term dominates and . For polymers close to the glass transition temperature, we have intermediate values of between 2 and 1000 . Stress intensity factor Another significant achievement of Irwin and his colleagues was to find a method of calculating the amount of energy available for fracture in terms of the asymptotic stress and displacement fields around a crack front in a linear elastic solid. This asymptotic expression for the stress field in mode I loading is related to the stress intensity factor following: where are the Cauchy stresses, is the distance from the crack tip, is the angle with respect to the plane of the crack, and are functions that depend on the crack geometry and loading conditions. Irwin called the quantity the stress intensity factor. Since the quantity is dimensionless, the stress intensity factor can be expressed in units of . Stress intensity replaced strain energy release rate and a term called fracture toughness replaced surface weakness energy. Both of these terms are simply related to the energy terms that Griffith used: and where is the mode stress intensity, the fracture toughness, and is Poisson’s ratio. Fracture occurs when . For the special case of plane strain deformation, becomes and is considered a material property. The subscript arises because of the different ways of loading a material to enable a crack to propagate. It refers to so-called "mode " loading as opposed to mode or : The expression for will be different for geometries other than the center-cracked infinite plate, as discussed in the article on the stress intensity factor. Consequently, it is necessary to introduce a dimensionless correction factor, , in order to characterize the geometry. This correction factor, also often referred to as the geometric shape factor, is given by empirically determined series and accounts for the type and geometry of the crack or notch. We thus have: where is a function of the crack length and width of sheet given, for a sheet of finite width containing a through-thickness crack of length , by: Strain energy release Irwin was the first to observe that if the size of the plastic zone around a crack is small compared to the size of the crack, the energy required to grow the crack will not be critically dependent on the state of stress (the plastic zone) at the crack tip. In other words, a purely elastic solution may