J-integral theory

Many materials are subject to plastic deformation, i.e. they show elasto-plastic behavior so that there is no guaranteed linear correlation between stresses and elongation. Recently, this has resulted in the development of elasto-plastic fracture mechanics and ductile fracture mechanics. The most important of these methods are:

  • COD: measurement of the crack opening displacement,
  • Determination of the J-integral (as the path-independent line integral around a crack tip), and
  • Establishing the crack resistance curves and the rupture modulus.

These methods allow better conclusions to be made regarding the material behavior in components than this was previously possible. The material characteristics obtained by means of the COD and J-integral method can be converted to KIc values.

When describing the temperature dependence of fracture toughness for ductile materials, it has been common to indicate KIc values in the lower temperature range and KJc or KQ values (COD) in the upper temperature range, without separating the two (Fig. 1).

The fracturing properties of high-graphite cast iron materials are considerably influenced by the quantity, form (see Graphite form) and size of the graphite particles, by the structure formation and also by the chemical composition of the metal matrix.

The following values are indicated for the behavior at room temperature:

for cast steel, up to 5000 N/mm3/2,
for nodular graphite cast iron up to 3350 N/mm3/2,
for malleable cast iron up to 1800 N/mm3/2,
for vermicular graphite cast iron up to 1575 N/mm3/2 and
for flake graphite cast iron up to 630 N/mm3/2.


  • Fig. 1: Correlation between temperature and fracture toughness based on different testing concepts (according to O. Liesenberg and D. Wittekopf)
Back to list