# Elasticity, Plasticity and Yield

#### Elasticity and Plasticity

The graph shown in the previous section shows the difference between stiff and flexible materials. This is shown again below.

No material can continue to deform infinitely, or undergo infinite stress, so surely there is an upper limit of the lines presented. The upper limit of the stress vs strain is a property of each material, in addition the manner in which failure of the material occurs is also a property of a given material. To understand the manner of failure of a material it is important to understand the material’s elastic and/or plastic behaviour.

Under load, most materials will initially deform in an elastic manner: when a load is applied to an object the object deforms, when the load is removed the object returns back to its original shape. A good way to picture this is the behaviour of a spring or an elastic band.

However, some materials can also deform in a plastic manner, any deformation caused by an applied load will result in a permanent deformation and the object will not return to its original shape.

Some materials will behave in a purely elastic manner, some will behave in a purely plastic manner and some will behave initially elastically and then plastically, often called elasto-plastic. Examples of each given below:

• Elastic only – An elastic band – will return to it’s originally shape until it is overstretched and breaks.
• Plastic only – Soils – These will often behave in a predominately plastic manner, when a load is removed the soil stays in it’s newly deformed shape.
• Elastoplastic – Steel – Steel will initially behave elastically, beams will deflect under load and then rebound, but above certain loading permanent deformations of the steel will occur.

#### Yield point / Yield Stress

The stress value at which an elasto-plastic materials transitions from an elastic behaviour to a plastic behaviour has a special name, its is called a material “Yield Point” or “Yield Stress”. Below the yield stress the material will behaviour in an elastic manner, when the stress is removed the material will deflect back to its original shape. Above the yield stress any deformations will be permanent, plastic deformations.

But why is this important? Broadly speaking, failure of a material will typically be in one of two ways, Ductile Failure or Brittle Failure

#### Ductile Failure

The ductility of a material is a measure of how well a material can respond to plastic deformations. Toffee is a ductile material, it can withstand a large amount of plastic deformation under load. A ductile failure occurs when a material has undergone its elastic deformation, then undergone plastic deformation and then finally reached a limiting failure strain at which the material ultimately ruptures.

Ductile failures can only occur in materials which can take plastic strains.

#### Brittle Failure

Brittle failures occur in materials that either do not behave plastically at all or only have a limited capacity to undergo plastic strains. As the material cannot undergo plastic strain failure of the material is often sudden with little or no warning of imminent failure. Ductile failure can often fail in an explosive manner as elastic energy is released suddenly.

Ductile failure is a lot more favourable in Engineering materials as it shows signs of deformation prior to failure, this allows time for the structure to be evacuated or a replacement of a failing part. Materials that fail in a brittle manner, such as cast iron or ceramics need to be designed and monitored very carefully to avoid sudden catastrophic failure.

#### Temperature effects

The ductility or brittleness of a material is often related to the temperature of the material. At room temperature glass is a brittle material, however when heated it can become ductile. Ultimate tensile strengths and yield strengths of materials also change with temperature, a blacksmith heats metal objects prior to working them in order to make the material more malleable.