Mechanical APDL Structural Analysis Guide

=

πσ^2

At the moment of fracture, G is equal to the critical energy-release rat e Gc, a function of the fracture

toughness. The value of Gc for a material can be determined via a relatively straightforward set of crack

experiments.

For a single-fracture mode, the stress-intensity factor and the energy-release rat e are related by:

=

′

where G is the energy-release rate,

′=

−ν
 for plane strain, and ′= for plane stress. (E is the

material Young’s modulus, and ν is the Poisson’s ratio.)

For more information, see VCCT Energy-Release Rat e Calculation (p. 356).

11.1.2.3. Stress-Intensity Factor

Limited to linear elastic material, the stress and strain fields ahead of the crack tip are expressed as:

σij= − ijθ

ε= − θ

where K is the stress-intensity factor, r and θ are coordinates of a polar coordinate system (as shown in
Figure 11.2: Schematic of a Crack Tip (p. 342)). These equations apply to any of the three fracture modes.

Figure 11.2: Schematic of a Crack Tip

Crack

y

x

r

θ

For a Mode I crack, the stress field is given as:

σ

π

θ θ θ



= I 









 −





































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Fracture Mechanics