AMME1362 Chap.2 Stress, Strain and Tensile Testing
Stress, Strain and Tensile Testing
A tensile test converts force and extension into engineering stress and strain using original specimen geometry. The resulting curve identifies elastic slope, yielding, strain hardening, ultimate tensile strength, necking and fracture. Interpretation depends on knowing which dimensions and conventions were used.
Laboratory evidence also includes specimen geometry, machine alignment, strain measurement and observed deformation, not merely the plotted curve.
What this chapter covers
- 01
Engineering stress and strain
- 02
Elastic slope and modulus
- 03
Yield and offset conventions
- 04
Ultimate strength and necking
- 05
True versus engineering measures
- 06
Tensile laboratory evidence
Worked example · free
Calculate an elastic tensile point
- 1Engineering stress is 12,000 N divided by 80.0 mm², or 150 MPa.
- 1Engineering strain is 0.40 mm divided by 50.0 mm, or 0.0080.
- 1Modulus is 150 MPa divided by 0.0080, or 18,750 MPa.
- 1Convert 18,750 MPa to 18.75 GPa and state that the point must be elastic for this interpretation.
Key terms
- Gauge length
- The reference length over which tensile extension or strain is measured.
- Engineering stress
- Force divided by original cross-sectional area.
- Necking
- Localised reduction of cross-sectional area during tensile deformation.
- Offset yield
- A conventional yield value found using a specified parallel offset line.
- Machine compliance
- Deformation in grips and the testing frame that can be included in crosshead travel even though it is not specimen gauge extension. Direct extensometer measurement and a stated fitting region reduce its effect on calculated strain and modulus.
- True stress
- Instantaneous force divided by the current cross-sectional area. It differs increasingly from engineering stress as area changes, especially after necking makes deformation local and a single original-area measure hides the shrinking load path.
- Strain hardening
- Increasing resistance to continued plastic deformation as dislocations multiply and interact. On an engineering curve it follows yielding and can raise carried load until localisation begins, but the exact response depends on material and condition.
Stress, Strain and Tensile Testing FAQ
Why does the engineering curve fall after its maximum?
After necking begins, the original-area definition spreads load over a fixed denominator while the carried load can fall. Local true stress in the shrinking neck can follow a different trend.
How is elastic modulus found from a curve?
Use the slope of the linear elastic region with consistent stress and strain units. A single secant point is valid only if the response from the origin to that point is elastic and linear.
What laboratory observations belong with the graph?
Record specimen dimensions, loading direction, alignment, extension method, surface condition and visible yielding, necking or fracture. Those observations help explain scatter and whether the curve represents the intended test.
Exam move
Start by drawing an engineering stress-strain curve on blank axes without notes. Label the linear elastic region, yield convention, strain hardening, ultimate engineering stress, necking and fracture. Under every graph label, write the specimen event that creates it.
The slope represents recoverable bond stretching at small strain; yielding begins sustained plastic deformation; strain hardening increases resistance to further plastic flow; necking localises area reduction. Redraw the curve until the graph and physical sequence can be recalled together. Make a definition sheet that contains force, extension, original area, original gauge length, current area and current length.
Derive engineering stress and strain from the original quantities before using any values. Then calculate four points with different unit combinations, including kilonewtons with square millimetres and metres with millimetres. Check that newtons per square millimetre become megapascals and that strain remains dimensionless.
For modulus practice, select two points in the stated linear region and calculate a slope rather than automatically dividing one stress by one strain. Explain why a secant through the origin is acceptable only when the response is linear from zero.
Add an uncertainty note beside each calculation: area error changes stress, gauge-length error changes strain, machine compliance can distort crosshead extension, and misalignment can create bending. Use the laboratory rubric themes to rehearse evidence reporting.
For a hypothetical metal and polymer specimen, describe geometry before testing, expected curve features, final specimen appearance and one reason two nominally identical curves might differ. Sketch the fractured specimens and label uniform extension, necking or stretching only when the observations support them. Practise converting between engineering and true concepts qualitatively.
Before necking, decreasing area means true stress exceeds engineering stress. After necking, a single gauge-average strain no longer represents the intense local deformation. Do not memorise a universal post-necking curve; explain which geometry each definition uses and why local measurement becomes necessary. Finish with timed curve diagnoses.
For each unlabeled curve, state whether it suggests high stiffness, early yielding, large ductility or brittle fracture, but attach every claim to an axis feature. Then write one sentence on what cannot be concluded, such as toughness without the full area or material identity without conditions. Review errors by category: definition, geometry, units, graph region or interpretation.
Repeat only the failed category with fresh numbers, and require the rebuilt answer to end with units and a physical check.
