# Experimental Investigation of the Failure Rate Dependency of Composite Materials Using Off-Axis Tensile Tests

Thomas Fourest, Julien Berthe

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Thomas Fourest, Julien Berthe. Experimental Investigation of the Failure Rate Dependency of Composite Materials Using Off-Axis Tensile Tests. 2020 SEM Annual Conference & Exposition on Experimental and Applied Mechanics, Sep 2020, Orlando, United States. pp.25-27, 10.1007/978-3-030-59947-8_5. hal-03642506

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# Experimental Investigation of the Failure Rate Dependency of Composite Materials Using Off-Axis Tensile Tests

Thomas Fourest and Julien Berthe

**Abstract** The present study investigates the mechanical response of T700/M21 Carbon Fiber Reinforced Polymers submit-
ted to coupled shear and transverse tension at intermediate strain-rates ranging from 0.001 to 15 s⁻¹. The experimental inves-
tigation is performed using transverse and oblique tabs off-axis tension specimens with a low aspect ratio. The axial
stress-strain curves are successfully simulated using Finite Elements simulations with a viscoelastic model. The numerical
simulations enable the calculation of corrections to take into account the effect of end constraints for such low aspect ratio
specimens. Finally, an increase of the material strength with the strain-rate is observed.

**Keywords** Off-axis tensile test · Unidirectional composite · Failure criteria · Viscoelasticity

**5.1 Introduction**

Reliable predictions of crash and impact scenarios rely on the knowledge of the material behavior at high solicitation speeds. In the case of laminated composites, the physical justification of the different rate effects introduced in these models is clas- sically based on compressive high strain-rate tests on off-axis specimens. Off-axis specimens permit to induce a coupling between tension and shear in the specimen by using a single actuator and simple specimens which explain the interest of the different authors for the dynamic testing.

**5.2 Off-Axis Tension Tensile Tests**

The advantage of off-axis specimens is the apparent simplicity of the test; however, their drawback is that they induced an unwanted transverse load to the testing device. In addition to increasing the complexity of the analysis, it could prevent the use of such specimens on servo-hydraulic jacks since they are usually not built to sustain high transverse loads. One way of dealing with this drawback is the use of long specimens and of corrective factors. However, such long specimens are not suitable for high strain-rate tests, since it would lead to smaller strain-rates for the same actuator speed and it would amplify resonance of the load chain and pollute the load signal recording. It would also lead to larger times to reach mechanical equilibrium. The investigated solution in this study is the use of oblique tabs on such specimens (Fig. 5.1). Several studies [1, 2] have shown that the use of oblique tabs results in more homogeneous stress fields. In these specimens, the tab angle $\phi$ is determined to follow the iso-displacement line induced by the testing of a specimen with fibers oriented with an angle $\theta$ from the specimen length. Table 5.1 summarizes the numerical values used for both angles in this study.

<footnote>T. Fourest (✉) · J. Berthe
DMAS, ONERA, Lille, France
e-mail: thomas.fourest@onera.fr; julien.berthe@onera.fr</footnote>
<figure><img src="image_2.png" /><figcaption>**Table 5.1** Correspondence between the off-axis angle $\theta$ and the oblique tab angle $\phi$ for T700/M21</figcaption></figure>

<table><caption>**Fig. 5.2** Comparison between axial stress-strain curves recorded in the experiments and the one computed with finite elements simulations using a viscoelastic model for tests at 5 mm/min, 500 mm/min and 1 m/s</caption><tr><td>θ</td><td>15°</td><td>30°</td><td>45°</td><td>60°</td><td>75°</td></tr><tr><td>φ</td><td>23.5°</td><td>37°</td><td>56°</td><td>74°</td><td>85°</td></tr></table>

<figure><img src="image_3.png" /></figure>

## 5.3 Finite Elements Simulations of the Tests

Since in this study the specimen aspect ratio (length/width) is small, finite elements simulations are used to determine the local stress state in off-axis specimens. Linear elastic FE simulations do not reproduce the experimental observations. So the introduction of the end-constrain is not sufficient to explain this phenomenon. Since it is known that CFRP is time-dependent material and there is no clear damage mechanism to consider in UD composites, a viscoelastic model is considered. The considered model is a viscoelastic spectral model taken from Maire [3]. The parameters of the model have been identified by performing FE model updating using *Z-opt* which is part of the *Z-set* software [4]. Figure 5.2 compares the finite elements simulations with the experimental results for 30° off-axis tests.

The agreement between the finite elements load-based axial stress and the experimental one has been found quite reasonable. The increase of the apparent modulus with the strain-rate observed experimentally is well reproduced by the model. Globally the nonlinear behavior is also reasonably well predicted. Then these finite elements simulations have been used to determine the local stress state at the center of the specimen. Figure 5.3 illustrates the failure stresses determined for all angles and strain-rates tested.

## 5.4 Conclusion

In the present study, off-axis and transverse tests have been performed on T700/M21 CFRP material. It has been shown that finite elements simulations using spectral viscoelastic model permit to describe the axial stress-strain curves at all tested strain-rates. It has been identified using all tests, with a fairly good agreement.
<figure><img src="image_4.png" /><figcaption>**Fig. 5.3** T700/M21 tensile strength corrected using Finite Elements simulations presented in shear stress versus transverse stress graph (uncorrected values in transparency)</figcaption></figure>

Using this model, corrections of the stress field have been computed to take into account the effect of the end constraint. The effect of the correction is maximal for the 15° off-axis test and it decreases while the off-axis angle increase becoming negligible for the 75° and 90° tests. Globally an increase in the axial failure stress with the strain-rate has been observed for all specimen orientations.

## References

1. Sun, C.T., Chung, I.: An oblique end-tab design for testing off-axis composite specimens. Composites. **24**(8), 619–623 (1993)

2. Pierron, F., Vautrin, A.: The 10 off-axis tensile test: a critical approach. Compos. Sci. Technol. **56**(4), 483–488 (1996)

3. Maire, J.-F.: Etudes expérimentales et théoriques du comportement de matériaux composites en contraintes planes. Thèse de doctorat. Doctorate Thesis of Franche-Comté University, Besançon (1992)

4. Missoum-Benziane, D., Chiaruttini, V., Garaud, J.-D., Feyel, F., Foerch, R., Osipov, N., Quilici, S., Rannou, J., Roos, A., Ryckelynck, D.: Z-set/ZeBuLoN: une suite logicielle pour la mécanique des matériaux et le calcul de structures. 10e colloque national en calcul des structures (2011)