Statistical modeling of 3D fiber geometry in pultruded GFRP composite: A multi-scale approach

The fiber geometry is a crucial determinant of the fiber reinforced polymer composites' mechanical properties. Specifically, the manufacturing process of stretching and gradual curving in pultruded composites invariably results in complex 3D fiber geometries. Despite its significance, there is still lacking a statistical method to accurately describe these spatially curved fiber shapes. This paper presents a novel multi-scale mathematical approach for modeling the complex 3D fiber geometry in pultruded glass fiber reinforced polymer (GFRP) composites, which includes the analysis of fiber misalignment and waviness at two scales. At the mesoscopic level, a modified elliptical symmetry angular Gaussian (ESAG) model effectively characterizes the fiber misalignment. Simultaneously, at the micro scale, a cosine series representation is employed for capturing local fiber waviness. The approach is verified with XCT scanning results of pultruded GFRP specimens. The current statistical modeling method provides a multi-scale approach for geometry analysis and further simulation of pultruded composite materials.