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Parametric studies

Zencrack can readily be used to conduct parametric studies of crack sizes. Cases where this type of parametric study may be important include:

  • through-thickness crack analysis of welds in pipelines
  • leak before break studies
  • investigations to determine critical crack size
  • comparison against theoretical solutions where the crack shape is defined by an equation.

In the example shown here an investigation of stress intensity factors is carried out for an elliptic surface crack in which the depth is fixed and the length along the surface is varied. This results in stress intensity factor as a function of surface crack length for the deepest point and the surface point.

Stress intensity factors as a function of a/c

This analysis is conducted using the same initial mesh for all crack sizes. The only change is in the initial crack specification in the Zencrack input file. Once a suitable initial mesh is generated the analysis can therefore be conducted very quickly and efficiently.

Another situation in which a parametric study can be required is comparison with existing published solutions. In some cases the approach of modifying the Zencrack input is not the most convenient and instead the various crack shapes can be developed by carrying out a "pseudo-crack-growth" analysis. For this type of analysis the initial crack is defined and instead of advancing by the normal means of stress intensity factors and a crack growth law, the crack is advanced in a user subroutine in order to control the shape of each generated crack profile.

The example below shows such an analysis. An initial surface elliptic defect is present in a circular cross section shaft loaded by cyclic bending. In order to compare stress intensity factors against published data for different specified ellipse sizes a pseudo growth run is carried out to generate a sequence of elliptic profiles in a single Zencrack analysis. The "true" profiles based on stress intensity factors and crack growth data are somewhat different.

Psuedo crack growth analysis with forced elliptic profiles
Pseudo crack growth analysis with forced elliptic profiles (controlled via a user subroutine)
Real crack growth analysis
Real crack growth analysis with Paris crack growth data
Ellipse with a/c=0.5
Ellipse with a/c=0.5

Ellipse with a/c=2
Ellipse with a/c=2

Ellipse with a/c=3
Ellipse with a/c=3

Ellipse with a/c=5
Ellipse with a/c=5

Ellipse with a/c=7
Ellipse with a/c=7
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