Understanding the mechanical properties of materials like steel is crucial in engineering. One important property is the yield stress, which indicates the stress at which a material begins to deform plastically (permanently).

For many types of steel, especially low-carbon structural steel, the stress-strain curve shows a distinct point or region where the material yields. This is called the yield plateau. After reaching the upper yield point, the stress might drop slightly (lower yield point) and then remain relatively constant as the material deforms before strain hardening begins. The yield stress is typically taken as the lower yield point in such cases.

Proof Stress for Steel

However, not all steel bars exhibit a clear yield plateau. High-strength steel or certain steel alloys may show a stress-strain curve where the transition from elastic to plastic behavior is gradual. In such cases, defining the yield stress at a distinct point becomes difficult.

For materials without a well-defined yield plateau, an alternative method is used to specify the yield strength. This method uses a concept called "proof stress" or "offset yield strength".

0.2 Percent Proof Stress

Proof stress is defined as the stress at which a material undergoes a specified amount of permanent (plastic) strain. This is determined by drawing a line parallel to the initial elastic portion of the stress-strain curve, offset by a specific strain value, and finding where this offset line intersects the stress-strain curve.

For steel bars that lack a well-defined yield plateau, the yield stress is conventionally specified at the 0.2 percent proof stress. This means the stress required to produce a permanent strain of 0.2% (or 0.002). The procedure involves:

• Plotting the stress-strain curve from a tensile test.
• Drawing a line parallel to the initial linear elastic portion of the curve.
• Ensuring this parallel line starts at a strain offset of 0.002 (0.2% strain) on the strain axis.
• The stress value at the point where this offset line intersects the stress-strain curve is defined as the 0.2 percent proof stress, which is taken as the yield stress.

This 0.2 percent offset method is widely adopted in standards (like ASTM, ISO, etc.) for determining the yield strength of materials, including steel, that do not show a clear yield point.

The other options (1 percent, 0.1 percent, 2 percent proof stress) represent different levels of permanent deformation and are not the standard values used to define the yield stress for steel bars lacking a distinct yield plateau.

Summary of Yield Stress Definition

In summary, the definition of yield stress depends on the material's stress-strain behavior:

• For steel with a clear yield plateau, the yield stress is typically the lower yield point.
• For steel bars lacking a well-defined yield plateau, the yield stress is defined as the 0.2 percent proof stress.

Therefore, in steel bars lacking a well-defined yield plateau, yield stress is specified at 0.2 percent proof stress.