Finite similitude approach for fatigue crack growth

Abstract

Fatigue crack growth in large-scale engineering structures is difficult to assess directly because full-scale testing is often expensive, time-consuming and technically impractical. Laboratory-scale specimens and numerical simulations are therefore widely used, but their direct transfer to larger structures is not straightforward when size effect and incomplete mechanical similarity are present. This thesis develops and validates a finite similitude framework for the cross-scale description and prediction of fatigue crack growth within the context of linear elastic fracture mechanics. The work first establishes a finite similitude-based similar-state description for fatigue crack growth. On this basis, cross-scale projection relations are derived for key fracture and fatigue quantities, including crack length, stress-intensity-factor (SIF) range, cycle number and crack-growth rate. These relations provide a systematic route for connecting scaled specimens and physical structures when classical geometrical similarity alone is insufficient. When the zeroth-order projection is not sufficiently accurate, the first-order finite similitude formulation provides the higher-order correction required for full-scale prediction. The formulation also clarifies the applicability conditions of the framework, including the role of crack-tip driving force, geometry scaling and local fracture-process scales. The deterministic part of the thesis develops and assesses first-order prediction methods for fatigue crack growth. Both \(R\)-form and \(H\)-form finite similitude relations are examined, with particular attention given to the determination and use of the parameter \(H\). Numerical simulations are used to verify the extraction of fracture parameters and to assess the internal consistency of the derived scale-transfer relations. The framework is then evaluated using available experimental fatigue crack-growth data from geometrically scaled compact-tension specimens. The comparisons examine the prediction of crack-growth rate, SIF range and reconstructed Paris-law parameters. In addition, an inverse parameter-determination approach is developed to infer or assess fatigue crack-growth parameters through cross-scale relations. The final part of the thesis extends the deterministic framework to stochastic modelling. Random variability in fatigue crack growth is incorporated through stochastic descriptors of scatter, with particular attention to the distinction between fixed-scale stochastic evolution and cross-scale stochastic transfer. A fixed-scale diffusion model describes how scatter may evolve with a fatigue-process variable at one specimen size, whereas the finite similitude transfer rule describes how a stochastic descriptor changes with scale at corresponding fatigue crack-growth states. This distinction avoids interpreting the diffusion model itself as a scale-transfer law. Overall, the thesis shows that first-order finite similitude provides a structured basis for cross-scale fatigue crack-growth prediction. The proposed framework does not replace conventional fracture mechanics, Paris-law analysis or finite element modelling; rather, it provides a means of connecting these tools across scales when zeroth-order finite-similitude transfer alone is insufficient to transfer the full fatigue crack-growth response. The work also identifies the need for future experimental programmes with repeated crack-growth histories at multiple geometrically scaled sizes to provide stronger validation of the stochastic extension.

Date of Award	18 Sept 2026
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Keith Davey (Main Supervisor), Rooholamin Darvizeh (Co Supervisor) & Kali-Babu Katnam (Co Supervisor)