Mechanical Properties of MatterMechanical Properties of Matter

The area under a force-extension (or compression) graph gives the work done. This is transferred to elastic potential energy within the material.

Elastic potential energy is given by:

E = frac{1}{2}Fx

E = frac{1}{2}kx^{2}

Tensile stress is defined as the force applied per unit cross sectional area of the wire. The unit of stress is pascals.

sigma = frac{F}{A}

Tensile strain is the fractional change in the original length of the wire. Strain is a ratio so has no units.

varepsilon = frac{x}{L}

Within the limit of proportionality, stress is directly proportional to strain, The ratio of stress to strain for a particular material is constant and is known as the Young modulus, E.

E = frac{sigma }{epsilon }

 =frac{f}{A}div frac{x}{L}=frac{FL}{Ax}

The unit of Young modulus is the same as stress, Pa or Nm-2. It is equivalent to the gradient of the linear region of the stress-strain graph and a property of a material, not an object. 

Stress-strain graph features:

  1. Limit of proportionality, P: the point up to which the material obeys Hooke’s Law (the graph is linear).
  2. Elastic limit, E: the point up to which the stress can be increased before the onset of permanent, plastic deformation,                                                                                                                                   
  3. Yield points, Y1 and Y2: points where the material extends rapidly.
  4. Ultimate tensile strength, UTS: the maximum stress a material can withstand when being stretched before breaking. Beyond this point, the material may become longer and thinner at its weakest point (necking) before eventually snapping.
  5. Breaking point, B: the point at which the material snaps.
  6. Breaking strength: the stress vale at the point of fracture.


Characteristics of matter:

  1. Strong: a strong material that has a high UTS.
  2. Stiff: a material with a large Young’s modulus (and large force constant). Large gradient on stress-strain graph.
  3. Brittle: shows elastic behaviour up to its breaking point, without plastic deformation. Breaks when linear region ends.

Break due to spreading of cracks. 

  1. Ductile: can be drawn into a wire, so shows plastic deformation. Linear region ends quickly.
  2. Polymeric: consists of long molecular chains. Behave differently depending on structure and temperature. Can stretch a great deal before breaking, but may show elastic or plastic behaviour.
  3. Tough: deforms plastically to reduce the spread of cracks. Requires a large amount of work (area under forceextension graph) to break.
  4. Hard: resistance to scratching and surface indentation.

Types of deformation:

  1. Elastic: returns to original length when force causing deformation is removed.

Plastic: permanent deformation/extension. Doesn’t return to original length when force is removed. Flow, slip or slide internally before breaking.