4.6 Stress, Strain & The Young Modulus

Stress

• Stress is the applied force per unit cross sectional area of a material
• Forces can be;
  • Tensile forces, which pull on an object and extend it
  • Compressive forces, which push onto an object and compress (or squash) it

•  The equation for stress is the force per unit area, and so the units are N m⁻², or Pascals, the same unit as pressure

Stress equation

 

• The ultimate tensile stress is the maximum force per original cross-sectional area a wire is able to support until it breaks

 

Strain

• Strain is the extension per unit length

Strain is the ratio of the extension (or compression) and the original length

• This is a deformation of a solid due to stress in the form of elongation or contraction
• Note that strain is a dimensionless unit because it’s the ratio of lengths

Strain equation

 

Young Modulus

• The Young modulus (sometimes called Young's Modulus) is the measure of the ability of a material to withstand changes in length with an added load ie. how stiff a material is
• This gives information about the elasticity of a material
• The Young Modulus is defined as the ratio of stress and strain

Young Modulus equation

 

• Its unit is the same as stress: Pa (since strain is unitless)
• Just like the Force-Extension graph, stress and strain are directly proportional to one another for a material exhibiting elastic behaviour

A stress-strain graph is a straight line with its gradient equal to Young modulus

 

• The gradient of a stress-strain graph when it is linear is the Young Modulus