Analytical fractal model for rugged fracture surface of brittle materials

• General fractal fracture surfaces model for brittle materials (heavy clay and mortar).
• Rugged crack affects fracture resistance curve and stress field around a rough crack.
• The local and the global ruggedness exponents of fracture surfaces were obtained.
• The rugged profile length and other parameters were obtained by fitting the model.
• Increasing rugged crack length of heavy clay and mortar correlates microstructure.

The fractal modeling of a rugged fracture surface has received different purposes. However none definitive model for the most of materials has been reached. Therefore, a general self-affine fractal model is proposed for fracture surfaces and applied to heavy clay and mortar. An analytical expression for the rugged crack length is obtained for application on fractal fracture mechanics. Stereoscopic images are obtained for each tested specimens. Image processing filters are used to extract the rugged profile of the cracks. The box-counting and sand-box methods are used on the crack profile to obtain the local and the global roughness exponents. Specimens prepared under different conditions validated the model. Mortars and heavy clay specimens were characterized by measuring their modulus of rupture and the rugged crack profile under 3-point bending tests. A good agreement between the model and the experimental results was observed. A strong correlation between the fractal dimension and the sintering temperature for heavy clay specimens was verified. The results also showed that the increasing rugged crack length of the profile of the fractured mortar specimens is well correlated with the increase in water/cement ratio. These results validate the application of the proposed model for estimating the fracture strength of brittle materials.

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