page_title: Fracture mechanics
section_title: Irwin's modification
hierarchical_section_title: Fracture mechanics / Linear elastic fracture mechanics / Irwin's modification
context_page_description: Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.
  In modern materials science, fracture mechanics is an important tool used to improve the performance of mechanical components. It applies the physics of stress and strain behavior of materials, in particular the theories of elasticity and plasticity, to the microscopic crystallographic defects found in real materials in order to predict the macroscopic mechanical behavior of those bodies. Fractography is widely used with fracture mechanics to understand the causes of failures and also verify the theoretical failure predictions with real life failures. The prediction of crack growth is at the heart of the damage tolerance mechanical design discipline.
  There are three ways of applying a force to enable a crack to propagate:
  Mode I – Opening mode,
  Mode II – Sliding mode, and
  Mode III – Tearing mode.
context_section_description: Griffith's theory provides excellent agreement with experimental data for brittle materials such as glass.  For ductile materials such as steel, although the relation  still holds, the surface energy (γ) predicted by Griffith's theory is usually unrealistically high.  A group working under G. R. Irwin at the U.S. Naval Research Laboratory (NRL) during World War II realized that plasticity must play a significant role in the fracture of ductile materials.
  In ductile materials (and even in materials that appear to be brittle), a plastic zone develops at the tip of the crack.  As the applied load increases, the plastic zone increases in size until the crack grows and the elastically strained material behind the crack tip unloads. The plastic loading and unloading cycle near the crack tip leads to the dissipation of energy as heat.  Hence, a dissipative term has to be added to the energy balance relation devised by Griffith for brittle materials.  In physical terms, additional energy is needed for crack growth in ductile materials as compared to brittle materials.
  Irwin's strategy was to partition the energy into two parts:
  the stored elastic strain energy which is released as a crack grows.  This is the thermodynamic driving force for fracture.
  the dissipated energy which includes plastic dissipation and the surface energy (and any other dissipative forces that may be at work).  The dissipated energy provides the thermodynamic resistance to fracture.  Then the total energy is
  where  is the surface energy and  is the plastic dissipation (and dissipation from other sources) per unit area of crack growth.
  The modified version of Griffith's energy criterion can then be written as
  For brittle materials such as glass, the surface energy term dominates and .  For ductile materials such as steel, the plastic dissipation term dominates and .  For polymers close to the glass transition temperature, we have intermediate values of  between 2 and 1000 .
caption: The plastic zone around a crack tip in a ductile material