I. Core Breakthroughs

Breakthrough 1 : Innovatively developed a predictive model for analyzing and forecasting filament bundle lift-off, enabling proactive defect prediction during the path‑design phase.

Previous studies have only provided qualitative descriptions of the buckling and uplift phenomena, lacking quantitative computational tools. This paper is based on Kirchhoff’s thin-plate theory. +  Rayleigh -  The Ritz energy method is used to formulate analytical equations; by directly inputting material moduli, fiber dimensions, resin viscosity, and curing temperature, one can calculate the minimum turning radius that prevents delamination, eliminating the need for extensive trial layups, and in… CAM Defects are proactively avoided during the path-planning phase.

Breakthrough 2 : Identify the two primary influencing factors of defects and correct the one-sided perception of curvature.

The industry generally holds that the critical radius of curvature solely determines delamination onset. This paper quantitatively demonstrates, through sensitivity analysis, that the length of the fiber‑layup segment and the viscoelastic properties of the prepreg (i.e., matrix stiffness) exert far greater influence than fiber modulus and Poisson’s ratio. Specifically, lower viscosity and longer layup segments correspond to a larger critical turning radius, making it exceedingly difficult to form minimal‑surface structures. These findings provide a quantitative basis for material selection and segmented ply‑layup design.

Breakthrough 3 : Graded test quantitative heating / The regulatory mechanism of viscosity on the forming limit

Establish a four-level evaluation standard for delamination defects (no delamination). /  End lifting up /  Large-area lifting /  Complete debonding), as demonstrated by comparing two types of prepregs: higher heating power increases resin viscosity, and under the same curvature, defect levels are significantly reduced; for materials with high resin content and high viscosity, the minimum feasible turning radius can be reduced from 2m Zoom out to 1.8m , providing a clear direction for optimizing the heat input process.

Breakthrough 4 : Establishing a novel physical mechanism for tensile buckling defects

Unlike conventional studies on internal wrinkling, this work focuses on the mechanism of tensile instability at the outer edge of the tow: the difference in arc lengths between the inner and outer regions of the tow generates a linearly distributed tensile load; when this load exceeds the critical adhesive strength of the resin matrix, outward buckling occurs, thereby refining… AFP A comprehensive theoretical framework for directional defects, distinguishing between two distinct failure modes: folding and buckling.

II. Technological Innovation

Innovation 1  Experimental System for Characterizing Lift-Off Defects in Level‑4 Standardization

• Test platform: AFP-XS Gen2 Headpiece pairing KUKA KR210 Robot, fixed-speed paving 0.05m/s , Compaction Force 375N , the variable is only the turning radius ( 0.5~2m ), heating power level;
• Two types of control materials: TC700 Carbon fiber prepreg tape, material 1  Resin 35% Low viscosity, material 2  Resin 33% High viscosity;
• Visual defect grading: perfect adhesion, lifting only at the edges, large‑area delamination, and complete debonding throughout—standardized test evaluation criteria ensure data are comparable across tests.

Innovation 2  Rayleigh - Ritz Energy Analysis Modeling Framework

• Geometric-mechanical equivalence: the steering cable bundle is simplified as an orthotropic thin plate on an elastic foundation, and the difference in inner and outer arc lengths is converted into a linearly distributed in-plane tensile load.
• Energy functional formulation: integrates the bending strain energy of the thin plate, the elastic potential energy of the resin matrix, and the work done by the tensile external force.
• A custom deflection trial function is employed to match the actual warping surface, and explicit analytical expressions are derived for the critical buckling load and the critical yaw radius.
• Batch sensitivity analysis for a single variable, providing an intuitive visualization of the relative influence of each parameter on the forming limit.

Innovation 3  A New Approach to Characterizing the Viscous-Equivalent Elastic Substrate

Innovatively converts the resin tackiness of prepregs into the normal stiffness of the substrate. k Without requiring complex adhesion tests, it infers the resin’s bonding performance solely from the critical molding radius, establishing a quantitative link between material adhesion and forming limits, thereby streamlining the material‑selection testing process.

Innovation 4  Engineering Application Logic for Path Design

The model is embeddable. AFP Offline routing software ADDPath It automatically verifies the radius of each segment of the turning curve, and for areas with radii below the critical threshold, it promptly suggests segmenting the curve, increasing the tow width, or boosting the heating power—thereby reducing rework at the design stage and lowering the scrap rate during prototype manufacturing of pressure vessels.

III. Application Scenarios

• Aviation / Aerospace Composite Pressure Vessel (Core Application Scenario)

Verification of the double‑curvature layup paths for the vehicle’s oxidizer tank, the satellite’s high‑pressure gas bottle, and the rocket’s liquid hydrogen tank; early assessment of whether fiber‑bundle lifting may occur in transition zones; optimization of layup segmentation and curvature design to minimize delamination defects during molding.

• Airframe / Dual-curved variable stiffness inlet duct AFP Component

Saddle‑shaped skin of the aircraft, complex curved surfaces of the inlet duct, verification of layup processes in confined turning zones, matching the viscosity of prepregs with heating power, and balancing weight reduction with forming quality.

• AFP Lamination CAM Software Algorithm Development

The model formula can be integrated with offline path-planning software to automatically calculate the critical turning radius for each area, enabling intelligent path optimization and reducing the man-hours required for manual, iterative curve adjustments.

• Research and Development of Prepreg Formulations and Storage Processes

Resin content and surface tack are optimized through benchmarking, and the critical radius metric is used to assess the lay-up compatibility of prepregs. Additionally, the risk of reduced molding limits due to tack degradation in aged materials is evaluated.

• AFP Optimized Design of the Head Heating System for Laying Down

Quantify the benefits of increasing heating power based on the model, and provide guidance for infrared applications. /  Laser heating source power and temperature-zone design enhance the forming window for curved surfaces.

IV. Summary of the Article

(1) Core Research Findings

• AFP Stretching the outer edge of a tow during directional layup can induce stretch‑induced buckling–type delamination, leading to edge lifting defects. This paper presents an analytical model that directly computes the critical minimum turning radius, with predicted results in good agreement with experimental data.
• The layup length and the resin viscosity of the prepreg are the two most critical parameters influencing the forming limit, while fiber modulus and Poisson’s ratio have only a minor effect.
• Increasing the curing temperature and selecting high-resin-impregnation prepregs can significantly reduce the minimum allowable bend radius and enhance the capability for forming curved surfaces.
• Curl‑up defects are classified into four morphological levels and can serve as a unified acceptance criterion for in‑line quality inspection and process debugging.

(II) Engineering Application Value

Traditional prototyping of hyperbolic pressure vessels relies on repeated layup trials, resulting in high costs and long development cycles. The analytical model presented in this paper enables early prediction of fiber‑bundle lift‑off risks during the digital design phase, allowing for proactive optimization of ply curvature, segment length, and heating protocols. Furthermore, it establishes a quantitative method for evaluating prepreg viscosity, providing a robust tool for material selection and for optimizing the thermal systems of layup equipment, thereby significantly reducing R&D and iteration costs for composite pressure vessels.

(3) Current Research Limitations

Only thermoset prepregs; thermoplastics are not covered. AFP System; the model currently cannot directly and accurately measure the viscosity of the resin matrix. k , there is a lack of rapid adhesion testing methods; only plate‑based tests have been conducted, with no validation on the three‑dimensional curved surfaces of complete tank bodies.

(IV) Future Expansion Directions

• Develop a rapid quantitative testing device for the tack of prepregs and refine the procedure for experimentally determining model input parameters.
• Expand CF/PEEK Under thermoplastic steering conditions, a critical radius model specific to thermoplastics is established.
• Full-scale model verification was completed on the hyperbolic shell of a complete pressure vessel.
• Encapsulate the analytical formula into a commercial product. AFP Path-planning software that enables automated defect detection and path optimization.

(5) Industry Insights

Variable‑stiffness lightweight composite designs rely heavily on curved‑surface‑oriented ply layups, yet fiber‑bundle lifting remains the key bottleneck hindering mass production of complex curved parts. During the design phase, forming feasibility cannot be judged solely on geometric curvature; it must be evaluated in conjunction with prepreg viscosity and layup length. Increasing heating input and selecting high‑viscosity prepregs are cost‑effective strategies for broadening the process window on curved surfaces. This analytical prediction tool enables a “simulation‑first, minimal physical prototyping” approach, significantly boosting the development efficiency of high‑end composites such as pressure vessels.

Image and Text Guide

Figure 1. AFP Test Results: Overall Pressure Vessel and Results of Various Tensile‑Drag Tests

Figure 2. Tensile results observed in experiments under varying material types, turning radii, and heating conditions.

Figure 3. Geometric description of the sling, schematic diagram of the plate model, and representation of the deflection function.

Figure 4. Materials 1  Sensitivity Analysis of Different Model Parameters