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Figure 2: Failure of Liberty type ship “Schenectady” /5/

Figure 3. Welding arc strike. Cracks about 2 mm in size developed in hard heat-affected-zone

(HAZ) surrounding fusion starter /6/

2.1. Linear elastic fracture mechanics (LEFM)

Considering the crack in homogeneous material, FM developed models for descrip-

tion of stress and strain distribution ahead the crack tip, the singular location in the field,

and corresponding parameters for mathematical analysis. Intensive theoretical and

experimental, and later on numerical investigation of stress concentration in elastic range

around geometry transition and defects in loaded components enabled to involve crack

and its size in the stress analysis. This was done for elastic behaviour (linear-elastic

fracture mechanics – LEFM), using primarily the results of Grifith /8/ and of Irwin and

Kies /9/. In this way theoretically supported crack analysis allowed to define crack

parameters for plain strain condition, corresponding to generally accepted material

properties expressed in strength parameters.

In the analysis of fracture strength Griffith /8/ recognized that it is possible to derive a

thermodynamic criterion for fracture by considering the total energy change with

increasing crack length in a cracked body. Only if the total energy decreased would the

crack extend spontaneously under the applied stress. Using energetic approach in the

body as a whole, it is possible to neglect local stress concentration around the crack tip

and derive a useful expression for the fracture stress. The analysis performed by Griffith

is based on the situation shown in Fig. 4. He analyzed the changes in energy, which

occur if the crack is infinitesimally extended. New crack surfaces are created and since

the stresses and displacements immediately ahead of the infinitesimally extended crack

tip are identical to those ahead of the initial crack tip, the energy increase during crack

extension is simply the unit "work to fracture", 2

, multiplied by the area of produced

new crack surfaces. Based on that, Griffith proposed that the crack driving force (CDF)

is involved by the difference between the energy released for crack extension and that