Key Definitions:
Term | Definition |
|---|---|
Stress (σ) | Force per unit area acting on a material, σ = Force/Area (units = Pa) |
Strain (ε) | Fractional change in dimension, strain = change in length / original length |
Elastic | Deformation is fully recoverable |
Elastic limit | Highest stress where the stress-strain curve remains linear |
Yield stress | Stress where permanent (plastic) deformation begins (often estimated by 0.2% proof stress) |
Young's modulus (E) | Gradient of linear elastic region of stress-strain curve, E = stress/strain |
Hooke's law | Stress is proportional to strain |
Ultimate tensile strength | Maximum stress sustained in tension |
Fracture strength | Stress at which the specimen breaks |
Ductility | Plastic strain at fracture (often reported as % elongation) |
Necking | Localised reduction in cross-sectional area that precedes fracture in ductile materials |
Resilience | Elastic energy absorbed per unit volume, area under linear elastic region of stress-strain curve |
Toughness | Total energy to fracture, entire area under stress-strain curve |
Hardness | Resistance to indentation |
Fatigue | Failure under cyclic stresses below the yield stress |
Creep | Gradual increase in strain under constant stress, especially at elevated temperature relative to softening |
Stress relaxation | Reduction in stress under constant strain |
Poisson's ratio (ν) | Ratio of lateral strain to axial strain when a material is stretched or compressed. It describes how much a material becomes thinner when stretched, or wider when compressed. |
Why stress and strain (not just force and extension)?
A raw load–extension record depends on a specimen’s size and shape: a thick, short rod looks “stronger” than a thin, long one even if both are made from the same material. Stress (normalising load by area) and strain (normalising extension by original length) remove those geometric effects. With a stress–strain curve you can predict how any cross-section and length of that material will behave under tension and, crucially, compare materials on an equal footing.
Different stress states are clinically relevant: enamel and ceramics thrive under compression, while tension and shear are far more dangerous for brittle phases. Restorations experience mixed stress fields as occlusal loads distribute through complex geometries.
Poisson’s ratio
Materials do not just change length when loaded, they also change width. If you stretch a specimen, it gets longer and usually thinner; if you compress it, it gets shorter and wider. Poisson’s ratio (ν) measures how much sideways deformation occurs relative to lengthwise deformation. In simple terms, it tells you how much a material “bulges” or “necks” sideways when loaded. This is useful because dental materials in the mouth experience complex loading, so sideways strain can affect marginal seal, stress distribution, and bonding.
Reading a stress–strain curve
Most materials begin with a linear elastic segment. Here, the slope is Young’s modulus (E), the stiffer the material, the steeper the slope. Beyond the elastic/proportional limit, the curve departs from linearity as plastic flow begins. The yield stress marks the onset of permanent deformation; in practice we often use the 0.2% proof stress (an offset method) to locate it.
As loading continues, ductile metals show a peak (ultimate tensile strength) and then necking, concentrating strain until fracture. Brittle materials (e.g., plaster, ceramics) typically show a linear elastic rise and then abrupt fracture with little to no plastic deformation. Elastomers display large, recoverable strains with low tensile strength and no obvious linear segment at small strains.
Key measures pulled from the curve:
Young's modulus (E): stress / strain.
Proof stress: the stress a material can withstand without plastic deformation, defined as the stress that causes a specific, small amount of permanent extension, usually set at 0.2%
Ultimate tensile strength: maximum stress sustained in tension.
Ductility (% elongation): formability and warning before fracture. Measured by drawing a line parallel to the linear elastic region from the fracture point to the strain (x) axis.
Resilience: area under linear (elastic) region of stress-strain curve.
Toughness: total area under stress-strain curve.
Energy measures: resilience and toughness
If you bend a wire and let go, it snaps back because it stored elastic energy. The modulus of resilience estimates how much energy per volume a material can store without permanent set; useful for springs, orthodontic wires, and clasps. Toughness reads the whole journey: how much energy the material can absorb before it breaks, vital when you need resistance to crack initiation and growth.