Refined Engineering Theory of Fracture with a Two-Parameter Strength Criterion

We present a refined engineering theory of cracks based on a two-parameter strength criterion. Unlike the basic theory, the refined approach utilizes an improved algorithm for the regular stress component computation. This improvement allows extending the engineering theory to longer cracks. The two-parameter Leonov–Panasyuk–Dugdale fracture criterion serves as a basis. A coupled fracture criterion includes a strain-based criterion, which is formulated at the tip of the true crack, as well as a stress-based criterion, formulated at the tip of the fictitious crack. Based on the refined criterion, quasi-brittle fracture curves are constructed for a compact specimen, a strip with an edge crack, and a four-point bending beam. To validate the new refined fracture criterion, we present simulation results of quasi-brittle fracture for structures made from various virtual materials. The corresponding virtual materials are modeled using a nonlocal damage theory accounting for the average size of the aggregate state of the material. Additionally, various classes of damage accumulation hypotheses are considered. Analysis of various types of virtual materials provides insights into the impact of hypotheses behind the engineering theory. For each type of material, the influence of the microstructural length scale on the overall structural strength is investigated. The analysis shows that the refined engineering theory has a wider range of applicability as compared to the basic theory based on two-parameter strength criteria.