A finite similitude approach to fatigue crack growth across the scales

Testing materials housing defects such as cracks presents difficulties for traditional experimental methods due to the presence of size effects, where the response of specimens can differ at different sizes. This issue has been addressed recently with the arrival of the finite similitude scaling theory, which is a theory for relating information across the scales, accounting for any scale effect that might be present. The theory introduces an infinite number of possible similitude rules with lower-order rules (e.g., zeroth, first, and second) having the most practical value, with zeroth order being equivalent to dimensional analysis, and first order able to accommodate the theories of fracture mechanics and fatigue. The first-order finite-similitude rule can be applied experimentally by performing tests at two distinct scales but also analytically at an arbitrary scale but involving additional equations. To confirm that the approach has practical value it is tested in this work against experimental-fatigue data that has appeared recently in the open literature. Numerical simulation is performed with a commercially available finite-element package in support of the study to assess the robustness of the scaled-experimental tests and compliance with the finite-similitude theory. The response of the empirical Paris crack-growth law under scaling is examined to test the criticality of using either scale-invariant or scale-variant parameters in crack-growth predictions. Introduced as part of the work is a method for the experimental determination of Paris-law parameters under the sound assumption that the correct similarity law for fracture-fatigue studies is the first-order finite-similitude rule. The results presented here confirm the veracity and applicability of the finite-similitude scaling theory returning analytical and numerical confirmations to within a few percent of published experimental results.