Fracture Mechanics Analysis
The trend towards integrally machined structure can result in complex geometric features which are often associated with 3D stress 'hotspots' - stress concentrations. Cracks at such locations are not really amenable to handbook solutions without a lot of idealisation of both geometry and stress fields. However in the top picture you can see a boundary element model of such a configuration, with a crack located at the position of the highest nodal stress. The model incorporates both the local geometry and stress distribution and allows the crack tip stress intensity to be determined; the crack can also be 'grown' in the model just like it would do in the real structure. More information can be found here (1.053 MB pdf).
Another case in which a handbook solution may only be an approximation occurs with pin loaded lugs. Both the lug shape and pin fit have a significant effect on the stress concentration factor and the crack tip stress intensities; the boundary element model, as shown in the middle picture, has included the pin fit (using contact) and the shape (the model geometry) and gives the most representative stress intensity factors.
Cracks found in-service often have a different aspect ratio or shape to those assumed during any analysis. This is often due to multiple cracks growing into each other. Such shapes are often outside the limits of the handbook solutions, but these situations are exactly when the best possible estimate of the stress intensities are needed, for example to allow a comparison with striation counts obtained from fractography. The lower picture shows a boundary element model representing an in-service crack which has been inserted into a flat test plate (because only the surfaces are modelled, the shape of the crack can only be seen by looking 'inside' the plate). Of course most real cracks happen at stress concentrations, and these are included explicitly in the model as well.
If you have a situation in which you have either a crack or geometry (or both!) outside the range of the standard handbook solutions, please email us your enquiry, or phone 07941 125 445 or use our contact form.
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