# Stresses and strains in steel

When an effort or combination of forces is applied to the material, including, to steel, then this material - steel - reacts to this by manifesting deformations, that is, changing its size, often in a very complex way.

## What is deformation

Each of us saw on TV, how extreme jumpers jump from a height of two hundred meters - from a bridge or a special platform, tied by the legs to a rubber rope. This rubber rope is stretched right before our eyes and you can clearly see how its section is significantly reduced. This rope stretches like this, so as not to hit the jumper on the ground, and then shrinks back. In this example deformation rubber rope - the change in its length and thickness is clearly visible.

But this is not always the case. for instance, if a sufficiently heavy load is suspended on a vertical steel wire, then the length of this wire, of course, increase, and its cross section will decrease. However, this deformation - changing the dimensions of the wire – not easy to notice. This requires special careful measurements of the length and diameter of this wire., as before hanging the load, so then, when he already hangs on it.

Mechanical properties of the material, including, become, describe the relationship between stresses, which act on the material due to applied loads and deformations, which this material experiences as a result of these stresses.

## What is voltage

Stress in its most general form is effort or load., divided by area, on which it acts. It's better to put it mathematically here, which gives the following expression:

σ = F / A,

where F is the effort (force), which affects the area A,
A - area, which is affected by the force F,
σ - stress on a site with area A.

Stresses in our time are expressed in units of MPa, which means a million (106) units N / m2 (newton per square meter).

There are two different ways to describe these very stresses.: engineering and true.

## Engineering stresses

Engineering stresses are commonly used in engineering calculations. They are based on the original cross-sectional area of ​​the part or product, which is considered. Since engineering stresses are calculated for the original - unloaded - area, then they do not take into account, that this cross-sectional area changed after a load was applied to the part. When the material is under stress, the resulting change in cross-sectional area depends on the mechanical properties of the material and the magnitude of the applied load.

## True voltages

True stresses are based on the actual at each instant - instantaneous - cross-sectional area. Therefore this, basically, more accurate method for describing stresses. However, since the magnitude of the true stresses is much more difficult to determine, than engineering stresses, then in practice they are rarely used.

## Deformation is a dimensionless number

The use of the concept of "deformation" allows you to quantitatively describe changes in the size and shape of the body, which arise when stresses are applied, which, in its turn, occur when some load is applied. It is important to note, that deformation is "pure", dimensionless number. Deformation does not have any units of measurement. To calculate the deformation, you need to compare the initial, original dimensions or shape of a body before applying a load with the same dimensions or shape of the same body under load.

formula, by which the deformation is calculated, has quantities of the same dimension (meters, centimeters, millimeters) as in the denominator, and in the numerator. therefore, understandable from school physics, that these dimensional units cancel each other out, and as a result we get a dimensionless number. This procedure is clearly visible when calculating stresses and strains for a simple tensile test..

## Tensile testing of metals

In conventional engineering tensile testing of metallic materials, including, become, get an engineering stress-strain diagram. This diagram is plotted from load-elongation measurements., which perform on the sample, which is gradually stretched (picture 1). Picture 1 - Standard sample for tensile test, which is used to determine the mechanical properties of metallic materials, including, steels.

## Stretch diagram

Engineering stress σ, which is applied in the stress-strain diagram in the figure 2, is the average or rated stress in the ruptured specimen. It is obtained by dividing the value of the load F by the original - not loaded - area A0 cross section of this sample.

σ = F / A0. Picture 2 - Engineering stress-strain diagram. More commonly referred to as a stretch diagram.. The intersection of the dotted line with the stress-strain diagram gives the value of the yield point at permanent deformation, usually, 0,2 %.

As the stress in the rupture specimen increases, the distance between the base length marks changes under the influence of the applied stresses. Resulting deformation ɛ, which is indicated on the stress-strain engineering diagram, is average or nominal linear - uniaxial - deformation. The magnitude of this deformation is obtained by dividing the change in the base length of the sample δ by the original base length of the sample L0:

ɛ = δ / L0 = ΔL/L0 = (L – L0)/L0

Since the engineering stress (σ) and deformation (ɛ) obtained by dividing the load on the sample and the elongation of the sample by the same constant value L0, then the shape of the load-elongation diagram and the stress-strain diagram have the same shape.

The shape and size of the tensile diagram of steel depends on:

• chemical composition of steel,
• the form of heat treatment,
• modes of plastic deformation,
• temperature and
• stress state during tensile test.

Mechanical properties of steel is most often determined by tensile testing, which is described above. Steel characteristics, which are commonly used to describe the tensile diagram of a particular steel include:

• strength limit (temporary tensile strength),
• yield point,
• elongation of sample base length (in percentages),
• narrowing of the cross-sectional area of ​​the sample (in percentages).

Different types of tests, which involve applying different loads to a steel specimen, also used to determine other mechanical properties of steel. Examples of such mechanical properties of steel are the elastic modulus, hardness, fatigue resistance and impact strength.

## All mechanical properties of steel

An almost complete list of mechanical properties for steel includes:

• Hardness. A measure of resistance to indentation
• Linear elastic coefficients for tensile, compressive and shear loads
• Yield point (when stretching, compressive and shear loads). Shows voltage level, at which irreversible plastic deformations occur
• Strength limit (when stretching, compressive and shear loads). Shows the maximum engineering stress, which material can withstand without breaking. Tensile strength - tensile strength - usually associated with the onset of necking on a ruptured specimen (cm. picture 2)
• Fatigue strength. Shows the level of cyclic stress, which cause fatigue failure of the metal after a specified number of loading cycles, eg, 1 million
• Impact strength. Shows the level of absorption of shock energy from loads, which is able to absorb the metal to destruction
• Fracture toughness. Shows the level of resistance to destruction, when the product contains defects and stress concentrators
• Resistance to high temperature creep and fracture.
• Wear resistance. 