at least 10: 1 along the deformation axis). This is done in the same way as when calculating the elastic limit (see Figure 2.47), only a segment OK = 0,2l 0/100.

The conditional limits of proportionality, elasticity and fluidity characterize the resistance of the material to small deformations. Their magnitude slightly differs from the true stresses corresponding to the corresponding deformation tolerances. The technical significance of these limits comes down to assessing the stress levels under which

this or that part can work without undergoing permanent deformation (proportionality limit) or deforming by some small allowable value determined by the operating conditions (σ 0.01, σ 0.05, σ 0.2, etc.). Considering that in modern technology the possibility of residual changes in the dimensions of parts and structures is more and more strictly limited, it becomes clear that there is an urgent need for accurate knowledge of the limits of proportionality, elasticity and fluidity, which are widely used in design calculations.

The physical meaning of the proportionality limit of any material is so obvious that it does not require special discussion. Indeed, σ nu for a single- and polycrystal, a homogeneous metal, and a heterophase alloy is always the maximum stress, up to which Hooke's law is observed during stretching and no macroplastic deformation is observed. It should be remembered that before σ nu is reached in individual grains of a polycrystalline sample (with their favorable orientation, the presence of stress concentrators), plastic deformation may begin, which, however, will not lead to a noticeable elongation of the entire sample until the majority of the grains are covered by the deformation.

The elastic limit corresponds to the initial stages of specimen macroelongation. For a favorably oriented single crystal, it should be close to the critical shear stress. Naturally, for different crystallographic orientations of the single crystal, the elastic limit will be different. In a sufficiently fine-grained polycrystal in the absence of texture, the elastic limit is isotropic, the same in all directions.

The nature of the conditional yield stress of a polycrystal is, in principle, similar to the nature of the elastic limit. But it is precisely the yield point that is the most common and important characteristic of the resistance of metals and alloys to small plastic deformation. Therefore, the physical meaning of the yield point and its dependence on various factors must be analyzed in more detail.

A smooth transition from elastic to plastic deformation (without a tooth and yield area) is observed when tensile of such metals and alloys, in which there is a sufficiently large number of mobile, unfixed dislocations in the initial state (before the start of the test). The stress required for the onset of plastic deformation of polycrystals of these materials, estimated through the conditional yield stress, is determined by the forces of resistance to the movement of dislocations within the grains, the ease of transferring deformation through their boundaries, and the size of the grains.

The same factors determine the value physical yield pointσ t - stress at which the sample is deformed under the action of a practically unchanged tensile load P t (see Fig. 2.45, yield area on the dashed curve). The physical yield strength is often referred to as the lower, as opposed to the upper yield point calculated from the load corresponding to the tip of the yield tooth. and(see fig. 2.45): σ t.w = P t.v / F 0.

The formation of a tooth and a yield area (the so-called phenomenon of sharp fluidity) looks like this. Elastic tension leads to a gradual rise in the resistance to deformation up to σ t.w, then a relatively sharp drop in stresses to σ tn occurs, and the subsequent deformation (usually by 0.1-1%) proceeds with a constant external force - a yield area is formed. During the elongation corresponding to this area, the sample at the working length is covered with characteristic Chernoff - Luders stripes, in which deformation is localized. Therefore, the amount of elongation at the yield point (0.1 - 1%) is often called the Chernov - Luders deformation.

The phenomenon of sharp fluidity is observed in many technically important metallic materials and therefore is of great practical importance. It is also of general theoretical interest from the point of view of understanding the nature of the initial stages of plastic deformation.

In recent decades, it has been shown that a tooth and a yield point can be obtained by stretching single and polycrystals of metals and alloys with various lattices and microstructures. Sharp fluidity is most often recorded when testing metals with a bcc lattice and alloys based on them. Naturally, the practical importance of sharp fluidity for these metals is especially great, and most of the theories were also developed in relation to the characteristics of these metals. The use of dislocation concepts to explain sharp fluidity was one of the first and very fruitful applications of dislocation theory.

Initially, the formation of a tooth and a yield area in bcc metals was associated with the effective blocking of dislocations by impurities. It is known that in a bcc lattice, interstitial impurity atoms form elastic stress fields that do not have spherical symmetry and interact with dislocations of all types, including purely screw dislocations. Already at low concentrations [<10 -1 - 10 -2 % (ат.)] примеси (например, азот и углерод в железе) способны блокировать все дислокации, имеющиеся в металле до деформации. Тогда, по Коттреллу, для начала движения дислокаций и для начала пластического течения необходимо приложить напряжение, гораздо большее, чем это требуется для перемещения дислокаций, свободных от примесных атмосфер. Следовательно, вплоть до момента достижения верхнего предела текучести заблокированные дислокации не могут начать двигаться, и деформация идет упруго. После достижения σ тв по крайней мере часть этих дислокаций (расположенных в плоскости действия максимальных касательных напряжений) отрывается от своих атмосфер и начинает перемещаться, производя пластическую деформацию. Последующий спад напряжений - образование зуба текучести - происходит потому, что свободные от примесных атмосфер и более подвижные дислокации могут скользить некоторое время под действием меньших напряжений σ тн пока их торможение не вызовет начала обычного деформационного упрочнения.

The results of the following simple experiments confirm the correctness of Cottrell's theory. If you deform an iron sample, for example, to a point A(Fig. 2.48), unload it and immediately stretch it again, then the tooth and the yield area will not arise, because after preliminary stretching in the new initial state, the sample contained many mobile dislocations free from impurity atmospheres. If now after unloading from the point A keep the sample at room or slightly elevated temperature, i.e. allow time for the condensation of impurities on dislocations, then with a new tension, a tooth and a yield area will again appear on the diagram.

Thus, Cottrell's theory associates sharp fluidity with strain aging - fixing of dislocations by impurities.

Cottrell's hypothesis that, after unblocking, plastic deformation, at least in the beginning, is carried out by sliding these "old" but now freed from impurities dislocations, turned out to be not universal. For a number of materials, it has been established that the initial dislocations can be so firmly fixed that they cannot be unblocked, and plastic deformation at the yield point occurs due to the motion of newly formed dislocations. In addition, the formation of a tooth and a yield area is observed in dislocation-free crystals - "whiskers". Consequently, Cottrell's theory describes only a particular, albeit important, case of sharp fluidity.

The basis of the modern theory of the namesake fluidity, which cannot yet be considered finally established, is the same position put forward by Cottrell: the tooth and the yield area are caused by a sharp increase in the number of mobile dislocations at the beginning of plastic flow. This means that for their appearance, two conditions must be met: 1) the number of free dislocations in the initial sample must be very small, and 2) it must be able to rapidly increase by one or another mechanism at the very beginning of plastic deformation.

The lack of mobile dislocations in the initial sample can be associated either with the high perfection of its substructure (for example, in the whiskers) or with the pinning of most of the existing dislocations. According to Cottrell, such anchorage can be achieved by the formation of impurity atmospheres. Other methods of fixing are possible, for example, with particles of the second phase.

The number of mobile dislocations can sharply increase:

1) By unblocking previously fixed dislocations (separation from impurity atmospheres, bypassing particles by transverse sliding, etc.);

2) By the formation of new dislocations;

3) By their reproduction as a result of interaction.

In polycrystals, the yield point strongly depends on the grain size. Grain boundaries serve as effective barriers to moving dislocations. The finer the grain, the more often these barriers are encountered on the path of gliding dislocations and higher stresses are required for the continuation of plastic deformation already at its initial stages. As a result, as the grain is refined, the yield stress increases. Numerous experiments have shown that the lower yield strength

σ tn = σ i + K y d -½, (2.15)

where σ i and K y - material constants at a certain test temperature and strain rate; d- grain size (or subgrain for a polygonized structure).

Formula 2.15, called after its first authors the Petch - Hall equation, is universal and well describes the effect of grain size not only on σ so-called, but also on the conditional yield stress and, in general, any stress in the region of uniform deformation.

The physical interpretation of the empirical equation (2.15) is based on the already considered ideas about the nature of sharp fluidity. The constant σ i is considered as the stress required to move the dislocations inside the grain, and the term K y d -½- as the voltage required to activate dislocation sources in adjacent grains.

The value of σ i depends on the Peierls - Nabarro force and the obstacles to the sliding of dislocations (other dislocations, foreign atoms, particles of the second phase, etc.). Thus, σ i - "friction stress" - compensates for the forces that have to be overcome by dislocations during their movement inside the grain. For the experimental determination of σ i, you can use the primary tension diagram: the value of σ i corresponds to the point of intersection of the tension curve extrapolated to the region of small deformations behind the yield area with the straight section of this curve (Fig. 2.49, a). This method for estimating σ i is based on the idea that the site ius tensile diagrams are the result of polycrystalline properties of the stretched specimen; if it were a single crystal, then the plastic flow would begin at the point i .

Figure 2.49. Determination of the flow stress σ i from the tension diagram (a) and the dependence of the lower yield stress on the grain size (b).

The second method for determining σ i is extrapolation of the straight line σ tn - d -½ to the value d -½ = 0 (see fig. 2.49, b). Here it is already directly assumed that σ i is the yield stress of a single crystal with the same intragranular structure as polycrystals.

Parameter K y characterizes the slope of the straight line σ t - d- ½. According to Cottrell,

K y = σ d(2l) ½,

where σ d stress required to unblock dislocations in a neighboring grain (for example, separation from an impurity atmosphere or from a grain boundary); l is the distance from the grain boundary to the nearest dislocation source.

Thus, K y determines the difficulty of transferring deformation from grain to grain.

The creep effect depends on the test temperature. Its change affects both the height of the yield tooth, and the length of the platform, and, most importantly, the value of the lower (physical) yield stress. As the test temperature rises, the tooth height and yield pad length usually decrease. This effect, in particular, manifests itself in the stretching of bcc metals. The exceptions are alloys and temperature ranges in which heating leads to increased blocking of dislocations or hindering their generation (for example, during aging or ordering).

The lower yield stress drops especially sharply at temperatures when the degree of blocking of dislocations changes significantly. In bcc metals, for example, a sharp temperature dependence of σ tn is observed below 0.2 T pl, which is precisely what determines their tendency to brittle fracture at low temperatures (see Section 2.4). The inevitability of the temperature dependence of σ tn follows from the physical meaning of its components. Indeed, σ i must depend on temperature, since the stresses required to overcome the frictional forces decrease with increasing temperature due to the facilitation of bypassing the barriers by transverse sliding and climbing. The degree of blocking of dislocations, which determines the value K y and, therefore, the term K y d -½ in the formula (2. 15), should also decrease with heating. For example, in bcc metals this is due to the smearing of impurity atmospheres even at low temperatures due to the high diffusion mobility of interstitial impurities.

The conventional yield stress is usually less dependent on temperature, although it also naturally decreases when pure metals and alloys are heated, in which phase transformations do not take place during testing. If such transformations (especially aging) take place, then the nature of the change in the yield point with increasing temperature becomes ambiguous. Depending on changes in the structure, both decline and rise, and a complex dependence on temperature are possible here. For example, an increase in the stretching temperature of a pre-quenched alloy - a supersaturated solid solution first leads to an increase in the yield stress up to some maximum corresponding to the largest amount of dispersed coherent precipitates of the decomposition products of the solid solution proceeding during testing, and with a further increase in temperature σ 0.2 will decrease due to the loss of coherence of particles with the matrix and their coagulation.

Tensile strength. After passing the point s in the stress-strain diagram (see Fig. 2.45), there is severe plastic deformation in the sample, which was previously considered in detail. Up to point “b” the working part of the sample retains its original shape. The elongation is here evenly distributed over the calculated length. At the point “at ” this macro-uniformity of plastic deformation is violated. In some part of the sample, usually near the stress concentrator, which was already in the initial state or formed under tension (most often in the middle of the calculated length), deformation begins to localize. It corresponds to a local narrowing of the cross-section of the sample - the formation of a neck.

The possibility of significant uniform deformation and "pulling back" of the moment of the onset of necking in plastic materials is due to strain hardening. If it were not there, the neck would begin to form immediately upon reaching the yield point. At the stage of uniform deformation, the increase in the flow stress due to strain hardening is fully compensated by the elongation and contraction of the calculated part of the sample. When the increase in stress due to a decrease in the cross-section becomes greater than the increase in stress due to strain hardening, the uniformity of deformation is disturbed and a neck is formed.

The neck develops from a point "in" up to destruction at a point k(see Fig. 2.45), at the same time the force acting on the sample is reduced. At maximum load ( P c, Fig. 2.44, 2.45) on the primary tension diagram, calculate temporary resistance(often called ultimate strength or conditional ultimate strength)

σ in = P b / F 0 .

For materials that collapse with necking, σ in is the conditional stress characterizing the resistance to maximum uniform deformation.

The ultimate strength of such materials does not determine σ in. This is due to two reasons. First, σ is much less than the true stress S in, acting in the sample at the moment of reaching the point "b" . By this time, the relative elongation has already reached 10-30%, the cross-sectional area of the sample F v "F 0. That's why

S v = P v / F v > σ in = P v / F 0.

But the so-called true tensile strength S c also cannot serve as a characteristic of ultimate strength, since beyond the point "c" in the tensile diagram (see Fig. 2.45), the true resistance to deformation continues to grow, although the force decreases. The fact is that this effort on the site in k concentrates on the minimum cross-section of the sample in the neck, and its area decreases faster than the force.

Figure 2.50- Diagram of true tensile stresses

If we rebuild the primary stretch diagram in coordinates S-e or S-Ψ (Fig. 2.50), it turns out that S increases continuously with deformation up to the moment of destruction. The curve in Fig. 2.50. allows for rigorous analysis of strain hardening and tensile strength properties. The true stress diagram (see Figure 2.50) for necked materials has a number of interesting properties. In particular, the continuation of the straight section of the diagram beyond the point “c” to the intersection with the stress axis makes it possible to approximately estimate the value of σ in, and the extrapolation of the straight section to the point c corresponding to Ψ = 1 (100%) gives S c= 2S v.

The diagram in Fig. 2.50 qualitatively differs from the previously considered strain hardening curves, since in the analysis of the latter we discussed only the stage of uniform deformation, at which the uniaxial tension pattern is retained, i.e. previously analyzed diagrams of true stresses corresponding to type II curves.

In fig. 2.50 it is seen that S in and even more so σ in is much less true tear resistance (S k = P k / F k) defined as the ratio of the force at the moment of failure to the maximum cross-sectional area of the sample at the point of rupture F k... It would seem that the value S k is an the best characteristic ultimate strength of the material. But it is also conditional. Payment S k assumes that at the moment of fracture, a uniaxial tension scheme operates in the neck, although, in fact, a volumetric stress state arises there, which cannot be characterized at all by a single normal stress (this is why concentrated deformation is not considered in the theories of strain hardening under uniaxial tension). Actually, S k determines only a certain average longitudinal stress at the moment of failure.

The meaning and significance of temporary resistance, as well as S in and S k change significantly when passing from the considered tension diagram (see Fig. 2.44, III) to the first two (see fig. 2.44, I, II). In the absence of plastic deformation (see Fig. 2.44, I) σ in ≈ S at ≈ S k... In this case, the maximum load before destruction P c determines the so-called actual peel strength or brittle strength of the material. Here σ in is no longer a conditional, but a characteristic that has a certain physical meaning, determined by the nature of the material and the conditions of brittle fracture.

For relatively low-plasticity materials giving the tensile curve shown in Fig. 2.44, II, σ in is the conditional stress at the moment of failure. Here S v = S k and rather strictly characterizes the ultimate strength of the material, since the sample is uniformly deformed under conditions of uniaxial tension up to rupture. The difference in the absolute values of σ in and S depends on the elongation before failure, there is no direct proportional relationship between them.

Thus, depending on the type and even quantitative characteristics of tension diagrams of one type, the physical meaning of σ in, S in and S k can change significantly, and sometimes even fundamentally. All these stresses are often referred to the category of characteristics of ultimate strength or fracture resistance, although in a number of important cases σ in and S c actually determine the resistance to significant plastic deformation, not fracture. Therefore, when comparing σ in, S in and S k of different metals and alloys, one should always take into account the specific meaning of these properties for each material, depending on the type of its tensile diagram.

- is the tensile stress at which, under conditions of short-term loading, irreversible plastic deformation of the reinforcement begins, in MPa, N / mm2. [Terminological dictionary for concrete and reinforced concrete. FSUE "Research Center" Construction "NIIZhB them. A. A ... Encyclopedia of terms, definitions and explanations of building materials

elastic limit- The characteristic of the deformation properties of elastic materials, expressed through the highest stress, at which residual deformations appear, the values of which do not exceed those allowed by the technical specifications [Glossary of ... Technical translator's guide

ELASTIC LIMIT- (Elastic limit) the highest stress value at which the body does not yet receive permanent deformations. In practice, the stress is taken as the elastic limit, at which the residual deformation after removing the load does not exceed a certain ... ... Marine Dictionary

Elastic limit- Elastic limit Elastic limit. The maximum stress that a material can withstand without plastic deformation remaining after full stress relief. The material exceeds the elastic limit when the load is sufficient to cause ... ... Metallurgical Glossary

elastic limit- tamprumo riba statusas T sritis fizika atitikmenys: angl. elastic limit; limit of elasticity vok. Elastizitätsgrenze, f rus. elastic limit, m pranc. élasticité limite, f; limite d'élasticité, f; limite élastique, f ... Fizikos terminų žodynas

elastic limit- conditional stress, corresponding to the appearance after unloading of a slight permanent deformation, usually equal to 0.05%. See also: Physical Yield Strength ... Encyclopedic Dictionary of Metallurgy

ELASTIC LIMIT- mechanical characteristics of materials: stress, at which the residual deformations for the first time reach a certain value, characterized by definition. tolerance established by technical. conditions (for example, 0.001; 0.005; 0.03%), denoted by bu. P. at. limits ... ... Big Encyclopedic Polytechnic Dictionary

ELASTIC LIMIT- characteristic of the deformation properties of elastic materials, expressed through the highest stress, at which residual deformations appear, the values of which do not exceed the limits allowed by the technical conditions (Bulgarian; Български) ... Construction vocabulary

ELASTIC LIMIT- stress at which permanent deformations for the first time reach a certain small value, characterized by a certain tolerance established by the technical conditions (for example, 0.001; 0.003; 0.005; 0.03%) ... Dictionary of Hydrogeology and Engineering Geology

ELASTIC LIMIT- conditional stress, corresponding to the appearance after unloading of a slight permanent deformation, usually equal to 0.05% ... Metallurgical Dictionary

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Optical method of investigation of voltages. , Cocker E. .. The book of Cocker and Fileon ʻOptical method of investigation of stresses` is of very great scientific and practical interest. The authors of this book, prominent specialists in the field of elasticity theory and ...

The formulas derived in § 2.13 are valid only when the stresses in the material caused by the critical force do not exceed the proportionality limit, i.e. when This follows from the fact that the derivation of the formulas is based on the differential equation of an elastic line, which can be used only within the limits of applicability of Hooke's law.

We substitute in the condition okrapts the value of ocr according to the formula (13.13):

From this equation

(14.13)

The right-hand side of expression (14.13) represents the smallest value of the flexibility of the rod, at which the Euler formula is still applicable - this is the so-called limiting flexibility:

Ultimate flexibility depends only on the physical mechanical properties rod material - its modulus of elasticity and proportionality limit.

Condition (14.13) for the applicability of Euler's formulas, taking into account expression (15.13), can be represented in the form

So, Euler's formula for determining the critical force of a compressed bar is applicable provided that its flexibility is greater than the limiting one.

Here are the values for different materials.

For steel and therefore

For wood for cast iron For steel with an increased value, the limiting flexibility is reduced by expression (15.13). In particular, for some grades of alloy steel.

When the flexibility of the rod is less than the limiting one, the critical stress, if it is determined by the Euler formula, is obtained above the proportionality limit cpc. So, for example, with the flexibility of a steel rod (made of steel) according to the formula (13.13)

those. the value is significantly greater than not only the proportionality limit, but also the yield point and ultimate strength (ultimate strength).

The actual critical forces and critical stresses for rods, the flexibility of which is below the limit, are significantly less than the values determined by the Euler formula. For such rods, the critical stresses are determined using empirical formulas.

Professor of the St. Petersburg Institute of Railway Engineers F.S. Yasinsky proposed an empirical formula for critical stresses for rods with flexibility I, less

(17.13)

where a and b are experimentally determined coefficients that depend on the properties of the material. For example, for steel

Formula (17.13) is applicable for rods made of mild steel with flexibility In flexibility, the stress is considered approximately constant and equal to the yield strength.

Metals are characterized by high plasticity, heat and electrical conductivity. They have a characteristic metallic luster.

The properties of metals are possessed by about 80 elements of the D.I. Mendeleev. For metals, as well as for metal alloys, especially structural ones, mechanical properties are of great importance, the main of which are strength, ductility, hardness and impact toughness.

Under the action of an external load, stress and deformation arise in a solid. relative to the original cross-sectional area of the specimen.

Deformation - this is a change in the shape and size of a solid under the action external forces or as a result of physical processes occurring in the body during phase transformations, shrinkage, etc. Deformation can be elastic(disappears after removing the load) and plastic(remains after unloading). With an ever increasing load, elastic deformation, as a rule, transforms into plastic, and then the sample is destroyed.

Depending on the method of applying the load, methods for testing the mechanical properties of metals, alloys and other materials are divided into static, dynamic and alternating ones.

Strength - the ability of metals to resist deformation or destruction of static, dynamic or alternating loads. The strength of metals under static loads is tested in tension, compression, bending and torsion. Tensile testing is mandatory. Strength under dynamic loads is estimated by specific impact strength, and under alternating loads - by fatigue strength.

To determine the strength, elasticity and ductility, metals in the form of round or flat samples are tested for static tension. The tests are carried out on tensile testing machines. As a result of the tests, a tensile diagram is obtained (Fig.3.1) . The abscissa of this diagram is the deformation values, and the ordinate is the stress values applied to the sample.

It can be seen from the graph that no matter how little the applied stress, it causes deformation, and the initial deformations are always elastic and their magnitude is in direct proportion to the stress. On the curve shown in the diagram (Fig. 3.1), elastic deformation is characterized by the line OA and its continuation.

Rice. 3.1. Deformation curve

Above the point A the proportionality between stress and deformation is violated. Stress causes not only elastic, but also residual, plastic deformation. Its value is equal to the horizontal segment from the dashed line to the solid curve.

During elastic deformation under the action of an external force, the distance between atoms in the crystal lattice changes. Removing the load eliminates the cause that caused the change in the interatomic distance, the atoms become on former places and the deformation disappears.

Plastic deformation is a completely different, much more complex process. During plastic deformation, one part of the crystal moves in relation to the other. If the load is removed, then the moved part of the crystal will not return to its old place; the deformation will persist. These shifts are detected by microstructural examination. In addition, plastic deformation is accompanied by crushing of mosaic blocks inside the grains, and at significant degrees of deformation, a noticeable change in the shape of the grains and their location in space is also observed, with voids (pores) appearing between the grains (sometimes inside the grains).

Submitted addiction OAV(see Fig. 3.1) between the externally applied voltage ( σ ) and the relative deformation caused by it ( ε ) characterizes the mechanical properties of metals.

Slope straight OA shows metal hardness, or a characteristic of how a load applied from the outside changes the interatomic distances, which in a first approximation characterizes the forces of interatomic attraction;

Tangent of an angle of inclination of a straight line OA proportional to the modulus of elasticity (E), which is numerically equal to the quotient of dividing the stress by the relative elastic deformation:

Voltage, which is called the proportionality limit ( σ pts), corresponds to the moment of appearance of plastic deformation. The more accurate the strain measurement method, the lower the point lies. A;

In technical measurements, a characteristic called yield point (σ 0.2). This is the stress causing permanent deformation equal to 0.2% of the length or other size of the sample, product;

Maximum voltage ( σ c) corresponds to the maximum stress achieved during stretching, and is called temporary resistance or ultimate strength .

Another material characteristic is the amount of plastic deformation that precedes fracture and is defined as a relative change in length (or cross-section) - the so-called relative extension (δ ) or relative narrowing (ψ ), they characterize the plasticity of the metal. Area under the curve OAV proportional to the work that must be expended to destroy the metal. This indicator, determined different ways(mainly by impact on a notched sample), characterizes viscosity metal.

When the sample is stretched to failure, the dependences between the applied force and the elongation of the sample are graphically recorded (Fig. 3.2), as a result of which the so-called deformation diagrams are obtained.

Rice. 3.2. Force (stress) - elongation diagram

The deformation of the specimen under loading of the alloy is first macroelastic, and then gradually and in different grains under unequal loading transforms into plastic deformation, which occurs by shears according to the dislocation mechanism. The accumulation of dislocations as a result of deformation leads to the hardening of the metal, but at their significant density, especially in certain areas, the centers of destruction appear, leading, ultimately, to the complete destruction of the sample as a whole.

The tensile strength is evaluated by the following characteristics:

1) tensile strength;

2) proportionality limit;

3) yield strength;

4) elastic limit;

5) modulus of elasticity;

6) yield point;

7) relative elongation;

8) relative uniform elongation;

9) relative narrowing after rupture.

Tensile strength (tensile strength or ultimate tensile strength) σ in, Is the voltage corresponding to the highest load P B preceding the destruction of the sample:

σ in = P in / F 0,

This characteristic is mandatory for metals.

Proportional limit (σ pc) Is the conditional voltage R pts, at which a deviation from the proportional relationship between deformation and load begins. It is equal to:

σ pts = P pts / F 0.

The values σ pts is measured in kgf / mm 2 or in MPa .

Yield point (σ t) is the voltage ( R T) at which the sample deforms (flows) without a noticeable increase in the load. Calculated by the formula:

σ t = R T / F 0 .

Elastic limit (σ 0.05) is the stress at which the residual elongation reaches 0.05% of the length of the section of the working part of the sample, equal to the base of the tensometer. Elastic limit σ 0.05 is calculated by the formula:

σ 0,05 = P 0,05 / F 0 .

Elastic modulus (E) – the ratio of the stress increment to the corresponding elongation increment within the elastic deformation. It is equal to:

E = Pl 0 / l cf F 0 ,

where ∆Р- load increment; l 0- the initial calculated length of the sample; l Wed- average increment of elongation; F 0 – initial cross-sectional area.

Yield point (conditional) - stress at which the residual elongation reaches 0.2% of the length of the sample section on its working part, the elongation of which is taken into account when determining the specified characteristic.

Calculated by the formula:

σ 0,2 = P 0,2 / F 0 .

The conditional yield stress is determined only if there is no yield area in the tensile diagram.

Relative extension (after the break) - one of the characteristics of the plasticity of materials, equal to the ratio of the increment in the calculated length of the sample after fracture ( l to) to the initial calculated length ( l 0) in percents:

Relative uniform elongation (δ p)- the ratio of the increment in the length of the sections in the working part of the specimen after rupture to the length before the test, expressed as a percentage.

Relative constriction after rupture (ψ ), as well as the relative elongation - a characteristic of the plasticity of the material. Defined as the ratio of the difference F 0 and minimum ( F to) cross-sectional area of the sample after fracture to the initial cross-sectional area ( F 0), expressed as a percentage:

Elasticity – the property of metals to restore their old form after removal of external forces causing deformation. Elasticity is the opposite of plasticity.

Very often, to determine the strength, they use a simple, non-destructive product (sample), a simplified method - measuring the hardness.

Under hardness material means the resistance to the penetration of a foreign body into it, i.e., in fact, hardness also characterizes the resistance to deformation. There are many methods for determining hardness. The most common is Brinell method (Fig. 3.3, a), when the test body under the action of force R a ball with a diameter is embedded D... Brinell hardness number (HB) is the load ( R) divided by the area spherical surface print (diameter d).

Rice. 3.3. Hardness test:

a - according to Brinell; b - according to Rockwell; c - according to Vickers

When measuring hardness Vickers method (Fig. 3.3, b) the diamond pyramid is pressed in. By measuring the diagonal of the print ( d), judge the hardness (HV) of the material.

When measuring hardness Rockwell method (Fig. 3.3, c) a diamond cone (sometimes a small steel ball) serves as an indenter. The hardness number is the reciprocal of the indentation depth ( h). There are three scales: A, B, C (Table 3.1).

The Brinell and Rockwell B methods are used for soft materials, the Rockwell C method is used for hard materials, and the Rockwell A method and Vickers method are used for thin layers(sheets). The described methods of measuring hardness characterize the average hardness of the alloy. In order to determine the hardness of individual structural components of the alloy, it is necessary to sharply localize the deformation, to press the diamond pyramid into a certain place found on the thin section at a magnification of 100 - 400 times under a very low load (from 1 to 100 gf), followed by measurement under a microscope of the diagonal of the imprint ... The resulting characteristic ( N) is called microhardness , and characterizes the hardness of a certain structural component.

Table 3.1 Test conditions when measuring hardness by the Rockwell method

Test conditions		T designation fidelity
R= 150 kgf
When tested with a diamond taper and load R= 60 kgf
Steel ball indentation and load R= 100 kgf

The HB value is measured in kgf / mm 2 (in this case, the units are often not indicated) or in SI - in MPa (1 kgf / mm 2 = 10 MPa).

Viscosity – the ability of metals to resist shock loads. Viscosity is the opposite of brittleness. Many parts during operation experience not only static loads, but also shock (dynamic) loads. For example, such loads are experienced by the wheels of locomotives and carriages at the joints of the rails.

The main type of dynamic testing is impact loading of notched specimens under bending conditions. Dynamic loading by impact is carried out on pendulum impact devices (Fig. 3.4), as well as by a falling load. In this case, the work spent on deformation and destruction of the sample is determined.

Typically, in these tests, the specific work expended on deformation and destruction of the sample is determined. It is calculated by the formula:

KS =K/ S 0 ,

where KS- specific work; TO- full work of deformation and destruction of the sample, J; S 0 – transverse section sample in the place of the notch, m 2 or cm 2.

Rice. 3.4. Pendulum Impact Tests

The width of all types of specimens is measured prior to testing. The height of samples with a U- and V-notch is measured before testing, and with a T-shaped notch after testing. Accordingly, the specific work of fracture deformation is designated KCU, KCV and KST.

Fragility metals at low temperatures are called coldness . In this case, the impact strength is significantly lower than at room temperature.

Another characteristic of the mechanical properties of materials is fatigue strength. Some parts (shafts, connecting rods, springs, springs, rails, etc.) during operation experience loads that vary in magnitude or simultaneously in magnitude and direction (sign). Under the influence of such alternating (vibration) loads, the metal seems to get tired, its strength decreases and the part collapses. This phenomenon is called tiredness metal, and the resulting fractures - fatigue. For such details, you need to know endurance limit, those. the value of the highest stress that the metal can withstand without destruction for a given number of load changes (cycles) ( N).

Wear resistance - resistance of metals to wear due to friction processes. it important characteristic, for example, for contact materials and, in particular, for a contact wire and current collector elements of a pantograph of electrified vehicles. Wear consists in the separation from the rubbing surface of its individual particles and is determined by a change in the geometric dimensions or mass of the part.

Fatigue strength and wear resistance give the most complete picture of the durability of parts in structures, and toughness characterizes the reliability of these parts.

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