Research background

    With the increasing application of composite materials in structural engineering, studying fiber failure-driven fracture toughness has become fundamental to understanding their damage behavior. This involves not only evaluating overall energy absorption capacity but also comprehensively understanding related mechanisms such as fiber pull-out, delamination, and fiber bridging. The anisotropy and heterogeneity of composites, combined with impact loading conditions like hail, runway debris, and bird strikes, make failure processes highly complex. Current fracture toughness research is primarily confined to uniaxial loading conditions, with factors including sample configuration, size effects, lamination sequence, and data processing methods. Despite extensive research in this field, there remain significant limitations in guiding the design of damage-tolerant engineering structures for operation in complex and extreme environments.

    In 2025, Professor Cui Hao's research team at Northwestern Polytechnical University published a groundbreaking paper titled "Fracture Characterization of Composite Laminates under Dynamic Biaxial Loading" in the International Journal of Impact Engineering. This study represents the first systematic investigation into the fracture behavior of glass fiber reinforced plastics (GFRPs) under dynamic biaxial tensile loading. The team developed an experimental framework integrating high-speed imaging with a DIC-based J-integral method to directly determine fracture toughness during crack initiation and propagation. The research systematically examined how displacement rate and load ratio affect fracture toughness, cohesive strength, and failure mechanisms. By addressing the limitations of previous uniaxial studies, this work effectively fills a critical gap in biaxial dynamic fracture characterization. The findings significantly enhance the predictive accuracy of dynamic failure models for composite materials.

The test was performed on the Hercuil NOIA-150 biaxial testing machine and the biaxial electromagnetic Hopkinson rod.

Materials and Tests

    In this study, laminates were manufactured using T700/LT03A unidirectional prepreg with an orthogonal symmetric [90/0]4s lamination configuration. In this configuration, the 0 fiber is subjected to tensile stress. The laminates were prepared using the hot pressing autoclave curing method with a nominal thickness of 2 mm. After curing, each laminate was inspected via C-scanning to confirm the absence of major defects in the original specimens. This step was performed prior to mechanical processing to ensure internal quality assessment could be conducted without interference from geometric features such as notches or edges. The cross-shaped specimens were precisely machined using a CNC milling machine to achieve the desired geometry and pre-crack characteristics. A pre-crack with a width of 0.5 mm and length of 5 mm was introduced, aligned with the 90 fiber, to guide crack propagation along the intended path. The crack tip was sharpened using a diamond wire saw with a diameter of 0.1 mm, achieving a tip radius of<250 μm.

    The sample design in this study was based on the previously established cross-shaped geometry for biaxial tensile strength testing, further refined through finite element (FE) simulation under representative biaxial loading conditions. The corner geometry was optimized to minimize unintended stress concentrations and enhance the reliability of J-integral measurements. The final optimized cross-shaped geometry dimensions are shown in Figure 1.

   Figure 1 Geometric design of the cross-shaped specimen: (a) quasi-static (b) dynamic

    The quasi-static experiment was conducted using the Hercules NOIA-150 biaxial device at a fixed load ratio and a displacement rate of 3 × 10^−6 m/s, as shown in Figure 2. The camera was mounted perpendicular to the sample surface with a large constant optical system, capturing images at a frame rate of 1 fps and a resolution of 5210 × 5210 pixels.

Figure 2 Quasi-static experimental setup

    The dynamic test employed a novel electromagnetic biaxial Hopkinson rod system, as illustrated in Figure 3. This system utilizes four electromagnetic pulse generators to produce biaxial, four-directional stress waves with adjustable consistency and synchronization. Four identical incident rods (of the same material and geometry) were used to ensure uniformity of the stress waves.

                            Figure 3 (a) Schematic diagram of the electromagnetic biaxial four-directional Hopkinson rod loading system (b) Partial schematic of the test

results and discussion

   Figure 4 presents DIC analysis results from representative stages of high-speed biaxial tensile failure (loading ratio f = 1). Throughout the loading process, both the displacement field calculated via DIC and the strain fields at crack tips on both sides of the central crack exhibited excellent symmetry. A distinct high-strain-rate region was observed at the crack tip, clearly reflecting the intense localized deformation during crack initiation and propagation. Furthermore, after crack initiation, a pronounced negative-strain-rate region emerged behind the crack tip. This phenomenon indicates rapid localized unloading and stress release in the material at that location.

Figure 4 DIC analysis results of displacement, strain, and strain rate during high-speed damage in the typical critical stage (f = 1)

    Transverse fracture toughness is a critical factor influencing the damage tolerance and notch sensitivity of fiber-reinforced composites. As shown in Figure 9, during the early stage of crack propagation, when stress waves propagate through the material, this energy is redistributed and partially converted into kinetic energy, resulting in a significant increase in strain rate near the crack tip. The redistribution of energy during stress wave propagation causes a substantial rise in strain rate at the crack tip, leading to localized rapid deformation and stress redistribution. Additionally, a local inertial lag effect emerges at the crack tip, reflecting instantaneous acceleration resistance due to dynamic inertia. As the crack accelerates and the material responds dynamically, local stress undergoes further redistribution, causing a temporary decrease in kinetic energy. In the later stages of crack growth, inertial effects become more pronounced, ultimately affecting crack stability and propagation trajectory.

Figure 5 Comparison of dynamic J-integral terms under different load rates

    By differentiating CTOD data obtained under dynamic loading conditions, the cohesive law curve is derived from the CTOD-J relationship. This method effectively captures localized damage behavior at crack tips. Due to its precision and computational efficiency, it is particularly suitable for high-rate applications. As shown in Figure 6, under biaxial tensile loading, the presence of transverse stress alleviates stress concentration at crack tips, thereby reducing material sensitivity to crack initiation and delaying failure onset. Consequently, the critical condition for crack initiation is elevated, effectively suppressing early crack propagation. Initial fracture toughness increases with the rise in transverse load ratio.

Figure 6 CTOD-J replicas and corresponding fitting curves under different dynamic load ratios: (a) f = 0, (b) f = 0.25, (c) f = 0.5, (d) f = 1, (e) CTOD-J fitting curves, (f) Cohesion zone law curves under different dynamic load ratios

    Figure 7 presents representative R-curves under varying displacement rates and load ratios. Compared to quasi-static conditions, both crack initiation and propagation toughness values show significant reduction under high-speed loading. This observed decrease in toughness is primarily attributed to the limited activation of time-dependent toughening mechanisms (e.g., fiber bridging), which require sufficient time and deformation to fully manifest. Under rapid crack propagation conditions, these mechanisms are markedly suppressed, resulting in reduced energy dissipation.

Figure 7 Comparison of R-curves for fiber tensile failure under quasi-static and high-speed loading conditions at different load rates: (a) f = 0, (b) f = 0.25, (c) f = 0.5, (d) f = 1

    X-ray CT examinations of typical failure specimens under varying loading ratios and strain rates are shown in Figure 8. Under biaxial tensile loading, the primary failure mode transitions from fiber fracture near the surface to internal fiber pull-out, reflecting a progressive failure evolution mechanism. The fiber pull-out process enhances crack growth resistance by promoting additional energy dissipation through fiber bridging. This fracture behavior aligns with R-curve results, where increased fiber bridging under quasi-static loading leads to more pronounced toughening effects.

Figure 8 CT tomographic window positioning and representative cross-sectional images: A and B represent the XY section (0° slice), while C shows the YZ section of the crack surface.

conclusion

1.The displacement rate significantly affects fracture behavior. Under high strain rate loading, the dynamic fracture toughness is approximately 30% lower than that under quasi-static conditions. This reduction indicates a diminished energy dissipation capacity during rapid crack propagation.

2.The load ratio also plays a key role. With the increase of the transverse load ratio, both the initial fracture toughness and the strength of the softening segment in the cohesive strength law curve show a significant upward trend. This indicates that transverse loading alleviates stress concentration at the crack tip and enhances fracture energy absorption.

3.X-ray CT revealed a distinct rate-dependent fracture mechanism. High strain rate loading inhibited fiber bridging, as evidenced by shorter pull-out lengths. In contrast, quasi-static loading promoted extensive fiber pull-out and sustained bridging, resulting in greater energy dissipation. These microstructural differences explain the reduction in fracture energy under dynamic conditions.

    These findings provide new insights into the dynamic fracture behavior of multi-axial stress states in real-world applications such as aerospace, automotive, and defense structures. More importantly, the proposed experimental method demonstrates strong reproducibility, high temporal resolution, and robust stress equilibrium, establishing a reliable foundation for future multi-axial fracture modeling. Future work will focus on optimizing specimen geometry and improving control precision to enable multi-rate testing under a wider range of loading conditions.

Article source

Feng Y, Lei C, Shi J, et al. Fracture characterization of composite laminates under dynamic biaxial tensile loading[J]. International Journal of Impact Engineering, 2025: 105526.

Original link

https://doi.org/10.1016/j.ijimpeng.2025.105526