Mechanical properties

Why it matters

The tensile test is the most common mechanical test in materials engineering. A carefully machined sample is pulled in a machine until it breaks, while force and elongation are recorded. Converted to stress and strain, the record becomes a stress-strain curve, and nearly every number on a material datasheet (modulus, yield strength, tensile strength, elongation) is read from it. Being able to read one is a basic skill for engineers and materials scientists alike.

From the test to the curve

Engineering stress is force divided by the sample's original cross-sectional area, σ = F/A0, and engineering strain is the change in gauge length divided by the original length, ε = ΔL/L0. Test standards such as ASTM E8 (metals) and ASTM D638 (plastics) fix the sample shape and speed so labs get comparable results.

Reading the curve for a ductile metal

Walking along a typical curve from the origin:

1. Elastic region. A straight line: stress is proportional to strain. Its slope is Young's modulus E. Unload here and the sample returns to its original length.
2. Yield. The curve bends over as planes of atoms start to slip (dislocation motion). Many metals have no sharp yield point, so engineers use the 0.2 % offset yield strength: draw a line parallel to the elastic line, starting at a strain of 0.002, and read the stress where it crosses the curve.
3. Strain hardening. Stress keeps rising as dislocations multiply and tangle, so more force is needed for more deformation.
4. Ultimate tensile strength (UTS). The highest point on the engineering curve. Beyond it the sample starts to neck: deformation concentrates in one region, the local area shrinks, and the force needed falls.
5. Fracture. The sample breaks. The elongation at fracture (often written as % elongation) measures ductility. It is the plastic strain at fracture: the total strain minus the elastic part that springs back when the sample breaks.

Two other properties come from the area under the curve: resilience (energy absorbed elastically, the area under the elastic part) and toughness (energy absorbed up to fracture, the total area). Ductile metals are tough because they deform a lot before breaking.

Worked example

A test on an aluminium alloy gives these points (strain, stress in MPa):

(0.001, 70)  (0.002, 140)  (0.003, 210)  (0.004, 280)  ...
(0.0065, 285)  ...  (0.080, 310)  ...  (0.120, 280) fracture

Modulus. The early points lie on a line through the origin with slope 70 MPa / 0.001 = 70,000 MPa = 70 GPa, a normal value for aluminium.

0.2 % offset yield. The offset line is σ = 70,000 × (ε − 0.002). At ε = 0.0065 it gives 315 MPa, already above the measured 285 MPa, while at ε = 0.006 it gives 280 MPa, below the curve. So the offset line crosses the curve between these points, at about 285 MPa: the yield strength.

UTS. The highest stress is 310 MPa, reached at a strain of 0.08.

Elongation at fracture. Total strain at fracture is 0.120. The elastic strain that springs back is 280 / 70,000 = 0.004. Plastic strain is 0.116, so elongation ≈ 11.6 %.

How different materials look

• Brittle ceramics and glass: a straight line to fracture, with almost no plastic region. Their tensile strength is very sensitive to surface flaws, so it scatters widely between samples.
• Ductile metals: a long plastic region, a clear UTS and necking.
• Polymers: strongly depend on temperature and test speed. Some neck and draw a long way (polyethylene), others are brittle (polystyrene), and elastomers stretch hundreds of percent with a curved, non-linear response.

True stress and strain

Engineering stress uses the original area, so it drops after necking even though the material in the neck is still getting stronger. True stress (force over the actual area) keeps rising. Engineering values are used for design data; true values are used for modelling forming processes.

Common mistakes

• Reading yield where the curve first looks curved. Use the 0.2 % offset method unless a standard says otherwise.
• Quoting total strain as elongation. Subtract the elastic recovery.
• Treating datasheet values as guaranteed. Typical values vary with grade, temper, product form and direction; designs use specified minimum values from the relevant material standard.

Recap

• Elastic slope = E; 0.2 % offset gives yield strength; the peak gives UTS.
• Elongation at fracture is plastic strain and measures ductility.
• The area under the curve measures toughness.

Try it

On the Do tab, you will analyse a full set of tensile test data in Python. The code finds UTS, offset yield and elongation; you write the modulus fit.