Questions: Hardness Testing Methods and Hardness Equivalence

Question 1

A Vickers hardness test is performed on the same steel sample using loads of 1 kgf (microhardness) and 50 kgf (macrohardness). What result would you expect?

• A. Significantly different values, because larger loads probe deeper material with different microstructure
• B. Approximately equal values, because the pyramidal indenter is geometrically self-similar at all scales — the same shape produces the same hardness number regardless of load
• C. Identical only if the same operator performs both tests under controlled temperature
• D. Values differing by a factor proportional to the ratio of loads applied

Answer: (B)

The Vickers indenter is a square pyramid. Because a pyramid scaled up or down maintains the same angular geometry, the ratio of impression diagonal to contact depth is constant regardless of load. This self-similarity means the calculated Vickers Hardness Number (HV) is load-independent — the same value results from micro and macro loads on homogeneous material. This is Vickers's key advantage over Brinell (where the sphere geometry changes the stress state at different scales).

Question 2

An engineer measures a new titanium alloy on the Rockwell C scale, then uses ASTM E140 tables to report an equivalent Vickers value as an accurate characterization. A materials scientist raises a concern. What is the strongest objection?

• A. The Rockwell C scale is calibrated only for non-ferrous metals and cannot be applied to alloys
• B. ASTM E140 conversion tables are derived empirically from steel specimens; applying them to titanium — which has different deformation mechanisms — may give significantly inaccurate results
• C. Vickers and Rockwell measure fundamentally incompatible quantities and can never be meaningfully compared
• D. The conversion is accurate as long as the applied load and indenter type are correctly specified in the report

Answer: (B)

ASTM E140 hardness conversion tables are built from parallel measurements on a large set of steel alloys. They encode the correlation between scales specifically for steel's deformation behavior. Titanium has different elastic modulus, yield strength anisotropy, and work-hardening characteristics — the Rockwell-to-Vickers correlation is simply different for titanium. Using steel tables introduces systematic error of unknown magnitude. The correct practice is to measure directly in the desired scale or develop material-specific conversions.

Question 3

Hardness testing is considered approximately nondestructive because the indentation is small relative to part dimensions, yet the resulting hardness number still correlates meaningfully with the material's yield strength.

• T. True
• F. False

Answer: True

The indentation is localized and leaves only a small residual impression on the part surface, which is why hardness testing is practical for quality control on finished parts. Despite its small scale, the plastic zone beneath the indenter reflects the same material resistance to plastic flow that governs yield strength in a tensile test. The empirical correlation (UTS ≈ HV × 3.3 MPa for steels) makes hardness a powerful proxy for tensile properties without consuming a dedicated specimen.

Question 4

Because both hardness testing and tensile testing measure resistance to plastic deformation, a single universal hardness-conversion table can reliably translate between Vickers, Rockwell, and Brinell scales for any metallic material.

• T. True
• F. False

Answer: False

Conversion tables are material-specific because each hardness test probes a different volume at a different strain rate under a different stress state (triaxial for indentation, uniaxial for tension). The empirical correlations are calibrated for a specific class of materials — typically steels in the published ASTM tables. For aluminum alloys, titanium, ceramics, or polymers, the deformation mechanisms differ enough that cross-scale conversions using steel tables can be substantially wrong. No physics-based universal conversion exists.

Question 5

Why is converting between Vickers, Rockwell, and Brinell hardness scales inherently approximate, and why do conversion tables fail when applied to materials other than those they were derived from?

Model answer: Each hardness method probes a different volume of material (microhardness vs. macro), uses a different indenter geometry (pyramid, cone, sphere), applies load at a different rate, and creates a different triaxial stress state beneath the indenter. The correlations between these methods are empirical — they reflect how a specific set of steel alloys happened to rank on each scale, not a universal physical law. For different materials, the plastic zone geometry, work-hardening rate, and elastic recovery differ, changing the relationship between scales. Conversion tables derived from steels encode steel-specific behavior; applying them to titanium, aluminum, or ceramics introduces systematic errors of unpredictable magnitude.

The deeper point is that different hardness numbers are not measuring exactly the same thing — they are correlated proxies for resistance to plastic flow, each biased by its own measurement geometry. The conversion is an approximation valid within a material class, not an exact unit conversion.