Online calculator for determining the permissible stresses of materials: steels and alloys of aluminum, copper and titanium.

The online calculator determines the calculated permissible stresses σ depending on the design temperature for various grades of materials of the following types: carbon steel, chromium steel, austenitic steel, austenitic-ferritic steel, aluminum and its alloys, copper and its alloys, titanium and its alloys according GOST-52857.1-2007 [1].

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I. Calculation method:

Allowable stresses were determined according to GOST-52857.1-2007 [1].

for carbon and low alloy steels

St3, 09G2S, 16GS, 20, 20K, 10, 10G2, 09G2, 17GS, 17G1S, 10G2S1:

1. At design temperatures below 20°C, the permissible stresses are taken to be the same as at 20°C, subject to the permissible use of the material at a given temperature.
2. For intermediate design wall temperatures, the permissible stress is determined by linear interpolation with rounding the results down to 0.5 MPa.
3. For steel grade 20 at Re/20e/20/220.
4. For steel grade 10G2 at Rр0.2/20р0.2/20/270.
5. For steel grades 09G2S, 16GS, strength classes 265 and 296 according to GOST 19281, the permissible stresses, regardless of the sheet thickness, are determined for thicknesses over 32 mm.
6. The permissible stresses located below the horizontal line are valid for a service life of no more than 105 hours. For a design service life of up to 2*105 hours, the permissible stress located below the horizontal line is multiplied by the coefficient: for carbon steel by 0.8; for manganese steel by 0.85 at temperatures <450 °C and by 0.8 at temperatures from 450 °C to 500 °C inclusive.

Allowable stresses for carbon steels of ordinary quality in the hot-rolled state

table 1

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for heat-resistant chromium steels

12XM, 12MX, 15XM, 15X5M, 15X5M-U:

1. At design temperatures below 20 °C, the permissible stresses are taken to be the same as at 20 °C, subject to the permissible use of the material at a given temperature.
2. For intermediate design wall temperatures, the permissible stress is determined by linear interpolation with rounding the results down to 0.5 MPa.
3. The permissible stresses located below the horizontal line are valid for a service life of 105 hours. For a design service life of up to 2 * 105 hours, the permissible stress located below the horizontal line is multiplied by a factor of 0.85.

Types of tensile strength

Tensile strength is one of the main mechanical parameters of steel, as well as any other structural material.

This value is used in strength calculations of parts and structures; based on it, it is decided whether a given material is applicable in a particular area or whether a more durable one needs to be selected.

The following types of tensile strength are distinguished:

• compression - determines the ability of a material to resist the pressure of an external force;
• bending - affects the flexibility of parts;
• torsion - shows how suitable the material is for loaded drive shafts that transmit torque;
• stretching

Types of material strength tests

The scientific name for the parameter used in standards and other official documents is tensile strength.

for heat-resistant, heat-resistant and corrosion-resistant austenitic steels

03X21H21M4GB, 03X18H11, 03X17H14M3, 08X18H10T, 08X18H12T, 08X17H13M2T, 08X17H15M3T, 12X18H10T, 12X18H12T, 10X17H13M2T, 10X 17H13M3T, 10X14G14H4:

1. At design temperatures below 20 °C, the permissible stresses are taken to be the same as at 20 °C, subject to the permissible use of the material at a given temperature.
2. For intermediate design wall temperatures, the permissible stress is determined by interpolating the two closest values ​​​​indicated in the table, with the results rounded down to the nearest 0.5 MPa.
3. For forgings made of steel grades 12Х18Н10Т, 10Х17Н13M2T, 10Х17Н13М3Т, the permissible stresses at temperatures up to 550 °C are multiplied by 0.83.
4. For long rolled steel grades 12Х18Н10Т, 10Х17Н13M2T, 10Х17Н13М3Т, permissible stresses at temperatures up to 550 °С are multiplied by the ratio (R*p0.2/20) / 240. (R*p0.2/20 - the yield strength of the long rolled material is determined by GOST 5949).
5. For forgings and long products made of steel grade 08X18H10T, the permissible stresses at temperatures up to 550 °C are multiplied by 0.95.
6. For forgings made of steel grade 03X17H14M3, the permissible stresses are multiplied by 0.9.
7. For forgings made of steel grade 03X18H11, the permissible stresses are multiplied by 0.9; for long products made of steel grade 03X18H11, the permissible stresses are multiplied by 0.8.
8. For pipes made of steel grade 03Х21Н21М4ГБ (ZI-35), the permissible stresses are multiplied by 0.88.
9. For forgings made of steel grade 03Х21Н21М4ГБ (ZI-35), the permissible stresses are multiplied by the ratio (R*p0.2/20) / 250. (R*p0.2/20 is the yield strength of the forging material, determined according to GOST 25054).
10. The permissible stresses located below the horizontal line are valid for a service life of no more than 105 hours.

For a design service life of up to 2*105 hours, the permissible voltage located below the horizontal line is multiplied by a factor of 0.9 at temperatures <600 °C and by a factor of 0.8 at temperatures from 600 °C to 700 °C inclusive.

Mechanical properties and permissible stresses of alloy structural steels

table 3

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for titanium and its alloys

VT1-0, OT4-0, AT3, VT1-00:

1. At design temperatures below 20 °C, the permissible stresses are taken to be the same as at 20 °C, subject to the permissibility of using the material at a given temperature.
2. For forgings and rods, the permissible stresses are multiplied by 0.8.

II. Definitions and notations:

Re/20 - minimum value of the yield strength at a temperature of 20 °C, MPa; Rр0.2/20 - minimum value of the conditional yield strength at a permanent elongation of 0.2% at a temperature of 20 °C, MPa. permissible stress - the highest stress that can be allowed in a structure, subject to its safe, reliable and durable operation. The value of the permissible stress is established by dividing the tensile strength, yield strength, etc. by a value greater than one, called the safety factor. design temperature - the temperature of the wall of equipment or a pipeline, equal to the maximum arithmetic mean value of the temperatures on its outer and inner surfaces in one section under normal operating conditions (for parts of nuclear reactor vessels, the design temperature is determined taking into account internal heat releases as the average integral value of the temperature distribution over the thickness of the vessel wall ( PNAE G-7-002-86, clause 2.2; PNAE G-7-008-89, appendix 1).

Design temperature

• [1], clause 5.1. The design temperature is used to determine the physical and mechanical characteristics of the material and permissible stresses, as well as when calculating strength taking into account temperature effects.
• [1], clause 5.2. The design temperature is determined on the basis of thermal calculations or test results, or operating experience of similar vessels.
• The highest wall temperature is taken as the design temperature of the wall of the vessel or apparatus. At temperatures below 20 °C, a temperature of 20 °C is taken as the design temperature when determining permissible stresses.
• [1], clause 5.3. If it is impossible to carry out thermal calculations or measurements and if during operation the wall temperature rises to the temperature of the medium in contact with the wall, then the highest temperature of the medium, but not lower than 20 °C, should be taken as the design temperature.
• When heating with an open flame, exhaust gases or electric heaters, the design temperature is taken equal to the ambient temperature increased by 20 °C for closed heating and by 50 °C for direct heating, unless more accurate data are available.
• [1], clause 5.4. If a vessel or apparatus is operated under several different loading modes or different elements of the apparatus operate under different conditions, for each mode its own design temperature can be determined (GOST-52857.1-2007, clause 5).

III. Note:

The source data block is highlighted in yellow, the intermediate calculation block is highlighted in blue, and the solution block is highlighted in green.

How is strength testing performed?

Strength tests for tensile strength are carried out on special test benches.
One end of the test sample is fixedly fixed in them, and a drive mount, electromechanical or hydraulic, is attached to the other. This drive creates a smoothly increasing force that acts to break the sample, or to bend or twist it. Tensile test

The electronic control system records the tensile force and relative elongation, and other types of deformation of the sample.

Harmful impurities

These primarily include: phosphorus,

which, forming a solution with ferrite, increases the brittleness of steel, especially at low temperatures (cold brittleness) and reduces ductility at elevated temperatures;

sulfur,

making steel red-brittle (prone to cracking at temperatures of 800 - 1000 C) due to the formation of low-melting iron sulfide. Therefore, the content of sulfur and phosphorus in steel is limited; So in carbon steel St 3, sulfur is up to 0.05% and phosphorus is up to 0.04%.

The mechanical properties of steel are adversely affected by saturation with gases that can enter the metal in a molten state from the atmosphere. Oxygen acts like sulfur, but to a greater extent and increases the brittleness of steel. Unfixed nitrogen also reduces the quality of steel. Hydrogen, although retained in an insignificant amount (0.0007%), but concentrating near inclusions in intercrystalline regions and located mainly along the boundaries of blocks, causes high stresses in microvolumes, which leads to a decrease in the resistance of steel, brittle fracture, a decrease in tensile strength and plastic properties become. Therefore, molten steel (for example during welding) must be protected from exposure to the atmosphere.

Proof of Yield

In addition to the tensile strength, the related concept of yield strength, denoted σt, is widely used in engineering calculations. It is equal to the amount of tensile strength that must be created in the material in order for the deformation to continue to increase without increasing the load. This state of the material immediately precedes its destruction.

At the microlevel, at such stresses, interatomic bonds in the crystal lattice begin to break, and the specific load on the remaining bonds increases.

Alloying additives in alloys

These are substances deliberately added to the melt to improve the properties of the alloy and bring its parameters to the required ones. Some of them are added in large quantities (more than a percent), others in very small quantities. I most often use the following alloying additives:

• Chromium. Used to increase hardenability and hardness. Share - 0.8-0.2%.
• Bor. Improves cold brittleness and radiation resistance. Share - 0.003%.
• Titanium. Added to improve the structure of Cr-Mn alloys. Share - 0.1%.
• Molybdenum. Increases strength characteristics and corrosion resistance, reduces fragility. Share - 0.15-0.45%.
• Vanadium. Improves strength parameters and elasticity. Share - 0.1-0.3%.
• Nickel. Promotes an increase in strength characteristics and hardenability, but at the same time leads to an increase in fragility. This effect is compensated by the simultaneous addition of molybdenum.

Metallurgists also use more complex combinations of alloying additives, achieving unique combinations of physical and mechanical properties of steel. The cost of such grades is several times (or even tens of times) higher than the cost of conventional low-carbon steels. They are used for particularly critical structures and assemblies.

Using the properties of metals

Two important indicators - plasticity and PP - are interrelated. Materials with a large first parameter degrade much more slowly. They change their shape well and are subjected to various types of metal processing, including die stamping - that’s why car body elements are made from sheets. With low ductility, alloys are called brittle. They can be very hard, but at the same time have poor stretching, bending and deformation, for example, titanium.

Resistance

There are two types:

• Regulatory - prescribed for each type of steel in GOSTs.
• Calculated – obtained after calculations in a specific project.

The first option is rather theoretical; the second is used for practical tasks.

Young's modulus of elasticity and shear, Poisson's ratio values ​​(Table)

Elastic properties of bodies

Below are reference tables for commonly used constants;
if two of them are known, then this is quite sufficient to determine the elastic properties of a homogeneous isotropic solid. Young's modulus or modulus of longitudinal elasticity in dyn/cm2.

Shear modulus or torsional modulus G in dyn/cm2.

Compressive modulus or bulk modulus K in dynes/cm2.

Poisson's ratio µ is equal to the ratio of transverse relative compression to longitudinal relative tension.

For a homogeneous isotropic solid material, the following relationships between these constants hold:

Poisson's ratio has a positive sign and its value is usually between 0.25 and 0.5, but in some cases it can go beyond these limits. The degree of agreement between the observed values ​​of µ and those calculated using formula (b) is an indicator of the isotropy of the material.

Tables of Young's Modulus of Elasticity, Shear Modulus and Poisson's Ratio

Values ​​calculated from relations (a), (b), (c) are given in italics.

The experimental results given below are for common laboratory materials, mainly wires.