When discussing “elastic design,” we might not focus on the material’s tensile strength or its elongation after fracture, but we cannot overlook the material’s yield strength.
Today, let’s talk about “yield strength.”
I wonder if you’ve ever noticed that “yield strength” is also categorized.
Here, I would like to briefly mention that the categories of “yield strength” include the commonly known—upper yield strength (ReH), lower yield strength (ReL), and the specified plastic extension strength (Rp0.2), which refers to the strength corresponding to a 0.2% strain.
Upper and Lower Yield Strength
The upper yield strength (ReH) and lower yield strength (ReL) are located at different points on the stress-strain curve of the same material.
As shown in Figure 1, the stress-strain curve of a certain steel material, ReH and ReL represent the maximum and minimum values in the yield phase of the material, respectively.
In the figure, the light blue curve is an enlarged version (100x horizontally) of the dark blue curve in the elastic phase.
Rpl = 241 MPa refers to the elastic limit, where the material behaves purely linearly under external load, and once the load is removed, it can completely return to its original state. The strain corresponding to the elastic limit is 0.0012. Then comes ReH—the upper yield strength, which is 262 MPa, followed by a sharp drop in stress to ReL—the lower yield strength, which is 248 MPa. At this point, the strain is 0.03, 25 times that of the elastic limit. After that, the material undergoes strain hardening until it reaches the tensile limit, Ru = 434 MPa. Finally, in the necking process, the material reaches fracture at Rf—the fracture strength, which is 324 MPa. The corresponding strain here is 0.38, which is 317 times the elastic limit.
For different materials, some require the use of upper yield strength, while others require lower yield strength. For example, bolts with weaker ductility fail more suddenly, so the lower yield strength ReL is generally used conservatively. On the other hand, alloy steels like Q355B, which have better ductility, fail more visibly, so the upper yield strength ReH is typically used.
Generally, for low-alloy steels, the upper yield strength is about 10% higher than the lower yield strength, as shown in Table 1, where the measured ReH and ReL for a certain low-alloy steel are listed.
Table 1 Measured Mechanical Properties of a Low-Alloy Steel
Specified Plastic Extension Strength (Rp0.2)
The last one is the specified plastic extension strength, Rp0.2.
This parameter is used for materials with stress-strain curves that are not as standardized, making it difficult to determine the yield strength (whether ReH or ReL), such as aluminum.
For materials with less distinct yield points, industries generally use the “offset method” to determine the yield strength.
What is the “Offset Method”?
Although the stress-strain curve of such materials may not be as typical as that of low-carbon steel, there is one thing in common—the initial part of the curve is always linear. The industry takes advantage of this by shifting the purely linear part of the curve along the strain axis by 0.002 (i.e., 0.2%) and then defining the point where the shifted line intersects with the original curve as the material’s yield strength (as shown in Figure 2).
Figure 2 The “Offset Method”
It is worth mentioning that, besides metals, the yield strength of plastics can sometimes also be determined using the 0.2% offset method. Additionally, for some metal materials, the yield strength is not based on the strength corresponding to 0.2% strain, but rather to a larger strain (such as 0.4%).