1.5 Solids under stress

State Hooke’s law.

Extension is directly proportional to the applied force, provided the limit of proportionality is not exceeded (F = kx).

What is the spring constant k?

Force per unit extension. Unit: N m⁻¹.

What does a large spring constant mean?

The spring is stiffer.

What is tensile stress?

Force per unit cross-sectional area. Stress = F / A. Unit: Pa (N m⁻²).

What is tensile strain?

Extension ÷ original length. Strain = ΔL / L. It has no units.

What is the Young modulus?

Stress ÷ strain (in the linear region). Unit: Pa.

What does the gradient of the linear part of a stress-strain graph represent?

The Young modulus.

What does the area under a force-extension graph represent?

Work done in stretching the material (= elastic energy stored).

What is the elastic limit?

The maximum stress from which the material can still return to its original length.

What is plastic deformation?

Permanent deformation that remains after the force is removed.

What is elastic deformation?

Temporary deformation – the material returns to its original shape when the force is removed.

What is a ductile material?

A material that can undergo large plastic deformation before breaking (e.g. copper, mild steel).

What is a brittle material?

A material that breaks with little or no plastic deformation (e.g. glass, cast iron).

What is the yield point?

The point after which large plastic deformation occurs with little increase in stress.

Name the three main classes of solid.

Crystalline, amorphous and polymeric.

What is a crystalline solid?

Atoms arranged in a regular lattice (long-range order). Example: metals.

What is an amorphous solid?

Atoms arranged randomly with no long-range order. Examples: glass, ceramics.

What is a polymeric solid?

Made of long chain molecules. Examples: rubber, polythene.

What is the limit of proportionality?

The point up to which stress is proportional to strain (Hooke’s law is obeyed).

What happens to the cross-sectional area during necking in a ductile material?

It decreases, so stress increases even if the force stays the same or decreases.

What is the difference between the elastic limit and the limit of proportionality?

The limit of proportionality is where the graph stops being linear. The elastic limit is where permanent deformation begins (they are often very close).

What does the area under a stress-strain graph represent?

Energy stored per unit volume.

What is the unit of the Young modulus?

Pascals (Pa) or N m⁻².

What happens to a material if it is stretched beyond its elastic limit?

It suffers plastic (permanent) deformation.

What is meant by “necking”?

Local reduction in cross-sectional area that occurs in ductile materials just before they break.