4.2.1 Bulk properties of solids

Density

• Density is defined as the mass per unit volume of a material.
• It provides a measure of how compact a substance is.

Hooke's Law

• Hooke's Law states that extension is directly proportional to the force applied (assuming environmental factors like temperature remain constant).
• This relationship can be seen as a straight line through the origin on a force-extension graph.
• Formula: $F = k \Delta L$
  • Where:
  • $F$ = force,
  • $k$ = spring constant (a measure of the material's stiffness),
  • $\Delta L$ = extension.

Limit of Proportionality

• The limit of proportionality is the point on a force-extension graph beyond which Hooke's Law no longer applies.
• Beyond this point, if force is further increased, the material reaches the elastic limit and may deform plastically (permanent deformation).

Stress and Strain

1. Tensile Stress is defined as the force applied per unit cross-sectional area.

• Formula: $\text{Stress} = \frac{F}{A}$
• $F$ = force, $A$ = cross-sectional area.

2. Tensile Strain is the extension per unit original length.

• Formula: $\text{Strain} = \frac{\Delta L}{L}$
• $\Delta L$ = extension, $L$ = original length.

Elastic Strain Energy

• When a material is stretched or compressed, energy is stored as elastic strain energy.
• For variable forces, this energy can be calculated as the area under the force-extension graph.
• Formula for Elastic Strain Energy: $\text{Elastic Strain Energy} = \frac{1}{2} F \Delta L$.

Breaking Stress

• Breaking Stress is the stress level at which a material will fracture.
• It varies with conditions such as temperature.

Behaviour of Materials on Force-Extension Graphs

• Plastic: Materials that exhibit significant extension with load beyond the elastic limit.
• Brittle: Materials that extend very little and tend to fracture at low extensions.

Elastic vs. Plastic Behaviour

• Elastic Behaviour: The material returns to its original shape when the force is removed, storing energy as elastic strain energy.
• Plastic Behaviour: The material undergoes permanent deformation; energy is dissipated as heat rather than stored as strain energy.

Application of Elastic Strain Energy

• In safety features like crumple zones in cars:
  • These deform plastically, absorbing energy during collisions, which reduces the impact force experienced by passengers.

Stress-Strain Graphs

• Stress-strain graphs represent the behaviour of materials rather than specific objects.
  • They indicate ultimate tensile stress (UTS) – the maximum stress a material can withstand.
• The graph's shape can also reveal if a material is:
  • Ductile (undergoes a large amount of plastic deformation),
  • Brittle (fractures easily without much deformation),
  • Plastic (exhibits significant deformation before breaking).