Materials

• • You need to pair of equal & opposite forces to alter the shape of an object
• Tensile forces --> forces that produce extension
• Compressive forces --> Two or more forces together that reduce the length or volume of an object
• Strength --> The ability to resist fracture
• Stiffness --> The ability to resist deformation
• Ductility --> The ability to permanently deform before failure
• Brittleness --> The opposite of ductility
• Toughness --> The ability to absorb energy before breaking
• Hardness --> The ability to resist indentation, abrasion & wear
• Deformation --> Change the shape or size of an object
• Elasticity --> Property of a body to return to its original shape or size once the deforming forces or stress has been removed
• Plastic --> The object will not return to its original shape when the deforming force is removed. It becomes permanently distorted.
• Shear deformation --> occurs when an object changes shape because forces are applied to it and does not just become longer or shorter
• Compression --> The decrease in length of an object when a compressive forces is exerted on it
• Hooke's law:

  • A helical spring undergoes tensile deformation when tensile forces are exerted & compressive deformation when compressive forces are exerted
  • The force - extension graph is a straight line from the origin up to the elastic limit of the spring In this linear region, the spring undergoes elastic deformation
  • The spring will return to its original length when the force is removed. Beyond point A, the spring undergoes plastic deformation: permanent structural changes to the spring occur and it doesn't return to its original length when the force is removed
• Hooke's law --> the extension of the spring is directly proportional to the force applied. This is true as long as the elastic limit of the spring is not exceeded.
• Force constant, k:

  • For a spring obeying Hooke's law, the applied force F is directly proportional to the extension, x
  • F = kx
• • K is called the force constant of the spring ( SI unit newton per metre Nm^-1)
  • This is the measure of the stiffness of a spring
  • A spring with a large force constant is difficult to extend and you would refer to it as a stiff spring
  • You can also use the equation F= kx for a compressible spring: x then represents the compression of the spring
• Investigating Hooke's law


  1. Attach the spring at one end using a clamp, boss and clamp stand secured to the bench using a G - clamp or a large mass

  2. Set up a metre rule with a resolution of 1mm close to the spring

  3. Suspend slotted masses from the spring and as you add each one, record the total mass added and the new length of the spring

  4. Improve the accuracy of the length measurements using a set square, and by taking readings at eye level to reduce parallax errors

  5. Measure the mass of each slotted mass using a digital balance

  6. Take at least six different readings and repeat each one at least once
• Material compressed or extended without going beyond elastic limit


  • Work done on the material can be fully recovered
• Material has gone through plastic deformation


  • Some of the work done on the material can be fully recovered
• Material has gone through plastic deformation


  • Some of the work done on the material has gone into moving its atoms to new permanent positions
  • This energy is not recovered
• Area under a force - extension curve graph


  Work done
• Work done on the spring

  1. Transferred to elastic potential energy within the spring

  2. This energy is fully recoverable because of the elastic behaviour of the spring
• Elastic potential energy:

  • E = area under graph = area of shaded triangle
  • E = 1/2 Fx where F is the force producing an extension, x
  • E = 1/2Kx^2
  • For a given spring, E is directly proportional to x^2, so doubling the extension quadruples the energy stored
• Tensile stress --> the force applied per unit cross-sectional area of the wire

  • tensile stress = force / cross-sectional area
  • Sigma = F/A
  • where sigma is the tensile stress, F is the applied force and A is the cross sectional area
• Tensile strain --> the fractional change in the original length of the wire

  • tensile strain = extension / original length
  • e = X / L
  • where e is the tensile strain, x is the extension and L is the original length
  • Tensile strain is the ratio of 2 lengths, so has no units
• Stress - strain graph for a metal:

  • The stress is directly proportional to the strain from the origin to the limit of proportionality
  • The ultimate tensile strength is the maximum stress that a material can withstand when being stretched before it breaks
  • Beyond the UTS, the material may become longer & thinner at its weakest point , a process called necking
  • The material eventually snaps at its breaking point
  • The stress value at the point of fracture is known as the breaking strength of the material
  • A strong material is one with a high ultimate tensile strength
• The Young modulus, E:

  • Within the limit of proportionality, stress is directly proportional to strain.
  • The ratio of stress to strain for a particular material is a constant & is known as its Young modulus, E.
  • Young modulus = tensile stress / tensile strain
  • the unit of the Young modulus is the same as that for stress, Nm^-2 or Pa
• Polymeric materials --> materials that consist of long molecular chains.

  • These behave differently depending on their molecular structure & temperature
• Ultimate tensile strength (UTS) --> the maximum stress a material can withstand before breaking
• Elastic deformation —> the material returns to its original shape after the force is removed
• Plastic deformation —> the material does not return to it original shape after the force is removed
• Ductile material —> a material which can easily be drawn into wires
• • Rubber doesn't experience plastic deformation, doesn't obey Hooke's law
  • The area between the loading & unloading curves is a hysteresis loop
  • This area represents the energy that was required to stretch the material out, which was transferred to thermal energy when the force was removed
• • Polythene is a polymeric material. Doesn't obey Hooke's law, experiences plastic deformation when any force is applied to it
  • Makes it very easy to stretch it into new shapes