Using fractal voids to understand Mode I compressive fracture in brittle materials – A two-dimensional analysis

• Published in: Theoretical and applied fracture mechanics Vol. 133; p. 104648
• Main Authors: Ahmed, A., Shrive, N.G.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2024
• Subjects: Compressive fracture; Fractal void; Shape effect; Size effect; Stress intensity factor; Shape effect; Fractal void; Stress intensity factor; Compressive fracture; Size effect
• ISSN: 0167-8442
• DOI: 10.1016/j.tafmec.2024.104648

•A comprehensive idealization of a void as a fractal surface is presented.•The “small flaw assumption” is defined and used to analyze fractal voids.•Fractal void analysis is shown capable of satisfying the stress and energy criteria.•Via fractal void analysis KI is computed for voids in compression without iteration.•Fractal void analysis predicts shape and size effects in 2D compressive fracture. Unlike cases of direct or indirect tensile loading, analysis of Mode I fracture in cases of compressive loading must necessarily consider two-dimensional flaw geometries. The consequent analytical complications have resulted in little theoretical evolution towards understanding Mode I fracture in compressive loading. Researchers have recently observed that the linear elastic (LE) stress fields surrounding two-dimensional flaws in compression appear to have indicative value regarding Mode I fracture, but no rational framework has yet been proposed for their interpretation. Herein it is demonstrated that by idealizing void surfaces as fractal, and using what will be called the “small flaw assumption,” LE stress fields can be interpreted to obtain significant insight regarding brittle Mode I compressive fracture. Using fractal voids, a rational and consistent explanation for the satisfaction of the stress and energy criteria at the surface of two-dimensional flaws is presented. The discussion resolves many typical theoretical issues in the literature in a manner consistent with fundamental Griffith theory, and accounts for size and shape effects. The framework further enables the computationally efficient prediction of peak KI values associated with the propagation of line cracks from two-dimensional flaws from a brittle medium subject to macroscopic uniaxial compression via LE stress fields.