The Reduction of Area (RA) is a fundamental, quantitative measure of ductility obtained from a tensile test on a material specimen. It expresses the extent to which a material can plastically deform (i.e., stretch) in a localized region before it fractures.
1. Definition
Reduction of Area is defined as the percentage decrease in the cross-sectional area of a tensile specimen at the point of fracture compared to its original cross-sectional area.
2. How It Is Determined
The test is performed by pulling a standardized specimen (often with a machined “gauge section”) in a tensile testing machine until it breaks.
Original Cross-sectional Area (A₀): The area of the specimen’s narrowest part before the test.
Final Cross-sectional Area (Aƒ): The area of the specimen at the fractured surface after the test. For a round specimen, this is measured by fitting the broken pieces together and measuring the smallest diameter.
3. The Formula
The Reduction of Area is calculated using the following formula:
RA (%) = [(A₀ – Aƒ) / A₀] × 100
Where:
RA (%) is the Percentage Reduction of Area.
A₀ is the original cross-sectional area.
Aƒ is the final cross-sectional area at the fracture point.
4. Physical Significance and Interpretation
Indicator of Ductility: A high RA value indicates a highly ductile material. Such materials can undergo significant permanent deformation (necking) before failure. Examples include mild steel, copper, and aluminum.
Indicator of Brittleness: A low RA value (close to 0%) indicates a brittle material. Brittle materials fracture with little to no plastic deformation. Examples include cast iron and glass.
Necking: RA is a direct measure of the “necking” phenomenon in ductile materials, where the specimen significantly and locally contracts before fracture.
5. Key Differences from Elongation
While both RA and Percent Elongation (%EL) measure ductility, they provide different insights:
| Feature | Reduction of Area (RA) | Elongation (%EL) |
| What it measures | Localized deformation at the neck. | Uniform and localized deformation over the entire gauge length. |
| Sensitivity | Often considered a more fundamental and accurate measure of true ductility, as it is less sensitive to the specimen’s gauge length. | Can be influenced by the gauge length of the specimen; longer gauge lengths can give lower %EL values. |
| Result | Gives a direct measure of the material’s ability to deform plastically under triaxial stresses at the neck. | Represents the overall “stretchability” of the material. |
6. Practical Importance in Engineering
Material Selection: Helps engineers choose materials for applications where plastic deformation is expected or required without fracture (e.g., metal forming, car crash zones).
Quality Control: Used to verify that a material batch meets specified ductility requirements.
Failure Analysis: A low RA value in a failed component can indicate issues like embrittlement, improper heat treatment, or the wrong material being used.
Example:
If a round steel bar with an original diameter of 10 mm (A₀ ≈ 78.54 mm²) fractures and the diameter at the neck is measured to be 6 mm (Aƒ ≈ 28.27 mm²), the Reduction of Area is:
RA (%) = [(78.54 – 28.27) / 78.54] × 100 = 64%
This high RA value confirms that the steel is very ductile.
In summary, the Reduction of Area (RA) is a crucial mechanical property that quantifies a material’s ductility by measuring the permanent contraction of its cross-section at the point of fracture during a tensile test.
