Miscellaneous materials react differently to an external force applied to them, causing a change in their shape and linear dimensions. This change is called plastic deformation. If the body, after the termination of the impact, independently restores its original shape and linear dimensions, such a deformation is called elastic. Elasticity, toughness, strength and hardness are the main mechanical characteristics solid and amorphous bodies and determine the changes that occur with the physical body during deformation under the action of an external force and its limiting case - destruction. The yield strength of a material is the value of stress (or force per unit cross-sectional area) at which plastic deformation begins.
Knowledge of the mechanical properties of a material is extremely important for a designer who uses them in his work. It determines the maximum load on a particular part or structure as a whole, above which plastic deformation will begin, and the structure will lose its strength and shape with a howl and can be destroyed. Destruction or serious deformation of building structures or elements of transport systems can lead to large-scale destruction, material losses and even human casualties.
Yield strength is the maximum load that can be applied to a structure without it deforming and failing. The higher its value, the greater the load the structure can withstand.
In practice, the yield strength of a metal determines the performance of the material itself and products made from it under extreme loads. People have always predicted the maximum loads that the structures they erect or the mechanisms they create can withstand. In the early stages of the development of the industry, this was determined empirically, and only in the 19th century the foundation was laid for the creation of the theory of strength of materials. The issue of reliability was solved by creating a multiple margin of safety, which led to the weight and rise in the cost of structures. Today it is not necessary to create a model of a product of a certain scale or in full size and conduct experiments on failure under load on it - computer programs CAE (calculation engineering) families can accurately calculate strength parameters finished product and predict limit values loads.
The value of the yield strength of the material
With the development of atomic physics in the 20th century, it became possible to calculate the value of a parameter theoretically. This work was first done by Yakov Frenkel in 1924. Based on the strength of interatomic bonds, he determined the amount of stress, which was sufficient for the onset of plastic deformation of bodies of a simple shape, by means of calculations that were difficult for that time. The value of the yield strength of the material will be equal to
τ τ =G/2π. , where G is the shear modulus , which determines the stability of bonds between atoms.
Calculation of the yield strength
The ingenious assumption made by Frenkel in the calculations was that the process of changing the shape of the material was considered as driven by shear stresses. For the beginning of plastic deformation, it was considered sufficient that one half of the body shifted relative to the other to such an extent that it could not return to starting position under the action of elastic forces.
Frenkel suggested that the material tested in a thought experiment has a crystalline or polycrystalline structure, characteristic of most metals, ceramics and many polymers. Such a structure implies the presence of a spatial lattice, in the nodes of which atoms are located in a strictly defined order. The configuration of this lattice is strictly individual for each substance, the interatomic distances and the forces binding these atoms are also individual. Thus, in order to cause plastic shear deformation, it will be necessary to break all interatomic bonds passing through the conditional plane separating the halves of the body.
At a certain stress value equal to the yield strength , bonds between atoms from different halves of the body will break, and a number of atoms will shift relative to each other by one interatomic distance without the possibility of returning to their original position. With continued exposure, such a microshift will continue until all the atoms of one half of the body lose contact with the atoms of the other half.
In the macrocosm, this will cause plastic deformation, change the shape of the body and, if the impact continues, will lead to its destruction. In practice, the line of the beginning of destruction does not pass in the middle of the physical body, but is located at the locations of material inhomogeneities.
Physical yield strength
In the theory of strength for each material, there are several values of this important characteristic. The physical yield strength corresponds to the stress value at which, despite the deformation, the specific load does not change at all or changes insignificantly. In other words, this is the stress value at which the physical body is deformed, “flows”, without increasing the force applied to the sample
A large number of metals and alloys during tensile testing show a yield diagram with no or weakly expressed "yield area". For such materials, one speaks of a conditional yield strength. It is interpreted as the stress at which deformation occurs in the range of 0.2%.
Such materials include alloyed and high-carbon steel alloys, bronze, duralumin and many others. The more ductile the material, the higher the residual deformation index for it. Examples of ductile materials are copper, brass, pure aluminum, and most low carbon steel alloys.
Steel, as the most popular mass-produced structural material, is under the close attention of specialists in calculating the strength of structures and the maximum allowable loads on them.
Steel structures during their operation are subjected to large and complex in shape combined loads of tension, compression, bending and shear. Loads can be dynamic, static and periodic. Despite the most difficult conditions of use, the designer must ensure that the structures and mechanisms designed by him are durable, fail-safe and a high degree of safety for both personnel and the surrounding population.
Therefore, steel is presented increased requirements by mechanical properties. From point of view economic efficiency, the company seeks to reduce the cross-section and other dimensions of its products in order to reduce material consumption and weight and thus increase performance characteristics. In practice, this requirement must be balanced with the safety and reliability requirements set out in standards and specifications.
The yield strength for steel is a key parameter in these calculations, as it characterizes the ability of a structure to withstand stresses without irreversible deformation and failure.
Effect of carbon content on the properties of steels
According to the physicochemical principle of additivity, the change in the physical properties of materials is determined by the percentage of carbon. Increasing its proportion to 1.2% makes it possible to increase the strength, hardness, yield strength and threshold cold capacity of the alloy. A further increase in the proportion of carbon leads to a noticeable decrease in such technical indicators as the ability to weld and limit deformation during stamping work. Low carbon steels exhibit the best weldability.
Nitrogen and oxygen in the alloy
These non-metals from the beginning of the periodic table are harmful impurities and reduce mechanical and physical characteristics steels, such as, for example, toughness threshold, ductility and brittleness. If oxygen is contained in an amount of more than 0.03%, this leads to accelerated aging of the alloy, and nitrogen increases the brittleness of the material. On the other hand, the nitrogen content increases strength by lowering the yield strength.
Manganese and silicon additives
An alloying additive in the form of manganese is used to deoxidize the alloy and compensate for the negative effect of harmful sulfur-containing impurities. Due to its similarity in properties to iron, manganese does not have a significant independent effect on the properties of the alloy. Typical manganese content is about 0.8%.
Silicon has a similar effect, it is added during the deoxidation process in a volume fraction not exceeding 0.4%. Since silicon significantly worsens such a technical indicator as the weldability of steel. For structural steels intended for welding, its proportion should not exceed 0.25%. Silicon does not affect the properties of steel alloys.
Sulfur and phosphorus impurities
Sulfur is an extremely harmful impurity and adversely affects many physical properties and specifications.
The maximum permissible content of this element in the form of brittle sulfites is 0.06%
Sulfur impairs ductility, yield strength, impact strength, wear resistance and corrosion resistance of materials.
Phosphorus has two effects on physical and mechanical properties steels. On the one hand, with an increase in its content, the yield strength increases, but on the other hand, the viscosity and fluidity simultaneously decrease. Usually the phosphorus content is in the range from 0.025 to 0.044%. Phosphorus has a particularly strong negative effect with a simultaneous increase in the volume fractions of carbon.
Alloy additives in the composition of alloys
Alloying additives are called substances that are deliberately introduced into the composition of the alloy to purposefully change its properties to the right indicators. Such alloys are called alloy steels. best performance can be achieved by adding several additives at the same time in certain proportions.
Common additives are nickel, vanadium, chromium, molybdenum and others. With the help of alloying additives, the value of the yield strength, strength, viscosity, corrosion resistance and many other physical, mechanical and chemical parameters and properties are improved.
Metal melt flow
The fluidity of a metal melt is its property to completely fill the mold, penetrating into the smallest cavities and relief details. The accuracy of the casting and the quality of its surface depend on this.
The property can be enhanced by placing the melt under excess pressure. This physical phenomenon used in injection molding machines. This method can significantly increase the productivity of the casting process, improve the surface quality and uniformity of the castings.
Sample test to determine the yield strength
To carry out standard tests, use a cylindrical specimen 20 mm in diameter and 10 mm high, fix it in the test apparatus and subject it to tension. The distance between the marks applied on the side surface of the sample is called the estimated length. During measurements, the dependence of the relative elongation of the sample on the magnitude of the tensile force is recorded.
The dependence is displayed as a conditional stretch diagram. At the first stage of the experiment, the increase in force causes a proportional increase in the length of the sample. Upon reaching the limit of proportionality, the diagram turns from linear to curvilinear, and the linear relationship between force and elongation is lost. In this section of the diagram, the sample, when the force is removed, can still return to its original shape and dimensions.
For most materials, the values of proportionality limit and yield strength are so close that in practical applications the difference between them is not taken into account.
The area of stresses at which only elastic deformation occurs is limited by the limit of proportionality σpc. In this region, only elastic deformations take place in each grain, and for the sample as a whole, Hooke's law is satisfied - the deformation is proportional to the stress (hence the name of the limit).
With an increase in stress, microplastic deformations occur in individual grains. Under such loads, the residual stresses are insignificant (0.001% - 0.01%).
The stress at which residual deformations appear within the specified limits is called the conditional elastic limit. In its designation, the index indicates the amount of residual deformation (in percent), for which the elastic limit was determined, for example, σ 0.01.
The stress at which plastic deformation already takes place in all grains is called the conditional yield strength. Most often, it is determined at a residual strain of 0.2% and is denoted σ 0.2.
Formally, the difference between the limits of elasticity and yield is associated with the accuracy of determining the "boundary" between the elastic and plastic state, which reflects the word "conditional". It is obvious that σ pc<σ 0.01 <σ 0.2 . Однако значения этих пределов определяется разными процессами. Поэтому термообработка или обработка давлением по-разному влияют на их величину. Отметим, что именно предел пропорциональности или упругости определяет степень проявления неупругих свойств и величину предела усталости.
The absence of a sharp boundary between the elastic and plastic states means that both elastic and plastic deformations occur in the stress range between σpc and σ 0.2.
The elastic state exists as long as the dislocations in all grains of the metal are immobile.
The transition to the plastic state is observed in such an interval of loads, in which the movement of dislocations (and, consequently, plastic deformation) occurs only in individual crystal grains, while the mechanism of elastic deformation continues to be realized in the rest.
The plastic state is realized when the movement of dislocations occurs in all grains of the sample.
After the rearrangement of the dislocation structure (completion of plastic deformation), the metal returns to the elastic state, but with changed elastic properties.
The above designations of the limits correspond to uniaxial tension, the diagram of which is shown in fig. 7.6. Limits similar in meaning are determined for compression, bending and torsion.
The considered diagram is typical for metals, in which the transition from the elastic state to the plastic one is very smooth. However, there are metals with a pronounced transition to the plastic state. The tensile diagrams of such metals have a horizontal section, and they are characterized not by a conditional, but by a physical yield strength.
The most important parameters of the elastic state are the elastic limit σ y and the elastic moduli.
The elastic limit determines the maximum allowable operational loads at which the metal experiences only elastic or small allowable elastic-plastic deformations. Very roughly (and in the direction of overestimation), the elastic limit can be estimated from the yield strength.
Elastic moduli characterize the resistance of a material to the action of a load in an elastic state. Young's modulus E determines the resistance to normal stresses (tensile, compression and bending), and the shear modulus G - to shear stresses (torsion). The greater the moduli of elasticity, the steeper the elastic section on the deformation diagram, the smaller the magnitude of elastic deformations at equal stresses and, consequently, the greater the rigidity of the structure. Elastic deformations cannot be greater than the value of σ y /E.
Thus, the elastic moduli determine the maximum allowable operational deformations (taking into account the magnitude of the elastic limit and the rigidity of the products. The elastic moduli are measured in the same units as the stress (MPa or kgf / mm 2).
Structural materials must combine high values of yield strength (withstand high loads) and elastic moduli (provide greater rigidity). The modulus of elasticity E has the same value in compression and tension. However, the compressive and tensile elastic limits may differ. Therefore, with the same stiffness, the ranges of elasticity in compression and tension can be different.
In the elastic state, the metal does not experience macroplastic deformations, however, local microplastic deformations can occur in its individual microscopic volumes. They are the cause of the so-called inelastic phenomena, which significantly affect the behavior of metals in an elastic state. Under static loads, hysteresis, elastic aftereffect and relaxation appear, and under dynamic loads, internal friction.
Relaxation– spontaneous reduction of stresses in the product. An example of its manifestation is the weakening of tension connections over time. The lower the relaxation, the more stable the acting stresses. In addition, relaxation leads to the appearance of permanent deformation after the load is removed. Susceptibility to these phenomena is characterized by relaxation resistance. It is estimated as the relative change in voltage over time. The larger it is, the less the metal is subject to relaxation.
Internal friction determines the irreversible energy loss under variable loads. Energy losses are characterized by damping factor or coefficient of internal friction. Metals with a large damping factor effectively dampen sound and vibrations, are less susceptible to resonance (one of the best damping metals is gray cast iron). Metals with a low coefficient of internal friction, on the contrary, have a minimal effect on the propagation of vibrations (for example, bell bronze). Depending on the purpose, the metal must have high internal friction (shock absorbers) or, conversely, low internal friction (measuring instrument springs).
As the temperature rises, the elastic properties of metals deteriorate. This manifests itself in a narrowing of the elastic region (due to a decrease in the elastic limits), an increase in inelastic phenomena, and a decrease in the elastic moduli.
Metals that are used for the manufacture of elastic elements, products with stable dimensions must have minimal manifestations of inelastic properties. This requirement is better met when the elastic limit is much higher than the working stress. In addition, the ratio of elastic and yield strengths is important. The greater the ratio σ у / σ 0.2, the less the manifestation of inelastic properties. When a metal is said to have good elastic properties, it usually means not only a high elastic limit, but also a large value of σ y / σ 0.2.
TENSILE STRENGTH. At stresses exceeding the yield strength σ 0.2, the metal passes into a plastic state. Outwardly, this is manifested in a decrease in resistance to the acting load and a visible change in shape and size. After removing the load, the metal returns to the elastic state, but remains deformed by the amount of residual deformations, which can far exceed the limiting elastic deformations. A change in the dislocation structure in the process of plastic deformation increases the yield strength of the metal - its strain hardening occurs.
Usually, plastic deformation is studied in uniaxial tension of the specimen. In this case, the temporary resistance σ in, the relative elongation after the break δ and the relative narrowing after the break ψ are determined. The tensile pattern at stresses exceeding the yield strength is reduced to two options, shown in Figure 7.6.
In the first case, uniform stretching of the entire sample is observed - uniform plastic deformation occurs, which ends with sample rupture at stress σv. In this case, σ is the conditional tensile strength, and δ and ψ determine the maximum uniform plastic deformation.
In the second case, the sample is first stretched uniformly, and after reaching the stress σ in a local narrowing (neck) is formed and further stretching, up to a break, is concentrated in the neck area. In this case, δ and ψ are the sum of uniform and concentrated deformations. Since the “moment” of determining the tensile strength no longer coincides with the “moment” of sample rupture, then σ in determines not the ultimate strength, but the conditional stress at which uniform deformation ends. However, the value of σ in is often called the conditional tensile strength, regardless of the presence or absence of a neck.
In any case, the difference (σ in - σ 0.2) determines the range of conditional stresses in which uniform plastic deformation occurs, and the ratio σ 0.2 / σ V characterizes the degree of hardening. In the annealed metal σ 0.2 / σ B = 0.5 - 0.6, and after strain hardening (hardening) it increases to 0.9 - 0.95.
The word "conditional" in relation to σ in means that it is less than the "true" stress S In acting in the sample. The fact is that the stress σ is defined as the ratio of the tensile force to the area of the initial cross section of the sample (which is convenient), while the true stress S must be determined in relation to the cross section area at the moment of measurement (which is more difficult). In the process of plastic deformation, the sample becomes thinner and, as it stretches, the difference between the conditional and true stress increases (especially after the formation of a neck). If you build a stretch diagram for true stresses, then the stretch curve will pass over the curve drawn in the figure and will not have a falling section.
Metals can have the same value of σ in, but if they have different tensile diagrams, the destruction of the sample will occur at different true stresses S B (their true strength will be different).
The tensile strength σ in is determined under a load acting for tens of seconds, therefore it is often called the short-term strength limit.
Plastic deformation is also studied under compression, bending, torsion, the deformation diagrams are similar to those shown in the figure. But for many reasons, uniaxial tension is generally preferred. The least laborious is the determination of the parameters of uniaxial tension σ in and δ, they are always determined during mass factory tests, and their values are necessarily given in all reference books.
Fig.7.7. Bar uniaxial tension diagram
A description of the methodology for testing metals in tension (and the definition of all terms) is given in GOST 1497-73. The compression test is described in GOST 25.503-97, and for torsion - in GOST 3565-80.
PLASTICITY AND VISCOSITY. Plasticity is the ability of a metal to change shape without violating its integrity (without cracks, tears, and even more destruction). It manifests itself when elastic deformation is replaced by plastic, i.e. at stresses greater than the yield strength σ in.
The possibilities of plastic deformation are characterized by the ratio σ 0.2 / σ c. At σ 0.2 / σ в \u003d 0.5 - 0.6, the metal allows large plastic deformations (δ and ψ are tens of percent). On the contrary, at σ 0.2 / σ в = 0.95 - 0.98, the metal behaves as brittle: the plastic deformation region is practically absent (δ and ψ are 1-3%).
Most often, plastic properties are evaluated by the relative elongation at break δ. But this value is determined under static uniaxial tension and therefore does not characterize plasticity under other types of deformations (bending, compression, torsion), high strain rates (forging, rolling) and high temperatures.
An example is brass L63 and LS59-1, which have practically the same values of δ, but significantly different plastic properties. The incised rod from L63 bends at the cut point, and from LS59-1 it breaks off with little effort. Wire from L63 is easily flattened without cracking, and from LS59-1 it cracks after several blows. Brass LS59-1 can be easily hot rolled, and L63 is rolled only in a narrow temperature range, beyond which the billet cracks.
Thus, plasticity depends on temperature, speed and method of deformation. Plastic properties are strongly affected by many impurities, often even at very low concentrations.
In practice, to determine the plasticity, technological samples are used, in which such deformation methods are used that are more consistent with the relevant technological processes.
A common assessment of plasticity is the angle of bending, the number of kinks or twists that a semi-finished product can withstand without cracking or tearing.
The test for extrusion of the hole from the tape (an analogy with stamping and deep drawing) is carried out until tears and cracks appear.
Good plastic properties are important in metal forming processes. During normal operation, the metal is in an elastic state and its plastic properties do not appear. Therefore, it makes no sense at first glance to focus on plasticity indicators during normal operation of products.
But if there is a possibility of occurrence of loads exceeding the yield strength, then it is desirable that the material be ductile. A brittle metal breaks down immediately after exceeding a certain limit, and a ductile material is able to absorb enough excess energy without breaking down.
The concepts of viscosity and plasticity are often equated, but these terms characterize different properties:
Plastic- determines the ability to deform without destruction, it is evaluated in linear, relative or conventional units.
Viscosity- determines the amount of energy absorbed during plastic deformation, it is measured using units of energy.
The amount of energy required to break the material is equal to the area under the strain curve in the true stress-true strain diagram. This means that it depends both on the maximum possible deformation and on the strength of the metal. The method for determining the energy intensity during plastic deformation is described in GOST 23.218-84.
HARDNESS. A generalized characteristic of elastic-plastic properties is hardness.
Hardness- this is the property of the surface layer of the material to resist the introduction of another, more solid body, when it is concentrated on the surface of the material. The "other, harder body" is an indenter (steel ball, diamond pyramid, or cone) pressed into the metal being tested.
The stresses caused by the indenter are determined by its shape and the indentation force. Depending on the magnitude of these stresses, elastic, elastic-plastic or plastic deformations occur in the surface layer of the metal. In the first case, the removal of the load leaves no trace on the surface. If the stress exceeds the elastic limit of the metal, then after removing the load, an imprint remains on the surface.
The smaller the indentation, the higher the indentation resistance and the higher the hardness is considered. By the magnitude of the concentrated effort, which has not yet left an imprint, it is possible to determine the hardness at the yield point.
Numerical determination of hardness is carried out according to the methods of Vickers, Brinell and Rockwell.
In the Rockwell method, hardness is measured in HR units, which reflect the degree of elastic recovery of the indentation after the removal of the load. Those. the Rockwell hardness number determines the resistance to elastic or small plastic deformations. Depending on the type of metal and its hardness, different scales are used. The most commonly used scale is C and the hardness number HRC.
In terms of HRC, requirements for the surface quality of steel parts after heat treatment are often formulated. The HRC hardness best reflects the level of performance of high-strength steels, and given the ease of Rockwell measurement, it is very widely used in practice. Details about the Rockwell method with a description of the different scales and hardness of different classes of materials.
Vickers and Brinell hardness is defined as the ratio of the indentation force to the contact area of the indenter and the metal at the maximum penetration of the indenter. Those. the hardness numbers HV and HB have the meaning of the average stress on the surface of an unrecovered imprint, are measured in units of stress (MPa or kgf / mm 2) and determine the resistance to plastic deformation. The main difference between these methods is related to the shape of the indenter.
The use of a diamond pyramid in the Vickers method (GOST 2999-75, GOST R ISO 6507-1) provides a geometric similarity of pyramidal prints under any load - the ratio of the depth and size of the print at maximum indentation does not depend on the applied force. This makes it possible to fairly strictly compare the hardness of different metals, including the results obtained under different loads.
Ball indenters in the Brinell method (GOST 9012-59) do not provide a geometric similarity of spherical indentations. This leads to the need to choose the load value depending on the diameter of the ball indenter and the type of material being tested according to the tables of recommended test parameters. The consequence of this is ambiguity when comparing hardness numbers HB for different materials.
The dependence of the determined hardness on the magnitude of the applied load (small for the Vickers method and very strong for the Brinell method) requires that the test conditions be specified when recording the hardness number, although this rule is often not respected.
The area of influence of the indenter on the metal is comparable to the size of the imprint, i.e. hardness characterizes the local properties of a semi-finished product or product. If the surface layer (clad or hardened) differs in properties from the base metal, then the measured hardness values will depend on the ratio of the indentation depth and the layer thickness - i.e. will depend on the measurement method and conditions. The result of the hardness measurement can refer either only to the surface layer or to the base metal, taking into account its surface layer.
When measuring hardness, the resulting resistance to the penetration of the indenter into the metal is determined without taking into account individual structural components. Averaging occurs if the imprint size exceeds the size of all inhomogeneities. The hardness of individual phase components (microhardness) is determined by the Vickers method at low indentation forces.
There is no direct relationship between different hardness scales, and there are no reasonable methods for transferring hardness numbers from one scale to another. The available tables, formally linking the various scales, are built on the basis of comparative measurements and are valid only for specific categories of metals. In such tables, hardness numbers are usually compared with HV hardness numbers. This is due to the fact that the Vickers method allows you to determine the hardness of any materials (in other methods, the range of measured hardness is limited) and provides a geometric similarity of prints.
Also, there is no direct relationship between hardness and yield strength or strength, although in practice the ratio σ in \u003d k HB is often used. The values of the coefficient k are determined on the basis of comparative tests for specific classes of metals and vary from 0.15 to 0.5 depending on the type of metal and its condition (annealed, hard-worked, etc.).
Changes in elastic and plastic properties with temperature changes, after heat treatment, work hardening, etc. appear as a change in hardness. Hardness is measured faster, easier, allows non-destructive testing. Therefore, it is convenient to control the change in the characteristics of the metal after various types of processing precisely by changing the hardness. For example, hardening, increasing σ 0.2 and σ 0.2 / σ in, increases hardness, and annealing reduces it.
In most cases, hardness is determined at room temperature with an indenter exposure of less than a minute. The hardness determined in this case is called short-term hardness. At high temperatures, when the phenomenon of creep develops (see below), long-term hardness is determined - the reaction of the metal to prolonged exposure to the indenter (usually within an hour). Long-term hardness is always less than short-term hardness, and this difference increases with increasing temperature. For example, in copper, short-term and long-term hardness at 400 o C is 35HV and 25HV, and at 700 o C - 9HV and 5HV, respectively.
The considered methods are static: the indenter is introduced slowly, and the maximum load acts long enough to complete the plastic deformation processes (10–180 s). In dynamic (impact) methods, the impact of the indenter on the metal is short-term, and therefore the deformation processes proceed differently. Various variations of dynamic methods are used in portable hardness testers.
When colliding with the material under study, the energy of the indenter (striker) is spent on elastic and plastic deformation. The less energy spent on plastic deformation of the sample, the higher should be its "dynamic" hardness, which determines the resistance of the material to elastic-plastic deformation upon impact. Primary data are converted into numbers of "static" hardness (HR, HV, HB), which are displayed on the device. Such recalculation is possible only on the basis of comparative measurements for specific groups of materials.
There are also hardness ratings for abrasion or cutting resistance that better reflect the respective processing properties of the materials.
From what has been said, it follows that hardness is not a primary property of a material; rather, it is a generalized characteristic that reflects its elastic-plastic properties. In this case, the choice of method and measurement conditions can mainly characterize either its elastic or, conversely, plastic properties.
2. Elastic limit
3. Yield strength
4. Tensile strength or tensile strength
5. Tension at break
Drawing. 2.3 - View of a cylindrical sample after fracture (a) and a change in the zone of the sample near the rupture site (b)
In order for the diagram to reflect only the properties of the material (regardless of the size of the sample), it is rebuilt in relative coordinates (stress-strain).
Arbitrary ordinates i-th the points of such a diagram (Fig. 2.4) are obtained by dividing the values of the tensile force (Fig. 2.2) by the initial cross-sectional area of \u200b\u200bthe sample (), and the abscissas are obtained by dividing the absolute elongation of the working part of the sample by its initial length (). In particular, for the characteristic points of the diagram, the ordinates are calculated using formulas (2.3) ... (2.7).
The resulting diagram is called conditional stress diagram (Fig. 2.4).
The convention of the diagram lies in the method of determining the stress not by the current cross-sectional area, which changes during the test, but by the original one -. The stress diagram retains all the features of the original tensile diagram. The characteristic stresses of the diagram are called ultimate stresses and reflect the strength properties of the material under test. (formulas 2.3…2.7). Note that the yield strength of the metal taught in this case corresponds to the new physical state of the metal and is therefore called the physical yield strength
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Drawing. 2.4 - Stress diagram
From the stress diagram (Fig. 2.4) it can be seen that
i.e. tensile modulus E numerically equal to the tangent of the angle of inclination of the initial straight section of the stress diagram to the abscissa axis. This is the geometric meaning of the modulus of elasticity in tension.
If we relate the forces acting on the sample at each moment of loading to the true value of the cross section at the corresponding moment of time, then we get a diagram of true stresses, often denoted by the letter S(Fig. 2.5, solid line). Since the diameter of the sample decreases insignificantly in the section of the diagram 0-1-2-3-4 (the neck has not yet formed), the true diagram, within this section, practically coincides with the conditional diagram (dashed curve), passing somewhat higher.
Drawing. 2.5 - Diagram of true stresses
The construction of the remaining section of the true stress diagram (section 4-5 in Fig. 2.5) makes it necessary to measure the diameter of the sample during the tensile test, which is not always possible. There is an approximate method for constructing this section of the diagram, based on determining the coordinates of the point 5 () of the true diagram (Fig. 2.5), corresponding to the moment of sample rupture. First, the true breaking stress is determined
where is the force on the sample at the moment of its rupture;
is the cross-sectional area in the sample neck at the moment of rupture.
The second coordinate of the point - relative deformation includes two components - true plastic - and elastic - . The value can be determined from the condition of equality of the volumes of the material near the point of rupture of the sample before and after the test (Fig. 2.3). So, before testing, the volume of material of a sample of unit length will be equal to , and after rupture, . Here, is the elongation of a sample of unit length near the rupture site. Since the true deformation is here, and 
, That . The elastic component is found according to Hooke's law: . Then the abscissa of point 5 will be equal to . Drawing a smooth curve between points 4 and 5, we get the full view of the true diagram.
For materials whose tension diagram in the initial section does not have a pronounced yield point (see Fig. 2.6), the yield strength is conditionally defined as the stress at which the residual deformation is the value established by GOST or technical conditions. According to GOST 1497–84, this value of permanent deformation is 0.2% of the measured sample length, and conditional yield strength denoted by the symbol - .
When testing samples for tension, in addition to strength characteristics, plasticity characteristics are also determined, which include relative extension sample after rupture, defined as the ratio of the increment in the length of the sample after rupture to its original length:
And relative narrowing , calculated by the formula
% (2.10)
In these formulas - the initial estimated length and cross-sectional area of the sample, - respectively, the length of the calculated part and the minimum cross-sectional area of the sample after rupture.
Instead of relative deformation, in some cases the so-called logarithmic deformation is used. Since the sample length changes as the sample is stretched, the length increment dl refer not to , but to the current value . If we integrate the extension increments when changing the length from to , then we get the logarithmic or true deformation of the metal
Then – strain at break (i.e. . = k) will
.
It should also be taken into account that the plastic deformation in the sample proceeds unevenly along its length.
Depending on the nature of the metal, they are conditionally divided into very ductile (annealed copper, lead), ductile (low-carbon steels), brittle (gray cast iron), and very brittle (white cast iron, ceramics).
Load application rate V deform affects the appearance of the diagram and the characteristics of the material. σ T And σ V increases with increasing load speed. Deformations corresponding to the tensile strength and fracture point are reduced.
Ordinary machines provide deformation speed
10 -2 …10 -5 1/sec.
With decreasing temperature T Spanish for pearlitic steels increases σ T and decreases.
austenitic steels, Al And Ti alloys are less responsive to lowering T.
As the temperature increases, the deformations change with time at constant stresses, i.e. creep occurs, and than > σ , topics< .
There are usually three stages of creep. For mechanical engineering, stage II is of greatest interest, where έ = const (steady stage of creep).
To compare the creep resistance of various metals, a conditional characteristic is introduced - the creep limit.
creep limit σ pl called the stress at which the plastic deformation for a given period of time reaches the value established by the technical conditions.
Along with the concept of “creep”, the concept of “stress relaxation” is also known.
The process of stress relaxation proceeds at constant deformations.
A specimen under constant load at high T can fail either with the formation of a neck (ductile intercrystalline fracture) or without it (brittle transcrystalline fracture). The first is characteristic of lower T and high σ .
Material strength at high T evaluated by the limit of long-term strength.
Tensile strength(σdp) is the ratio of the load at which the tensile sample collapses after a certain period of time, to the initial cross-sectional area.
When designing welded products operating at elevated T, are guided by the following quantities when assigning [ σ ]:
a) at T 260 o C for ultimate strength σ V ;
b) when T 420 ° C for carbon steels T < 470 о С для стали 12Х1МФ, T< 550 о С для 1Х18Н10Т – на σ T ;
c) at higher T to the limit of long-term strength σ dp .
In addition to the above test methods under static loads, bending, torsion, shear, compression, crushing, stability, and hardness tests are also performed.
Tensile properties, as in other static tests, can be divided into three main groups: strength, plasticity and viscosity characteristics. Strength properties - these are the characteristics of the resistance of the material of the sample to deformation or destruction. Most standard strength characteristics are calculated from the position of certain points on the tension diagram, in the form of conditional tensile stresses. Section 2.3 analyzed diagrams in the coordinates true stress - true strain , which most accurately characterize strain hardening. In practice, the mechanical properties are usually determined from the primary tension 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 a first approximation to three types (Fig. 2.44).
Figure 2.44- Types of Primary Stretch Curves
Type I tensile diagram is typical for specimens that fail without noticeable plastic deformation. A type II diagram is obtained by stretching specimens that are uniformly deformed up to failure. Finally, the type III diagram is typical for specimens that fail after necking as a result of focused deformations. Such a diagram can also be obtained in the case of stretching of samples that fail without the formation of a neck (at high-temperature stretching); plot bk here it can be strongly stretched and almost parallel to the deformation axis. The increase in load until the moment of destruction (see Fig. 2.44, II) or up to the maximum (see Fig. 2.44, III) can be either smooth (solid lines) or broken. In the latter case, in particular, a tooth and a yield plateau 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. On fig. 2.44 (type III diagram) characteristic points are plotted, along the ordinates of which 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 can be plotted.
The limit of proportionality. The first characteristic point on the stretch diagram is the point p(See Figure 2.45). The force P nu determines the value proportional limit - the stress that the sample material can withstand without deviating from Hooke's law.
Approximately, the value of P nu can be determined by the point where the divergence of the stretching curve and the continuation of the straight section begins (Fig. 2.46).
Figure 2.46- Graphical ways to determine the limit of proportionality.
In order to unify the methodology and improve the accuracy of calculating the proportionality limit, it is estimated as a 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 decreasing the tangent of the slope angle formed by the tangent to the tension curve at the point p with the strain axis, compared with the tangent in the initial elastic section. The standard tolerance is 50%, 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 proportionality limit can be determined graphically directly on this diagram (see Fig. 2.46). First of all, continue the straight section until it intersects with the axis of deformation at the point 0, which is taken as the new origin of coordinates, thus excluding the initial section of the diagram distorted due to insufficient rigidity of the machine. Then you can use two methods. According to the first of them, at an arbitrary height within the elastic region, a perpendicular is restored AB to the load axis (see Fig. 2.46, A), lay a segment along it BC=½ AB and draw a line OS. In this case, tg α′= tg α/1.5. If we now draw a tangent to the stretch curve in parallel OS, then the point of contact R determine the desired load P nu .
In the second method, a perpendicular is lowered from an arbitrary point of the rectilinear section of the diagram KU(see fig. 2.46, b) on the x-axis and divide it into three equal parts. Through the dot C and the origin of coordinates draw a straight line, and parallel to it - a tangent to the stretching curve. touch point p corresponds to the effort P nu (tan α′= tan α/1.5).
You can more accurately determine the proportionality limit using strain gauges - special devices for measuring small deformations.
Elastic limit. The next characteristic point on the primary stretch diagram (see Fig. 2.45) is the point e. It corresponds to the load, according to which the conditional is calculated 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 tension diagram. Therefore, in cases where high accuracy is not required, the elastic limit is taken equal to the proportional limit. If an accurate quantitative assessment of σ 0.05 is required, then strain gauges are used. The procedure for determining σ 0.05 is largely similar to that described for σ nu , but there is one fundamental difference. Since, when determining the elastic limit, the tolerance is specified by the value of residual deformation, after each loading stage, 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 with a strain gauge.
If the scale of recording the tension diagram along the elongation axis is 50:1 or more, and along the load axis ≤10 MPa per 1 mm, a graphical determination of σ 0.05 is allowed. To do this, a segment is laid along the axis of elongation from the origin of coordinates OK= 0,05 l 0 /100 and through a dot TO draw a straight line parallel to the rectilinear section of the diagram (Fig. 2.47). Point ordinate e will correspond to the load R 0.05, which determines the conditional elastic limit σ 0.05 = P 0.05 / F 0 .
Yield limit. In the absence of a tooth stretching diagram and a yield platform, calculate conditional yield strength - the stress at which the residual elongation reaches a given value, usually 0.2%. Accordingly, the conditional yield strength is denoted σ 0.2. As you can see, this characteristic differs from the conditional elastic limit only by the tolerance value. 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 the calculation of the nominal yield strength is relatively large, it is often determined graphically from the tension diagram, if the latter is recorded on a sufficiently large scale (at least 10:1 along the strain axis). This is done in the same way as when calculating the elastic limit (see Fig. 2.47), only the segment OK = 0,2l 0 /100.
The conditional limits of proportionality, elasticity and yield characterize the resistance of the material to small deformations. Their value slightly differs from the true stresses corresponding to the corresponding strain tolerances. The technical significance of these limits is to assess the stress levels under which
one or another part can work without being subjected to permanent deformation (proportionality limit) or deformed by some small allowable value determined by operating conditions (σ 0.01, σ 0.05, σ 0.2, etc.). Considering that in modern technology the possibility of a residual change in the dimensions of parts and structures is more and more strictly limited, the urgent need for accurate knowledge of the limits of proportionality, elasticity and fluidity, which are widely used in design calculations, becomes clear.
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 tension and macroplastic deformation is not 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 most of the grains are covered by deformation.
The initial stages of sample macroelongation correspond to the elastic limit. For a favorably oriented single crystal, it should be close to the critical shear stress. Naturally, for different crystallographic orientations of a 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 strength of a polycrystal is in principle similar to the nature of the elastic limit. But it is the yield strength that is the most common and important characteristic of the resistance of metals and alloys of small plastic deformation. Therefore, the physical meaning of the yield strength and its dependence on various factors must be analyzed in more detail.
A smooth transition from elastic to plastic deformation (without a tooth and a yield plateau) is observed during tension of such metals and alloys, in which there is a sufficiently large number of mobile, loose dislocations in the initial state (before testing). The stress required for the onset of plastic deformation of polycrystals of these materials, estimated through the conditional yield strength, is determined by the forces of resistance to the movement of dislocations inside the grains, the ease of transfer of deformation through their boundaries, and the size of the grains.
These factors also determine the value physical yield strengthσ t - stress at which the sample is deformed under the action of an almost constant tensile load P t (see Fig. 2.45, yield point on the dotted curve). The physical yield point is often referred to as the lower yield point, in contrast to the upper yield point, calculated from the load corresponding to the top of the yield tooth. And(see Fig. 2.45): σ t.v = P t.v / F0.
The formation of a tooth and a yield platform (the so-called sharp yield phenomenon) externally looks as follows. Elastic tension leads to a smooth rise in the resistance to deformation up to σ t.v, then a relatively sharp drop in stresses to σ t. During the elongation corresponding to this area, the sample on the working length is covered with characteristic Chernov-Luders bands, in which deformation is localized. Therefore, the value 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 is therefore 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 different lattices and microstructures. Most often, a sharp fluidity is recorded when testing metals with a bcc lattice and alloys based on them. Naturally, the practical significance of abrupt fluidity for these metals is especially great, and most of the theories have also been developed in relation to the features of these metals. The use of dislocation concepts to explain abrupt fluidity was one of the first and very fruitful applications of dislocation theory.
Initially, the formation of a tooth and a yield plateau in bcc metals was associated with the effective blocking of dislocations by impurities. It is known that interstitial impurity atoms in a bcc lattice form fields of elastic stresses that do not have spherical symmetry and interact with dislocations of all types, including purely screw dislocations. Even 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 correctness of Cottrell's theory is confirmed by the results of the following simple experiments. If an iron sample is deformed, for example, to a point A(Fig. 2.48), unload it and immediately stretch it again, then the tooth and the yield point 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. to give time for the condensation of impurities on the dislocations, then with a new tension, a tooth and a yield plateau will again appear in the diagram.
Thus, Cottrell's theory links abrupt fluidity to deformation aging - pinning of dislocations by impurities.
Cottrell's suggestion that after unblocking, plastic deformation, at least initially, is carried out by the slip of 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 strongly fixed that their unblocking does not occur, and plastic deformation at the yield point occurs due to the movement of newly formed dislocations. In addition, the formation of a tooth and a yield plateau is observed in dislocation-free crystals - "whiskers". Consequently, Cottrell's theory describes only a particular, albeit important, case of abrupt fluidity.
The basis of the modern theory of the namesake yield, which cannot yet be considered finally established, is the same position put forward by Cottrell: the tooth and the yield plateau are due to a sharp increase in the number of mobile dislocations at the beginning of plastic flow. This means that two conditions must be met for their appearance: 1) the number of free dislocations in the initial sample must be very small, and 2) it must be able to increase rapidly by one mechanism or another at the very beginning of plastic deformation.
The lack of mobile dislocations in the original sample can be associated either with the high perfection of its substructure (for example, in whiskers) or with the pinning of most of the existing dislocations. According to Cottrell, such pinning can be achieved by the formation of impurity atmospheres. Other ways of fixing are also possible, for example, by particles of the second phase.
The number of mobile dislocations can sharply increase:
1) Due to the unblocking of previously pinned dislocations (separation from impurity atmospheres, bypassing particles by cross slip, etc.);
2) By the formation of new dislocations;
3) By their reproduction as a result of interaction.
In polycrystals, the yield strength strongly depends on the grain size. Grain boundaries serve as effective barriers to moving dislocations. The finer the grain, the more often these barriers occur in the path of gliding dislocations, and high stresses are required to continue plastic deformation even at its initial stages. As a result, as the grain is refined, the yield strength increases. Numerous experiments have shown that the lower yield strength
σ t.n. = 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 in case of polygonized structure).
Formula 2.15, called the Petch-Hall equation after its first authors, is universal and well describes the effect of grain size not only on σ so, but also on the conditional yield strength 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 dislocations inside the grain, and the term K y d -½- as the stress required to drive dislocation sources in neighboring grains.
The value of σ i depends on the Peierls-Nabarro force and obstacles to dislocation slip (other dislocations, foreign atoms, particles of the second phase, etc.). Thus, σ i - "friction stress" - compensates for the forces that dislocations have to overcome when moving inside the grain. To experimentally determine 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 plateau with the straight section of this curve (Fig. 2.49, A). This method of estimating σ i is based on the notion that the plot ius tension diagrams are the result of the polycrystalline nature of the stretched sample; 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 according to the tension diagram (a) and the dependence of the lower yield strength on the grain size (b).
The second way to determine σ i - extrapolation of the straight line σ so-called - d-½ up to value d-½ = 0 (see Fig. 2.49, b). Here it is directly assumed that σ i is the yield strength 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 the stress required to unblock dislocations in an adjacent grain (for example, detachment 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 abrupt flow 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 strength. As the test temperature increases, the tooth height and yield plateau length generally decrease. Such an effect, in particular, manifests itself during tension of bcc metals. The exceptions are alloys and temperature ranges in which heating increases the blocking of dislocations or hinders their generation (for example, during aging or ordering).
The lower yield strength is especially sharply reduced at such temperatures, when the degree of blocking of dislocations changes significantly. In bcc metals, for example, a sharp temperature dependence of σt.n. is observed below 0.2 T pl, which just causes their tendency to brittle fracture at low temperatures (see Section 2.4). The inevitability of the temperature dependence of σ t 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 ease of bypassing the barriers by cross-sliding and creeping. The degree of blocking of dislocations, which determines the value K y and hence the term K y d -½ in formula (2. 15), should also decrease when heated. For example, in bcc metals, this is due to the smearing of impurity atmospheres already at low temperatures due to the high diffusion mobility of interstitial impurities.
The conditional yield strength is usually less dependent on temperature, although it naturally decreases when pure metals and alloys are heated, in which phase transformations do not occur during testing. If such transformations (especially aging) take place, then the nature of the change in the yield strength with increasing temperature becomes ambiguous. Depending on changes in the structure, both a decline and an increase, and a complex dependence on temperature, are possible here. For example, an increase in the tensile temperature of a pre-hardened alloy - a supersaturated solid solution, first leads to an increase in the yield strength up to some maximum corresponding to the largest amount of dispersed coherent precipitates of the decomposition products of the solid solution that occurs during testing, and with a further increase in temperature σ 0.2 will decrease due to the loss of coherence of the particles with the matrix and their coagulation.
Tensile strength. After passing the point s in the tensile diagram (see Fig. 2.45), there is severe plastic deformation in the sample, which was previously considered in detail. Up to the “c” point, the working part of the sample retains its original shape. The elongation here is evenly distributed along the effective length. At the point "in ” this macrouniformity 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 during tension (most often in the middle of the calculated length), the localization of deformation begins. It corresponds to the local narrowing of the cross section of the sample - the formation of the neck.
The possibility of significant uniform deformation and "delay" of the moment of the beginning of neck formation in plastic materials are due to strain hardening. If it were not there, then 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 narrowing of the calculated part of the sample. When the increase in stress due to the decrease in the cross section becomes greater than the increase in stress due to work hardening, the uniformity of deformation is disturbed and a neck is formed.
The neck develops from the point "in" up to the destruction at the point k(see Fig. 2.45), at the same time, the force acting on the sample is reduced. According to the maximum load ( P c, fig. 2.44, 2.45) on the primary stretching diagram calculate temporary resistance(often called tensile strength or conditional tensile strength)
σ in = Pb /F0 .
For materials that fail with the formation of a neck, σ in is a conditional stress characterizing the resistance to maximum uniform deformation.
The ultimate strength of such materials σ in does not determine. 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 “in” . By this moment, the relative elongation reaches 10-30%, the cross-sectional area of the sample F V “F0. That's why
S V = P V /F V > σ in = P V / F0 .
But the so-called true tensile strength S c also cannot serve as a characteristic of the ultimate strength, since beyond the point “c” in the tension diagram (see Fig. 2.45), the true resistance to deformation continues to increase, although the force decreases. The fact is that this effort on the site in k concentrates on the minimum 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 neck-failing materials has a number of interesting properties. In particular, the continuation of the rectilinear 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 rectilinear section to the point c corresponding to Ψ = 1 (100%) gives S c= 2S V.
The diagram in fig. 2.50 is qualitatively different 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 scheme is preserved, i.e. previously, true stress diagrams corresponding to type II curves were analyzed.
On fig. 2.50 shows that S in and even more so σ in much less true tear resistance (Sk =Pk / Fk) defined as the ratio of the force at the moment of failure to the maximum cross-sectional area of the specimen at the point of failure F k. It would seem that the magnitude Sk is the best characteristic of the ultimate strength of the material. But it is also conditional. Calculation Sk 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 one normal stress (which is why concentrated deformation is not considered in the theories of strain hardening in uniaxial tension). In fact, Sk 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 Sk change significantly upon transition from the considered stretching 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 in ≈ Sk. In this case, the maximum load before failure P c determines the so-called real tear resistance or brittle strength of the material. Here, σ in is no longer 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 ductility materials, giving the stretching curve shown in fig. 2.44 II, σ in is the conditional stress at the moment of destruction. Here S V = S k and quite 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 c depends on the elongation before failure, there is no direct proportional relationship between them.
Thus, depending on the type and even quantitative characteristics of tensile diagrams of one type, the physical meaning of σ in, S in and Sk can significantly, and sometimes fundamentally change. All these stresses are often referred to as characteristics of ultimate strength or fracture resistance, although in a number of important cases σ in and S in fact determine the resistance to significant plastic deformation, and not to destruction. Therefore, when comparing σ in, S in and Sk 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 tension diagram.
To date, there are several methods for testing samples of materials. At the same time, one of the simplest and most revealing are tensile (tensile) tests, which allow determining the proportionality limit, yield strength, elastic modulus and other important characteristics of the material. Since the most important characteristic of the stressed state of a material is deformation, the determination of the value of deformation for known dimensions of the sample and the loads acting on the sample makes it possible to establish the above characteristics of the material.
Here the question may arise: why not just determine the resistance of the material? The fact is that absolutely elastic materials that collapse only after overcoming a certain limit - resistance, exist only in theory. In reality, most materials have both elastic and plastic properties, what these properties are, we will consider below using the example of metals.
Tensile tests of metals are carried out in accordance with GOST 1497-84. For this, standard samples are used. The test procedure looks something like this: a static load is applied to the sample, the absolute elongation of the sample is determined Δl, then the load is increased by some step value and the absolute elongation of the sample is again determined, and so on. Based on the data obtained, a graph of elongation versus load is plotted. This graph is called a voltage diagram.
Figure 318.1. Stress diagram for a steel sample.
In this diagram, we see 5 characteristic points:
1. Limit of proportionality R p(point A)
Normal stresses in the cross section of the sample upon reaching the limit of proportionality will be equal to:
σ p \u003d P p / F o (318.2.1)
The proportional limit limits the area of elastic deformations in the diagram. In this section, the deformations are directly proportional to the stresses, which is expressed by Hooke's law:
P p \u003d kΔl (318.2.2)
where k is the stiffness factor:
k = EF/l (318.2.3)
where l is the sample length, F is the cross-sectional area, E is Young's modulus.
Modulus of elasticity
The main characteristics of the elastic properties of materials are Young's modulus E (modulus of elasticity of the first kind, tensile modulus), modulus of elasticity of the second kind G (shear modulus) and Poisson's ratio μ (transverse strain coefficient).
Young's modulus E shows the ratio of normal stresses to relative strains within proportionality
Young's modulus is also determined empirically when testing standard tensile specimens. Since the normal stresses in the material are equal to the force divided by the initial cross-sectional area:
σ \u003d P / F about (318.3.1), (317.2)
and relative elongation ε - the ratio of absolute deformation to the initial length
ε pr \u003d Δl / l o (318.3.2)
then Young's modulus according to Hooke's law can be expressed as follows
E \u003d σ / ε pr \u003d Pl o / F o Δl \u003d tg α (318.3.3)
Figure 318.2. Stress diagrams of some metal alloys
Poisson's ratio μ shows the ratio of transverse deformations to longitudinal
Under the influence of loads, not only the length of the sample increases, but also the area of the considered cross section decreases (assuming that the volume of the material in the region of elastic deformations remains constant, then an increase in the length of the sample leads to a decrease in the cross-sectional area). For a sample having a circular cross section, the change in cross-sectional area can be expressed as follows:
ε pop \u003d Δd / d o (318.3.4)
Then Poisson's ratio can be expressed by the following equation:
μ = ε pop /ε pr (318.3.5)
The shear modulus G shows the shear stress ratio T to the shear angle
The shear modulus G can be determined empirically when testing specimens for torsion.
With angular deformations, the section under consideration does not move linearly, but at a certain angle - the shear angle γ to the initial section. Since shear stresses are equal to the force divided by the area in the plane of which the force acts:
T= P/F (318.3.6)
and the slope angle tangent can be expressed by the absolute strain ratio Δl to the distance h from the place of fixation of the absolute deformation to the point about which the rotation was carried out:
tgγ = ∆l/h (318.3.7)
then for small values of the shear angle, the shear modulus can be expressed by the following equation:
G= T/γ = Ph/FΔl (318.3.8)
Young's modulus, shear modulus and Poisson's ratio are related by the following relationship:
E = 2(1 + μ)G (318.3.9)
The values of the constants E, G and µ are given in table 318.1
Table 318.1. Guide values for the elastic properties of some materials
Note: The moduli of elasticity are constant values, however, the manufacturing technologies of various building materials change and more accurate values of the modulus of elasticity should be specified according to the current regulatory documents. The elastic moduli of concrete depend on the class of concrete and therefore are not given here.
Elastic characteristics are determined for various materials within the limits of elastic deformations, limited by point A on the stress diagram. Meanwhile, several more points can be distinguished on the stress diagram:
2. Elastic limit Р y
Normal stresses in the cross section of the sample when the elastic limit is reached will be equal to:
σ y \u003d P y / F o (318.2.4)
The elastic limit limits the area on which the emerging plastic deformations are within a certain small value, normalized by the technical conditions (for example, 0.001%; 0.01%, etc.). Sometimes the elastic limit is indicated according to the tolerance σ 0.001, σ 0.01, etc.
3. Yield strength P t
σ t \u003d P t / F o (318.2.5)
Limits the section of the diagram in which the deformation increases without a significant increase in load (yield state). In this case, a partial rupture of internal bonds occurs throughout the entire volume of the sample, which leads to significant plastic deformations. The sample material is not completely destroyed, but its initial geometric dimensions undergo irreversible changes. On the polished surface of the samples, flow figures are observed - shear lines (discovered by Professor V. D. Chernov). For different metals, the slope angles of these lines are different, but are in the range of 40-50 o. In this case, part of the accumulated potential energy is irreversibly spent on a partial rupture of internal bonds. In tensile testing, it is customary to distinguish between upper and lower yield points - respectively, the largest and smallest of the stresses at which plastic (residual) deformation increases at an almost constant value of the acting load.
The stress diagrams show the lower yield point. It is this limit for most materials that is taken as the normative resistance of the material.
Some materials do not have a pronounced yield point. For them, the conditional yield stress σ 0.2 is taken to be the stress at which the residual elongation of the sample reaches the value ε ≈ 0.2%.
4. Tensile strength P max (tensile strength)
Normal stresses in the cross section of the sample upon reaching the tensile strength will be equal to:
σ in \u003d P max / F o (318.2.6)
After overcoming the upper yield strength (not shown in the stress diagrams), the material again begins to resist loads. At the maximum force P max, the complete destruction of the internal bonds of the material begins. In this case, plastic deformations are concentrated in one place, forming a so-called neck in the sample.
The stress at maximum load is called the tensile strength or tensile strength of the material.
Tables 318.2 - 318.5 show the approximate values of the tensile strengths for some materials:
Table 318.2 Approximate limits of compressive strength (tensile strength) of some building materials.
Note: For metals and alloys, the value of tensile strength should be determined in accordance with regulatory documents. The value of temporary resistance for some steel grades can be viewed.
Table 318.3. Approximate tensile strengths (tensile strengths) for some plastics
Table 318.4. Approximate tensile strengths for some fibers
Table 318.5. Approximate tensile strengths for some tree species
5. Destruction of material Р р
If you look at the stress diagram, it seems that the destruction of the material occurs when the load decreases. This impression is created because, as a result of the formation of the "neck", the cross-sectional area of the sample in the region of the "neck" changes significantly. If we build a stress diagram for a sample of mild steel depending on the changing cross-sectional area, it will be seen that the stresses in the considered section increase to a certain limit:
Figure 318.3. Stress diagram: 2 - in relation to the initial cross-sectional area, 1 - in relation to the changing cross-sectional area in the neck region.
Nevertheless, it is more correct to consider the strength characteristics of the material in relation to the area of the initial section, since changes in the initial geometric shape are rarely provided for in strength calculations.
One of the mechanical characteristics of metals is the relative change ψ of the cross-sectional area in the neck region, expressed as a percentage:
ψ = 100(F o - F)/F o (318.2.7)
where F o - the initial cross-sectional area of the sample (cross-sectional area before deformation), F - cross-sectional area in the "neck". The larger the value of ψ, the more pronounced the plastic properties of the material. The smaller the value of ψ, the greater the brittleness of the material.
If we add up the broken parts of the sample and measure its elongation, it turns out that it is less than the elongation in the diagram (by the length of the segment NL), since after rupture, elastic deformations disappear and only plastic deformations remain. The amount of plastic deformation (elongation) is also an important characteristic of the mechanical properties of the material.
Beyond the limits of elasticity, up to fracture, the total deformation consists of elastic and plastic components. If the material is brought to stresses exceeding the yield strength (in Fig. 318.1 there is some point between the yield strength and the tensile strength), and then unloaded, then plastic deformations will remain in the sample, but upon reloading after some time, the elastic limit will become higher, since in this case, a change in the geometric shape of the sample as a result of plastic deformation becomes, as it were, the result of the action of internal bonds, and the changed geometric shape becomes the initial one. This process of loading and unloading the material can be repeated several times, while the strength properties of the material will increase:
Figure 318.4. Hardening stress diagram (oblique straight lines correspond to unloading and reloading)
Such a change in the strength properties of the material, obtained by repeated static loading, is called work hardening. However, as the strength of the metal is increased by work hardening, its plastic properties decrease, and its brittleness increases, therefore, as a rule, a relatively small work hardening is considered useful.
Work of deformation
The strength of the material is the higher, the greater the internal forces of interaction of the particles of the material. Therefore, the value of elongation resistance per unit volume of the material can serve as a characteristic of its strength. In this case, the tensile strength is not an exhaustive characteristic of the strength properties of a given material, since it characterizes only the cross sections. At rupture, the interconnections over the entire cross-sectional area are destroyed, and during shears that occur with any plastic deformation, only local interconnections are destroyed. A certain work of internal forces of interaction is expended on the destruction of these bonds, which is equal to the work of external forces expended on displacement:
A \u003d РΔl / 2 (318.4.1)
where 1/2 is the result of the static action of the load, increasing from 0 to P at the time of its application (average value (0 + P) / 2)
With elastic deformation, the work of forces is determined by the area of \u200b\u200bthe triangle OAB (see Fig. 318.1). The total work spent on the deformation of the sample and its destruction:
A = ηP max Δl max (318.4.2)
where η is the coefficient of completeness of the diagram, equal to the ratio of the area of the entire diagram, limited by the curve AM and straight lines OA, MN and ON, to the area of \u200b\u200bthe rectangle with sides 0Р max (along the P axis) and Δl max (dashed line in Fig. 318.1). In this case, it is necessary to subtract the work determined by the area of the triangle MNL (relating to elastic deformations).
The work expended on plastic deformation and destruction of the sample is one of the important characteristics of the material that determines the degree of its brittleness.
Compression deformation
Compressive deformations are similar to tensile deformations: first, elastic deformations occur, to which plastic ones are added beyond the elastic limit. The nature of deformation and fracture under compression is shown in Fig. . 318.5:
Figure 318.5
a - for plastic materials; b - for brittle materials; c - for a tree along the fibers, d - for a tree across the fibers.
Compression tests are less convenient for determining the mechanical properties of plastic materials due to the difficulty of fixing the moment of failure. Methods for mechanical testing of metals are regulated by GOST 25.503-97. When testing for compression, the shape of the sample and its dimensions can be different. Approximate values of tensile strengths for various materials are given in tables 318.2 - 318.5.
If the material is under load at constant stress, then additional elastic deformation is gradually added to the almost instantaneous elastic deformation. When the load is completely removed, the elastic deformation decreases in proportion to decreasing stresses, and the additional elastic deformation disappears more slowly.
The resulting additional elastic deformation at constant stress, which does not disappear immediately after unloading, is called elastic aftereffect.
The influence of temperature on the change in the mechanical properties of materials
The solid state is not the only aggregate state of matter. Solids exist only in a certain range of temperatures and pressures. An increase in temperature leads to a phase transition from a solid to a liquid state, and the transition process itself is called melting. Melting points, like other physical characteristics of materials, depend on many factors and are also determined empirically.
Table 318.6. Melting points of some substances
Note: The table shows the melting points at atmospheric pressure (except for helium).
The elastic and strength characteristics of materials given in tables 318.1-318.5 are usually determined at a temperature of +20 ° C. GOST 25.503-97 allows testing of metal samples in the temperature range from +10 to +35 ° C.
When the temperature changes, the potential energy of the body changes, which means that the value of the internal forces of interaction also changes. Therefore, the mechanical properties of materials depend not only on the absolute value of the temperature, but also on the duration of its action. For most materials, when heated, the strength characteristics (σ p, σ t and σ c) decrease, while the plasticity of the material increases. As the temperature decreases, the strength characteristics increase, but the brittleness increases. When heated, the Young's modulus E decreases, and the Poisson's ratio increases. When the temperature drops, the reverse process occurs.
Figure 318.6. The effect of temperature on the mechanical characteristics of carbon steel.
When non-ferrous metals and their alloys are heated, their strength immediately drops and at a temperature close to 600 ° C, it is practically lost. The exception is aluminothermic chromium, the tensile strength of which increases with increasing temperature and at a temperature equal to 1100 ° C reaches a maximum σ in 1100 \u003d 2σ in 20.
The ductility characteristics of copper, copper alloys and magnesium decrease with increasing temperature, while those of aluminum increase. When plastics and rubber are heated, their tensile strength decreases sharply, and when cooled, these materials become very brittle.
Influence of radioactive irradiation on the change in mechanical properties
Radiation exposure affects different materials differently. Irradiation of materials of inorganic origin in its effect on the mechanical characteristics and characteristics of plasticity is similar to lowering the temperature: with an increase in the dose of radioactive irradiation, the tensile strength and especially the yield strength increase, and the plasticity characteristics decrease.
Irradiation of plastics also leads to an increase in brittleness, and irradiation has a different effect on the tensile strength of these materials: it has almost no effect on some plastics (polyethylene), in others it causes a significant decrease in tensile strength (katamen), and in others it increases the tensile strength (selectron ).
