Characterization of ubiquitiform crack fracture parameters based on ubiquitiform theory

Ubiquitiform geometry, as an important tool to study complex and irregular configurations, provides an important theoretical basis for solving nonlinear problems. In this paper, considering the ubiquitiformal characteristics of crack propagation, two key ubiquitiformal parameters of complexity and yardstick length were introduced into the theoretical derivation of Mode I crack propagation. The effects of complexity on the stress intensity factor and crack propagation forces were also analyzed using numerical examples. Furthermore, the uniaxial tensile failure behavior of cast iron materials under different crack forms was studied. The fracture surface morphology of a tensile specimen was measured using a laser confocal microscope, and the complexity of cross-section contours and the statistical self-similar interval was calculated via the box-counting method. Experimental results verified the accuracy of the expression of ubiquitiform critical stress. It is demonstrated that ubiquitiform theory fundamentally solves the difficulties in application of fractal theory. More rational results can be obtained when ubiquitiform fracture parameters are adopted in fracture problems.