Fracture Mechanics

The object of fracture mechanics is to provide quantitative answers to specific problems concerning cracks in structures. Finite element analysis may be used to determine the stress intensity factor of a crack, predict the rate of propagation and growth path, and provide solutions to many other fracture mechanics related questions.

Case Studies:

• Cracks in tubular intersections
• Local approach
• Prediction of pipe burst pressure
• The V-factor

Cracks in tubular intersections

A linear elastic fracture mechanics analysis was undertaken to determine the stress intensity factor and the crack opening area from fully penetrating cracks around intersecting cylinders. A 3D mesh of the components was generated using CADfix. Because the problem is symmetrical, only a half model was created, as shown in Fig.1.

Fig.1. CADfix generated model of intersecting cylinders

Internal pressure was applied to both cylinders, and additional axial loading allowed the loading from the end caps to be simulated. The stress intensity factor of the crack through the thickness of the wall of the main cylinder was calculated from the J-integral solutions provided by the finite element analysis. The J-integral characterises the energy release rate associated with crack growth. The crack opening area was obtained using displacements of nodes along the crack.

The figures below show the maximum principal stress distribution around the crack tip when the pressure loading is applied ( Fig.2), and the shape of the crack opening ( Fig.3).

Fig.2. Maximum principal stress distribution at crack tip

Fig.3. Displaced mesh plot

Local approach

The Beremin model is a statistical micro-mechanical concept ('Local Approach') for prediction of cleavage failure. One of its advantages over conventional fracture prediction methods is that it allows the scatter in fracture toughness to be quantified in failure predictions. TWI has been using finite element analysis to link with material-specific fracture parameters obtained using small-scale specimens in order to develop micro-mechanical failure models. Combining experiments and modern finite element methods has enabled the assessment of structures which was previously not possible, or very expensive.

Prediction of pipe burst pressure

TWI has used finite element analysis to model 'corrosion' pits ( Fig.4), typical of those that may be found in pipe-lines. Results were used to relate the critical pressure condition ('burst' pressure) in the pipe to the remaining ligament thickness, for a range of pit diameters. It was assumed that failure occurred by plastic collapse when the von Mises stress level on the outside wall at the corroded pit reached the material UTS.

Fig.4. Corroded pit modelled to predict pipe burst pressure

The V-factor

Within a European programme (SINTAP), TWI developed a factor, V, which may be applied to the secondary stress intensity factor resulting from thermal and residual stresses, K _I ^S to account for plasticity effects. This means that the parameter K _r, used in failure assessment diagram (FAD) methods may be evaluated using Eq [1]. In this equation, K _I ^P is the stress intensity factor due to primary (applied) loads, and K _mat is the fracture toughness of the material in which the crack is located.

[1]

The use of the V-Factor for this application has been validated using finite element methods.

To find out more about how TWI could benefit your company, please contact us at nmo@twi.co.uk