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3D fracture mechanics analysis

Zencrack provides a general 3D fracture mechanics analysis capability. But what is meant by "3D" in the context of a fracture mechanics or crack growth simulation? The term is widely used - sometimes in a misleading way. Are you sure that your analysis methodology is providing a truly general 3D solution?

3D structural model

For finite element or boundary element analysis it is immediately obvious by visual inspection whether or not the structural model is 2D or 3D. However, a 3D model does not necessarily mean a 3D analysis. For example, boundary conditions may constrain the model to behave in a 2D fashion. In most cases Zencrack would be used to analyse a true 3D structural model. However, the application of appropriate boundary conditions allows Zencrack to be used to analyse axi-symmetric and 2D problems.

3D crack front

A 3D crack front is, in general, an arbitrary line in space with a non-planar crack surface. For a true 3D crack front capability, the crack must be able to develop into an arbitrary line if that is what the geometry, applied loading and materials data deliver. A subset of the general 3D crack is a crack in a 2D plane that may be modelled in a 3D structural model e.g. a planar semi-elliptic surface crack. The analysis of this type of 2D planar defect can often only be completed successfully via a 3D structural model.

3D state of stress along the crack front

Any textbook on fracture mechanics will very quickly introduce plane stress or plane strain conditions in theoretical derivations. The true state of stress varies along the length of a crack front and at any point can be plane stress, plane strain or something in between. Many factors influence this condition including surface proximity, geometry and loading.

Zencrack prefers to use an energy based approach in which the state of stress is embodied in the structural solution provided by the finite element analysis. In some cases it is necessary to make assumptions about the state of stress (for example when converting displacements to stress intensity factors) and options are available to give flexibility to the user for these cases.

3D crack growth

3D crack growth could be considered to mean several things:

  • planar crack growth in a 3D structural model
  • non-planar or mixed mode crack growth in which the growth direction is the same along the length of a crack front
  • non-planar or mixed mode crack growth in which growth can occur in any direction depending upon the geometry and loading.

Only the third description provides a full 3D capability.

In many applications, particularly forensic studies and leak-before-break, the trajectory of the crack is a critical outcome of the analysis which simply cannot be calculated with anything less than a full 3D solution.

Complex load history

Real components experience complex loading which may generate non-planar crack growth. The load history can range from simple constant amplitude loading through increasing degrees of complexity to the most general case of complex thermo-mechanical load cycles in which mixed mode effects and non-linearities (e.g. contact) can occur. Zencrack has a "load system" approach to allow handling of a range of load histories. The process requires that:

  • One or more load increments are defined in the f.e. analysis and a "type" of load history is defined in the Zencrack input file
  • The "type" of load history must be given information about how it relates to the load increments in the f.e. analysis
  • The end result is a sequence of (counted) load cycles that are integrated with a fatigue crack growth law (e.g. Paris, Walker etc)
  • This integration process is carried out at each corner node on the crack front to ensure consistent cycle counts as the crack advances (see below) - the growth at each node will, in general, be different in both magnitude and direction.

The approach therefore gives the correct crack shape development during the integration process. A time dependent crack growth option is also available. This integrates directly through a load vs time history using a da/dt growth law. Fatigue and time dependent integration can also be combined in the same analysis.

Crack shape development with proper account of load spectrum cycles and crack growth data

A general 3D crack growth capability requires a "consistent dN" approach during fatigue crack growth integration. A general 3D crack in a finite element model has many nodes along the crack front. All of these crack front nodes must grow by the same number of cycles over an integration step. In general each node would have a different da over this step. This integration must be done as the analysis progresses in order that any change in crack shape due to non-uniform growth is properly taken into account. For a true 3D analysis it is not sufficient to attempt a pseudo-growth analysis to generate K vs a curves and then to apply integration as a secondary procedure to calculate life.

Summary


3D capability
Zencrack
Your software or methodology
3D structural model
yes
?
3D structural model constrained to behave like a 2D or axisymmetric model
yes
?
3D crack front
yes
?
Changing state of stress along the crack front
yes
?
Non-planar or mixed mode crack growth in any direction
yes
?
Complex load history
yes
?
Crack shape development and consistent dN calculation
yes
?
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