Limitations when using a plasticity model based on deformation theory. Mechanical and plastic properties of materials Properties of mortar mixtures


Naturally, the properties of a freshly prepared mortar mixture and a hardened mortar are completely different. The main properties of the mortar mixture are workability, plasticity (mobility) and water-holding capacity, and of hardened mortars - density, strength and durability.
The correct choice of application area for solutions depends entirely on their properties.

Properties of mortar mixtures

Workability- the property of the mortar mixture to be easily laid in a dense and thin layer on a porous base and not to delaminate during storage, transportation and pumping.
It depends on the plasticity (mobility) and water-holding capacity of the mixture.

Plasticity of the mixture characterized by its mobility, i.e. the ability to spread under the influence of its own weight or external forces applied to it. The mobility of almost all mortar mixtures is determined by the immersion depth (in cm) of a standard cone weighing (300:4:2) g.
Cone height 180 mm, base diameter 150 mm, apex angle 30 °.
In the laboratory, the cone is mounted on a tripod (Fig. 1,a); in a construction site, it is suspended on a chain with a ring (Fig. 1,6).


Fig.1. Tripod

Cone 3, held by the ring, is brought to the mixture so that its apex touches its surface. Then the cone is released and it sinks into the mixture under its own weight.
Using the divisions on a scale of 6 or on the surface of the cone, the depth of its immersion in the mixture is determined. If the cone is immersed to a depth of 6 cm, this means that the mobility of the mortar mixture is 6 cm.

Mobility of the mortar mixture depends primarily on the amount of water and binder, the type of binder and filler, the ratio between binder and filler. Fatty mortar mixtures are more mobile than thin ones. All other things being equal, solutions based on lime and clay are more mobile than solutions based on cement; solutions on natural sand are more mobile than solutions on artificial (crushed) sand.
The type of binder is selected and the composition of the mortar is set depending on the required strength of the mortar and the operating conditions of the building.

The mobility of the mortar mixture can be adjusted by increasing or decreasing the consumption of binder or water. By increasing the content of water and binder in the mortar mixture, more plastic (mobile) and workable mixtures are obtained

A workable mortar mixture is obtained with the correctly assigned grain composition of its solid components (sand, binder, additives). The binder dough not only fills the voids between the grains of sand, but also evenly envelops the grains of sand with a thin layer, reducing internal friction.
A mortar mixture with normal water-holding capacity is workable and easy to lay, soft, the plasterer does not reach for the shovel, and ensures high labor productivity.

The quality of masonry and plaster depends on the workability of the mixture.
A correctly selected and well-mixed mortar mixture tightly fills uneven areas, depressions, and cracks in the base, so a large contact area is obtained between the mortar and the base, as a result, the solidity of the masonry and plaster increases, and their durability increases.

Delamination- the ability of the mortar mixture to separate into solid and liquid fractions when transporting and pumping it through pipes and hoses.
The mortar mixture is often transported by dump trucks and moved through pipelines using mortar pumps. At the same time, it is not uncommon for the mixture to separate into water (liquid phase) and sand and binder (solid phase), as a result of which plugs can form in pipes and hoses, the removal of which is associated with large losses of labor and time.
The stratification properties of the mortar mixture are determined in the laboratory.

A simple way to check the mixture for stratification is as follows. The mortar mixture is placed in a bucket in a layer about 30 cm high and its mobility is determined with a standard cone. After 30 minutes, remove the upper part of the solution (about 20 cm) and determine the immersion depth of the cone again. If the difference in the immersion values ​​of the cone is close to zero, then the mortar mixture is considered non-separating; if it is within 2 cm, the mixture is considered to be of medium delamination.
A difference in cone immersion values ​​of more than 2 cm indicates that the mortar mixture is stratifying.

If the composition of the mortar mixture is selected correctly and the water-binding ratio is set correctly, then the mortar mixture will be mobile, workable, it will have good water-holding capacity and will not delaminate.
Plasticizing additives, both inorganic and organic, increase the water-holding capacity of mortar mixtures and reduce their delamination

Clay- a plastic natural material used in construction, folk crafts, treatment and healing of the body and in other areas of human life. It is this widespread use that is determined by certain qualities and properties of clay. And the properties of clay are largely influenced by its composition.

Application of clay

Clay is very accessible, and its benefits are invaluable, and therefore it has been used by people since ancient times. There are many mentions of this wonderful material in history textbooks 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 brick. In some countries and regions, clay is still used to build houses - mud huts; the use of clay is widespread in the construction of brick ovens, where clay serves as a binder (as cement). The same clay is also used for plastering stoves.

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 the beneficial elements of clay. Of course, not all clay will work here.

Souvenirs and dishes. I combine two large directions into one, since many examples of dishes are only of a souvenir nature. Plates, pots, jugs and vases are present in abundance in modern stores. Not a single fair is complete without the sale of clay souvenirs - smoky toys, whistles, signs, keychains and much more. You and I will try to create a lot of things ourselves.

Clay can be included in composition of other materials. Finely ground Chasovoyar clay, for example, is an element of artistic paints (gouache), sauce, pastels and sanguine. Read about this in the "Help to the Artist" articles.

Properties of clay

Color. Clay of various compositions has many shades. The clay is called by its colors: red, blue, white... However, upon 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 retain the shape given to it that allowed man to find the use of clay in his everyday life. It is worth noting here that everything depends on the consistency - the ratio of the amount of water, clay and sand. For various works different compositions are needed. So, for sculpting, sand may be completely unnecessary.

Hygroscopicity allows 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 earthenware and porcelain, which are indispensable in the modern world.

Fire resistance. A property used more in construction than in artistic crafts, except for the firing of products. The firing technology is different for a particular clay composition. Closely related to drying and firing is the property of clay shrinkage or compressibility - 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 a lot of iron oxides. Clay basically contains certain substances - clay minerals - which are formed during various natural phenomena. The format of the article does not provide for consideration of the chemical properties and composition of clay, so I will not go into detail.

The composition of clay suitable for use in folk crafts, as already mentioned, is determined by three important elements: clay minerals, water and sand.

The proportions of these elements can be changed, although it is much easier to add than to 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. Sand is very easy to add, but removing it from the clay is a non-trivial task.

There are “lean” and “fat” clays. The “fat content” scale determines the plasticity coefficient, and the binding properties of the clay allows you to adjust the fat content by mixing it with others natural materials, for example, with sand. Lean clay has less plasticity, its binding force is weaker, but it shrinks less during drying and firing.

Clay deposits are found in varying states around the world. This ensured its use by artisans of different nationalities, and contributed to the emergence of such a variety of products and technologies.

Craftsmen have learned to control the behavior and condition of clay through various additions to the composition. This way you can thin the clay, elutriate it, give it greater fire resistance, and reduce shrinkage. As a result of such manipulations, an experienced craftsman will be able to ultimately obtain a high-quality, highly artistic product.

Essay

by discipline:

"Technology of structural materials"

"Physical basis of plasticity and strength of metals"

Is done by a student

Checked by the teacher


Introduction

The main mechanical properties are strength, plasticity, elasticity, viscosity, hardness.

Knowing the mechanical properties, the designer, when designing, reasonably selects the appropriate material that ensures the reliability and durability of machines and structures with their minimum weight.

Plasticity and strength are among the most important properties solids.

Both of these properties, mutually related to each other, determine the ability of solids to resist irreversible shape changes and macroscopic destruction, i.e., the division of a body into parts as a result of microscopic cracks appearing in it under the influence of external or internal force fields.

For a technologist, plasticity is very important, determining the possibility of manufacturing products. different ways pressure treatments based on plastic deformation of metal.

Materials with increased ductility are less sensitive to stress concentrators and other embrittlement factors.

Based on indicators of strength, ductility, etc., a comparative assessment of various metals and alloys is carried out, as well as quality control during the manufacture of products.

In physics and technology, plasticity is the ability of a material to obtain residual deformations without destruction and retain them after the load is removed.

The property of plasticity is crucial 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 changes 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 basis of the plasticity and strength of metals.

1. Physical basis of the strength of metals

Strength is a fundamental property of solids. It determines the body’s ability to withstand the action of external forces without destruction. Ultimately, as is known, strength is determined by the magnitude 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 remains unclear about the nature of strength, about the essence of the processes occurring in a material under load. In matters of strength, not only is there no complete physical theory, but even on the most basic ideas there are differences of opinion and opposing opinions.

The ultimate goal of studying the mechanism of destruction should be to clarify the basic principles of creating new materials with given properties, improving existing materials and rationalizing 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 temporary resistance, determined at the rupture of a cylindrical sample that has been previously annealed. Based on their strength, metals can be divided into the following groups:

fragile (temporary resistance does not exceed 50 MPa) - tin, lead, bismuth, as well as soft alkali metals;

durable (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 does not apply to mercury, since it is a liquid.

The tensile strength of metals is indicated in Table 1.


Table 1.

Strength of metals

Majority technical characteristics strength is determined as a result of a static tensile test. The sample, fixed in the grips of the tensile testing machine, is deformed under a static, gradually increasing load. During testing, as a rule, a tensile diagram expressing the relationship between load and deformation is automatically recorded. Small deformations are determined with very high accuracy by strain gauges.

To eliminate the influence of sample sizes, tensile tests are carried out on standard samples with a certain ratio between the calculated length l0 and cross-sectional area F0.

The most widely used samples round section: long with l 0 /d 0 = 10 or short with l 0 /d 0 = 5 (where d 0 is the original diameter of the sample).

In Fig. 1a shows the tensile diagram of low-carbon annealed steel. At 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 effective stress

where P is the applied load; F o is the initial cross-sectional area of ​​the sample.

The load at point a, which defines the end of the straight section of the tensile diagram, corresponds to the limit of proportionality.

Theoretical limit of proportionality- maximum stress up to which the linear relationship between stress (load) and deformation is maintained

σ pc = P pc / F 0.

Since there may be errors when determining the position of point a on the diagram, they usually use conditional limit of proportionality, which is understood as the voltage that causes a certain amount of deviation from linear dependence, for example tg alpha changes to 50% of its original value.

The linear relationship between stress and strain can be expressed by Hooke's law:

σ = E epsilon,

where epsilon = (delta l/l o) 100% - relative deformation;

delta l - absolute elongation, mm;

l 0 - initial length of the sample, mm.

Fig. 1 Tensile diagram of low-carbon steel (a) and diagram for determining the conditional yield strength σ0.2 (b)

The proportionality coefficient E (graphically equal to tg alpha), which characterizes the elastic properties of the material, is called the normal elastic modulus.

At a given stress value, as the modulus increases, the magnitude of elastic deformation decreases, i.e., the rigidity (stability) of the structure (product) increases. Therefore, modulus E is also called stiffness modulus.

The magnitude of the modulus depends on the nature of the alloy and changes slightly with changes in its composition, structure, and heat treatment.

For example, for various carbon and alloy steels after any processing E = 21000 kgf/mm 2.

Theoretical elastic limit- the maximum stress up to which the sample receives only elastic deformation:

σ up = P up /F 0 .

If the effective stress in a part (structure) is less than σ unit, then the material will work in the region of elastic deformations.

Due to the difficulty of determining σ unit, they practically use conditional elastic limit, which is understood as the stress that causes a residual deformation of 0.005-0.05% of the initial calculated length of the sample. The designation of the conditional elastic limit indicates the amount of residual deformation, 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 strength- physical and conditional - characterizes the material’s resistance to small plastic deformations.

Physical yield strength- stress at which an increase in deformation occurs under constant load

σ t = P T /F 0 .

In the tensile diagram, the yield strength corresponds to the horizontal section c - d, when plastic deformation (elongation) is observed - the “flow” of the metal under constant load.

Most technical metals and alloys do not have a yield plateau. For them it is most often determined proof strength- stress causing residual deformation equal to 0.2% of the initial design length of the sample (Fig. 1, b):

σ0.2 =P 0.2 /F 0

With further loading, plastic deformation increases more and more, being evenly distributed throughout the entire volume of the sample.

At point B, where the load reaches its maximum value, at the most weak point the sample begins to form a “neck” - a narrowing of the cross section; the deformation is concentrated in one area - it goes from uniform to local.

The stress in the material at this point in the test is called the tensile strength.

When designing structural elements and machine parts, it is necessary to know the mechanical and plastic properties of materials. For this purpose they are made standard samples, which are subject to destruction in the testing machine. For tensile testing, it is recommended to use cylindrical and flat samples. The calculated length of cylindrical samples should be equal to ℓ 0 =5d 0 or ℓ 0 =10d 0. Samples with a design length ℓ 0 =5d 0 are called short, and samples with ℓ 0 =10d 0 are called long. The use of short samples is preferable. Samples with a diameter d 0 = 10 mm are used as the main ones. Specimens with smaller (sometimes larger) diameters or non-circular cross-sections are called proportional. The estimated length ℓ 0 on the sample differs in risks.

The estimated length of the sample can be expressed in terms of the cross-sectional area:

So for short samples:

for long samples:

These relationships are used to determine the design length of specimens of rectangular cross-section.

The relationships between the working ℓ and calculated ℓ 0 lengths take:

for cylindrical samples: from ℓ = ℓ 0 + 0.5d 0 to ℓ = ℓ 0 + 3d 0 ;

for flat samples with a thickness of 4 mm and more:

The main objective of a tensile test is to construct a stress-strain diagram, i.e., the relationship between the force acting on the sample and its elongation.

The testing machine imparts a forced elongation to the sample and records the resistance force of the sample, i.e. the load corresponding to this elongation. The results of the experiment are recorded using a diagramming apparatus on paper in the form of a tensile diagram in coordinates F – Δℓ. A sample tensile curve typical for mild steel is shown in the figure.

This curve can be divided into four plots. The straight section of OA is called area of ​​elasticity. Here the sample material experiences only 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 section is called site general fluidity, and segment VK – turnover platform. Here there is a significant change in the length of the sample without a noticeable increase in load. The presence of a yield plateau is characteristic of low-carbon steel.

The section of the CS is called hardening area. Here the material again exhibits the ability to increase resistance with increasing deformation. The region of material hardening on the tensile diagram extends to point C, the ordinate of which is equal to the greatest load on the sample F max.

Starting from point C, the nature of the deformation of the sample changes sharply. As the load on the sample increased from 0 to F, all sections of the sample elongated equally—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 sample occurs with a decrease in force (SD section). In this case, the elongation of the sample is local in nature. In this place of the sample, the cross-sectional dimensions intensively decrease (a so-called neck is formed) and the length of this section increases. Therefore, the SD section is called site of local turnover. Dot D corresponds to in the diagram destruction of the sample.

If the test sample is not brought to destruction, but is unloaded (for example, at point H), then during the unloading process the relationship between the force P and the elongation Δℓ will be represented by a straight line NM, which will be parallel to OA. The length of the unloaded sample will be greater than the original length by OH. The segment OM represents residual or plastic elongation. When the sample is reloaded, the tensile diagram takes the form of a straight line NM and then an NSD curve, as if there was no intermediate unloading.

A range of plastic materials(alloy steels, bronzes, brass, aluminum alloys, titanium alloys, etc.) have no physical yield strength. In the stress-strain diagram of such materials, after point B there is a rapid increase in plastic deformation. Ultimate yield strength F t corresponds to point B on the tension diagram, is defined as the load at which the plastic deformation is 0.2%.

To quantify the mechanical properties of a material, the stress-strain diagram F= f(Δℓ) (rebuilt in coordinates. For this, the force values ​​F are divided by the original area of ​​the sample A 0, i.e. = F/ A 0, and the elongation Δℓ is divided by the original length of the calculated part of the sample ℓ 0,

As a result, we obtain a diagram of the dependence of normal stress on relative longitudinal strain, which will characterize the properties of the material, and not the properties of a particular sample. This diagram is called conditional, since the calculation does not take into account changes in the length and cross-sectional area of ​​the sample during stretching.

The main mechanical characteristics are:

Proportionality limit: σ pts = F pts / A 0

Yield strength: σ t = F t / A 0

Tensile strength: σ in = F in / A 0

Plasticity characteristics:

relative extension

relative narrowing

where A w is the cross-sectional area of ​​the sample (neck) at the narrowest point after destruction.

Specific work of deformation: a = F in Δℓ/V,

where V is the volume of the test sample,

V = A 0 ·ℓ 0 .

Let us recall that the maximum stresses σ in cannot exceed 1200 MPa for structural materials.

Compression diagram of plastic materials

Steel samples are placed in a testing machine and subjected to compression.

In the first stage of loading a steel sample, the material experiences elastic deformation. The relationship between applied force and deformation in the diagram is linear. Some time after the start of the test, the material reaches a state of fluidity. At the same time, the arrow of the strength meter stops, and the ordinates on the diagram stop growing. The sample is deformed under constant load. The load corresponding to the fluidity state F T of the material is recorded in the test log. With further compression of the sample, the strength meter readings 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 explained by the fact that there is a frictional force between the support plates and the ends of the sample, which does not allow parts of the sample adjacent to the support plates to move in the transverse direction. This phenomenon can be weakened by lubricating the ends of the sample.

It is not possible to bring a steel sample to destruction. The test stops at a load approximately twice the yield strength F T. The appearance of the samples before and after the test is shown in the figure. A typical compression diagram of low-carbon steel in coordinates F – Δℓ is shown in Fig. on right.

Diagram of tension and compression of brittle materials

The testing procedure for brittle materials is the same as for testing ductile materials. Therefore, let us dwell 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 lack a yield plateau, although many materials have certain plastic properties. For these materials the tensile strength is taken as a dangerous condition. It should always be remembered that The tensile strength of brittle materials is many times greater in compression. For cast iron this value reaches 3-4 times. As for building materials, this difference can reach tenfold.

Experiments have shown that the Genki-Ilyushin equations underlying the plasticity model describe the process of monotonic loading quite well. With this process, at all stages of loading ( external forces, temperatures, etc.) the intensity of stress increases all the time.

Monotonic loading is usually realized with simple loading, when all external force factors change in proportion to one increasing parameter. With simple loading, the relationship between external loads during the loading process remains unchanged. If the unloading process begins, when the intensity of stress decreases at all points of the body (for example, when external forces are removed), then the increase (decrease) in stress and strain at the unloading stage is determined on the basis of elasticity equations (law of unloading; see Fig. 5.15). The main limitations of the plasticity model under consideration are related to the fact that the plasticity equations refer to the end point of the process and therefore do not take into account the loading history.

If it is clear from physical relationships that monotonic loading occurs, then this drawback is insignificant.

Within the framework of the applied plasticity model, it is possible to take into account the actual loading history if we consider loading as a set of several stages. If unloading occurs at any intermediate stage, then the calculation is carried out using elasticity equations.

Rice. 5.15. Unloading process during elastoplastic deformation

Other models of plasticity.

More advanced, but also much more complex, is the plasticity model based on the plastic flow theory of Saint-Venant, Misesat Prandtl and Reis. In accordance with this theory, the increments of elastic and plastic deformations are considered separately:

The increment in plastic deformation is taken to be proportional to the stress deviator components:

where is the increment in stress intensity. The function is determined based on experimental data when the samples are stretched.

A presentation of the theory of plastic flow and other models of plasticity can be found in the specialized literature.