Research background

      Fiber-reinforced composites are increasingly prominent in aerospace applications, widely used in manufacturing critical structures such as fuselages and wings. In these applications, composites typically endure combinations of multiple stresses or loads to achieve desired structural performance. Among the various failure modes observed in laminated composites, fiber failure under tensile loads remains a major concern, often leading to catastrophic failure and complete loss of load-bearing capacity. Experimental determination of fracture toughness under fiber-dominated tensile failure serves as a critical parameter for characterizing composite properties and ensuring structural safety design. However, most existing research is based on uniaxial tensile conditions, which may not accurately predict fracture behavior under real-world multi-axial stress states. To comprehensively understand the mechanical behavior of composites under complex stress conditions, conducting biaxial and multi-axial testing is essential.

     In 2025, Professor Cui Hao's research team at Northwestern Polytechnical University published a paper titled "Translaminar Fracture Toughness of Carbon Fiber Reinforced Polymer Composite Laminates with Cross-Ply Configuration under Biaxial Tensile Loading" in Engineering Fracture Mechanics. The researchers developed a novel testing method to evaluate the fiber tensile fracture toughness of composite laminates under biaxial loading. They fabricated cross-shaped specimens with central pre-cracks and applied varying load ratios simultaneously in both longitudinal and transverse directions. Using digital image correlation (DIC) to obtain full-field strain data, the team calculated fracture toughness during crack initiation and propagation through the J-integral method. The study revealed that crack initiation and propagation were load-dependent, with longitudinal fiber tensile fracture toughness increasing as transverse stress rose. Mechanistic analysis indicated that the enhanced fracture toughness likely resulted from transverse stress reducing stress concentration at crack tips, which stabilized the fracture process zone (FPZ) and increased fiber pull-out length.

    The experimental study conducted by the researchers in this study was performed using the Hercuil NOIA-150 biaxial testing machine provided by our company.

Sample Preparation and Experimental Setup

    The specimen design proposed in this study represents an improvement over the previously developed cross-shaped specimens for biaxial failure strength testing. A central crack spanning the thickness is introduced to induce interlayer fracture, which can propagate in two directions. Cross-laying was employed to allow the crack to propagate along the Y-axis through the longitudinal fibers, while the X-axis fibers guide the crack along the desired path. To enhance load transfer and minimize stress concentration, 2 mm thick quasi-isotropic GFRP reinforcement sheets were bonded to the cross-shaped specimen using 3M DP420 epoxy adhesive. A 330 × 330 mm² composite plate was fabricated using T700/LT03A unidirectional prepreg with a [90/0]4s lamination configuration and a nominal thickness of 2 mm.

Figure 1 Geometric dimensions of the cross-shaped specimen

    The biaxial tensile tests were conducted using the Herculi NOIA-150 biaxial testing machine, which has a loading capacity of 150 kN. The tests were performed at a constant loading rate of 0.18 mm/min, with load and displacement values recorded at a frequency of 10 Hz. Experiments were conducted under four different biaxial load ratios, denoted as f = F1: F2, where F1 and F2 represent the loads applied laterally (TD) and axially (AD), respectively. The parameter f ranged from 0, 0.25,0.5, and 1.

Figure 2 (a) Double-axis loading test device; (b) Schematic diagram of the integral domain and contour lines on both sides of the crack tip.

Results Discussion

    During the initial loading phase, the specimen exhibited stable deformation with linear elastic behavior and consistent stiffness across different loading ratios. As the load increased, the curve showed slight nonlinearity before crack initiation, indicating the onset of minor matrix or interface damage. After crack initiation, a sudden but minor load drop was observed, typically accompanied by audible crack formation signs. However, the total load on the specimen continued to increase until subsequent crack propagation triggered another load drop. Increasing the loading ratio resulted in a slight rise in both crack initiation load and peak load, suggesting that transverse stress partially enhanced the load-bearing capacity.

    During crack propagation, fiber bridging becomes clearly observable, playing a pivotal role in delaying crack growth. At crack initiation, the crack tip extends into the fiber bundle region where intact fibers effectively bridge the crack. These bridging fibers redistribute stress, slowing crack propagation and enabling incremental expansion. However, when the crack tip propagates beyond the fiber bundle region, the bridging effect gradually diminishes. Subsequently, the bridging fibers fracture, causing rapid crack propagation across the entire gauge length until ultimate failure occurs. 

Figure 3 (a) Representative load-displacement curves under different load ratios (f=0,0.25,0.5,1), (b) Representative failure specimens under biaxial tensile loading (f=1)

    Research demonstrates that the average initial fracture toughness under varying loading ratios exhibits distinct dependence on loading modes. Specifically, biaxial loading yields higher fracture toughness than uniaxial loading, indicating that the presence of transverse stress enhances crack propagation resistance. Furthermore, fracture toughness values show a positive correlation with loading ratios. However, while this trend persists across different biaxial stress conditions, the rate of increase in fracture toughness gradually diminishes with higher loading ratios. This suggests that although transverse stress effectively suppresses crack initiation, its marginal effect diminishes under elevated biaxial loading conditions.

    The lfpz values derived from R-curve analysis demonstrate a gradual increase with rising loading ratios, consistent with the trend observed in lfpz values estimated using the J-integral iteration method. However, under uniaxial loading conditions, the instability of crack propagation and limited crack growth within the specimen may result in insufficient data points, making it difficult to establish a distinct R-curve. Under biaxial loading conditions, the enhanced toughening effect of the R-curve primarily stems from the combined influence of matrix cracking at the crack tip and fiber bridging behind the crack. This interaction stabilizes crack propagation and extends the FPZ, leading to larger lfpz values compared to those obtained by the J-integral method.

Figure 5 R-curves under different loading ratios (① germination zone, ② unstable expansion zone)

    Near the crack tip, distinct fiber clusters or columns are observed being pulled out, indicating the stable crack propagation phase. In contrast, regions farther from the tip exhibit relatively smooth fracture surfaces, symbolizing the unstable crack propagation phase, which typically corresponds to brittle fracture behavior. Under uniaxial loading, the fiber pull-out length shows minimal variation between the stable and unstable propagation phases. However, as the loading ratio increases, the fiber pull-out height at the crack tip gradually rises, ranging from 0.68 mm to 1.48 mm.

Figure 6 Fracture morphology under optical microscope

    The fracture surface consistently exhibits two distinct zones: a stable extension zone and an unstable extension zone. In the stable extension zone, prominent fiber bundle extraction features are observed, accompanied by grooves left after fiber detachment. This progressive fracture process is driven by fiber extraction and interfacial delamination, facilitating stable crack propagation. Conversely, the fracture surface in the unstable extension zone appears relatively smooth, indicating brittle fracture behavior. Although the diameter of extracted fiber bundles remains consistent across different loading ratios, the extraction height increases with rising loading ratios. This behavior demonstrates that frictional slip at the fiber-matrix interface becomes more pronounced with increasing transverse stress, promoting energy dissipation and enhancing fracture resistance.

Figure 7 Representative SEM images of the fracture surface: (a) (f = 1) Low magnification of the crack initiation zone and unstable propagation zone, (b) Crack initiation zone under different loading ratios

    Under varying loading ratios, distinct shadow bands perpendicular to the crack direction are observed near the crack tip. These shadow bands emerge prior to crack initiation, indicating the onset of localized strain concentration caused by fiber-matrix interface damage. This strain concentration originates from the high modulus of the 0 fiber, which restricts crack propagation while inducing localized stress accumulation at the fiber-matrix interface. The resulting delamination leads to strain localization, manifested as visible shadow bands. These shadow bands serve as visual indicators of the evolving FPZ, marking regions of microcracks, interface delamination, and localized damage accumulation.

Figure 8 (a) Crack tip of the shaded band, (b) Mechanism of fiber bundle damage evolution

Full text summary

    This study employed full-field strain measurement and J-integral method to determine the fiber tensile fracture toughness of cross-shaped specimens under different loading ratios. Additionally, the lfpz was estimated under biaxial loading conditions to enhance the understanding of material damage evolution and failure mechanisms under complex stress states.

    This study on fiber-dominated failure yielded several noteworthy findings. The DIC-J method demonstrated effective and reliable calculation of fracture toughness under biaxial tensile loading conditions. Loading mode proved to be a critical factor influencing fracture toughness. Specifically, values obtained under biaxial loading significantly exceeded those observed under uniaxial loading. Although the sensitivity of biaxial fracture toughness to incremental loading ratio increments remained limited, an overall upward trend was consistently observed. This positive correlation aligns well with the growth of the fracture length per unit area (lfpz). The observed trend primarily relates to the magnification of fiber bundle pull-out length during damage processes and the enhanced frictional dissipation effect.

    Future biaxial loading studies should consider expanding the gauge length range of cross-shaped specimens to broaden the collection of crack propagation data, thereby facilitating the creation of comprehensive R-curves. Furthermore, investigating the effects of mixed-mode crack propagation at different angles under biaxial loading conditions holds significant potential. These research directions are expected to provide deeper insights for the safe and robust design of composite structures.

Article source

Feng Y, Wang J, Zhao Y, et al. Translaminar fracture toughness of carbon fibre reinforced polymer composite laminates with cross-ply configuration under biaxial tensile loading[J]. Engineering Fracture Mechanics, 2025: 111386.

Original link

https://doi.org/10.1016/j.engfracmech.2025.111386