Biaxial tensile test
Biaxial tensile test is a tensile testing in which the sample is stretched in two distinct directions. This technique is used to obtain the mechanical characteristics of anisotropic materials, such as composite materials, textiles, and soft biological tissues. There are three main types of biaxial tensile testing:
- Bursting test, based on a circular specimen clamped along the edge and inflated by air or water under pressure until the specimen bursts;
- Cylinder test, based on a hollow cylinder subjected to internal pressure and axial pressure or tension;
- Plane biaxial test which offers the best result because of the independent force introduction in the two main directions.
Scope of the test method
The scope of the test represents one of the most crucial aspects in developing the relative testing protocol. For foils and coated fabrics there are several areas of interest: the initial behaviour, the service behavior, the behavior at break, the long term behaviour (creep) and the dynamic behavior. The material response can be significantly different according to the loading condition considered.
A protocol on the initial behavior aims to investigate the material behaviour of the fabric at the early stages of the structure’s life span during the erection phase. The results represent a fundamental support for the compensation of the panels of fabric in order to refine the erection and pre-tensioning processes.
The service behaviour is another aspect of great interest because it represents the overall material response to load conditions occurring during the entire life span of the structure. The result of this type of test represents a fundamental input data for the software used for structural analysis and the determination of the stress distribution in the structure. The biaxial behaviour at breaking load is an important open issue that has not been investigated thoroughly until now. Previous researches demonstrate the difficulties concerning the rupture of a biaxial sample, it has been noted that generally the maximum biaxial tensile strength is lower than the corresponding ultimate tensile strength obtained by means of a monoaxial test. However, the test can be focused on the resistance of a joint, evaluating the strength of welded (high frequency welding, hot element welding), glued and sewn seams or the resistance of clamping plates and Keder rail joints or looped and laced joints.
Another field of research is the appearance and propagation of tears in the fabric, this issue has been partially investigated  and represents a fundamental data in the determination of the safety factor which should be used for a specific structure. Because tear propagation generally occurs at 25% UTS, the safety factor is generally higher than four. The test is carried out on a sample taken from a dismounted structure or by using conditioned samples of fabric which aim to reproduce the in-situ conditions. The load profile should reproduce the expected overload by pulling the sample until breakage, which should start far from the sample edge and the clamping system. The repetition of the test and different temperatures (generally -20°C and +70°C) offers important information about the joint behaviour at extreme conditions, such as heavy snow fall with temperatures below zero or a blast of wind during a hot summer. This type of test is generally required by designers and manufacturers and those in charge of the evaluation of the structure behaviour and the final test of the structure. Finally, in order to prevent collapses due to ponding and fluttering, the creep behaviour should be carefully considered in the design, choosing anchorages which enable periodical re-tensioning according to the predicted fall in the level of pre-stress. It is based on a monoaxial test but an accurate investigation requires the use of virgin cruciform samples of fabric and the force is applied by means of counter weights. The creep is defined as the “increase in strain with time when a constant force is applied”  and aims to describe the material behaviour when a constant force is applied over a long period of time. This has a considerable effect on the design and realisation of the membrane structure because a progressive increase in the material strain leads to a considerable reduction in the level of pre-stress initially induced in the structure. The sample should be maintained at a constant temperature and for specific applications it may require a proper climatic chamber for investigations at high and low temperatures. There are no complete studies about the dynamic behaviour of coated fabric and foils for structural applications. A dynamic test on coated fabrics can evaluate the response under fast loading and unloading cycles due to blasts of wind or other sources of stress. It should consider a conditioned fabric which reproduces the in-situ conditions and the testing apparatus should be able to apply a high speed load profile which is generally not possible with a common testing rig equipped with electric servomotors. The results of this type of test, despite the absence of research which can support these expectations, can highlight anomalies in the fabric strength and in the tear propagation with consequent adjustments in the safety factor applied.
One of the key aspects is the sample mounting, which should consider the initial gauge length, the correct positioning of the fabric into the clamps and the correct application of the strain transducers in the central area.
The next crucial stage is load application. This issue has been widely investigated but there is no loading path universally adopted by the testing laboratories. It has to be said that the loading cycles mainly depend on the scope of the test and it is unrealistic to consider the possibility of elaborating a single loading path able to fulfil at the same time all the requirements imposed by the investigation of the initial behaviour, the service behaviour, the behaviour at breaking load and long term behaviour. This part of the procedure should provide a valid approach to the establishment of a load profile, describing the effects of the parameters involved, in order to fully investigate the material response according to the required repeatability. Since coated fabrics do not follow an elastic behaviour, once the stress is removed the sample maintains a certain level of permanent strain, a plastic deformation. This behaviour is known as residual strain and is present both in monoaxial and biaxial tests. The main value of residual strain is shown between the first and second load cycle, decreasing to zero after a number of cycles that depends on the material properties, the applied load and the time for which it has been applied. This is due to the creep of the yarns and the coating material and to the internal frictional effects. In order to obtain a realistic description of the material the strain should be measured within a unique load cycle, assuming equal to zero the strain at pre-stress. For this reason the loading cycle considered for the strain measure is generally preceded by identical cycles in a number sufficient to stabilise the sample response. In order to remove the residual strain previous researches considered adequate the application of five identical loading and unloading cycles, the TensiNet design guide consider three or five repetitions to be sufficient, depending on the testing protocol. While the Membrane Structures Association of Japan prescribes the repetition of the cycles three times, but only for the 1:1 load ratio which separates the others. This offers several advantages in the comparison of readings carried out within the same test and with other tests.
For the investigation of the typical behaviour of an in-situ fabric, it is proposed a test protocol divided into: pre-stress, conditioning and a final radial test regime. The prestress was considered fundamental in order to reproduce the typical stress state of a membrane structure after the initial pre-tensioning is concluded, it is held for a certain amount of hours and generally set at 1.3% UTS for PVC/polyester fabric and 2.5% UTS for PTFE/glass fibre fabric.
A second issue which should be taken into account is the effect of the load history on the response of the fabric. This may have important consequences for the structure of the load profile, which may turn out be inadequate for the investigation of in-situ conditions of fabrics which have not yet undergone the maximum stress state applied during conditioning.
Thirdly, it is crucial to determine the possible effects of the recent load history on the fabric response, in particular whether the load sequence followed by approaching a particular stress state result in a different level of strain. The effects due to the level of minimum pre-stress, load history and the recent load history should be carefully considered when developing the testing load regime. The aim is to assure the repeatability of the test and that the data obtained are in accordance with the scope of the test.
- Reinhardt, H.W. 1976, "On the biaxial testing and strength of coated fabrics", Experimental Mechanics, vol. 16, no. 2, pp. 71-74;
- Happold, E. 1987, "Design and construction of the Diplomatic Club, Riyadh", Structural Engineer, vol. 65, no. 10, pp. 377-382.
- EN ISO 899−1, 2003
- Minami, H. 2006, "A Multi-Step Linear Approximation Method for Nonlinear Analysis of Stress and Deformation of Coated Plain-Weave Fabric", Journal of Textile Machinery Society of Japan, vol. 52, no. 5, pp. 189-195
- Foster, B. & Mollaert, M. 2004, European design guide for tensile surface structures, Tensinet, Brussels
- MSAJ/M-02 Testing method for elastic constants of membrane materials 1995, Standard of Membrane Structures Association of Japan edn, Tokyo, Japan
- Seidel, M. 2009, Tensile Surface Structures A Practical Guide to Cable and Membrane Construction. Materials, Design, Assembly and Erection, Wiley-VCH, Weinheim