Knowledge- 8 Materials

• Density is the mass per unit volume
• Hooke's law states that the extension of a spring is directly proportional to the force exerted on it.

  • F=k x change in length
• Hooke's law:

  • only applies up to a certain point- the limit of proportionality
  • is obeyed by wires and solid objects made of most materials
  • can be applied to the compression of a spring , where change in l is the amount the spring gets shorter.
• Elastic deformation occurs when a material can return to its original shape and size once any forces on it are removed.
• Plastic deformation occurs when a material remains permanently deformed, so does not return to its original shape and size once any forces on it are removed.
• The elastic limit of a spring or material is the point beyond which it becomes permanently deformed.
• the Youngs modulus is a measure of stiffness of a material.
• The stress and strain of a material are proportional to each other up to the limit of proportionality.
• Stress and strain:

  work done to stretch or compress an object.
• When an object is elastically deformed , the energy transferred when it is stretched or compressed is stored as elastic strain energy.

  • Ep = 1/2 F x change in length
  • since Ep = k x change in length^2
• An object is under tension if the forces acting on it are stretching it. An object is under compression if the forces acting on it are squashing it.
• The tensile stress on an object is the force stretching F it divided by the cross-sectional area A: F/A.
• The unit of stress is the pascal (Pa).
• The tensile strain on an object is the ratio of its extension change in length over its original length. e = change in length /length
• Stress-strain graph: shows the general behavior of a material.
• On a stress-strain graph:

  where OP is a line from origin straight to P

  • OP: Stress and strain proportional to each other; material obeys Hooke's law, gradient constant and equal to Youngs modulus ; area under section = energy stored in the material per unit volume.
• On stress-strain graph:

  where P is the point before line on graph goes from straight to curved

  • P: limit of proportionality - stress and strain no longer proportional; deformation still elastic.
• On stress-strain graph:

  Where E is a point on the curved section of the graph

  • E: elastic limit- deformation plastic from this point.
• On stress-strain graph:

  where y1 is where curve has negative gradient

  • Y1: yield point 1- stress at which material weakens and stretches plastically without additional force
• On stress-strain graph:

  Where Y2 is a point on the graph before line increases again with a curve.

  • Y2: yield point 2- stress at which material undergoes plastic flow, where small stress leads to large strain because cross-sectional area of material is decreasing rapidly.
• On stress-strain graph:

  UTS: ultimate tensile stress- maximum stress the material experiences; measure of the materials strength.
• On stress-strain graph:

  • B: breaking point- stress in material at which it breaks.
• Properties of materials:

  • stiff materials have steep initial gradients , large Youngs modulus
  • strong materials have high UTS and breaking point
  • brittle materials break without much plastic deformation.
  • Ductile materials undergo high plastic deformation before breaking.
• Force-extension graphs show the behavior of a sample of a material , with a particular shape and size
• Metal stretched past beyond its elastic limit:

  • unloading line do not go through the origin- wire is permanently stretched.
  • Loading and unloading lines parallel because Youngs modulus is constant.
  • Area between loading and unloading is the work done to permanently deform the wire.
• Rubber band:

  • unloading line goes through the origin- rubber band returns back to its original length.
  • area under loading curve is the work done to stretch rubber bands.
  • area under unloading curve is the work done by the rubber band when unloaded.
  • Area between loading and unloading curves is the difference in energy stored and energy recovered when unstretched