Fracture mechanics: A two-experiment theory

Built into the founding theory of fracture mechanics is a size effect with the size of defects influencing or dictating the structural response of materials. Larger structures can fail at lower loads than might be anticipated from the results obtained from smaller scaled versions made of the same material. The explanation for this phenomenon is that larger defects can exist in the bigger structure and consequently failure loads are correspondingly relatively lower. A slightly different viewpoint is that a single scaled experiment does not adequately capture the response of a defect-ridden structure. This paper introduces a two-experiment theory for fracture mechanics underpinned by experimental tests performed at two distinct scales. It is shown how the size effect associated with defect size is immediately accounted for providing significantly improved representative behaviour than can be otherwise achieved through experiments at a single scale. Two appropriately designed scaled experiments are shown to provide the correct focus in fracture mechanics. It is contended therefore that the current focus on absolute fields (e.g., stress, strain) should be expanded to encompass field differences (or derivatives) with scale in quasistatic fracture mechanics. To demonstrate the importance of field differences classical fracture-mechanics theory is re-examined and stress intensity, J-integrals and cohesive zone models provide the focus. The work builds on the recently discovered finite-similitude theory and on the first-order similitude condition involving two scaled experiments. Standard tests are reanalysed using the finite element method to examine the theory and showcase the potential of the two-experiment approach.