Research background

    Background: Fiber-reinforced polymer (FRP) composites, renowned for their exceptional specific strength and stiffness, are increasingly utilized in high-end equipment sectors such as aerospace and transportation. The pure shear response characteristics of laminates in the in-plane principal material direction constitute fundamental data for structural design, damage prediction, and finite element simulation of composite structures, which directly determine the load-bearing safety and reliability of the structures.

    To fully comprehend the shear mechanical behavior of FRP, it is essential to precisely capture its shear stiffness, shear strength, and the full stress-strain evolution patterns, while also clarifying how factors such as fiber orientation and load types influence shear damage mechanisms (e.g., shear band formation and fiber bridging). However, the anisotropy and inhomogeneity of composites, combined with the susceptibility of traditional shear testing methods to stress concentration and load coupling, make it challenging to accurately simulate pure shear conditions. Current research predominantly relies on uniaxial loading tests to indirectly derive shear performance, yet these methods suffer from limitations such as overestimation of shear stiffness and distortion in response characterization during high-strain phases, failing to comprehensively reflect the material's true shear behavior under complex loading conditions.

    In 2023, a research team led by S. Horta Munoz at Spain's University of Castilla-La Mancha published a study in *Composites Part B*, proposing a tensile-compression biaxial test using ±45-degree symmetric cross-laminated specimens to systematically investigate the feasibility of measuring pure shear responses in the main material direction of laminates. The study developed an experimental framework integrating digital image correlation (DIC) technology with finite element simulation, conducting in-depth analysis of how displacement rates and loading patterns affect shear performance. This work effectively filled the technical gap in characterizing pure shear of composites under biaxial loading, providing critical support for structural design of composites under complex loading conditions.

Materials and Tests

1.Test Materials

    Test materials: UD carbon fiber-reinforced epoxy prepreg was selected, with a cured nominal thickness of 0.25mm and a fiber volume fraction of 58%. The in-plane elastic properties of the laminated panel were obtained through preliminary uniaxial tests. The elastic modulus and Poisson's ratio data under tensile and compressive conditions are presented in Table 1 and Table 2, respectively. Subscripts 1 and 2 denote the parallel and perpendicular fiber orientations, while superscripts T and C represent tensile and compressive conditions. Table 1: Average elastic properties of the laminated panel in the main material direction under tensile load.

Table 1 Average Elastic Properties of Main Material Direction of Laminated Panel under Tensile Load

Table 2 Average Elastic Properties of Laminated Panel in the Main Material Direction Under Compression Load

2. Sample Design and Preparation

    The geometric design of the cross-shaped specimen was developed based on the UNE 0074:2023 standard, incorporating finite element simulation optimization. The arm junction features a double-radius transition to effectively reduce stress concentration, while the central region is tapered to ensure damage initiation at the target area. Key design parameters include: nominal arm width of 30 mm, thickness of 4 mm; nominal central loading area dimensions of 22×20 mm² with 1 mm thickness; and an arm-to-center thickness ratio of 4:1 to suppress overall specimen buckling and maintain stable boundary conditions in the central region.

    To protect the clamped area and prevent slip damage during loading, a 3 mm thick, 50 mm long glass fiber reinforced polymer end plate was bonded to the specimen arm's end using Araldite©2000 epoxy adhesive, with the inner corner processed into a smooth transition structure. All specimens were fabricated as 300 mm× 300 mm laminated blanks through hand-pasting, then cured at 180°C under 7 bar pressure for 120 minutes. After CNC milling to the designed dimensions, ultrasonic testing confirmed the absence of initial defects.

Figure 1 Geometric shape and dimensions of the cross-shaped specimen

3. Test Equipment and Methods

    The Microtest electromechanical multi-axis testing machine, equipped with four independent closed-loop control electric actuators, operates at a loading rate of 20 N/s in load control mode. Real-time load data is collected through four 50 kN force sensors. A dual-axis anti-buckling fixture limits the lateral displacement of the specimen arm, while a reserved central observation window ensures unobstructed strain measurement. The fixture, specimen, and testing machine are calibrated and aligned via an L-shaped support base, with a loading direction deviation of no more than 0.1.

    Strain measurement was performed synchronously using the LaVision Strain-Master stereoscopic DIC system and Kyowa strain gauges. The DIC system camera had a pixel resolution of 2456×2058, with a calibrated scale factor of 30.59 pixels/mm. The central region of the specimen was coated with a black primer and white speckles. Post-processing employed a 51×51 pixel² subset size and a 16-pixel step size. A 0/45/90 strain gauge was affixed to the back of the central region, and local strain was measured synchronously using the Kyowa PCD-300B data acquisition instrument.

    The damage of the sample arm was detected by Olympus OmniScan SX phased array ultrasonic testing instrument. The shear failure morphology of the central region was observed by optical microscope. The finite element model was established by Abaqus/Standard to simulate the load transfer law and stress distribution characteristics, and the load transfer factor was determined.

Figure 2 Biaxial buckling fixture (a) Unassembled component (b) TC test setup with buckling fixture and test sample gripped

Results and discussion

1. DIC full-field strain analysis

    During the linear loading phase, the central region exhibited a uniformly distributed pure shear strain field with symmetrically arranged strain isoclines, demonstrating no significant stress concentration. This validated the experimental protocol's effectiveness in achieving pure shear conditions. When the load reached 93.9 MPa, localized strain concentration began to emerge, forming an initial shear band at a 45-degree angle to the loading direction, indicating the material's transition into the nonlinear response phase.

    As the load continues to increase, the shear band gradually expands and penetrates the entire central region, ultimately forming a shear failure plane oriented at 45 degrees. DIC measurements reveal that the maximum engineering shear strain reaches 40%, significantly exceeding the measurement range of traditional uniaxial tests. Furthermore, after crack initiation, a distinct negative strain rate region appears behind the crack tip, reflecting localized unloading and stress release effects during the shear damage process. This phenomenon is closely related to the energy dissipation mechanism of shear damage in composite materials.

Figure 3 (Left): Numerical shear strain field γ12 during the intermediate linear response stage of the TC test without fixture; (Right): Experimental shear strain field γ12 during the nonlinear stage of the TC test with fixture

2. Shear stress-strain response

    The shear stress-strain curves of all specimens showed two distinct phases: a linear elastic phase and a nonlinear strengthening phase. The linear phase exhibited a nearly linear stress-strain relationship, with an average shear modulus (G12) of 5.35±0.14 GPa obtained through linear fitting, which was in good agreement with the theoretical calculations of classical laminates.

    When the shear stress reaches 93.9±5.4 MPa, the curve slope begins to decline, entering a nonlinear phase. During this stage, micro-crack initiation and fiber orientation adjustment occur within the material, leading to a gradual reduction in stiffness. Comparing the test results with and without the fixture, specimens without the fixture exhibit lower initial stress for the nonlinear phase due to arm buckling, with a maximum shear strain of only 28%—significantly lower than the 40% observed with the fixture. This confirms that the anti-buckling fixture effectively suppresses overall specimen instability, ensuring the central region fully utilizes its shear performance.

    When the shear strain reaches 0.2, the corresponding shear strength is 115±5 MPa. The observed ultimate shear stress during testing was 130±5 MPa, indicating the material's excellent shear load-bearing capacity and energy absorption potential. The curve also shows that during the nonlinear phase, longitudinal strain in the x and y directions begins to diverge, with a maximum difference of 0.047. This phenomenon stems from the asymmetry between fiber orientation adjustment and shear band expansion within the material. However, the overall shear response remains stable, which does not affect the comprehensive evaluation of shear performance.

Figure 4 (a) Comparison of engineering shear stress-strain curves with actual shear stress-strain curves for a typical TC test (including both fixture application and non-application scenarios)

(b) Relationship between shear stress and DIC longitudinal strain in a typical TC test

3. Failure mechanism analysis

    Figure 5 presents the final failure mode of the TC test. The diagonal in the biaxial loading zone exhibits a distinct shear failure plane, with a smooth fracture surface at a 45-degree angle to the loading direction—characteristic of pure shear failure. The failure region shows no significant delamination or fiber breakage, primarily manifesting as matrix shear cracking and fiber slip. This confirms the test successfully achieved a pure shear-dominated failure mode, effectively avoiding interference from other failure mechanisms.

Figure 5 shows the final failure mode of the TC test

    The phased array ultrasonic testing results in the sample arm region demonstrated no damage signals, confirming that the damage was confined to the central loading zone. Throughout the test, the sample arm maintained linear elastic response without exhibiting pseudo-ductile deformation or stress concentration. These findings validate the rationality of the sample design, ensuring that shear property measurements remain unaffected by the sample arm's response and thereby enhancing the reliability of the experimental data.

Figure 6 Phased-array ultrasonic detection results of the sample arm region after testing

    Microscopic morphology analysis of failure specimens via optical microscopy and X-ray CT revealed that the shear failure mechanism of ±45 symmetric lamination composites primarily involves shear band formation, matrix cracking, and fiber slip. Under quasi-static loading, the fiber pull-out length was significantly longer (averaging approximately 0.8 mm), with pronounced fiber bridging effects resulting in rough fracture surfaces and substantial energy dissipation. In contrast, high-speed loading shortened the fiber pull-out length (averaging about 0.3 mm), reduced shear band width, and produced smoother fracture surfaces, exhibiting brittle failure characteristics. This microscopic mechanism difference elucidates how loading rate influences macroscopic shear performance.

Conclusion

1. The tensile-compression biaxial test of ±45 symmetrical cross-shaped specimens can successfully achieve uniform pure shear state in the central region. The DIC full-field strain analysis in the linear stage is highly consistent with the finite element simulation results. The measured average shear modulus G12=5.35±0.14 GPa and ultimate shear strength = 130±5 MPa provide a reliable method for characterizing the shear properties of composites.

2. The application of the anti-buckling fixture significantly enhances test stability by effectively suppressing out-of-plane buckling of the specimen arm, increasing the maximum shear strain in the central region from 28% to 40%, thereby ensuring complete capture of shear response during high-strain phases.

3. The load ratio and loading rate significantly affect the shear performance: Increasing the transverse load ratio alleviates stress concentration and enhances shear toughness; under high-speed loading, the shear strength slightly improves but the ultimate strain decreases, with the failure mode transitioning from ductile shear to brittle shear, providing critical references for structural design under complex load conditions.

4. Comparing the results of uniaxial and biaxial tests, uniaxial tests tend to overestimate shear stiffness (with a deviation of approximately 2%), whereas biaxial tensile-compression tests can more accurately capture the full stress-strain evolution and failure mechanisms of materials. This approach is particularly suitable for characterizing shear responses during high-strain stages, thereby addressing the limitations of traditional methods.

5. The shear failure mechanism of the composite is mainly composed of shear band formation, matrix cracking and fiber slip. The fiber bridging effect is significant under quasi-static loading, and the time-dependent toughening mechanism is inhibited under high-speed loading. This finding provides experimental support for the optimization of the damage model of the composite.

Article source:

Horta Muñoz S, Serna Moreno M C. Tension–compression biaxial test with ±45◦symmetric angle-ply laminates for determining the pure shear response in principal material directions of a lamina [J]. Composites Part B, 2023, 261: 110792.

Original link:

https://doi.org/10.1016/j.compositesb.2023.110792