Tensile Test: Procedure and Stress-Strain Curve

The tensile test is the most common mechanical test. It tells engineers how strong, stiff and ductile a material is, and whether a batch of steel, aluminium or plastic meets its specification. The data feed directly into design calculations of stress and strain and the choice of a factor of safety.

Test equipment and specimen

• Universal testing machine (UTM): a loading frame driven by hydraulics or electromechanical screws, with a load cell to measure force, and grips to hold the specimen.
• Extensometer: clipped to the specimen to measure elongation accurately over a defined gauge length, especially for modulus and yield.
• Specimen: round or flat, with enlarged ends for gripping and a reduced parallel section. Proportional round specimens often use a gauge length L₀ = 5.65√S₀, equivalent to 5 times the diameter. Specimens are machined from plate, bar, castings or welded joints according to the product standard.

Procedure

1. Measure the specimen’s original diameter or width and thickness, calculate the cross-sectional area S₀, and mark the gauge length.
2. Mount the specimen in the grips, aligned with the load axis, and attach the extensometer.
3. Apply load at a controlled strain or stress rate defined by the standard (slow in the elastic and yield region).
4. Record force and extension continuously until fracture. The extensometer is usually removed after yield to protect it.
5. Fit the broken pieces together and measure the final gauge length and the minimum cross-section at the neck.
6. Calculate properties and report them with test temperature and specimen details.

The stress-strain curve

Engineering stress and strain are:

$$\sigma = \frac{F}{S_0} \qquad \varepsilon = \frac{\Delta L}{L_0}$$

Download diagram (WebP)

Elastic region

At low stress, stress is proportional to strain (Hooke’s law), and the specimen returns to its original length when unloaded. The slope is Young’s modulus:

$$E = \frac{\sigma}{\varepsilon}$$

Typical values: steel about 200 to 210 GPa, aluminium about 70 GPa, copper about 120 GPa.

Yield

Beyond the elastic limit, permanent (plastic) deformation begins. Low carbon steels show an upper yield point, a sudden drop, and a yield plateau (Lüders band propagation). Other materials yield gradually; the 0.2% proof stress (R_p0.2) is found by drawing a line parallel to the elastic slope from 0.2% strain and reading where it crosses the curve.

Strain hardening and UTS

After yielding, the metal strengthens as dislocations multiply and tangle (work hardening). Stress rises to a maximum, the ultimate tensile strength (R_m):

$$R_m = \frac{F_\text{max}}{S_0}$$

Necking and fracture

At the UTS, deformation concentrates in one region, which narrows (necking). Engineering stress falls because the load drops, although true stress in the neck continues to rise. The specimen finally fractures, typically with a cup and cone surface in ductile metals.

Ductility measures

$$A = \frac{L_u - L_0}{L_0} \times 100\% \qquad Z = \frac{S_0 - S_u}{S_0} \times 100\%$$

where L_u is the final gauge length and S_u the minimum cross-section after fracture.

True stress and true strain

Engineering values use the original area and length. True stress and true strain account for the changing dimensions: σ_true = σ(1 + ε) and ε_true = ln(1 + ε), valid up to the onset of necking. True stress-strain curves keep rising until fracture and are used in metal forming simulations and crash analysis. The strain hardening exponent n from the relation σ_true = Kε_trueⁿ indicates how well a sheet metal can be stretched without local thinning.

Factors affecting tensile test results

• Temperature: strength usually falls and ductility rises with temperature; some steels become brittle at low temperatures.
• Strain rate: faster testing raises yield strength in many metals.
• Specimen orientation: rolled and forged products can differ along and across the grain.
• Specimen preparation: machining marks or misalignment cause early failure.
• Heat treatment and microstructure, as explained in heat treatment of steel.

Using tensile test data

Test certificates (mill certificates) supplied with steel and other metals report these tensile results for each heat or batch.

Design codes use yield strength (with safety factors) for static design and UTS in some checks. Material standards specify minimum yield, UTS and elongation, for example S355 structural steel requires a minimum yield strength of 355 MPa for thinner sections. Elongation and reduction of area indicate formability and toughness. For repeated loads, tensile data are complemented by fatigue tests described in fatigue failure, and for brittle fracture risk by Charpy impact tests. Tensile testing is a destructive test; components in service are checked instead with NDT methods.