Copper, properties, compounds, alloys, production, application

The main task of engineering design is the selection of the optimal profile section and structural material. It is necessary to find exactly the size that will ensure that the shape of the system is maintained with the minimum possible mass under the influence of load. For example, what kind of steel should be used as a span beam for a structure? The material may be used irrationally, installation will become more complicated and the structure will become heavier, and financial costs will increase. This question will be answered by such a concept as the elastic modulus of steel. It will also allow you to avoid these problems at a very early stage.

Modulus of elasticity of steel

►Elasticity modulus of steel
►Elasticity modulus of different steel grades

►Table of strength moduli of steel grades

►Elastic modulus for metals and alloys

►Elasticity of steels

►Strength limit

When designing steel products or structural elements, the ability of the alloy to withstand multidirectional types of loads is taken into account: impact, bending, tensile, compressive. The value of the elastic modulus of steel, along with hardness and other characteristics, shows resistance to these influences.

For example, in reinforced concrete construction, longitudinal and transverse reinforcing bars are used. In the horizontal plane they are subject to tension, and in the vertical plane they are subject to pressure from the entire mass of the structure. In places where stress is concentrated: corners, technological openings, elevator shafts and flights of stairs, more reinforcement is placed. The ability of concrete to absorb water causes constant changes in compressive and tensile loads.

Let's look at another example. During wartime, many developments in the field of aviation were created. The most common causes of accidents were engine fires. Taking off from the ground, the plane enters atmospheric layers with rarefied air and its body expands; the reverse process occurs during landing. In addition, the structure is affected by the resistance of air flows, the pressure of curved layers of air and other forces. Despite their strength, the alloys existing at that time were not always suitable for the manufacture of critical parts; this mainly led to ruptures of fuel tanks.

In various types of industry, parts of moving mechanisms are made from steel: springs, leaf springs. The grades used for such purposes are not prone to cracking under constantly changing loads.

Basic information

Young's modulus (also called the longitudinal modulus of elasticity and the modulus of elasticity of the first kind) is an important mechanical characteristic of a substance. It is a measure of resistance to longitudinal deformation and determines the degree of rigidity. It is designated as E; measured in n/m 2 or in Pa.

This important coefficient is used when calculating the rigidity of workpieces, assemblies and structures, and in determining their resistance to longitudinal deformations. Substances used for the manufacture of industrial and building structures, as a rule, have very large E values. And therefore, in practice, E values ​​for them are given in gigaPascals (10 12 Pa)

The value of E for rods can be calculated; for more complex structures it is measured during experiments.

Approximate values ​​of E can be obtained from the graph constructed during tensile tests.

Tensile test schedule

E is the quotient of normal stress σ divided by relative elongation ε.

Hooke's law can also be formulated using Young's modulus.

Modulus of elasticity of steel

The elasticity of solids is the ability to return to its original shape after the cessation of deforming influences. For example, a block of plasticine has zero springiness, while rubber products can be compressed and stretched. When various forces are applied to objects and materials, they become deformed. Depending on the physical properties of the body or substance, two types of deformation are distinguished:

• Elastic - the consequences disappear after the action of external forces ends;
• Plastic - irreversible change in shape.

The modulus of elasticity is the name of several physical quantities that characterize the tendency of a solid body to deform elastically.

The concept was first introduced by Thomas Young. The scientist suspended weights from metal rods and observed their elongation. Some samples doubled in length, while others were torn during the experiment.

Today the definition combines a number of properties of physical bodies:

Young's modulus: Calculated by the formula E= σ/ε, where σ is the stress equal to the force divided by the area of ​​its application, and ε is the elastic deformation, equivalent to the ratio of the elongation of the sample from the beginning of deformation to the compression after its cessation.

Shear modulus (G or μ): the ability to resist deformation while maintaining volume when the direction of loads is tangential. For example, when hitting the head of a nail, if it was not made at a right angle, the product becomes distorted. In sopromat, the value is used to calculate shifts and torsion.

Bulk modulus or bulk modulus (K): changes caused by the action of a confining stress, such as hydrostatic pressure.

Punch ratio (Ⅴ or μ): the ratio of transverse compression to longitudinal elongation, calculated for material samples. For absolutely fragile substances it is zero.

Lamé's constant: the energy that provokes a return to its original form is calculated through the construction of scalar combinations.

The modulus of elasticity of steel is correlated with a number of other physical quantities. For example, when conducting a tensile experiment, it is important to take into account the tensile strength, exceeding which results in destruction of the part.

• Ratio of rigidity and ductility;
• Impact strength;
• Yield strength;
• Relative compression and tension (longitudinal and transverse);
• Strength limits under shock, dynamic and other loads.

The use of a number of approaches is determined by the requirements for the mechanical properties of materials in various industries, construction, and instrument making.

Unit of measurement and formulas

The SI unit of Young's modulus is Newton per meter squared (N/m²), i.e. Pascal (Pa).

Formulas

There are several formulas from which you can calculate Young's modulus. For example, Hooke's law.

Hooke's law

You can calculate Young's modulus using these formulas (we will do this using an example). Because of this law, there are several interesting equalities that can be useful for calculations.

Hooke's law (this one describes phenomena in the body, in differential form):

• σ - mechanical stress
• E - Young's modulus (elastic modulus)
• ε—relative elongation

Hooke's Law (this one describes phenomena in the body)

• Fupr - elastic force
• k × Δl—body elongation

• Fupr - elastic force
• E - Young's modulus (elastic modulus)
• S - cross-sectional area
• l - initial body length
• Δl - body elongation

• Fpr/S - mechanical stress, denoted as σ
• Δl/l - relative elongation, denoted as ε

It should be noted that this law applies to the point where the material is irreversibly deformed and no longer returns to its original shape. At what point this happens depends on the material. If the material is very stiff (meaning a high elastic modulus reading), then this point may coincide with rupture/deformation.

Other formulas for calculating Young's modulus (elastic modulus)

• E - Young's modulus (elastic modulus)
• k - body stiffness
• l is the original length of the rod
• S - cross-sectional area

Or you can express k (body stiffness):

• k - body stiffness
• E - Young's modulus (elastic modulus)
• S - cross-sectional area
• l is the initial length of the rod/body

An example of solving the problem (via Hooke's law):

A wire 2.5 meters long and with a cross-sectional area of ​​2.5 millimeters² is elongated by 1 millimeter under a force of 50 newtons. Determine Young's modulus.

• l = 2.5 m
• F=50H
• E = ?

We will search through Hooke's law (σ = E × ε).

Remember from Hooke's law:

σ = F / S (remember that Fpr/S is mechanical stress, denoted as σ)

ε = Δl/l (and this is the relative elongation, denoted as ε)

Substitute into the formula (σ = E × ε):

For example, in our table, cadmium has such a Young’s modulus.

Elastic modulus of different steel grades

Spring steel alloys have the greatest ability to resist deformation. These materials are characterized by high yield strength. The value shows the stress at which the deformation increases without external influences, for example, when bending and twisting.

The elasticity characteristics of steel depend on alloying elements and the structure of the crystal lattice. Carbon imparts hardness to the steel alloy, but in high concentrations it reduces ductility and springiness. The main alloying additives that increase elastic properties: silicon, manganese, nickel, tungsten.

Often, the desired indicators can be achieved only with the help of special heat treatment modes. In this way, all fragments of the part will have uniform fluidity indicators, and weak areas will be eliminated. Otherwise, the product may break, burst or crack. Grades 60G and 65G have such characteristics as tensile strength, viscosity, wear resistance, they are used for the manufacture of industrial springs and musical strings.

The metallurgical industry has created several hundred grades of steel with different elastic moduli. The table shows the characteristics of popular alloys.

Table of strength moduli of steel grades

Modulus of elasticity for metals and alloys

Elasticity of steels

Material tensile strength

This is the limit of the stress that occurs, after which the sample begins to fail.

Static tensile strength is measured under prolonged application of deforming force, dynamic - under short-term, impact nature of such force. For most substances the dynamic limit is greater than the static limit.

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Tensile strength tool

In addition, there are limits to the material's compressive and tensile strength. They are determined experimentally on a test bench, by stretching or compressing samples with powerful hydraulic machines equipped with precise dynamometers and pressure meters. If it is impossible to achieve the required pressure hydraulically, a directed explosion in a sealed capsule is sometimes used.

Allowable tensile stress in some materials

From life experience we know that different materials resist changes in shape in different ways. The strength characteristics of crystalline and other solids are determined by the forces of interatomic interaction. As interatomic distances increase, the forces that attract atoms to each other also increase. These forces reach a maximum at a certain amount of stress, equal to approximately one tenth of Young's modulus.

Tensile test

This value is called theoretical strength; when it is exceeded, the destruction of the material begins. In reality, destruction begins at lower values, since the structure of real samples is heterogeneous. This causes an uneven distribution of stresses, and destruction begins from those areas where the stresses are maximum.

These numbers are taken into account by designers when choosing the material for parts of a future product. Strength calculations are also carried out using them. For example, cables used for lifting and transport operations must have a tenfold safety margin. They are periodically checked by hanging a load ten times greater than the cable's rated load capacity.

The safety margins built into critical structures are also multiple.

Safety factor

To quantify the safety factor during design, a safety factor is used. It characterizes the product’s ability to withstand overloads above rated loads. For household products it is small, but for critical components and parts that, if destroyed, can pose a danger to human life and health, it is made multiple times.

Accurate calculation of strength characteristics makes it possible to create a sufficient safety margin and at the same time not to overweight the structure, worsening its performance characteristics. For such calculations, complex mathematical methods and sophisticated software are used. The most important designs are calculated on supercomputers.

Types of loads

When using metals, different static and dynamic loads are applied. In the theory of strength, it is customary to define the following types of loads.

• Compression - an acting force compresses an object, causing a decrease in length along the direction of application of the load. This deformation is felt by frames, supporting surfaces, racks and a number of other structures that can withstand a certain weight. Bridges and crossings, car and tractor frames, foundations and reinforcement - all these structural elements are under constant compression.

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• Tension - the load tends to lengthen the body in a certain direction. Lifting and transport machines and mechanisms experience similar loads when lifting and carrying loads.

• Shear and shear - such loading is observed in the case of forces directed along the same axis towards each other. Connecting elements (bolts, screws, rivets and other hardware) experience this type of load. The design of housings, metal frames, gearboxes and other components of mechanisms and machines necessarily contains connecting parts. The performance of devices depends on their strength.

• Torsion - if a pair of forces acting on an object are located at a certain distance from each other, then a torque occurs. These forces tend to produce torsional deformation. Similar loads are observed in gearboxes; the shafts experience just such a load. It is most often inconsistent in meaning. Over time, the magnitude of the acting forces changes.

• Bending – a load that changes the curvature of objects is considered bending. Bridges, crossbars, consoles, lifting and transport mechanisms and other parts experience similar loading.