Yield Strength

In plain English

If you bend a steel wire slightly and let go, it springs back. Bend it further and it stays bent. The stress at which the material stops springing back and starts to change shape permanently is its yield strength. Most machine parts are designed so that they never reach it in service.

Technical definition

Yield strength is the stress at which a material begins to deform plastically. Some steels show a distinct yield point, reported as the upper yield strength R_eH and lower yield strength R_eL (ISO 6892-1). Materials without a clear yield point are characterised by the 0.2% proof strength R_p0.2: the stress at which the permanent (plastic) extension equals 0.2% of the gauge length. ASTM E8 calls this the yield strength by the 0.2% offset method.

How it works and where it is used

In a tensile test, a standard specimen is stretched while force and extension are recorded. The force is divided by the original cross-sectional area to give engineering stress. For the offset method, a line parallel to the elastic part of the curve is drawn from 0.2% strain; where it meets the curve is R_p0.2. Yield strength depends on composition, heat treatment, cold work, section size and temperature, so it is taken from the material certificate or standard for the actual product.

Formula

R_e (or R_p0.2) = F_yield ÷ S₀

F_yield = force at yield (or at 0.2% plastic extension), S₀ = original cross-sectional area of the specimen. A typical allowable design stress = yield strength ÷ factor of safety.

Worked example

An example tensile test on a round specimen of 10.0 mm diameter (S₀ = 78.54 mm²) reaches 0.2% plastic extension at 21.2 kN.

R_p0.2 = 21 200 ÷ 78.54 = 270 MPa. With a factor of safety of 2 chosen by the designer, the allowable stress would be 135 MPa. (The test values here are illustrative only.)

In the workshop and in practice

Yield strength is the basis for most static strength checks: shafts, brackets, bolts (through proof strength), pressure parts and structures. In the workshop it explains why parts bend permanently when overloaded, why cold-worked bar is stronger than annealed bar, and why heat treatment changes how a part behaves.

Common mistakes and misconceptions

• Confusing yield with tensile strength. Tensile (ultimate) strength is the maximum stress; yield comes earlier and is usually the design limit for static loads.
• Using a “typical” value for design. Use the minimum guaranteed value from the material standard or certificate.
• Ignoring fatigue. Parts with repeated loading can fail far below the yield strength.
• Ignoring temperature and size. Strength falls at high temperature and can be lower in thick sections.

Related calculators

• Shaft Torsional Stress Calculator — Torsional shear stress and angle of twist of a round shaft, or the diameter needed.
• Parallel Key Length Estimator — Minimum parallel-key length for shear and crushing, or the stresses in a given key.
• Bolt Tightening Torque Estimator — Tightening torque from preload (T = K·F·d), preload from torque, or a preload target from proof strength.

Related topics

• Tensile Strength — The maximum stress a material withstands in a tensile test before it necks and breaks.
• Stress and Strain — Internal force per unit area, and the stretch per unit length it causes.

References

• ISO 6892-1: Metallic materials — Tensile testing — Part 1: Method of test at room temperature (ReH, ReL, Rp)
• ASTM E8/E8M: Standard Test Methods for Tension Testing of Metallic Materials
• Callister and Rethwisch, Materials Science and Engineering: An Introduction