To change the shape of an object, two equal and opposite forces are required. Tensile forces stretch an object, causing extension, while compressive forces act towards the centre of an object.
In elastic deformation, a material temporarily changes shape, and regains its original shape after deforming forces are removed. In plastic deformation, a material permanently changes shape, and does not regain its original shape after deforming forces are removed.
For a material within its elastic limit, the force applied is directly proportional to the extension of the material. Past the elastic limit, there will be plastic deformation, causing permanent deformation.
A point beyond which behaviour no longer conforms to Hooke's law. It comes at a lower extension than the elastic limit.
A point beyond which the spring will no longer return to its original shape once the force is removed. It comes at a higher extension than the limit of proportionality.
When a material is deformed elastically, work is done and stored as elastic potential energy. The energy is equal to the area under a force-extension graph. If plastic deformation occurs, work is done to achieve the deformation by rearranging atoms into new permanent positions.
The hysteresis loop in a loading-unloading force-extension graph has an area bound by two curves, which represents the work being done. This is transferred to thermal energy. Materials such as rubber exhibit this behaviour.
Springs in parallel share the load and have the same extension as a single spring with a combined spring constant:
Springs in series have the same force. The extensions add, giving the same extension as a single spring with a combined spring constant:
Stress is the force applied per unit cross-sectional area. It is measured in pascal (Pa). Where
The stress required to cause the material to begin to deform plastically.
Strain is the extension or compression of a material per unit of its original length. It has no units, and is sometimes written as a percentage. Where
The Young's modulus of a material is the ratio of stress to strain. It is the gradient of a stress-strain graph, and is a measure of stiffness. It is measured in Pascal (Pa).
The Young's modulus is the gradient of the straight part of a stress-strain graph.
The elastic limit is where elastic deformation ends and plastic deformation begins to occur (at the yield stress).
A point at which there is a large increase in the extension when the stress increases beyond the elastic limit.
The maximum stress experienced by a sample before breaking.
The point at which the material breaks (at the fracture stress).
Crystalline structures have regular, ordered particles.
Amorphous structures have random and disordered arrangements.
Polycrystalline structures have regular crystalline fragments (grains), but the grains are arranged in a disordered way.
Metals have a crystalline or polycrystalline structure.
Metals behave elastically for small strains. Up to the elastic limit, the spacing between positive ions increases. When the tensile force is removed, the metal returns to its original shape.
Metals are malleable and ductile. There are dislocations - missing ions in the regular lattice arrangement. These allow atoms to move along one at a time, causing the dislocation to move through the metal, causing ductility and plastic behaviour. As dislocations move, slips can occur, where some layers require less force to move.
In an alloy, there are other metals, and these ions are different sizes, pinning the dislocation and making slips more difficult.
Amorphous materials such as glass are brittle. This is because cracks can easily propagate. Two atoms are pulled apart at a crack, followed by the next two atoms. The atoms cannot move relative to each other - they are pinned in place, and the crack area is small, producing high stresses. This causes the crack to quickly grow.
Polymers are long chains of repeating monomers. Chains are entangled and when stresses are applied, they rotate and unravel around each other. Crosslinks between chains can reduce the rotation and unravelling of chains.
Bonds in ceramics are directional, making it harder for them to deform plastically, while bonds in metals are non-directional.
Rayleigh's oil drop experiment compares the diameter of an oil drop to the diameter of the oil layer floating on water. The assumptions are:
For an oil layer of radius