PSI - Issue 68

Gül Demirer et al. / Procedia Structural Integrity 68 (2025) 190–196 G. Demirer and A. Kayran / Procedia Structural Integrity 00 (2024) 000–000

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in the buckling load and an 81.31% reduction in the out-of-plane displacement through Variable Angle Tow (VAT) optimization. Further studies have illustrated the benefits of VS composites in delaying damage initiation, increasing fundamental frequencies, and enhancing flutter speed (Lopes et al., 2007; Blom-Schieber et al., 2008; Haddadpour and Zamani, 2012). Despite these advantages, AFP has limitations, such as constraints on maximum allowable curvature, smoothness of fiber paths, minimum cut-length and defects such as tow kinking, wrinkling, and gapping or overlapping. The current study focuses on gaps and overlaps which are referred to as the manufacturing signature (MS) of the AFP and a ff ect the strength and sti ff ness of VS Laminates. Both experimental and computational studies examining mechanical impact of defects emphasize the importance of identifying and thoroughly analyzing the presence of gaps and overlaps. For instance, tensile and compressive tests on straight fiber specimens with controlled gap and overlap imperfections of varying sizes are conducted in Nguyen et al. (2019). Test results revealed that gaps reduce sti ff ness and strength by inducing localized strain. On the other hand, overlaps improved tensile properties without significantly a ff ecting compressive properties. Several numerical approaches are developed to study the influence of manufacturing defects. A 3D meshing tool is presented in Li et al. (2015) to built models with defects of various sizes and distributions using cohesive elements. This study examines the fiber splitting and delamination where out-of-plane waviness and ply thickness variations are represented as well. Defect layer method is proposed in Fayazbakhsh (2013) where isolated e ff ect of gaps and overlaps on in-plane sti ff ness and buckling load are numerically investigated. The location and extent of defects are captured using a Matlab script. The defect layer method characterizes the change in properties of each layer by accounting for the defect area percentage. Alternatively, in Vijayachandran et al. (2020) and Vijayachandran and Waas (2022), simulations of as-manufactured behavior of steered fiber composites using pixelated finite element (FE) mesh is performed. Course boundaries are defined as closed polygons for each course, allowing the algorithm to determine how many courses pass through each element’s centroid, classifying elements as within gap, overlap, or composite material regions. In this study, a VS laminate, optimized for maximum achievable buckling load in Fayazbakhsh (2013), is analyzed. First, the distribution of gaps and overlaps is identified by the developed Matlab code. The VS laminate is then modeled in Abaqus, where the presence of gaps and overlaps are imposed to the FE model through defect layer and pixelation methods. Linear and nonlinear buckling analyses are performed in Abaqus to investigate the e ff ects of these defects on buckling load and in-plane sti ff ness. The capabilities and mesh dependency of methods are discussed, and the performance of the VS laminate is compared with that of a quasi-isotropic [45 | 0 | − 45 | 90] 2 s laminate. 2. Methods A constant-curvature fiber path is used in this study to model fiber orientation within the composite. The shifting method, combined with a one-sided tow-drop approach, is applied to adjust the top boundary of each course. Both 0% coverage (complete gap) and 100% coverage (complete overlap) strategies are implemented. The standard composite regions are assigned the material properties of G40-800 / Cycom 5276-1 prepreg slit tape, while Cycom 5276-1 resin properties are used for resin-rich gap areas (Marouene et al., 2016). Each course is assumed to have 8 tows, each 3.175 mm in width, with a uniform layer thickness of 0.1545 mm. The boundary conditions shown in Fig. 1a are applied to a panel measuring 254 mm in width and 406 mm in height, with the symmetric balanced stacking of [ ± < 27 | 46 | 27 > ] 4 s . Formulations in sections 2.1 and 2.2 will be presented for T 1 < T 0 consistent with the fiber path definition considered in this study.

2.1. Fiber path definition

The constant curvature fiber path definition by Gurdal et al. (2005), based on circular arcs, is adopted to describe the reference fiber path. The notation [ < T 1 | T 0 | T 1 > ] represents a single layer with constant curvature fiber path where T 0 is the fiber orientation angle at the plate center ( x = 0) and T 1 is the fiber orientation at the plate edges ( x = ± w / 2), with w representing the plate width, as illustrated in Fig. 1b. For the constant curvature reference fiber path, the fiber orientation at a location A(x,y) in the plate can be expressed as follows:

w / 2 cosT 1 − cosT 0

for T 1 < T 0 .

(1)

ρ =