Dynamic quantized fracture mechanics

Abstract

A new quantum action-based theory, dynamic quantized fracture mechanics (DQFM), is presented that modifies continuum-based dynamic fracture mechanics (DFM). The crack propagation is assumed as quantized in both space and time. The static limit case corresponds to quantized fracture mechanics (QFM), that we have recently developed to predict the strength of nanostructures. DQFM predicts the well-known forbidden strength and crack speed bands – observed in atomistic simulations – which are unexplained by continuum-based approaches. In contrast to DFM and linear elastic fracture mechanics (LEFM), that are shown to be limiting cases of DQFM and which can treat only large (with respect to the “fracture quantum”) and sharp cracks under moderate loading speed, DQFM has no restrictions on treating defect size and shape, or loading rate. Simple examples are discussed (i) strengths predicted by DQFM for static loads are compared with experimental and numerical results on carbon nanotubes containing nanoscale defects; (ii) the dynamic fracture initiation toughness predicted by DQFM is compared with experimental results on microsecond range impact failures of 2024-T3 aircraft aluminum alloy. Since LEFM has been successfully applied also at the geophysics size-scale, it is conceivable that DQFM theory can treat objects that span at least 15 orders of magnitude in size.