⚡ electrical engineering

Defect2Tree

The paper introduces Defect2Tree, a framework that converts complex 3D void morphologies in carbon-fibre-reinforced polymers into topology-preserving skeleton-tree representations to accurately predict crack-growth directions and assess structural integrity, overcoming the limitations of conventional defect idealizations.

Original authors: Yong Li, Fangxiang Yin, Yaao Di, Yihao Yin, Yan Fu, Junming Yan, Kai Zheng, Yanan Miao, Long Chen, Shanling Han

Published 2026-09-11

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CC BY 4.0

Original authors: Yong Li, Fangxiang Yin, Yaao Di, Yihao Yin, Yan Fu, Junming Yan, Kai Zheng, Yanan Miao, Long Chen, Shanling Han

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Strong, lightweight materials made from carbon fibers and plastic are the backbone of modern engineering, powering everything from the wings of airplanes to the frames of high-speed trains. These materials are prized for their strength-to-weight ratio, but their reliability hinges on a single, stubborn problem: tiny, invisible holes trapped inside them during manufacturing. These voids are not perfect spheres or neat circles; they are jagged, branching, and irregular, formed by trapped air or uneven curing. For decades, engineers have struggled to predict how these messy shapes will cause a material to fail. Traditional methods often force these complex defects into simple geometric shapes to make them easier to calculate, but in doing so, they strip away the very details—the sharp corners, the connected branches, and the curved edges—that actually determine where a crack will start and how it will spread. Without a way to see the true shape of these flaws, predicting when a part might break remains a guessing game.

A team of researchers from Shandong University of Science and Technology and CRRC Forming Technology has developed a new way to look at these hidden flaws, turning a chaotic three-dimensional mess into a clear, tree-like map. They call this method Defect2Tree. Instead of trying to fit a jagged void into a circle or a rectangle, the researchers used high-resolution X-ray scans to see the actual shape of the holes inside carbon-fiber parts. They then traced the outline of each hole and simplified it into a skeleton, much like stripping a tree down to its main trunk and branches. This process preserves the critical topological features that other methods lose: the way branches connect, the sharpness of the tips, and the curvature of the edges. By converting these irregular shapes into a network of nodes and lines, the team created a digital representation that keeps the defect's true identity intact.

To understand how these specific shapes affect the material, the researchers needed to test them in a controlled environment. They could not easily test the original carbon-fiber parts because the fibers themselves create too much variation. Instead, they took the exact outlines of the scanned voids and printed them as two-dimensional holes in blocks of clear, dental-grade resin. These resin blocks acted as stand-ins, allowing the team to pull them apart in a testing machine while watching exactly what happened at the edges of the holes. Using high-speed cameras, they recorded how the material stretched and where the plastic deformation began. They found that the sharp, branching tips of the voids acted like stress concentrators, creating intense local strain that eventually led to cracks. To measure this, they developed a new way to calculate the intensity of the strain field, focusing on the area around the crack tip where the material begins to yield. This allowed them to identify which specific branches of the void were most likely to trigger a failure.

The researchers then combined their tree-like maps of the defects with the experimental data to build a prediction model. They fed the geometric details of the voids—such as the length of the branches, the angles between them, and the sharpness of the tips—into a machine learning algorithm known as a random forest. This model learned to associate the specific shape of a defect with the direction in which a crack would grow. The results were strikingly accurate. For a cone-shaped defect, the model predicted the crack's path with 93.64 percent accuracy. When they tested the system on six different types of complex defect shapes, including ring-like, sickle-shaped, and V-shaped voids, the prediction accuracy remained high, ranging from 86.57 percent to 95.75 percent. The model successfully identified not just where a crack would start, but also the precise angle at which it would travel through the material.

This work offers a significant shift in how engineers might assess the safety of composite materials. By moving away from simplified geometric assumptions and embracing the true, irregular topology of manufacturing defects, the Defect2Tree framework provides a direct link between the physical shape of a flaw and its mechanical consequences. The researchers demonstrated that preserving the branching structure and boundary details of a void is essential for understanding its behavior. While the current study used resin surrogates to isolate the effect of the defect shape, the framework is designed to be transferable to real carbon-fiber components. The ability to predict crack growth with such precision suggests a future where manufacturers can inspect a part, map its internal flaws into a tree structure, and immediately know which defects are safe and which are likely to cause failure, bridging the gap between seeing a defect and understanding its danger.

Technical Summary of "Defect2Tree"

Problem Statement
Manufacturing-induced void defects in carbon-fibre-reinforced polymer (CFRP) components present a significant barrier to reliable production. These defects exhibit highly irregular three-dimensional morphologies that cannot be adequately represented by conventional idealizations (e.g., strips, circles, or ellipses). Such simplifications discard critical topological features—specifically branching, connectivity, boundary curvature, and crack-prone tips—thereby limiting topology-sensitive defect assessment and subsequent failure prediction. Existing methods often rely on isolated geometric parameters or macroscopic averages, failing to establish quantitative links between real defect topology and mechanical degradation or crack evolution. Furthermore, classical fracture criteria (stress-intensity factor, energy-release rate) show limitations when applied to complex void defects where plastic zones and local strain concentrations are heavily influenced by irregular boundaries.

Methodology
The study proposes Defect2Tree, a topology-preserving framework that converts CT-resolved void morphologies into skeleton-tree representations to link real defect topology with mechanically relevant crack responses. The methodology proceeds through four integrated stages:

Defect Reconstruction and Skeletonization:
- X-ray computed tomography (CT) is used to reconstruct internal voids in CFRP.
- A skeletonization process (using morphological erosion-dilation operations) transforms irregular void boundaries into a concise skeleton.
- Node identification utilizes complex network theory and cosine similarity to distinguish intersections (nodes) from edge points, ensuring accurate graph representation.
- A Minimum Spanning Tree (MST) algorithm is applied to eliminate loops and redundant edges, streamlining the structure into a tree formation that preserves connectivity while minimizing total edge weight.
Tree-Heterogeneous Tensor Construction:
- The skeleton is parsed into trunks, branches, and shoots (nascent offshoots representing potential crack initiation sites).
- A tree-heterogeneous tensor is assembled by integrating geometric descriptors (defect diameter, aspect ratio, minimum void curvature radius, minimum trunk angle, fractal dimension) and topological metrics (degree centrality).
- This tensor provides a quantitative representation of void morphology from geometric shape to edge-node topology.
Experimental Validation and Strain Field Analysis:
- To isolate the mechanical influence of defect topology from fiber heterogeneity, CT-derived void contours were reproduced as 2D through-holes in DLP-printed resin surrogate specimens.
- These specimens underwent in-situ tensile testing with real-time coaxial optical microscopy to capture strain evolution and crack propagation.
- A Boundary Attention Dilation (BAD) algorithm was developed to identify crack-tip plastic zones. It combines an initial Irwin-model radius with morphological-gradient attention and directional weighting to iteratively refine the plastic-zone radius ( $r_p$ ).
- A Strain-rate Intensity Factor ( $K_\varepsilon$ ) was introduced to account for viscoelastic rate effects, leading to the formulation of an E criterion for Strain field intensity. This criterion uses a "strain-intensity-factor moment" to rank branch-wise crack-initiation risk.
Physics-Guided Prediction:
- A Random Forest Regression (RFR) model was trained using the tree-heterogeneous tensor descriptors and experimental crack-propagation data.
- The model predicts crack-growth directions by treating the continuous prediction problem as a discriminative selection among discrete virtual-crack orientations within the plastic zone.

Key Contributions

Defect2Tree Framework: A novel method for converting complex, irregular 3D void morphologies into topology-preserving tree representations, retaining features like branching and connectivity that are lost in standard geometric simplifications.
Tree-Heterogeneous Tensor: A multi-dimensional data structure that quantitatively encodes both geometric details (e.g., curvature, fractal dimension) and network topology (e.g., degree centrality) to serve as a feature vector for machine learning.
E Criterion for Strain Field Intensity: A new fracture assessment metric based on a strain-intensity-factor moment, designed to evaluate crack-initiation risk in irregular voids where traditional stress-intensity criteria may be insufficient.
Boundary Attention Dilation (BAD) Algorithm: A computational approach for experimentally resolving plastic-zone radii near irregular defect boundaries by combining physics-based initial estimates with attention-guided morphological dilation.
Physics-Guided Machine Learning: The integration of the E criterion and tree-heterogeneous tensor into a Random Forest model to predict crack propagation directions with high accuracy.

Results

Crack Initiation Prediction: The E criterion successfully identified high-risk branches. In a conical defect specimen, the model correctly identified Branch 9 as the initiation site (CII > 1.2), which matched the experimental observation of crack initiation at approximately 34 minutes.
Prediction Accuracy:
- For the conical defect specimen, the Random Forest model achieved a 93.64% accuracy in predicting crack-growth direction.
- Across six representative defect morphologies (conical, ring, sickle, strip, hump, and V-shaped), prediction accuracies ranged from 86.57% to 95.75%, with an overall mean accuracy of 92.47%.
- The model demonstrated stable performance (R² between 0.834 and 0.954) throughout most of the loading process, with error spikes occurring only during unstable crack-propagation stages.
Robustness: The framework proved effective across diverse defect shapes, with the strip-shaped defect yielding the highest accuracy and the sickle-shaped defect the lowest, attributed to the latter's highly curved boundaries and local tip perturbations.

Significance
The paper establishes an integrated and mechanically interpretable route from CT-resolved defect topology to experimentally supported crack-growth assessment. By bridging CT-based defect detection and structural-integrity evaluation, Defect2Tree offers a transferable framework that moves beyond scalar porosity metrics and idealized geometric descriptors. It provides a topology-sensitive route for post-process CT assessment of irregular void defects, potentially supporting defect acceptance criteria and the comparative assessment of composite processing conditions. While the current validation utilizes controlled DLP-printed resin surrogates, the authors posit that the topology-based formulation is extendable to other porous materials and complex defect morphologies, provided they can be reliably reconstructed and mechanically characterized. Future work is identified as necessary to establish direct process–defect–performance relationships using CFRP specimens manufactured under systematically controlled conditions.

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