1.Abstract

In recent years, high-altitude balloons (HAA) have become an economical platform for Earth observation, communication, and space exploration, sparking widespread research interest in their envelope materials. Although uniaxial strength of these materials has been widely adopted, no testing method exists to accurately measure their biaxial strength. Previous studies have shown that specimen failure often occurs in non-central regions due to severe stress concentration effects. Since biaxial stress fields only appear in the central test zone, the aforementioned failure modes cannot adequately describe material failure characteristics under biaxial stress conditions.

In 2018, the journal *Composite Structures* published a study by Shanghai Jiao Tong University on the biaxial strength of airship-type composite fabricators. The research conducted uniaxial and 1:1 biaxial tests on three types of HAA fabricators, obtaining load-displacement curves and capturing failure modes with high-speed cameras. The findings revealed that materials reaching their strength limits would fail through single or cross-crack mechanisms. Through finite element simulations, the study established the failure patterns of fabricators and identified the failure envelope within the first quadrant.

2.Test method 

2.1 Material

To meet multiple performance requirements, the capsule material typically possesses a complex microstructure.

Fabric composites are typically fabricated by laminating multiple thin film materials. The load-bearing layer is woven from warp yarns (warp Yarns) and weft yarns (weft Yarns), with functional layers uniformly distributed on both inner and outer surfaces of the load-bearing layer to provide protective functions.

Figure 1 Typical structure of high-altitude airship envelope

In this experiment, three types of test specimen materials were selected and tested respectively. The material properties are shown in the table below.

Table 1 Material Properties of High-altitude Airship Cages

2.2 Single-axis specimen design

Based on ISO 1421 standard, the length of the single-axis specimen is 600mm and the width is 50mm. The two ends of the specimen are given 200mm clamping area to ensure sufficient clamping.

Six specimens (three warp and three weft) were fabricated for each material. The experiments were conducted using the SANSI-UTM-4000 testing machine.

Figure 2 Uniaxial test specimen and testing machine

2.3 Biphasic specimen design

Samples in both (a) and (b) forms were considered.

(a) is a gas bag fabricated by stitching two sheet-like woven composites, which is ruptured by injecting high-pressure gas to observe failure conditions. The loading force can be determined by the pressure inside the gas bag; (b) is a typical cross-shaped specimen with a slit cut into the loading arm to ensure stress transmission along the direction of the loading arm.

After discussion, the (b) type sample was ultimately selected for optimization.

Figure 3 Proposed two sample configurations

The final double-axis specimen designed is shown in the figure. The fabrication process of this specimen is relatively complex and includes the following five steps: (1) Preliminary selection: Remove the sac material containing significant initial damage such as breakage, spalling, or tearing, and lay the rolled material flat for 48 hours to reduce the warp and weft skew to below 3 mm/m.

(2) Sectioning: Cut the cyst material into sample shapes with an error below 0.5 mm/m.

(3) Adhesion: The outer layer (reinforcement sheet) is bonded to the base layer (test specimen). Since the tensile strength of the adhesive (approximately 1.7 MPa) is significantly lower than that of the capsule material, the effect of cured adhesive on biaxial strength can be disregarded. Additionally, the adhesive exhibits ideal shear stiffness and strength, enabling effective load transfer.

(4) Secondary bonding: The sample is affixed to the EPDM rod to facilitate clamping and enable effective load application.

(5) Cutting slits: On the loading arm, manually cut slits at intervals of 33mm with meticulous care. All slits must be strictly parallel to the loading direction to prevent yarn damage.

Attach the sample to the EPDM rod

Figure 4 Preparation process of biaxial tensile specimens

2.3 Biphasic test equipment

The loading was performed using a self-developed hydraulic servo dual-axis testing machine. The machine provided a maximum load of 30,000 N, which met the load required for specimen failure.

At the same time, a high-speed camera of SVSI-7 type with a resolution of 800 × 600 dpi and a sampling rate of 909fps was used to observe the failure state of the specimen at the fracture moment.

Other equipment: 400W supplementary lighting.

Figure 5 Layout of Biaxial Testing Device

3.Experiment Implementation

Uniaxial tensile test: Apply a preload of 0.5 N/mm and verify the vertical alignment. Subsequently, continue applying a load of 0.1 N/mm per second.

Biaxial stretching: First clamp the EPDM rod, then apply preload, check parallelism, and proceed to formal loading. Maintain the same loading parameters as described above while simultaneously capturing high-speed camera footage.

The temperature was 27±1℃ and the humidity was 57±3%.

4.Results and discussion

4.1 Failure mode 

In the biaxial failure mode, both specimens of Material 1 developed longitudinal cracks, with Specimen 1 exhibiting minor transverse crack propagation. The two specimens of Material 2 showed similar behavior, with longitudinal cracks forming and propagating within the test area. The specimens of Material 3 presented an intriguing scenario: Specimen 1 displayed clearly visible cracks, while Specimen 2 exhibited extensive cracks in both transverse and longitudinal directions. These cracks showed no discernible sequence, indicating simultaneous occurrence.

Meanwhile, all initial cracks in the tests were along the meridional direction, because the strength of the latitudinal direction is usually lower than that of the meridional direction, so the damage tends to expand along the direction of low strength under the 1:1 load ratio.

Figure 6 Failure mode of biaxial specimen captured by high-speed camera

4.2 Load-displacement curve

Overall, the load-displacement curves of the sac material exhibit a typical nonlinear constitutive relationship. During the initial loading phase, the sample's stiffness gradually increases, eventually stabilizing at a constant value as loading progresses. Under uniaxial loading, the longitudinal and transverse directions demonstrate good consistency, whereas significant differences emerge under biaxial loading.

In uniaxial tensile testing, both warp and weft yarns exhibit a brief "low-stiffness zone" where load increases occur very slowly. This phenomenon can be explained microstructurally: under uniaxial loading, the initial slack and spatial curling of warp or weft yarns gradually dissipate, with clamping displacement primarily arising from microstructural changes rather than material stretching. This mechanism explains why low-stiffness occurs during the initial loading phase. Notably, the weft yarns demonstrate more pronounced low-stiffness behavior, likely due to the weaving sequence during processing. When all yarns in the sample are fully loaded and straightened, the load-displacement curve gradually transitions into a linear segment.

The results of biaxial stretching show significant differences from uniaxial stretching. The load-displacement curve lacks a distinct low-stress zone, as the internal yarns are vertically aligned. Consequently, biaxial loading can only partially reduce micro-scale yarn distortion without complete elimination. Due to the interlaced yarn orientation and Poisson's effect, the tangential modulus in the warp and weft directions increases by 17.11 and 13.67 times, respectively, compared to uniaxial stretching. Under a 1:1 loading ratio, the weft's clamping displacement exceeds that of the warp, indicating lower weft strength. Thus, biaxial loading also results in higher warp strength than weft.

Note that the displacement data is collected via sensors on the fixture and does not fully represent the displacement at the sample arm end. Moreover, the biaxial load sample is a bonded multilayer structure, so the load-displacement curve cannot accurately reflect its internal stress-strain state. To obtain more precise data, numerical simulations were conducted.

4.3 Stress Analysis Based on Finite Element Software

The finite element model based on shell element modeling was used to reproduce the strength of the capsule material. The maximum stress of the specimen was generated in the protruding triangular region, which was consistent with the initial damage location in the test. The failure load was well fitted with the test results in Table 2.

Figure 8 Finite Element Model Results

Table 2 Biaxial Strength of Capsule Materials

4.4 Biaxial Strength and Failure Package Curve

The failure envelope in the stress space is drawn according to the failure strength of the double axis with the load ratio of 1:1.

Figure 9 Failure envelope in the first quadrant inferred

5.Summary

（1）A new type of cross-shaped specimen is designed and fabricated to measure the biaxial strength of airship envelope. The specimen consists of a double-layer loading arm and a single-layer central test area. After structural optimization, the biaxial failure occurs in the central test area.

（2）Uniaxial and biaxial tensile tests were conducted. The load-displacement curves revealed a distinct low-stiffness region in uniaxial tests, likely caused by the gradual elimination of initial relaxation and spatial distortion in the warp and weft yarns during the early loading phase. This phenomenon was less pronounced in biaxial tests. Under biaxial stress conditions, both warp and weft yarns exhibited increased tangential modulus, with the warp direction consistently demonstrating higher strength than the weft direction.

（3）The failure modes of the specimens were recorded by high-speed camera, which can be divided into two modes: single crack fracture and simultaneous transverse and longitudinal fracture.

（4）The maximum stress is calculated by the finite element simulation software. It is considered that the biaxial strength is 1.1~1.3 times of the uniaxial strength of the secondary axis under the 1:1 load ratio.

（5）Based on the 1:1 loading ratio, the failure envelope in the stress space is drawn.