Contents
In continuum mechanics the material is supposed to be a continuum where properties change continuously from one point to the other. However, a real material contains discontinuities like interfaces between different components, inclusions and defects. Resulting stress concentrations can provoke initiation and growth of cracks.
In fracture mechanics attention is focussed onto one crack. Theoretical concepts and experimental techniques have been and are being developed, which allow answers to questions like:
- Will a crack grow under the given load?
To answer these questions, the geometry of and the load on the crack must be known. In practice this must be determined experimentally. Some experimental techniques are discussed in the course.
First, concepts and theories are discussed in which linear elastic material behaviour is an essential assumption. This is the case for Linear Elastic Fracture Mechanics (LEFM). Prediction of crack growth is based on an energy balance. The Griffith criterion states that "crack growth will occur when there is enough energy available to generate new crack surface." The energy release rate (G) is an essential quantity in energy balance criteria.
The crack growth criterion can also be based on the stress state at the crack tip. This stress field can be determined analytically. It is characterised by the stress intensity factor (K).
It is important to predict whether a crack will grow or not. It is also essential to predict the speed and direction of its growth. Theories and methods for this purpose are discussed.
Assumption of linear elastic material behaviour leads to infinite stresses at the crack tip. In reality this is obviously not possible: plastic deformation will occur at the crack tip. Using yield criteria (Von Mises, Tresca), the crack tip plastic zone can be determined. When this zone is small enough (Small Scale Yielding (SSY)), LEFM concepts can be used.
When the plastic crack tip zone is too large, the stress and strain fields from LEFM are not valid any more. This is also the case when the material behaviour is nonlinear elastic (eg. in polymers and composites). Crack growth criteria can no longer be formulated with the stress intensity factor.
In the Elastic-Plastic Fracture Mechanics (EPFM) or Non-Linear Fracture Mechanics (NLFM) criteria are derived, based on the Crack Tip Opening Displacement (CTOD). Calculation of CTOD is possible using models of Irwin or Dugdale-Barenblatt for the crack tip zone.
Another crack growth parameter much used in NLFM is the J-integral (J), which characterises the stress/deformatiion state in the crack tip zone.
Analytical calculation of relevant quantities (G, K, CTOD, J) is only possible for some very simple cases. For more practical cases numerical techniques are needed. Numerical calculations are mostly done using the finite element method. Special quarter-point crack tip elements must be used to get accurate results.
In the course the above concepts are discussed. Attention is also given to the experimental determination of critical values of the calculated quantities (Gc, Kc, CTODc, Jc).
- When a crack grows, what is its speed and direction?
- Will crack growth stop?
- What is the residual strength of a construction (part) as a function of the (initial) crack length and the load?
- What is the proper inspection frequenc ?
- When must the part be repaired or replaced?
Learning objectives
Getting an overview of the whole field of "Fracture Mechanics". Be able to use crack growth criteria and calculate rest life for simple cases.