Tensile and hardness testing

Why it matters

A tensile test is the most common mechanical test in the world. Its results (modulus, yield strength, tensile strength, elongation) appear on every material certificate and data sheet, and designers use them directly. Hardness tests are faster and nearly non-destructive, so they are the everyday check on heat treatment and incoming material. Being able to compute these numbers yourself from raw data, and to spot a bad test, is a core skill.

From load and extension to stress and strain

A load frame pulls a specimen of known cross-section A0 and records force F; an extensometer measures the change in a gauge length L0.

engineering stress  sigma = F / A0        (N / mm^2 = MPa)
engineering strain  e     = delta_L / L0  (dimensionless; x100 for %)

"Engineering" means we divide by the original area and length. True stress and strain use the instantaneous values and matter for forming simulations, but certificates report engineering values.

The properties

• Young's modulus E: the slope of the initial straight part. Fit a line only to the clearly elastic region. Grip slack and specimen seating make the first few points unreliable, and a crosshead-displacement "strain" without an extensometer underestimates E badly.
• 0.2% offset yield strength: many metals have no sharp yield point. Draw a line with slope E starting at 0.2% strain (0.002) and find where it crosses the curve. That stress is the yield strength Rp0.2 (or sigma_y).
• Ultimate tensile strength (UTS): the maximum engineering stress. After it, the specimen necks and engineering stress falls.
• Elongation at break and reduction of area: measures of ductility, taken from the broken specimen fitted back together, or from the strain at fracture minus the elastic recovery.

Worked example

A round steel specimen has A0 = 20.0 mm^2 (about 5.05 mm diameter) and L0 = 25.0 mm.

1. At 4,000 N the extension is 0.0250 mm: sigma = 4000 / 20 = 200 MPa and e = 0.025 / 25 = 0.0010, so the slope is 200 / 0.0010 = 200,000 MPa (200 GPa), as expected for steel. In real data, fit a line through many elastic points rather than trusting one.
2. The 0.2% offset line sigma = 200,000 (e - 0.002) crosses the curve at about 350 MPa: the yield strength.
3. The peak force is 9,000 N: UTS = 9000 / 20 = 450 MPa.

The yield-to-tensile ratio, 350/450 = 0.78, is a quick indicator of how much strain hardening the material has left.

Hardness

Hardness tests press an indenter into the surface and measure the resulting dent (Brinell, Vickers, Knoop) or the depth (Rockwell).

• Vickers (HV): a square diamond pyramid. Measure both diagonals of the dent and average them as d (in mm). With the force F in kgf, HV = 1.8544 * F / d^2. Example: 10 kgf with diagonals 0.300 and 0.304 mm gives d = 0.302, HV = 1.8544 * 10 / 0.0912 = 203, reported as 203 HV10.
• Rockwell (HRC, HRB...): a depth-based number read straight from the machine; fast and common on the shop floor. The scale letter matters: HRC and HRB are not interchangeable.
• Brinell (HBW): a large ball and high load, which averages over coarse microstructures such as castings.

Hardness correlates with tensile strength for many steels, and published conversion tables exist, but conversions are approximate and material-specific. Do not use them to certify a part.

Specimens and methods

Specimen shape, gauge length, test speed and how you compute each property are set by the test standard (for metals, ASTM E8/E8M or ISO 6892-1; for Vickers, ASTM E92 or ISO 6507-1). Results from different gauge lengths or speeds are not directly comparable, which is why test reports always name the method. The next lessons cover finding and following these methods.

Common mistakes

• Fitting the modulus through grip-seating data or using crosshead displacement as strain.
• Using the actual (necked) area and calling it engineering stress.
• Reporting UTS as yield for a material with no clear yield point.
• Indenting too close to an edge or another indent, or on a rough or curved surface, which distorts hardness.
• Mixing scales: an HRC value from a soft material, or a converted value reported as measured.

Safety and training

Load frames store a lot of energy, and specimens can break suddenly and throw fragments. Hardness testers and specimen preparation (cutting, grinding, polishing) have their own hazards. You operate them only after your lab's training, with guards and eye protection, under its procedures. In this course you analyse data.

Recap

• Stress = F / A0, strain = delta_L / L0. E is the elastic slope, yield is the 0.2% offset crossing, UTS is the peak.
• Vickers hardness = 1.8544 F / d^2 (kgf, mm); always report the scale and load.
• The standard method defines specimens, speeds and calculations, so name it in every report.

Try it

Open the Do tab to compute modulus, offset yield, UTS and Vickers hardness from a synthetic steel test with numpy.