Finite similitude in fracture mechanics

Abstract

Scaled experimentation can potentially provide significant benefits such as reduced costs materials and time in testing but is afflicted by the phenomena of scale effects, where the behaviour at scale can be markedly different to that at full size. The design of scaled experiments is presently predominantly founded on the theory of dimensional analysis, which itself is grounded on the invariance of dimensionless governing equations with scale. The reality of fracture mechanics however is not invariant equations, but significant deviations and it is evident that scaled-fracture related experiments are presently limited by this affliction.This paper examines an advance in a new approach to scaled experimentation called finite similitude. The key question addressed here is whether it is possible to overcome the affliction of scale effects by performing not one but two scaled experiments at different scales. It is shown that finite similitude (unlike dimensional analysis) is able to capture all forms of scale dependency, which opens up the possibility of selecting alternative forms of scale invariance and consequently alternative forms of similitude.First-order finite similitude is investigated in the paper and applied to cracked compact-tension and three-point bending test specimens along with a cracked pressure vessel to illustrate the new concepts. These case studies reveal the veracity and potential of the new approach and highlight possibilities that hitherto would have been deemed impossible with the circumvention of scale effects (as traditionally defined).