Multi-factorial models of a carbon fibre/epoxy composite subjected to accelerated environmental ageing
Introduction
Composite materials are ultra-light structural materials, massively introduced in the recent years in aeronautical applications. In spite of their exceptional mechanical performances, they are vulnerable to aggressive natural ageing factors such as rough temperature changes, chemical corrosion, moisture and solar radiation. It is widely accepted that special caution needs to be observed when using these materials to manufacture mechanically critical airframe components inside a full-scale structure. Although an online health monitoring is strongly suggested by authors [1], [2], [3] to verify the state of a composite structure, a model could be useful to estimate the degradation extent when subjected to some frequently confronted weathering agents. Carbon fibre reinforced plastics (CFRP) are currently the most used composites in the aeronautical industry (for example in the Boeing 787 and the currently in development Airbus 350 XWB).
There is currently in scientific literature some lack of understanding of polymer-based composite materials behaviour to weathering. Research has been mainly centred about the effects of mechanical fatigue [4] and chemical corrosion [5], [6]. A quantitative model of the material ageing under other usual natural agents such as heat, moisture or solar radiation, when applied cyclically on a sample, has not yet been established. This is frequently due to the elevated number of factors that can potentially affect the life cycle of polymers. Considering the case of CFRP [7], [8], [9], [10], the polymer-based matrix and the fibre/polymer interface are the most vulnerable components of the composite. Specialised researchers in the field of composite ageing have described qualitatively the failure mechanisms [6], [9], [10] or presented empirical quantitative evidence of changes in constitutive properties of polymers [7], [8], [11], [12] when subjected to natural and/or artificial weathering. In more extensive treatises by Carraher [13] and Brinson [14], some chemical mechanisms that explain the degradation are reviewed. These changes lead to a progressive macroscopic degradation of the elastic properties of the composite, which could turn out to be critical if the proper safety precautions are not considered.
A method to evaluate systematically the ageing of polymer-based composites and establish a mathematical model is proposed, which can be interpreted to understand the contributions of isolated or combined factors on the ageing process of aerospace composite. It will be verified if it is possible to estimate quantitatively the extent of the ageing by estimating the parameters of the mathematical model, based only on theoretical assumptions and basic information about the subject material. According to the specialised literature in the design of experiments theory [15], [16], a multi-factorial model is useful to compare quantitatively the influence of the existent ageing factors on the composite panels. The elastic properties, which are the object of this study, are measured by indirect methods, using modal testing to obtain the natural frequencies of the working specimens [17], which in turn are processed by a mixed numerical–experimental identification algorithm to obtain the experimental elastic properties [18]. Physically, the modal testing is done using mainly integrated piezoelectric sensors and accelerometers, which can be inscribed in a global structural health monitoring (SHM) method, which in summary allows surveying the state of a structure using networks of dynamic sensors. The choice of a dynamic measurement method is motivated by its flexibility, robustness, readiness and non-destructiveness when compared to more classic static methods (tensile tests, bending tests, ultrasound), qualities that are appreciated in aeronautical applications.
The mathematical pattern of the aforementioned model can be hinted by visual inspection of the experimental pre-modelling plots after the identification of the constitutive properties. The notion of Prony series and asymptotically exponential increase or decrease are inspired from previous works on composite testing [11], [13], [14]. A deeper statistical analysis shows a correlation between the absorbed moisture mass and the loss of stiffness. This statement leads to the replacement of the number of cycles by the water concentration as the state variable in the model. The usefulness of this reasoning is evident in the final lines of this paper: it leads to a generalised model for mechanical parts with more complex shapes, and contributes to the future research on CFRP with an early estimation of the extent of their ageing using only some basic information about the material’s initial properties.
Section snippets
Accelerated ageing protocol due to environmental conditions
In order to reveal any changes in stiffness due to exposition to aggressive ageing factors, progressively demanding experimental campaigns took place. The ageing factors included temperature, relative humidity (RH) and ultraviolet (UV) radiation, since they are frequently met by full-scale CFRP aeronautical structures during a life cycle. The ageing protocols were inspired from previous works [7], [8], [9], [10] as well as in ASTM standard guidelines for cyclic ageing protocols [19], for the
CFRP specimens
The material for experimentation is the Carbon-PrePreg PR-UD CST 125/300 FT109, supplied by Suter-Kunstoffe© AG (Switzerland). It is originally a scroll of unidirectional (UD) carbon fibre tissue (Torayca© T700S carbon fibre), pre-impregnated in unhardened epoxy polymer (PREDO© FT109) with an areal weight of 125 g/m2 (60% of fibre volume fraction). The nominal after-curing elastic properties of this material are given in Table 2. A total of six different 30 × 30 cm2 surface plates were manufactured
Non-destructive test: modal analysis
There is a wide range of solutions to measure directly or indirectly the elastic properties of a structure. In the interest of SHM, it is imperative to restrict the choice to non-destructive, fast, robust techniques. Modal analysis is a simple but powerful tool to obtain information about the state of a structure, based on the measurement of the natural frequencies and the corresponding modes. Among the available technologies, it was found that piezoelectric transducers provide remarkable
Introduction to experimental results
For the sake of uniformity and clarity, the changes in the constitutive properties of the samples are tracked with respect to their initial value:
The 0 index denotes the nominal initial values of the elastic properties, summarised in Table 2. At first glance, the graphs suggest an exponential asymptotic behaviour (Fig. 5). An increase in the mass can be observed in the “humid” protocols (D-, EF1-, EF2- and J-series). As stated before, in a UD configuration,
Equivalent moisture absorption in cyclic ageing protocols
Unfortunately, mathematical models based on statistical treatment remain uninteresting from the experimental point of view. Indeed, they cannot be directly applied to more general cases since the geometry plays a determining role in several of the ageing mechanisms (moisture absorption, heat diffusion, penetration depth of UV radiation, etc.).
To remove this dependency, it is proposed to replace time by a state variable, such as moisture concentration. To do so, it is necessary to establish a
Linear regression between mass and elastic properties
In Fig. 12, a pattern of correlation between the mass variation and the elastic properties can be observed. Depending on the relative humidity, the evolution of the mass depends essentially on the existence/absence of moisture in the ageing environment. In the graphs, the ageing track of all of the 8 series can be distinguished. More particularly, it shows that the pattern of the stiffness evolution over the time is similar between ageing protocols that exhibit the same relative humidity
A predicting method for composite ageing
From a scientific point of view, the multi-factorial model presented in this paper can prove to be useful in two ways: for characterisation and design of experiments, for the experimenter to follow a similar method to characterise other composite materials using different combinations of fibre/resin, and for prediction, using this model to estimate the ageing of a composite structure with variable geometries, since the effect is known.
For characterisation/design of experiments: Based on all
Conclusions
The hereby presented macroscopic model, based on the Prony series, proposed a characterisation method for a set of simultaneous physical/chemical phenomena that intervene on the CFRP ageing. The parameters of that model, fitted on the basis of the NLLS criterium, were determined from experimental results. However, the application of these results was restricted to samples with the same geometrical dimensions and proportions.
Thus, the main contribution of this document is not only to suggest the
Acknowledgements
The authors would like to acknowledge the partial financial support from the Swiss National Science Foundation, Grant No. 200020-143968/1.
References (31)
Polymer ageing: physics, chemistry or engineering? Time to reflect
CR Chim
(2006)- et al.
Accelerated environmental ageing study of polyester/glass fiber reinforced composites (GFRPCs)
Compos Part B – Eng
(2008) - et al.
Investigation of failure mechanisms in aged aerospace composites
Eng Fail Anal
(2004) - et al.
Investigation of moisture diffusion in epoxy system: experiments and molecular dynamics simulations
Chem Phys Lett
(2005) - et al.
Inverse method based on modal analysis for characterizing the constitutive properties of thick composite plates
Comput Struct
(2007) Structural health monitoring with piezoelectric wafer active sensors
(2008)- Sohn H, Farrar C, Hemez F, Shunk D, Stinemates D, Nadler B, et al. A review of structural health monitoring literature:...
- et al.
Summary review of wireless sensors and sensor networks for structural health monitoring
Shock Vib Digest
(2006) - et al.
Modeling mechanical fatigue of UD composite: multiple fiber breaks and debond growth
IOP C Ser Mater Sci Eng
(2009) - et al.
Long-term durability of fiber-reinforced polymer matrix composite materials for infrastructure applications: a review
J Advan Mater
(1998)