Multifractal modeling for quality control and mechanical property assessment of fiberglass pipes

The object of research is the microstructure of fiberglass composite pipes and the relationship between the spectrum of their multifractal dimensions and mechanical properties. This study aims to establish a predictive framework for mechanical properties based on microstructural analysis using multifractal methodologies. Method. Physical experiments were conducted to measure the mechanical properties of fiberglass composite pipes, including tensile strength (ultimate axial tensile strength), ductility (relative elongation), and elasticity (modulus of elasticity). The material composition by mass consisted of 64–68% roving and 32–35% epoxy binder. A multifractal analysis was performed on the microstructure, specifically evaluating the Renyi multifractal spectrum dimensions with a scale resolution of 50 µm. Relationships between fractal, informational, correlation dimensions, and mechanical properties were quantitatively assessed using statistical modeling. Results. The research demonstrated a significant correlation between microstructural parameters and mechanical properties. Increases in the fractal dimension (D₀) of the fiber matrix from 1.836 to 1.911 corresponded to a 15% rise in tensile strength. A decrease in the informational dimension (D₁) from 1.907 to 1.833 resulted in a 30% increase in relative elongation, while an increase in the correlation dimension (D₂) from 1.829 to 1.905 led to a 14% improvement in the elastic modulus. Structural heterogeneity was assessed using the canonical singularity spectrum, with higher spectrum values indicating improved homogeneity. The Renyi spectrum dimensions ranged from 1.160 to 3.860, confirming structural heterogeneity quantitatively. Mathematical models were developed to predict mechanical properties, forming a knowledge base for refinement with additional experimental data. These results enable the development of an operational control method for fiberglass pipe properties, applicable during both operational life assessment and quality control at the manufacturing stage. Implementation involves a custom software solution and an optical microscope or digital camera, allowing automatic mechanical property predictions from fractal dimension analysis, significantly reducing resource demands.

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