An effective free-meshing and linear Step-Wise procedure to predict crack initiation and propagation

An automated procedure is proposed to calculate fracture initiation and propagation in two-dimensional structures. The application uses and enriches the Hybrid Semi-Analytical Method to calculate mixed-mode stress intensity factors in linear elastic fracture mechanics framework. The strategy does not necessitate prior knowledge of the starting crack tip location within the structure, resulting in suitable for analyzing structures without initial defects. When neither a priori invitation nor pre-existing notch is provided, the fracture initiation is assumed to occur when the structure reaches its elastic limit, and a non-linear analysis is conducted under the prescribed load to identify the first occurrence of permanent strain and to locate where the crack opening occurs. As the crack propagates, solely linear elastic analyses are performed to calculate the stress intensity factors. Relying upon these parameters, the procedure implements an evolutionary algorithm based on a step-by-step evaluation of the crack increment and direction. A global–local energy-based criterion is employed to drive fracture propagation. Neither local refinement nor mapped meshes around the crack tip are required, resulting in a streamlined and efficient free-meshing strategy. The calculation has been implemented in a standard finite element environment, and several numerical examples have been investigated, both from a qualitative and quantitative point of view. Qualitative crack paths have been shown for a square hollow plate under pure tensile and shear loads, and a modified Single Edge Notched specimen in bending, as a function of the mutual void positions, distance from the plate edges, and different notch lengths. Finally, an effective comparison in terms of forces-displacement curves has been presented between the proposed procedure, and a lab test for a modified Compact Tension specimen under tensile loading, demonstrating the overall accuracy and reliability of the presented strategy. It is felt that the proposed procedure could pave the way for designing hollowed structures and investigating the corresponding evolutionary laws that relate structural geometries to the insurgence and spread of fractures, and envisaging crack initiation and propagation within inhomogeneous media.