Materials

What is the force constant?

• Force per unit extension

• Unit is Nm^-1

• It is called the constant of proportionality (k) in Hooke's law

• A measure of the stiffness of a spring

What is the the limit of proportionality?

The value of force or stress beyond which an object doesn’t obey Hooke’s law and stress is no longer directly proportional to strain

What is a yield point?

A point on a stress-strain graph at which the material starts to extend rapidly as stress increases.

Define stiffness

The ability of an object to resist deformation

What is a polymeric material?

• A material comprising of long-chain moleules (polymers) that does not obey Hooke’s law

• May show large strains

• Polyethene and Rubber are examples.

Define stress

The force per unit cross sectional area, measured in pascals (Pa)

Define strain

The ratio of extension to original length.

What is the unit of strain?

Strain does not have a unit as it is a ratio.

What is the unit of young’s modulus?

Pa or Nm^-2

What is the equation for young’s modulus?

E = σ/ε

Young’s modulus = tensile stress / tensile strain

What is the equation for tensile strain?

ε = x/L

Tensile strain = extension / original length

What must be true about a material for hysteresis loop to be produced?

The loading and unloading curves must be different

What does the area of a hysteris loop represent on a force-extension graph?

• The energy transferred to the material over one cycle

• This energy is dissipated as heat to the surroundings.

What does the area of a hysteris loop represent on a stress-strain graph?

The energy absorbed by the material per unit volume

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

The energy absorbed by the object during loading

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

The energy released by the object during unloading

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

The energy absorbed per unit volume by the object during loading

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

The energy released per unit volume by the object during unloading

Hooke’s law

Force is proportional to extension provided the limit of proportionality is not exceeded

Hooke’s law equation, including meaning and unit of each term

F= kx

• F Is force in N

• k is the spring constant in Nm^-1

• x is the extension in m

Elastic limit

The maximum value of force or stress for which the object returns to its original shape after unloading.

Equation for tensile stress

σ = F / A

• Where σ is tensile stress in Pa

• F is the force acting through the object in N

• A is the cross-sectional area in m²

Define Young’s modulus

The ratio of tensile stress to tensile strain within the material's elastic limit

Elastic potential energy

Energy stored when an object is stretched elastically

Breaking stress

The value of stress just before fracture.

Label this stress–strain graph with stress, strain, elastic and plastic region, UTS and breaking stress

Brittle behaviour (description + graph)

When a material shows little or no plastic deformation before it brakes

Ductile behaviour (description + graph)

When a material undergoes a large plastic deformation before it breaks ∴ has a large plastic region in a stress-strain graph.

Ultimate Tensile Strength

The maximum tensile stress an object can withstand before it breaks

What does the gradient of a force-extension graph equal?

Force constant k

What does the gradient of a stress-strain graph equal?

Young’s modulus E when below the elastic limit

Elastic deformation

• The object returns to its original shape once the load has been removed.

• The elastic limit has not been exceeded.

Plastic deformation

• The object does not return fo its original shape once the load has been removed.

• The elastic limit has been exceeded.

Stress-strain curves of glass, steel, copper and polymer on one plot

Stress-strain curve of glass

Glass is brittle

Force-extension graph of polyphene (loading and unloading curves)

Force-extension graph of metal wire where max force > elastic limit (loading and unloading curves + elastic limit)

Stress strain graph of rubber