An investigation into the effects of scaling on structural integrity assessments

  • Paulo Orrock

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


The work described in this thesis investigates the effects that scaling has on key structural integrity concepts, namely, stress fields, stress intensity factors, and the J-integral. Scaled models are an attractive concept in scenarios where full scale testing is not possible, and they are used extensively in other engineering fields. Little research into the practical applications of scaling in a structural integrity context exist however, which provided the motivation for the work.
Scaling laws for these three structural integrity parameters are developed, such that the load can be scaled, along with the geometry, while maintaining the parameter of interest. Two sets of experiments and their results are described, which consist of simple aluminium beams in four point bend configurations, to verify the scaling laws for stress fields and stress intensity factors, and to highlight practical issues surrounding scaling in real life.

The scaling laws themselves do not take into account the effect of scaling on the other parameters. As each parameter follows a different law, and as all the parameters are capable of contributing to failure, it is shown that the scaling laws are not capable of describing the behaviour of a component for a complete range of scale factors. By extrapolating results, and with the use of failure assessment diagrams to visualise this, it is possible to see that depending on the geometry, material properties, and loading regime, there will come a point with which the failure mechanisms will change.

There are certain conditions however, in which scaling is an appropriate and useful tool. For specimens where fracture occurs, if the small scale yielding conditions at the crack tip are maintained across the sizes, then scaled models can be reliably used to produce a model that accurately replicates the fracture conditions, and from which results from the scaled model can be transferred across to the full size. For the small scale yielding conditions to be maintained, the limitation will be on how small the scaled model can be made. Similarly for models where failure is due to the global stress field, scaling can be used provided this remains the dominant contributor to failure. Where there are stress concentrating features, care must be taken if the scaled model is larger in sizes than the original specimen, as this can tend towards small scale yielding conditions, and consequently a change in failure mechanism. Where these conditions are met however, then scaled models may confidently be used to replicate and further investigate the failure conditions of the original specimens.

The case studies considered throughout the development of the scaling laws, and in the experiments, are relatively straightforward, and while representative of test specimens used in materials testing, they are not accurate representations of real components. A complex case study is finally considered, which relates the results and findings from the work to a real component, and subject to realistic constraints and boundary conditions. The case study consists of a parametric finite element study, which aims to replicate failure criteria in a scaled down component. The resultant models obtained are able to meet this criteria, however in do- ing so the geometry is altered, and drifts from what might be considered true scaling. No “all encompassing” scaling law is derived to describe how to produce the scaled component, and prior knowledge of the stress state is required for the parametric study. The methodology is deemed useful, however, for scenarios where full scale modelling is not possible, yet physical validation of the modelling methods are required.
Date of Award8 May 2018
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorChristopher E Truman (Supervisor), Julian D Booker (Supervisor) & David Smith (Supervisor)

Cite this