Elements of Fracture Mechanics

Griffith Crack Theory

• A balance must be struck between the decrease in potential energy and the increase in surface energy resulting form the presence of a crack.
• The surface energy arises from the fact that there is a non-equilibrium configuration of nearest neighbor atoms at any surface in a solid.
• There exists an energy balance between strain energy released as the crack extends (negative):
  
  and energy absorbed as crack grows:
  
  due to creation of new surface.
• Instability occurs when dU/da = 0 and the crack will always grow.
• Griffith Theory:
          plane stress:
  
          plane strain:
  
• The above is derived for an elastic material containing a very sharp crack.
• There's a need to incorporate an extra term due to difference in fracture energy and surface energy for metals and polymers.
• Irwin used the energy source term and denoting dU/da as G:
  
• At the point of instability the elastic energy release rate G (the crack driving force) reaches a critical value and fracture occurs.

Stress Analysis of Cracks

• Three major modes of loading:
          mode I – opening or tensile mode, where the crack surfaces move directly apart
          mode II – sliding or in-plane shear mode, where the crack surfaces slide over one another in a direction perpendicular to the leading edge of the crack
          mode III – tearing or antiplane shear mode, where the crack surfaces move relative to one another and parallel to the leading edge of the crack
• plane strain – thin plate and sz = 0; 2D strain / 3D stress
• plane stress – thick sections; 2D stress / 3D strain