AMME1362 Chap.3 Plastic Deformation and Mechanical Measures
Plastic Deformation and Mechanical Measures
Mechanical measures answer different design questions. Yield strength marks resistance to specified permanent deformation, tensile strength is the maximum engineering stress, ductility describes plastic strain to fracture, resilience is elastic energy per volume and toughness is total energy to fracture. Hardness probes local resistance to indentation.
These values cannot be substituted for one another, and each depends on its test definition and specimen condition.
What this chapter covers
- 01
Elastic and plastic deformation
- 02
Yield and tensile strength
- 03
Ductility measures
- 04
Resilience and toughness
- 05
Hardness testing
- 06
Strength-ductility trade-offs
Worked example · free
Estimate elastic resilience
- 1Use the triangular elastic area: yield stress squared divided by twice the modulus.
- 1Convert modulus to 75,000 MPa and calculate 300² divided by 150,000, giving 0.60 MPa.
- 1Recognise that 0.60 MPa equals 0.60 MJ/m³ of stored elastic energy density.
Key terms
- Plastic deformation
- Permanent shape change remaining after the load is removed.
- Ductility
- Capacity for plastic deformation before fracture under a stated test.
- Resilience
- Elastic strain energy absorbed per unit volume up to yielding.
- Toughness
- Energy absorbed per unit volume across the stress-strain curve to fracture.
- Reduction area
- The percentage decrease from original to minimum fractured cross-sectional area. It captures local contraction near fracture and can rank ductility differently from percentage elongation, which averages deformation over a stated gauge length.
- Indentation hardness
- Resistance measured by the size or depth of an impression under a defined indenter, load and dwell. It samples a local volume and can map gradients, but it does not reproduce the full tensile or fracture response.
- Permanent strain
- The deformation remaining after unloading from beyond the elastic range. An unloading path can recover an elastic portion with a modulus-like slope while leaving this offset, separating recoverable response from accumulated plastic change.
Plastic Deformation and Mechanical Measures FAQ
Is the strongest material always the toughest?
No. Strength is a stress level, while toughness depends on both stress and deformation across the path to fracture. A high-strength material can fail after little plastic strain and absorb less total energy.
Why must elongation include gauge length?
Localised deformation occupies a different fraction of short and long gauge lengths. Reporting gauge length makes percentage elongation comparable and prevents specimen geometry from being mistaken for a material difference.
What does a hardness value establish?
It establishes resistance to a defined indentation method and load. Correlations with tensile strength can be useful for particular material families, but hardness does not directly replace a complete tensile or fracture test.
Exam move
Construct a property ledger with rows for elastic modulus, yield strength, tensile strength, elongation, reduction in area, resilience, toughness and hardness. For each row, record its definition, graph location or test, units, design use and one limitation.
The ledger should make incompatible substitutions obvious: modulus is a slope, yield strength is a stress convention, ductility is deformation to fracture, and toughness is an energy density across the full path. Work resilience calculations from both a triangular linear-elastic approximation and a simple piecewise curve. State the integration limit and keep modulus and stress in compatible units.
Use the direction check that increasing yield stress at fixed modulus enlarges the elastic area, while increasing modulus at fixed yield stress reduces yield strain. For toughness, estimate rectangular or trapezoidal areas from printed curve segments and explain why the result includes plastic deformation. Practise ductility with both percentage elongation and percentage reduction in area.
Write the original and final dimensions beside each formula and carry the gauge length with elongation results. Invent two specimens with the same final extension but different starting gauge lengths to demonstrate why raw extension cannot be compared directly. Pair each strength change with a likely ductility consequence, then identify circumstances where the trade-off is not captured by one slogan.
Grain refinement, strain hardening and precipitation can all impede dislocations, but they produce different microstructures and thermal stability. Ask what motion is blocked, whether the obstacle persists on heating and which failure mode might become limiting. For hardness, make a method checklist covering indenter, load, dwell, surface preparation, spacing and thickness.
Explain why a local indentation can map a gradient or heat-affected zone yet cannot reconstruct an entire tensile curve. When using an empirical hardness-strength correlation, state the material family and calibration boundary instead of treating it as a definition. Build comparison prompts that deliberately change the ranking.
One candidate should win on yield strength while another wins on toughness; one should resist permanent set while another absorbs more fracture energy. Answer by naming the service consequence, not by calling either material better. Close with a graph annotation drill. Shade the elastic area, full fracture area and permanent strain after unloading from a plastic point.
Add unloading lines and explain why their slope is associated with elastic response even though the specimen retains strain. The finished page should let you move from any measure to its physical experiment, governing geometry, energy meaning and design limitation without relying on memorised adjectives.
