Coordinateurs du projet
Context
Numerous studies attest to the hydrophilic nature of the organic matrices used to manufacture composite materials. It is therefore crucial to study the process of moisture diffusion within these materials, as it leads to both a decline in mechanical properties and significant internal mechanical stresses. These high internal stresses can then promote damage to the material, manifesting as cracking. In addition, the complex physics of the problem is subject to significant uncertainties that must be taken into account. The project aims to combine innovative and powerful numerical approaches to study the coupling between water diffusion and damage, all within a random framework.
Scientific breakthroughs and innovation
The diffusion of water in composites has already been extensively studied by numerous research teams, who agree that it has a detrimental impact on the material. However, although experimental results exist, there are no effective numerical methods associated with relevant models that can predict the behavior of the structure in service. This project will enable progress to be made in the development of these models and methods. In addition, all of the proposed tools will be extended to the random framework in order to take into account uncertainties about physical phenomena or the geometry and propagation path of cracks. Such approaches will make it possible to characterize, in probabilistic terms, in the form of probability laws or statistical information, quantities of crucial interest in the design of MRE structures. They will also provide a better understanding of the coupling between water diffusion and composite wear.
Expected technical and economic impact
EMR structures are now largely composed of organic matrix composite materials with excellent mechanical properties but which can be damaged by various marine environmental factors. The aim of the project is to develop digital tools for engineers to study the impact of water diffusion on the damage to these materials. These tools will optimize the lifespan of MRE structures and reduce the cost of the energy produced.
Demonstrator
Development of digital tools for analyzing damage to composite materials used in MRE structures.
Results
Experimental campaign on damage to EMR composite materials in wet conditions:
The aim of the experimental campaign was to study the water behavior of glass/epoxy composite samples at different levels of damage. To do this, a protocol was put in place and a chamber dedicated to these samples was created (see Figure 1-left). Among the results obtained, we found that the level of damage modified the water behavior (diffusion rate and maximum absorption capacity), as shown in Figure 1-right. The diffusion coefficients and maximum absorption capacities were identified using a search algorithm developed in Matlab©.
Figure 1: (left) CAD model of the chamber developed for aging and (right) sorption curves obtained for samples with different levels of damage.
The study showed that these parameters increased with the level of damage: the presence of cracks affects the diffusion coefficient, while the increase in maximum absorption capacity is more likely due to the presence of porosity (see Figure 2).
Figure 2: (left) SEM observation with crack and (right) SEM observation of porosity on glass/epoxy samples from the project.
Deterministic and stochastic hygroscopic model taking cracks into account:
The aim of this initial work was to develop a hygroscopic model that takes into account so-called “open” cracks through which water can diffuse. Solving this type of problem required the implementation of dedicated numerical methods. In order to overcome meshing problems in particular, the extended finite element method (X-FEM) was chosen and adapted to the specific characteristics of the problem using a penalty technique and enrichment functions to impose a water content along the crack and capture the irregularities of the solution across the crack front. Figure 1 shows illustrations of the water content fields of a glass/epoxy composite during the transient regime at the same instant for a case without a crack and a case with a crack. It can be seen that water diffusion within the material is significantly more advanced in the case with a crack. Figure 2 shows a comparison of sorption kinetics (change in overall water content over time) for these two cases. We can see that diffusion is significantly faster in the case with a crack.
Figure 3: Comparison of water content fields [%H20] for a glass epoxy composite without a crack (left) and with a crack (right).
Figure 4: Sorption curves obtained by simulation for an undamaged case (without cracks) and a damaged case (with cracks).
The problem was then extended to the stochastic framework through probabilistic modeling in which variability is represented by a finite set of random variables. The propagation of uncertainties, which consists of determining the uncertainties at the model output based on the input uncertainties, is performed using stochastic spectral approaches that involve searching for the solution in functional form. This type of method is effective when the number of random input variables is relatively low. The proposed approach has been specifically developed to adapt to the framework of these approaches. Examples of results are shown in Figures 3 and 4. In this problem, the crack length and maximum absorption capacity are represented using random variables. The randomness in the crack length was chosen to be significant (coefficient of variation of 45%), as is often observed, while that in the maximum absorption capacity is significantly lower (coefficient of variation of 5%). Figure 3 shows the random sorption curve for the problem using its mean and a 95% confidence interval. This same figure illustrates the response surface of this random process at a given moment when dispersion is significant.
Figure 5: Random sorption curve (left) and response surface for a given time (right).
It can be seen that variability in crack length has a much greater impact than variability in maximum absorption capacity. Figure 4 shows a post-processing of the stochastic solution leading to a rapid evaluation of water content fields for different random realizations of crack length and maximum absorption capacity. As before, we see that the larger the crack, the more advanced the water diffusion.
Figure 6: Examples of local water content fields for two crack lengths obtained by post-processing the stochastic solution.
The proposed approach also made it possible to determine the evolution of the effective diffusion coefficient as a function of crack length by considering the study domain as a representative elementary volume. Two cases were studied: the case of epoxy resin alone in the presence of a crack and the case of a glass/epoxy composite in the presence of a crack. Figure 5 illustrates the results for these two cases. A significant increase in this effective diffusion coefficient can be observed in both cases. This type of result can be used in simulations at equivalent homogeneous scales.
Figure 5: Evolution of the effective diffusion coefficient as a function of the cracking coefficient (analogous to crack density) for epoxy resin alone (left) and glass/epoxy composite (right).
Deterministic and stochastic hygroelastic model taking cracks into account:
In this section, the objective was to take into account the hygroscopic deformation resulting from water diffusion in the elastic calculation. To do this, the X-FEM method was adapted to take into account the results of the hygroscopic calculation illustrated in the previous section. The following illustrations are from a stochastic study on the same glass/epoxy composite as in the previous section. Figure 6 shows the evolution of the maximum random vertical stress and its response surface as a function of crack length and maximum absorption capacity. Significant dispersion can be observed in the results, mainly due to the randomness of the crack length.
Figure 6: Evolution of the maximum random vertical stress (left) and response surface for a given time (right).
Figure 7: Evolution of random crack opening (left) and response surface at a given time (right).
Deterministic and stochastic hygroelastic model with crack propagation:
In this last section, we have improved the proposed model to take into account crack propagation during aging. A deterministic study was proposed to compare a hygroelastic calculation with and without crack propagation. Figure 8 shows the evolution of the water content field as a function of crack propagation resulting from water diffusion within the glass/epoxy composite material.
Figure 8: Evolution of the water content field in parallel with crack propagation
Figure 9 presents comparisons between a calculation without crack propagation and one with crack propagation. Firstly, we can see that the overall water content is greatly affected by crack propagation, with a higher diffusion rate and saturation reached earlier than in the case without crack propagation. In addition, Figure 69 (right) shows a much larger and faster crack opening in the case with crack propagation.
Figure 9: Comparison between a case without crack propagation and one with crack propagation: (left) comparison of the evolution of the overall water content and (right) evolution of the maximum crack opening.
Finally, we proposed a stochastic study of the behavior of the parameters driving crack propagation: the crack propagation angle and the increase in crack length in particular. Figures 10 and 11 present some stochastic results, in the form of characteristic processes and response surfaces, for these two quantities, considering the crack length and maximum absorption capacity as random variables.
Figure 10: Evolution of the crack propagation angle θC: (left) stochastic process with mean and confidence interval and (right) characteristic response surface as a function of crack length Lcrack and maximum absorption capacity C
Figure 11: evolution of the increase in crack length Δa: (left) stochastic process with mean and confidence interval and (right) characteristic response surface as a function of crack length Lcrack and maximum absorption capacity C∞.
In each of these last two figures, we can observe significant variability, as indicated by the very wide confidence intervals. However, a slight distinction should be noted: as shown by the response surfaces, this variability stems almost exclusively from the randomness of the crack length for the propagation angle, whereas the randomness of the maximum absorption capacity plays a significant role in the variability of the increase in crack length.