Empirical hardness–strength correlation for steels A carbon steel has a Brinell hardness number (BHN) of 100. Using the standard engineering correlation between BHN and ultimate tensile strength (UTS), the UTS is closest to which value (in N/mm²)?

Introduction / Context:
In shop-floor quality control and quick estimates, engineers often convert hardness readings into approximate tensile strengths. For plain carbon and low-alloy steels, a widely used empirical rule links Brinell hardness number (BHN) to ultimate tensile strength (UTS).

Given Data / Assumptions:

• Material: carbon steel.
• Measured hardness: BHN = 100.
• Use the common rule: UTS (MPa) ≈ k * BHN, with k around 3.45 for steels.
• Note: 1 MPa = 1 N/mm².

Concept / Approach:
The practical correlation is often stated as UTS (MPa) ≈ 3.45 * BHN for carbon/low-alloy steels in typical heat-treated or normalized conditions. While the constant can vary slightly (3.3–3.5) depending on condition, 3.45 is a standard mid-value for quick estimates. This allows rapid strength estimation without destructive tensile testing.

Step-by-Step Solution:
Write the rule: UTS ≈ 3.45 * BHN.Insert BHN = 100: UTS ≈ 3.45 * 100.Compute: UTS ≈ 345 MPa.Round to the nearest provided choice: 350 N/mm² (since 1 MPa = 1 N/mm²).

Verification / Alternative check:
Some handbooks use UTS (MPa) ≈ 3.5 * BHN; with BHN = 100, that gives 350 MPa—exactly matching the chosen option. The difference between 345 and 350 is within practical estimation tolerance for this rule of thumb.

Why Other Options Are Wrong:
100 and 200 N/mm² are too low for BHN 100 steel; 700 and 1000 N/mm² correspond to much higher hardness levels (BHN ~ 200–300+). Choosing these would ignore the established proportionality.

Common Pitfalls:
Treating the correlation as exact across all alloys and heat treatments. It is an estimate for common steels; tool steels, austenitic stainless, and nonferrous alloys deviate from this factor.

Final Answer:
350 N/mm²