ABE 3813: Biophysical Properties of Materials - Mechanical Properties of Solid Materials

This set covers the fundamental mechanical properties of solid materials, including stress-strain relationships, types of deformation, loading applications, and measurement techniques for Engineering and True stress.

Stress ($\sigma$)

The normalization of load to cross sectional area (\sigma = rac{F}{A}).

Strain ($\epsilon$)

The normalization of deformation to unit or original length (\epsilon = rac{\Delta \text{length}}{\text{original length}}).

Young’s modulus

A material property reflecting the same amount of strain for the same conditions of stress, regardless of geometry and size.

Total Strain ($\epsilon_{total}$)

The sum of reversible and permanent deformation, expressed as $\epsilon_{total} = \epsilon_{elastic} + \epsilon_{plastic}$.

Elastic Strain

Reversible strain resulting from small stretching of atoms away from equilibrium positions; atoms return to equilibrium when stress is removed.

Plastic Strain

Permanent, non-reversible change in atomic arrangements and object shape caused by exceeding the limits of elastic strain.

Elastic Limit

The point on a stress-strain curve where the behavior begins to deviate from linearity and plastic strain begins to occur.

Brittle materials

Classes of materials that exhibit little or no plastic deformation.

Ductile materials

Materials that undergo large amounts of plastic deformation under tension.

Malleable materials

Materials that undergo large amounts of plastic deformation under compression.

Normal Stress ($\sigma$)

The intensity of internal force acting normally or perpendicularly to an area, which can be applied in compression or tension.

Shear Stress ($\tau$)

The intensity of internal forces acting parallelly or tangentially to a plane (\tau = rac{F}{A}).

3- and 4-point bending tests

Tests used to estimate the tensile strengths of brittle materials by reducing the area of test samples under tension and minimizing the role of flaws like cracks.

Hardness

The resistance to plastic deformation by penetration or scratching; calculated as \text{Hardness} = rac{\text{max load}}{\text{residual indentation area}}.

Indentation testing

A technique used to determine the hardness of a material.

Engineering stress-strain

Curves representing loads and deformations normalized to the sample’s original cross sectional area, which may exhibit negative slopes.

True stress-strain

Curves representing loads and deformations normalized to the sample’s instantaneous cross sectional area, which do not exhibit negative slopes.

Digital image correlation (DIC)

An optical technique used to measure instantaneous strain.

Poisson’s Ratio ($\nu$)

A measure of lateral/transverse strain, with values such as $0.25-0.5$ for metals, $0.13-0.3$ for bone, and $0.39-0.49$ for rubbers.