WHAT IS YIELD EFFORT AND HOW TO OBTAIN IT? - PHYSICAL - 2025

The yield stress is defined as the effort necessary for an object to begin to permanently deform, that is, to undergo plastic deformation without breaking or fracturing.

As this limit can be a bit imprecise for some materials and the precision of the equipment used is a weight factor, in engineering it has been determined that the yield stress in metals such as structural steel is one that produces 0.2% permanent deformation in the object.

Figure 1. Materials used in construction are tested to determine how much stress they are capable of withstanding. Source: Pixabay.

Knowing the value of the yield stress is important to know if the material is appropriate for the use that you want to give to the parts manufactured with it. When a part has been deformed beyond the elastic limit, it may not be able to perform its intended function correctly and must be replaced.

To obtain this value, tests are usually carried out on samples made with the material (test tubes or specimens), which are subjected to various stresses or loads, while measuring the elongation or stretching they experience with each one. These tests are known as tensile tests.

To perform a tensile test, start by applying a force from zero and gradually increase the value until the sample breaks.

Strain stress curves

The data pairs obtained by the tensile test are plotted by placing the load on the vertical axis and the strain on the horizontal axis. The result is a graph like the one shown below (figure 2), called the stress-strain curve for the material.

From it many important mechanical properties are determined. Each material has its own stress-strain curve. For example, one of the most studied is that of structural steel, also called mild or low carbon steel. It is a material widely used in construction.

The stress-strain curve has distinctive areas in which the material has a certain behavior according to the applied load. Their exact shape can vary considerably, but they nevertheless have some characteristics in common, which are described below.

For what follows see figure 2, which corresponds in very general terms to structural steel.

Figure 2. Stress-strain curve for steel. Source: modified from Hans Topo1993

Elastic zone

The area from O to A is the elastic area, where Hooke's Law is valid, in which the stress and strain are proportional. In this zone the material is fully recovered after the application of the stress. Point A is known as the limit of proportionality.

In some materials, the curve that goes from O to A is not a straight line, but nevertheless they are still elastic. The important thing is that they return to their original shape when charging ceases.

Elastic-plastic zone

Next we have the region from A to B, in which the deformation increases more rapidly with the effort, leaving both of them not proportional. The slope of the curve decreases and at B it becomes horizontal.

From point B, the material no longer recovers its original shape and the value of the stress at that point is considered to be that of the yield stress.

The area from B to C is called the yield or creep zone of the material. There the deformation continues even though the load is not increasing. It could even decrease, which is why it is said that the material in this condition is perfectly plastic.

Plastic zone and fracture

In the region from C to D, strain hardening occurs, in which the material presents alterations in its structure at the molecular and atomic level, which require greater efforts to achieve deformations.

For this reason, the curve experiences a growth that ends when reaching the maximum stress σ _max.

From D to E there is still deformation possible but with less load. A kind of thinning is formed in the sample (specimen) called stricture, which eventually leads to the fracture being observed at point E. However, already at point D the material can be considered to be broken.

How to obtain the yield effort?

The elastic limit L _e of a material is the maximum stress that it can withstand without losing elasticity. It is calculated by the quotient between the magnitude of the maximum force F _m and the cross-sectional area of ​​sample A.

L _e = F _m / A

The units of the elastic limit in the International System are N / m ² or Pa (Pascals) since it is a stress. The elastic limit and the proportionality limit at point A are very close values.

But as said at the beginning, it may not be easy to determine them. The yield stress obtained through the stress-strain curve is the practical approximation to the elastic limit used in engineering.

Yield stress from the stress-strain curve

To obtain it, a line is drawn parallel to the line that corresponds to the elastic zone (the one that obeys Hooke's law) but displaced approximately 0.2% on the horizontal scale or 0.002 inch per inch of deformation.

This line extends until it intersects the curve at a point whose vertical coordinate is the desired yield stress value, denoted as σ _y, as shown in figure 3. This curve belongs to another ductile material: aluminum.

Figure 3. Stress-strain curve for aluminum, from which the yield stress is determined in practice. Source: self made.

Two ductile materials such as steel and aluminum have different stress-strain curves. Aluminum, for example, does not have the roughly horizontal section of steel seen in the preceding section.

Other materials considered fragile such as glass, do not go through the stages described above. Rupture occurs long before appreciable deformations occur.

Important details to keep in mind

- The forces considered in principle do not take into account the modification that undoubtedly occurs in the cross-sectional area of ​​the specimen. This induces a small error that is corrected by graphing the real stresses, those that take into account the reduction in area as the deformation of the specimen increases.

- The temperatures considered are normal. Some materials are ductile at low temperatures, while other brittle materials behave as ductile at higher temperatures.

References

1. Beer, F. 2010. Mechanics of materials. McGraw Hill. 5th. Edition. 47-57.
2. Engineers Edge. Yield Strength. Recovered from: engineersedge.com.
3. Creep stress. Recovered from: instron.com.ar
4. Valera Negrete, J. 2005. Notes on General Physics. UNAM. 101-103.
5. Wikipedia. Creep. Recovered from: Wikipedia.com