Limitations when using the deformation theory-based plasticity model. Mechanical and plastic properties of materials Application is based on plasticity property
When designing structural elements and machine parts, it is necessary to know the mechanical and plastic properties of materials. For this, standard samples, which are destroyed in a testing machine. For tensile testing, cylindrical and flat specimens are recommended. The calculated length of cylindrical specimens should be equal to ℓ 0 \u003d 5d 0 or ℓ 0 \u003d 10d 0. Samples with a design length ℓ 0 \u003d 5d 0 are called short, and samples with ℓ 0 \u003d 10d 0 are called long. Short samples are preferred. Samples with a diameter of d 0 \u003d 10 mm are used as the main ones. Samples with smaller (sometimes large) diameters or non-circular cross section are called proportional. Estimated length ℓ 0 on the sample has risks.
The calculated sample length can be expressed in terms of the cross-sectional area:
So for short samples:
for long samples:
These ratios are used to determine the calculated length of rectangular cross-section specimens.
The relationship between working ℓ and calculated ℓ 0 lengths is:
for cylindrical specimens: from ℓ \u003d ℓ 0 + 0.5d 0 to ℓ \u003d ℓ 0 + 3d 0;
for flat specimens with a thickness of 4 mm and more:
The main task of tensile testing is to plot the tension diagram, i.e., the relationship between the force acting on the sample and its elongation.
The testing machine imparts a forced elongation to the specimen and records the resistance force of the specimen, i.e. the load corresponding to this elongation. The results of the experiment are written on paper using a diagrammatic apparatus in the form of a tension diagram in the coordinates F - Δℓ. The sample tension diagram typical for mild steel is shown in the figure.
This curve can be conditionally divided into four sites. The straight section OA is called area of \u200b\u200belasticity. Here, the sample material only experiences elastic deformations. The relationship between the load on the sample and its deformation obeys Hooke's law:
The elongation Δℓ in the OA section is very small.
The VK site is called plot general fluidity, and the segment VK - a site of fluidity. Here, a significant change in the length of the sample occurs without a noticeable increase in the load. The presence of a yield area is characteristic of mild steel.
The CS section is called hardening site... Here the material again shows the ability to increase resistance with increasing deformation. The area of \u200b\u200bhardening of the material in the tensile diagram extends to point C, the ordinate of which is equal to the highest load on the sample F max.
Beginning from point C, the character of deformation of the sample changes sharply. As the load on the sample increased from 0 to F, all sections of the sample lengthened in the same way — the sample experienced uniform deformation. Upon reaching the maximum load, the deformation of the sample begins to concentrate in some weakest point along its length. Subsequently, the elongation of the specimen occurs with decreasing force (section SD). In this case, the elongation of the sample is of a local nature. In this place of the sample, the dimensions of the cross-section decrease intensively (a so-called neck is formed) and the length of this section increases. Therefore, the SD section is called site of local fluidity... Dot D on the diagram corresponds destruction of the sample.
If the test specimen is not brought to failure, unloaded (for example, at point H), then in the process of unloading the relationship between the force P and the elongation Δℓ will appear as a straight NM, which will be parallel to OA. The length of the unloaded sample will be greater than the initial one by the value of OH. The OM segment is a residual or plastic elongation. Upon repeated loading of the sample, the tensile diagram takes the form of a straight NM and then - an NSD curve, as if there was no intermediate unloading.
Range of plastic materials (alloyed steels, bronzes, brass, aluminum alloys, titanium alloys, etc.) do not have a physical yield point. On the tensile diagram of such materials, after point B, there is a rapid increase in plastic deformation. Catch limit F t corresponds to point B on the tension diagram, is defined as the load at which the plastic deformation is 0.2%.
To give quantification mechanical properties of the material tensile diagram F \u003d f (Δℓ) (rearranged in coordinates. For this, the values \u200b\u200bof the force F are divided by the initial area of \u200b\u200bthe sample A 0, i.e. \u003d F / A 0, and the elongation Δℓ is divided by the initial length of the calculated part of the sample ℓ 0,
As a result, we obtain a diagram of the dependence of normal stresses on relative longitudinal deformation, which will characterize material propertiesrather than properties specific sample... This diagram is called conditional, since the calculation of and does not take into account changes in the length and cross-sectional area of \u200b\u200bthe sample during stretching.
The main mechanical characteristics are:
Proportionality limit: σ pts \u003d F pts / A 0
Yield strength: σ t \u003d F t / A 0
Tensile strength: σ in \u003d F in / A 0
Plasticity characteristics:
relative extension
relative narrowing
where A w is the cross-sectional area of \u200b\u200bthe sample (neck) at the narrowest point after fracture.
Specific work of deformation: a \u003d F in Δℓ / V,
where V is the volume of the test sample,
V \u003d A 0 ℓ 0.
Recall that the maximum stresses σ in cannot exceed 1200 MPa for structural materials.
Compression diagram of plastic materials
Samples of steel are placed in a testing machine and compressed.
In the first stage of loading a steel sample, the material experiences elastic deformation. The relationship between the applied force and deformation in the diagram is linear. Some time after the start of the test, the material reaches the state of flow. At the same time, the arrow of the silometer stops and the ordinates stop growing in the diagram. The specimen deforms under constant load. The load corresponding to the state of yield F T of the material is recorded in the test log. With further compression of the sample, the readings of the silometer begin to increase again. The sample is continuously compressed, its cross section increases, and in the absence of lubrication at the ends of the sample, it acquires a barrel-shaped shape. This is due to the fact that a frictional force acts between the base plates and the ends of the sample, which does not allow the parts of the sample adjacent to the base plates to move in the transverse direction. This phenomenon can be mitigated by lubricating the ends of the sample.
Steel specimen cannot be brought to destruction... The test is terminated at a load approximately twice the yield strength F T. The view of the samples before and after testing is shown in the figure. A typical diagram of compression of mild steel in coordinates F - Δℓ is shown in Fig. on right.
Tension and compression diagram of brittle materials
The test procedure for brittle materials is the same as for testing plastic materials. Therefore, we will focus on the main differences in the behavior of brittle materials. The figure shows a diagram of compression (curve 1) and tension (curve 2).
Brittle materials always have no flow area, although many materials have certain plastic properties. For these materials tensile strength is taken as a dangerous state... It should always be remembered that the ultimate strength of brittle materials is many times greater in compression... For cast iron, this value reaches 3-4 times. Concerning building materials, then this difference can reach tenfold.
Plasticity is the property of a metal to deform plastically without being destroyed by external forces. Plastic deformation is understood as the ability of materials to change their shape and size under the influence of external forces and to maintain these changes after removing the load.
Plasticity characteristics - relative elongation δ and narrowing the cross-sectional area ψ ... Determined when testing materials for static axial tension on the same standard samples and equipment, which were used to determine the characteristics of static strength (see Fig. 1, 2).
Relative elongation is the ratio of absolute elongation, i.e. the increment in the calculated length of the sample after rupture ( l k − l 0), to its original calculated length l 0, mm, expressed as a percentage:
where - l k length of the calculated part of a standard sample after rupture, mm.
Estimated length l 0 - section of the working length of the specimen between the marks applied before the test, on which the elongation is determined (see Fig. 1).
Relative constriction is the ratio of absolute constriction, i.e. the decrease in the cross-sectional area of \u200b\u200bthe sample after rupture ( F 0 – F k), to the initial area of \u200b\u200bits cross-section F 0, mm 2, expressed as a percentage:
, (9)
where F k - cross-sectional area of \u200b\u200bthe sample at the point of rupture, mm 2.
3. Determination of hardness characteristics
Hardness - the ability of a material to resist plastic or elastic deformation when a harder body (indenter) is introduced into it.
The most widely used methods for measuring hardness, based on the indentation of an indenter in the form of a ball, a diamond cone and a diamond pyramid, into the metal being tested - the Brinell, Rockwell and Vickers methods (Fig. 8).
Brinell's method ( HB). Determination of hardness is performed on a Brinell press (hardness tester, type TSh). The essence of the method is that a ball with a diameter of 10; five; 2.5 or 1.0 mm under the action of a certain force applied perpendicular to the surface of the sample, is continuously pressed into the tested metal (Fig. 8, a). Test conditions are regulated by GOST 9012-59. For example, the hardness of steel is measured by pressing a ball D \u003d 10 mm under a load of 30 kN (3000 kgf).
Figure: 8. Scheme for determining hardness
brinell (a), Rockwell (b) and Vickers (c)
After removing the force, the diameter of the spherical imprint is measured using a reference microscope, on the eyepiece of which there is a scale with divisions corresponding to hundredths of a millimeter.
Brinell hardness is indicated by letters HB (when using a steel ball) or HBW(when using a hard alloy ball) and calculated as the ratio of the force Racting on the ball to the surface area of \u200b\u200bthe spherical imprint F, kgf / mm 2 or MPa:
, (10)
where P - force acting on the ball, N (kgf);
F - surface area of \u200b\u200ba spherical imprint, m 2 (mm 2 ) ;
D and d – diameter of the ball and print, mm.
The Brinell method is recommended for metals with a hardness not exceeding HB 450 kgf / mm 2 (4500 MPa), since the steel ball can deform, which will introduce an error in the test result. This method is mainly used to measure the hardness of workpieces and semi-finished products from unhardened metal.
Rockwell's method ( HR). Determination of hardness is performed on a Rockwell press (TK type hardness tester) (GOST 9013-59). The essence of the method lies in the fact that the indenter in the form of a diamond cone is for hard and superhard (more HRC 70) metals (hardened steel ball with a diameter of 1.58 mm - for soft metals) (Fig. 8, b) - under the action of a certain force applied perpendicular to the surface of the sample, it is pressed into the tested metal. Hardness is determined by the depth of the print h... The results of measurements, in conventional units, are determined by the indication of the arrow on the scale of the indicator of the hardness tester (Fig. 9).
Sh Figure: 9. Indications of the indicator of the TK device
When a steel ball is pressed in, the main load is 100 kgf, the hardness is read on the internal (red) scale "B" of the indicator, the hardness is НRВ... When the diamond cone is pressed into the test specimen, the hardness is determined by the indication of the arrow on the external (black) scale "C" of the indicator. For hard metals, the basic load is 150 kg. This is the main method for measuring the hardness of hardened steels. Hardness designation - HRC... For very hard metals, as well as materials of parts of small thickness, the main load is assumed to be 60 kg. Hardness designation - HRA, eg: HRC 40, HRA 90 - Rockwell hardness on the "C" scale - 40 conventional units; on the "A" scale - 90.
The Rockwell hardness test method allows you to test soft and hard metals, while the impressions from a ball or cone are very small, so using this method you can measure the hardness of the material of finished parts. The test surface should be ground. Measurements are performed quickly (within 30 - 60 s), no calculations are required, since the hardness value is read off the hardness indicator scale.
Vickers method ( HV). When testing for hardness by the Vickers method, a diamond tetrahedral pyramid with an apex angle of 136º is pressed into the ground or polished surface of the material (Fig. 8, c). To determine the hardness of ferrous metals and alloys, loads from 5 to 100 kgf are used, and for non-ferrous metals and their alloys - from 2.5 to 50 kgf. After removing the load, the diagonal of the print is measured using a microscope attached to the device. d and calculate the value of hardness in kgf / mm 2 or in MPa as the ratio of the load R, N (kgf), to the surface area of \u200b\u200bthe pyramidal imprint M, m 2 (mm 2):
, (11)
where d - length of the diagonal of the print, mm.
For example, 500 HV means that the Vickers hardness is 500 kgf / mm 2 (5000 MPa).
The Vickers method allows you to measure the hardness of both soft and very hard metals and alloys, as well as to determine the hardness of thin surface layers (for example, after chemical-thermal treatment, quenching with high-frequency currents, etc.).
To compare the values \u200b\u200bof hardness, determined in different ways, conversion tables are used (Table 1).
Brinell hardness can be used to evaluate the mechanical properties of materials and the approximate ultimate strength. The empirical ratio of ultimate strength and hardness, determined by Brinell tests, has the form:
σ in ≈ 0,33HB max, (12)
where σ c - temporary resistance;
HB max is the maximum value of hardness under load, from which a smooth decrease in hardness begins.
Table 1
Comparison of hardness values \u200b\u200bdetermined by different methods
|
Imprint diameter |
By Brinell |
By Rockwell |
According to Vickers |
||
|
HB, MPa | |||||
PLASTIC- the property of solids to change shape and size under the influence of external loads and to maintain it when the loads cease to act (after removing the loads).
The first idea of \u200b\u200bthe property of a material, called plasticity, is given by a lump of plasticine, which easily changes shape under the pressure of the fingers, and retains a new shape after acting on it (in contrast to a stretched spring, which again compresses if it is released In this sense, they say that a spring elastic, and plasticine is plastic. ”Plasticine and plasticity are words of the same root, from the Greek word for plastic, which means modeling, from the verb“ to mold ”(from clay).
To get a more accurate idea of \u200b\u200bthe property of plasticity, you can make (or imagine) a simple experiment. Let there be an elongated plasticine parallelepiped (rod), the long edge of which is approximately 10 cm, and the small edge is a 1 cm × 1 cm square. Let this rod rest on two supports ("bridge") at its ends. If you put metal weights (for example, coins) on the middle of the rod, then while the load is low, the change in the shape of the rod is imperceptible to the eye. With further loading, it is found that at some point the bar bends and becomes curved. If you remove all the weights, the curvilinear shape will still be preserved.
This experience shows that a rod made of a material with the property of plasticity resists the action of loads, almost without changing its shape, until the load exceeds a certain threshold, after which a noticeable change in shape occurs, which persists even after the load is removed. This is the essence of plasticity, but not all - the change in shape (deformation) depends only on the applied load and does not change by itself over time. If deformation still occurs at a constant load, then the material is called not plastic, but viscoplastic or viscoelastic ( cm... RHEOLOGY; CREEP). Of course, plasticine is familiar and illustrative example plastic material. It is important that the property of plasticity is inherent in very many structural materials. First of all, these are metals and alloys - steel, iron, copper, aluminum and others, but the idea of \u200b\u200bplastic deformation is also very useful for understanding the deformation processes of composite materials, including cermet, carbon and polymer.
The plasticity of the material is, as it were, opposed to elasticity: the plastic body retains the shape given to it, and the elastic body restores the original one. But plasticity is also opposed to fragility: a plastic body responds to an increase in load by a noticeable change in shape, and a fragile body (for example, glass) - by the appearance of cracks and destruction.
The study of plasticity is developing in two directions: one of them is connected, first of all, with technical problems and its purpose is to answer the question: if a structure is exposed to external forces of a known magnitude, what is the shape change? how does it deform? This is important for the designer to know, but there is another important circumstance: usually plasticity precedes failure, so that the study of plastic deformations is the basis for predicting the strength and durability of a structure.
The second direction in the study of plasticity is the study of what happens in a material, as they say, at the micro level, i.e., what happens inside the material, for example, during plastic bending of a beam. It is possible, by analogy with the experiment on the bending of a rod, to make an experiment on its tension: the upper end of the rod (it is usually called a sample) is fixed, and a load is applied to the lower end. In this case, it is difficult to notice by eye the change in the length of the sample, but if the deformations are measured with special instruments, then it is found that the deformation process turns out to be similar to that in the experiment with bending: with a gradual increase in the tensile load, very small elastic deformations first appear, when the load reaches a threshold value, then the deformations (now, mainly, plastic) become, firstly, more significant, and, secondly, irreversible (i.e., do not disappear after removing the load).
This reveals interesting phenomena. If a steel specimen is used in the tensile test in the form of a long plate with a polished (mirror) surface, then in the process of plastic deformation many close thin parallel straight lines appear on this surface, oriented at an angle of 45 ° to the specimen axis (the specimen axis is here a straight line passing in the middle of the plate, parallel to its long sides). These lines are called the Luders - Chernov lines (after the names of the scientists who discovered them).
Microscopic analysis of these lines shows that they appear as a result of a shift in the plate material, i.e. one thin layer seems to be shifted relative to the second, the second - relative to the third, etc., like cards in a deck. We can say that the Luders - Chernov lines are the boundaries of the shifting layers. Figure 1 schematically shows the pattern of such deformation. This scheme makes it possible to understand how such shears lead to plastic elongation of the sample and why plastic deformations do not disappear after removing the load. More complex and accurate experiments have shown that plastic deformations of metals and alloys are always caused by shears within the material. In addition, deformations occur in porous materials that are very similar in appearance to plastic ones, but associated with a decrease in pores. The most familiar porous material is foam; In technology, porous materials are created by powder metallurgy, where parts are pressed from metal powder.
It is possible to describe the deformation pattern quite accurately, assuming that the elastic deformations of a body are the result of a change in the distance between the atoms of which it is composed, and plastic deformations are the result of shears.
So plasticity is the result of shear. And how do the shifts themselves occur? This question (and many others) is answered by branches of physics: solid state physics, dislocation theory, physics of metals, etc.
These are the two directions in which plasticity is studied, the first is called phenomenological - it studies the phenomenon of plasticity as it can be observed in experiments with samples and loads, and does not rely on the results of microscopic experiments. The phenomenological study of the plasticity of metals begins with the classical tensile experiment. Its results are presented in the form of graphs (Fig. 2), where the stress s is plotted along the vertical axis, equal to the tensile force P, referred to the cross-sectional area of \u200b\u200bthe sample F, i.e.
s \u003d P/F
and horizontally - deformation of the sample e, equal to the elongation d l sample (by force P) referred to its original length l.
e \u003d d l/l
In fig. 2 depicts a graph called the "stretch curve"; material - one of the steel grades. At the beginning of loading (on the graph from the point O to the point A) stress and strain are proportional, i.e. Hooke's law holds. The aspect ratio is called the modulus of elasticity (or Young's modulus) E... Dot A on the graph it is called the elastic limit - after it, the proportionality inherent in elasticity is replaced by a curvilinear dependence, and now the deformation grows much faster than the stress. If at some point B we begin to reduce the voltage (this is called unloading), then the graph will show a curve that does not differ much from a straight line - BC with an arrow down. If, after bringing the voltage to zero, increase it again, the graph will show a curve CB1 (with an upward arrow), and further this curve will smoothly transform into the curve B1D, which would have resulted from deformation of the sample without unloading. For simplicity, usually both curves, BC and CB1 are replaced by a straight line segment B2Cwhich is parallel to the line segment OA.
There are several versions of the theory of plasticity, which differ, on the one hand, in how accurately they take into account the real features of the deformation process of an elastic-plastic material, and, on the other hand, in the mathematical apparatus used. Some theories are less accurate, but simpler and more convenient for calculations, which is very important, since the calculation of plastic deformations in bodies of complex shapes is a very difficult task even when using modern computers. Other theories could provide high accuracy, but lead to very great difficulties, both mathematical and experimental. Apparently, the creation of an "ideal" theory combining physical clarity, mathematical simplicity and at the same time providing an adequate description of plastic deformation processes is a matter of the future. But even "simple" theories of plasticity are actually quite complex, since they require knowledge and understanding of many experimental results and serious mathematical training. As an example, consider the idea of \u200b\u200bthe simplest theory of plasticity.
In the simplest case of a tensile test of a sample, the process of elastic deformation is described by Hooke's law
There is no proportionality beyond the elastic limit, but the experimental tension curve can be described if we assume that the elastic modulus E in this case, it ceases to be a constant value and becomes a function of deformation, i.e.
In these formulas, a new function w \u003d w (e) appears, which is called the plasticity function and must be found from experimental data.
It can be seen that the function w (e) is identically zero under elastic deformations and increases under plastic deformations. Then it is clear that both elastic and plastic deformations are described by an equation generalizing Hooke's law
s \u003d Ee
This equation describes the deformation curve from which it is, in essence, obtained and this is so, while we are talking only about the tensile test. But the theory of plasticity must "be able" to describe any deformation processes - for example, both torsion, and bending, and their joint manifestation, and for this the formula must be essentially generalized and formulated essentially analogous, but immeasurably more complex relations that would relate the six components of the tensor strains with six stress tensor components. This is where the difficulties begin.
The classical deformation theory is called "the theory of small elastoplastic deformations". This theory is based on three experimental facts:
1. At various elastoplastic deformations at each point of the body, there is a universal functional relationship between the rms value of shear deformations and a similar rms value of shear stresses.
2. During elastoplastic deformation of the material, the volume change always occurs elastically.
3. The first two statements are valid only under the condition that all external forces acting on the body increase in proportion to each other (more precisely, in proportion to one parameter, for example, time). This is the so-called "simple" or "proportional" loading.
To properly understand these three statements, you need to consider the following:
The theory of plasticity, like all empirical theories, is essentially an approximate theory. This means that under certain conditions, when it can describe physical reality (“conditions of applicability”), the empirical theory describes this reality with a relatively small, but always present error (in other words, with a small error).
The theory of plasticity in question can give an answer with an error close to 10%. And almost always such an error turns out to be quite acceptable - they say that "the theory works well."
Mathematical formulation of the theory: let is the strain tensor e ijand the stress tensor s ij... It is required to write formulas (ratios) that connect these tensors at small elastoplastic deformations, just as Hooke's law connects them at elastic deformations.
Taking into account the different regularities of volumetric and shear deformation, tensors can be divided into volume (spherical) and shear (deviatorial) parts:
e ij \u003d 1/3 Q d ij+ e ij
The next step is to establish a relationship between shear stresses and deformations, since plasticity is shear.
For the deviator of deformations, the root-mean-square shift at a given point is determined by the formula
Similarly, the rms shear stress is determined by:
This is the universal functional relationship between and, and it is universal in the sense that it takes place at any point of the body and for any kind of deformation (bending, torsion, their combination, etc.). The function is considered known, but in fact must be found from processing the results of the experiment. Since, due to its universality, it is always the same, in particular, in any experiment, it is convenient to use the experiment on torsion of the tube, from which this function is determined especially easily.
Within elasticity, and the relationship between
Clay - a plastic natural material used in construction, folk crafts, treatment and improvement of the body and in other areas of human life. It is this widespread use that determines certain qualities and properties of clay. And the properties of clay are largely influenced by its composition.
Clay application
Clay is very accessible, and its benefits are invaluable, and therefore it has been used by people since very ancient times. There are many references to this wonderful material in textbooks on the history of all countries of the world.
Construction... Currently, clay is used as a material for making red bricks. Clay of a certain composition is molded and fired using a certain technology to obtain a durable and inexpensive ingot - a brick. And buildings and structures are already being built from bricks. In some countries and regions, clay is still used to build a dwelling - a hut; it is widespread to use clay in the construction of brick ovens, where clay serves as a binder (as cement). The same clay is used for plastering ovens.
Medicine. Wellness and traditional medicine uses clay in the form of mud baths and masks. The whole point is to nourish the surface of the skin with beneficial clay elements. Of course, not all clay will work here.
Souvenirs and dishes... I combine two large directions into one, since many items of tableware have only a souvenir character. Plates, pots, jugs and vases are abundant in modern stores. Not a single fair is complete without the sale of clay souvenirs - smoky toys, svustulki, tablets, key chains and much more. We will try to mold many things on our own.
Clay can enter composition of other materials... Chasovoyarskaya clay of fine grinding, for example, is an element of artistic paints (gouache), sauce, pastels and sanguine. Read about it in the articles "Help for the artist".
Clay properties
Colour. Clay of various compositions has many shades. The clay is called by its color: red, blue, white ... True, during drying and further firing, the color can completely change. This is worth paying attention to when working with clay.
Plastic. It was the ability to deform and keep the shape given to it that allowed a person to find the use of clay in his life. It should be noted here that it all depends on the consistency - the ratio of the amount of water, clay and sand. Different compositions require different compositions. So, for sculpting, sand may be generally unnecessary.
Hygroscopicity allows the clay to absorb water, changing its viscosity and plasticity properties. But after firing, clay products acquire water resistance, strength and lightness. The development of technology has made it possible to obtain faience and porcelain, which are irreplaceable in the modern world.
Refractoriness... A property used in construction rather than in artistic crafts, except for the firing of products. The firing technology is different for a particular clay composition. The property of clay shrinkage or compressibility is closely related to drying and firing - a change in mass and size due to the removal of part of the water from the composition.
Clay composition
The properties of clay are determined by its chemical composition. For different types clays are characterized by different chemical compositions. For example, red clay contains many iron oxides. Clay basically contains certain substances - clay minerals - that are formed during various natural phenomena... The format of the article does not provide for consideration chemical properties and the composition of the clay, so I will not go into details.
The composition of clay suitable for use in folk crafts, as already mentioned, is determined by three essential elements: clay minerals, water and sand.
The proportions of these elements can be changed, although it is much easier to add than remove. So, for example, dry clay can be quickly dissolved, however, it is not at all easy to make clay as liquid as sour cream suitable for modeling. It is very easy to add sand, but removing it from clay is not a trivial task.
Distinguish between "skinny" and "fat" clays. The scale of "fatness" determines the coefficient of plasticity, and the binding properties of clay allows you to adjust the fat content by mixing it with others natural materialseg with sand. Skinny clay has less plasticity, its binding strength is weaker, but it gives less shrinkage when drying and firing.
Clay deposits are found in various states around the world. This ensured its use by artisans of different nationalities, and served as the emergence of such a variety of products and technologies.
Craftsmen have learned to control the behavior and condition of the clay through various additives in the composition. So you can thin the clay, torture it, give it greater refractoriness, and reduce shrinkage. As a result of such manipulations, an experienced craftsman will be able to end up with a high-quality highly artistic product.
abstract
by discipline:
"Technology of structural materials"
"Physical foundations of plasticity and strength of metals "
Is done by a student
Checked by the teacher
Introduction
The main mechanical properties are strength, plasticity, elasticity, toughness, hardness.
Knowing the mechanical properties, the designer, when designing, reasonably chooses the appropriate material that ensures the reliability and durability of machines and structures with their minimum weight.
Ductility and strength are related to essential properties solids.
Both of these properties, mutually related to each other, determine the ability of solids to resist irreversible deformation and macroscopic destruction, i.e., the separation of the body into parts as a result of microscopic cracks arising in it under the influence of external or internal force fields.
For a technologist, plasticity is very important, which determines the possibility of manufacturing products by various methods of pressure treatment based on plastic deformation of the metal.
Materials with increased ductility are less sensitive to stress concentrators and other embrittlement factors.
In terms of strength, ductility, etc., a comparative assessment of various metals and alloys is performed, as well as their quality control in the manufacture of products.
In physics and engineering, plasticity is the ability of a material to receive residual deformations without destruction and to maintain them after removing the load.
The property of plasticity is of decisive importance for such technological operations as stamping, drawing, drawing, bending, etc.
The strength of solids, in a broad sense, is the property of solids to resist destruction (separation into parts), as well as irreversible change in shape (plastic deformation) under the influence of external loads. In a narrow sense, resistance to destruction.
The purpose of this work is to study the physical foundations of the plasticity and strength of metals.
1. Physical foundations of the strength of metals
Strength is a fundamental property of solids, bodies. It determines the body's ability to resist the action of external forces without destruction. Ultimately, as you know, strength is determined by the size and nature of the interatomic bond, the structural and atomic-molecular mobility of the particles that make up the solid. The mechanism of this phenomenon remains unresolved at the present time. The question of the nature of strength, the essence of the processes taking place in a material under load remains unclear. In matters of strength, not only is there no complete physical theory, but even on the most basic concepts there are differences of opinion and opposite opinions.
The ultimate goal studying the mechanism of destruction should be the clarification of the basic principles of creating new materials with desired properties, improving existing materials and rationalizing the methods of their processing.
Strength is the property of solids that resists destruction, as well as irreversible changes in shape. The main indicator of strength is the tensile strength, determined at rupture of a cylindrical sample, previously subjected to annealing. By strength, metals can be divided into the following groups:
fragile (tensile strength does not exceed 50 MPa) - tin, lead, bismuth, as well as soft alkali metals;
strong (from 50 to 500 MPa) - magnesium, aluminum, copper, iron, titanium and other metals that form the basis of the most important structural alloys;
high-strength (more than 500 MPa) - molybdenum, tungsten, niobium, etc.
The concept of strength is not applicable to mercury, since it is a liquid.
The tensile strength of metals is shown in Table 1.
Table 1.
Strength of metals
Most technical characteristics the strengths are determined as a result of a static tensile test. The specimen, fixed in the grips of the tensile testing machine, is deformed under a static, smoothly increasing load. During testing, as a rule, a tensile diagram is automatically recorded, expressing the relationship between load and deformation. Small deformations are determined with very high accuracy by tensometers.
To exclude the influence of the size of the samples, tensile tests are carried out on standard samples with a certain ratio between the calculated length l 0 and the cross-sectional area F 0.
The most widely used samples of circular cross-section: long with l 0 / d 0 \u003d 10 or short with l 0 / d 0 \u003d 5 (where d 0 is the initial diameter of the sample).
In fig. 1, a shows the stress-strain diagram of low-carbon annealed steel. Under a load corresponding to the initial part of the diagram, the material experiences only elastic deformation, which completely disappears after the load is removed.
Up to point a, this deformation is proportional to the load or the effective stress
where P is the applied load; F o - the initial cross-sectional area of \u200b\u200bthe sample.
The proportional limit corresponds to the load at the point a, which defines the end of the straight section of the tensile diagram.
Theoretical proportional limit - maximum stress up to which a linear relationship between stress (load) and deformation is maintained
σ pts \u003d P pts / F 0.
Since when determining the position of point a on the diagram there may be errors, they usually use conditional proportionality limit , which is understood as a voltage that causes a certain amount of deviation from a linear relationship, for example, tg alpha changes by 50% from its original value.
The straight-line relationship between stress and strain can be expressed by Hooke's law:
σ \u003d E epsilon,
where epsilon \u003d (delta l / l about) 100% - relative deformation;
delta l - absolute elongation, mm;
l 0 - initial sample length, mm.
Fig. 1 Tension diagram of low-carbon steel (a) and diagram for determining the conventional yield stress σ0.2 (b)
The proportionality coefficient E (graphically equal to tg alpha) characterizing the elastic properties of the material is called the modulus of normal elasticity.
At a given value of stress, with an increase in the modulus, the value of elastic deformation decreases, i.e., the rigidity (stability) of the structure (product) increases. Therefore, the modulus E is also called the stiffness modulus.
The modulus value depends on the nature of the alloy and changes insignificantly with a change in its composition, structure, and heat treatment.
For example, for various carbon and alloy steels after any processing, E \u003d 21000 kgf / mm 2.
Theoretical elastic limit is the maximum stress up to which the sample receives only elastic deformation:
σ pack \u003d P pack / F 0.
If the acting stress in the part (structure) is less than σ yn, then the material will work in the area of \u200b\u200belastic deformation.
In view of the difficulty of determining σ yn, they practically use conditional elastic limit , which is understood as a stress causing a permanent deformation of 0.005-0.05% of the initial calculated length of the sample. In the designation of the conventional limit of elasticity, the value of the permanent deformation is indicated, for example, σ0.005, etc.
For most materials, the theoretical limits of elasticity and proportionality are close in magnitude. For some materials, such as copper, the elastic limit is greater than the proportional limit.
Yield point - physical and conditional - characterizes the resistance of the material to small plastic deformations.
Physical yield strength - stress at which there is an increase in deformation under constant load
σ t \u003d P T / F 0.
In the tensile diagram, the horizontal section c - d corresponds to the yield point, when plastic deformation (elongation) is observed - the "flow" of the metal under constant load.
Most of the technical metals and alloys do not have a yield area. For them, the most often determined conditional yield stress - stress causing permanent deformation, equal to 0.2% of the initial design length of the sample (Fig. 1, b):
σ0.2 \u003d P 0.2 / F 0
With further loading, plastic deformation increases more and more, being evenly distributed over the entire volume of the sample.
At point B, where the load reaches its maximum value, at the weakest point of the specimen, the formation of a "neck" begins - a narrowing of the cross section; the deformation is concentrated in one area - from uniform to local.
The stress in the material at this point in the test is called the tensile strength.
Strength limit (ultimate tensile strength) - voltage corresponding to the maximum load that the specimen can withstand until failure:
σ in \u003d P in / F 0.
In its physical essence, σ in characterizes strength as resistance to significant uniform plastic deformation.
Behind point B (see Fig. 1, a), due to the development of the neck, the load decreases, at point k under load P k, the sample is destroyed.
True resistance to destruction - the maximum stress that the material can withstand at the moment preceding the destruction of the sample
S K \u003d P to / F K,
where F K is the final cross-sectional area of \u200b\u200bthe sample at the site of failure.
Despite the fact that the load P to<Р в, вследствие образования шейки F K
True voltages ... The considered strength indicators: σ t, σ b, etc., with the exception of S k, are conditional stresses, since in their determination the corresponding loads are referred to the initial cross-sectional area of \u200b\u200bthe sample F 0, although the latter gradually decreases as the sample is deformed. A more accurate idea of \u200b\u200bthe stresses in the sample is given by the diagrams of true stresses (Fig. 2). Fig.2 Diagram of true (S) and conditional (σ) stresses: ψ - transverse constriction of the sample. The true stresses S i \u003d P i / F i are determined by the load P i and the cross-sectional area F i at the moment of testing. Approximately to point b (Fig. 2,), ie, point B in Fig. 72, a, the difference between true and conditional stresses is small and S B \u003d σ c. Then the true stresses increase, reaching the maximum value of S k at the moment preceding the failure. In tensile testing, in addition to strength characteristics, plasticity characteristics are also determined. 2.
Physical foundations of plasticity of metals The development of the theory of the mechanical properties of solids, as is known, proceeded from the mechanics of an absolutely rigid body, in which deformations are not taken into account at all, through the theory of elasticity, which is the first approximation and is suitable in cases of small and reversible deformations, to the theory of small elastic plastic deformations. The theory of interaction between atoms of the crystal lattice, developed over 40 years ago, was in sharp contradiction with the experimental data on the strength of crystals. Two ways out of this situation were proposed. Both of them are based on the fact that in a real crystal, as in solid materials in general, there are inhomogeneities and imperfections. It is due to the imperfection of the structure of real bodies that premature plasticity arises. Further, the opinions of different researchers differed. Some believed that a real crystal consists of pieces of a perfect crystal, between which there are weak points. Plastic flow occurs only in weak points. Others believed that weaknesses, if they play a role in plasticity, only as sources of overvoltage. In other words, plastic flow requires large local overvoltages, as has been shown, for example, in experiments on controlling the formation of plastic shears. Undoubtedly, the study of the structure of a real crystal and various defects that may exist in it is an important task. However, it is controversial whether it is necessary to base the theory of plasticity on taking these phenomena into account, or whether it is possible to develop a theory of plastic deformation of an ideally correct crystal lattice followed by consideration of the role of various defects. A number of authors prefer to proceed from the assumption that there are regularly distributed defects with special properties in the crystal lattice. It is assumed that the plastic flow of crystals is the movement of these defects (dislocations) in the crystal lattice. The latest experimental data to a certain extent confirm the dislocation concepts. However, the fundamental question of the appearance of dislocations in the process of plastic deformation remains insufficiently clarified. Therefore, it is necessary to pay special attention to experimental verification of the theory of dislocations. It is possible that such a test and the corresponding refinement of the theory will facilitate the convergence of different points of view. Various materials exposed to external mechanical forces change their size and shape reversibly at the very initial stages of loading. The deformations observed in this case are called elastic. Studying the elastic properties of solids is important due to the fact that elastic constants are a measure of interparticle forces in solids. The phenomena of the shape change of solids under the influence of external forces are very complex. The final changes occurring in solids under the influence of external forces are determined by the totality of a number of processes, each of which itself is still completely unclear due to the lack of satisfactory and complete ideas about the nature of the bonding forces in solids, about their structure, about the nature thermal motion, etc., in other words, in view of the absence of an exhaustive theory of the crystalline state. However, there is no doubt that the basic and general phenomena occurring in solids under the influence of external forces are atomic and molecular displacements. It is known that the phenomena occurring during the deformation of solids under the action of external forces are strongly dependent on the structure and are closely related to the processes of diffusion, relaxation, recrystallization, with phase transformations and to a very strong degree depend on temperature. Due to this, the problem of elastic and plastic deformation of solids - the problem of plasticity, in fact, is part of a more general problem - the problem of mobility of atoms and molecules in solids, which includes: elasticity, imperfect elasticity, plasticity, creep, twinning, phase transformations , diffusion, relaxation, recrystallization and other (similar) phenomena. Thus, the development of the physical theory of plasticity requires coverage of a wide range of phenomena, some of which were listed above, and is inseparable from the solution of the following fundamental problems: the problem of the general theory of the solid state; problems of interparticle forces in solids; problems of ideal and real structure of solids; problems of thermal motion in solids. Plastic - the ability of a body (metal) to plastic deformation, that is, the ability to receive a residual change in shape and size without breaking the continuity. This property is used in the processing of metals by pressure. The characteristics of plasticity are elongation and contraction. According to the degree of plasticity, metals are usually subdivided as follows: highly plastic - (relative elongation exceeds 40%) - metals that form the basis of most structural alloys (aluminum, copper, iron, titanium, lead) and "light" metals (sodium, potassium, rubidium, etc.); plastic - (relative elongation lies in the range between 3% and 40%) - magnesium, zinc, molybdenum, tungsten, bismuth, etc. (the most extensive group); fragile - (relative elongation less than 3%) - chromium, manganese, kolbat, antimony. High purification of brittle metals somewhat increases ductility. The alloys obtained on their basis are almost indestructible. Manufactured products from them are often made by casting. Relative extension ... Elongation is a conditional characteristic of plasticity. This is explained by the fact that the absolute elongation consists of two components: uniform elongation delta l p, proportional to the length of the sample, and local, concentrated elongation in the neck delta l w, proportional to the cross-sectional area of \u200b\u200bthe sample. Hence, it follows that the fraction of local deformation and, consequently, the values \u200b\u200bof delta l ost and δ are greater for short specimens than for long specimens. At the same time, for various materials, the relative value of uniform and local deformations fluctuates within wide limits. Most ductile materials deform to form a neck. At the same time, uniform deformation is 5-10% of local deformation, for alloys of the duralumin type 18-20%, for brass 35-45%, etc., but not more than 50%. For brittle materials or those in a brittle state, the neck does not form and practically delta l ost \u003d delta l p. The elongation of metals is characterized by table 2. Table 2. Plasticity of metals. Relative narrowing. In plastic materials, the relative narrowing more accurately characterizes their maximum plasticity - the ability to local deformation and often serves as a technological characteristic during sheet stamping, etc. 3.
Theoretical and technical strength The technical (real) strength of metals is 10-1000 times less than their theoretical strength, determined by the forces of interatomic adhesion. For example, for iron, the theoretically calculated value of the separation resistance S FROM \u003d 2100 kgf / mm 2. Technical strength of iron: S FROM \u003d 70 kgf / mm 2, σ in \u003d 30 kgf / mm 2. Such a large difference is explained by the fact that the theoretical strength corresponds to the ideal defect-free crystal lattice of the metal. Real metals always contain dislocations and other defects of the crystal lattice, inclusions, microcracks, etc., which reduce strength and initiate fracture (Fig. 3). Fig.3 Dependence of strength on the number of dislocations and other crystal lattice defects (IA Oding's scheme): 1 - pure, annealed metals; 2 - alloys strengthened by alloying, heat treatment, plastic deformation (work hardening), etc. Pure, annealed metals with a dislocation density of about 10 7 -10 8 cm -2 have the minimum strength. With a decrease in the number of dislocations, the resistance to deformation, i.e., the strength of the metal, increases and can reach the theoretical value. Convincing evidence of the validity of this position was obtained in the study of metal whiskers - whiskers 0.5-2 μm thick and up to 10 mm long with a practically defect-free (dislocation-free) crystal structure. Iron whiskers with a thickness of 1 μm have a tensile strength σ in \u003d 1350 kgf / mm 2, that is, almost theoretical strength. Due to its small size, the mustache is used to a limited extent. An increase in the size of the whiskers leads to the appearance of dislocations and a sharp decrease in strength. To the right of point 1 (see Fig. 3), with an increase in the number of dislocations (defects), the strength of metals increases. This is used in hardening methods such as alloying, heat treatment, cold plastic deformation, etc. The main reasons for hardening are an increase in the number (density) of dislocations, distortions of the crystal lattice, the appearance of stresses, refinement of metal grains, etc., i.e., everything that impedes the free movement of dislocations. The limiting dislocation density for hardening is about 10 12 cm -2. At higher density, submicroscopic cracks are formed in the metal, causing fracture. Conclusion The issues of plasticity and strength of solids are of paramount importance for many branches of technology. The ductility and strength of this material ultimately determine the possibility of using it in building structures, in machine parts, in instrument structures, in tools for mechanical processing of solids and in many other cases. These properties also determine the possibility of machining a given material by pressure (forging, rolling, stamping, cutting) and set the power of the machines used for this purpose. Currently, the problem of strength and plasticity of solids should be considered from the standpoint of two areas of interest - physical and technical. The first of them includes: a) elucidation of the physical nature of plasticity and strength of solids based on the study of elementary processes occurring during deformation and destruction, b) systematic accumulation and generalization of new facts and patterns of behavior of solids under conditions encountered in practice. The second area of \u200b\u200binterest includes all problems related to the use of solids in technology with a general phenomenological description of their strength and deformation behavior under different types of stress state and in diverse operating conditions with the use of this information to calculate the strength and plasticity of machine parts and structures on the basis of formal theories of strength and plasticity. Studies of the nature of the strength and plasticity of solids are necessary to create a rigorous physical theory of their plastic deformation and fracture. The construction of such a theory consists, first of all, in solving the problem of the deviation of the structure of solids from ideally correct ones under the influence of mechanical factors and the influence of violations of the ideal structure of solids on their plasticity and strength. It is quite obvious that the absence of a physical theory based on the variety of experimental facts that have been accumulated as a result of many years of work on the problem will continue to hamper the solution of a number of possible practical issues. The most important of them are as follows: in the development of principles for creating new materials with desired properties, in improving existing materials, in identifying ways to further rationalize their processing. The tremendous national economic significance of these tasks is obvious. Meanwhile, until now, there is a noticeable gap between the requirements of technology in relation to the strength and ductility of materials for various conditions of their operation in machines and structures and the possibilities of theory for finding ways to solve the problems at hand. Now, at best, we have at our disposal only sketches of a possible theory of individual phenomena, as well as some experimental foundations of the theory, which do not fully cover the questions before us. List of references 1. Aleksandrov, AV Fundamentals of the theory of elasticity and plasticity: textbook for universities. - M.: Higher school, 1990 .-- 399 p. - ISBN 5-06-000053-2. 2. Gul VE, Structure and strength of polymers, 2nd ed., M., 1971. 3. Zubchaninov, VG Fundamentals of the theory of elasticity and plasticity: a textbook for students of engineering specialties of universities / VG Zubchaninov. - M .: Higher school, 1990 .-- 368 p.: Ill. - ISBN 5-06-000706-5. 4. Indenbom VL, Orlov AN, The problem of destruction in the physics of strength, "Problems of strength", 1990, no. 12, p. 3; 5. G.V. Kurdyumov. Physical foundations of strength and plasticity of solids. - M .: - 1975. 6. Mechanical properties of materials, trans. from English, ed. G.I.Barenblatt, M., 1966; 7. Fundamentals of the theory of elasticity and plasticity: a textbook for students of engineering specialties of universities / VG Zubchaninov. - M.: Higher school, 1990 .-- 368 p. : ill. - ISBN 5-06-000706-5. 8. Regel VR, Slutsker AI, Tomashevsky EE, The kinetic nature of the strength of solid bodies, M., 1974. 9. Sokolovsky V.V., Theory of plasticity, 3rd ed., Moscow, 1969. 10. Feodosiev V.I. Strength of materials. - M .: Publishing house of MSTU im. N.E. Bauman, 1999.S. 86. ISBN 5-7038-1340-9. 11. Numerical methods in the theory of elasticity and plasticity: textbook. manual for high fur boots. / B.E. Victory. - M .: MGU, 1981 .-- 343 s
The relative elongation, determined on long samples, is designated δ 10, on short δ 5, and always δ 5\u003e δ 10.