Studying the effect of polymethyl methacrylate polymer opticals fibers (POFs) on the performance of composite materials based on the polyether ether ketone (PEEK) polymer matrix.

More recently, various techniques have been implemented for the sensors manufacturing purpose, such as fiber Bragg gratings fibers (FBG) that allows variable core refractive index suitable for a large scale of measurements types, fiber optic evanescent waves (FOEW) for water parameters measurement, microstructured and crystal photonic optical fibers, polymers optical fiber (POFs), and so on. In this perspective, the objective of this work is to study the reliability and the origin of the resistance of each fiber-matrix interface of the composite materials PMMA/PEEK, Topas/PEEK, and Topas-Zeonex/PEEK. The genetic simulation is based on the probabilistic approach of Weibull to calculate the damage at the interface by crossing the two damages of the matrix and the fiber respectively. The results show that the PMMA/PEEK composite is the most resistant to the mechanical stresses applied compared to those Topas/PEEK and Topas-Zeonex/PEEK; these results were confirmed by the level of damage to the interface observed for the studied materials. The performed calculations are in good agreement with the analytical results of Cox, where he demonstrated that Young's modulus of fibers have an important influence on the shear strength of the fiber-matrix interface of composite materials. Based on the obtained results, the present study gives the opportunity for the proposed materials (PMMA/PEEK and Zeonex/PEEK) to be as potential candidates for the smart digital applications and telecoms aims. © Qatar University and Springer Nature Switzerland AG 2022.

Introduction

Today, smart digital applications witnesses an enormous progress within a wide range of sensitive and critical domains [1-3]. This is closely related to the rapid evolving of smart sensing technology, especially in the last decade [4, 5]. These technologies are mainly based on smart sensors where the purpose is to gather the monitored parameters from a targeted environment [6], such as temperature, humidity, pressure, velocity, and acceleration [7-12]. Due to their high precision measurements, affordable costs, and easy installation aspect, sensing devices play more and more vital role across various industrial fields and today life, we can cite vehicles automation [13], smart cities [14], power and solar stations [15], oil and gas plants [16], healthcare [17], biomedical devices [18], smart education [19], and other various digital applications [20]. Among various settled technologies, the use of optical fibers remains an attractive solution and a key enable technology to manufacture low cost and high precision smart sensors to the aim of a wide range of applications [21-25]. Recent researches highlights the features offered by optical fibers for sensors production, even for vital sectors as COVID-19, cancer detection, and heart parameters measurement for cardiovascular diseases [26-28]. This is mainly due to their lower young modulus for different constraints that allows better strain ad sensitive performances, especially for sensing applications [29]. Therefore, different techniques have been implemented to produce various types of sensors, such as fiber Bragg gratings fibers (FBG) that allows a variable core refractive index suitable for a large scale of measurements types [30-33], Fiber optic evanescent waves (FOEW) for water parameters measurement [34, 35], microstructured optical fibers [36, 37], crystal photonic optical fibers [38-40], and polymers optical fibers (POFs) [41, 42]. Our work is focused on POFs essentially based on polymers. Actually, POFs present the key interest of various new researches, since they have more advantages in tensile and strain strength, flexibility, and affordable hazardous installation profitability [43, 44]. Instead of SOF (silica optical fibers), that are mainly oriented to the telecom domain, for both backbone and access networks, due to their transmission capability of high capacity streams with minimum attenuation losses and dispersion [45-47], POFs, and since their appearance in 1960s, have known a large scale evolution, where they have been categorized in different types regarding their application domains and characteristics [48]. Step index POFs (SI-POFs) have been widely used for video surveillance and transport automation [49, 50], where graded index POFs (GI-POFs) with an attenuation loss about 10 dB/km around the infrared wavelength is suitable for Giga-Ethernet Local Area Networks and Data centers [51]. In the literature, various recent researches have studied the effect of implementing naocomposites for various applications, such as zinc oxyde nanoparticles blended with CS/PVA for antimicrobial packaging purpose [52], polyanyline/sodium alginate-doped TiO2, Ag/TiO2-doped naoparticles with Cs/PEO for food packaging applications [53, 54], and SWCNTs/TiO2 nanostructure blended with CMC/PEO for semiconductor industry [55]. On the other hand, polymers has paid a special attention, especially for the optical fibers purpose, as PMMA [56-58], TOPAS [59], ZEONEX [60], PC [61], CYTOP [62, 63], and other polymers [64, 65]. Therefore, we are focusing in our present work to study the effect on associating fiber optics polymers with PEEK (polyether ether ketone) composite materials to propose improved materials in terms of mechanical and physical properties for the smart digital applications and telecoms aims. Recent studies have paid a special attention to study the PEEK properties as a resin matrix. Authors in [66] have shown attractive results to improve the mechanical properties between the adhesion of the carbon fibers (CF) and the PEEK, by adding the sulfonated-polyether sulfone (s-PSF) as a sizing agent to coat the fiber carbon. In [67], authors presented compared the aging properties between the PEEK and PI films, where the elastic modulus has been measured using the DMA at 85 °C. The results have shown an efficiency of the physical aging for PI at 300 °C and PEEK at 130 °C. In [68], authors investigated the effect of two different continuous carbon fiber reinforced by the PEEK prepreg tapes (CFF/PEEKPT), where they depicted an increase in the tensile strength with the increase of the carbon fiber content. Moreover, the crystallization and melting temperature pf he CCF/PEEKPT are moved to lower temperatures while adding the fiber content. Authors in [69] presented a mixture between the PEEK and various metal oxide additives into zinc oxide (ZnO) to produce varistors via cold sintering process, where gained results depicted a high improvements in terms of the electrical properties compared to pure oxide zinc, and a decrease of the elastic module by adding the PEEK. A recent study is presented in [70], where authors illustrate the sensitivity in terms of mechanical properties of four composites PLA, ABS, PEEK, and PETG for the FDM (fused deposition modelling) process using an analysis of variance. In the same context, authors in [71] have studied the mechanical properties of CF/PEEK and GF/PEEK for the FMD-3D purpose. In [72], authors highlighted the effect of adding the PEEK composite to the epoxy to form a PEEK/epoxy resin system, and the curing kinetics was evaluated under dynamical conditions, where results show an increase on the flexural, compression, and tensile properties compared to the pure resin composite. Other obtained results in [73] stipulate that the mechanical properties of 3D-printed composites PEEK, PMMA, PLA, and PETG are highly dependent to the temperature change of the human body. Moreover, PVDF and PP show a significant decrease when the temperature increases. Results of this study are oriented to the biomedical applications using polymer-enabled devices.

To our knowledge, no published research reports on the study of the fiber-matrix interface shear damage of composite materials based on Polyether ether ketone (PEEK) and Topas, PMMA, and Topas-Zeonex polymer optical fibers (POFs) for potential telecoms applications.

Our objective is to offer experimenters composite materials that they have the best mechanical properties among the materials that we have studied, namely PMMA/PEEK, Topas/PEEK, and Topas-Zonex/PEEK.

Methods and models

Weibull’s law

Weibull [74] has demonstrated that the average breaking stress decreases when the volume of the plasticized zone increases: plasticized zone, because the ruptures are triggered by a plastic deformation, and therefore they do not appear outside this zone. However, the larger this plasticized zone, the greater the probability of encountering a critical element for cleavage [75]. The quantitative treatment of the statistical distribution of the cleavage stresses is carried out by considering that this distribution follows the Weibull law (established in 1939 by W. Weibull in Germany) [74, 75]. This stems from the theory of the weakest link: the part that breaks is considered to be made up of more or less fragile elements that are perfectly independent of each other; the breakage of the whole occurs when the most fragile yields (this is the behavior of a chain made up of links). Weibull’s law makes intervene three parameters which depend on the material: an average breaking stress, a stress threshold, often considered as null, and the exponent of Weibull which characterizes the extent of the distribution [76].

For composite materials, Weibull presented two Eqs. 1 and 2 relating to fiber and matrix failure respectively [77].

With:

: applied stress;

: matrix volume;

Weibull parameters.

Initial volume of the matrix.

With:

: the maximum stress applied to the fiber;

: the initial stress applied to the fiber;

: Weibull parameters;

π*a2;

: the length of the fiber at equilibrium.

Interface fiber-matrix shear damage

The interface is a fairly critical area which plays a very important role in the mechanical behavior of the composite.The interface has different properties from those of the constituents (fiber and matrix), in particular with regard to the mechanical properties. However, it plays a very important role in the transfer of loads between the matrix and the fiber. The quality of the interface therefore conditions the final performance of composites [77, 78]. For this reason, the mechanical characterization of this strategic area is essential. The characterization of the interface consists in determining its mechanical properties as a function of the materials used fiber and matrix and possibly, as a function of the modifications (treatment) which they undergo [79]. The interface’s shear strength largely influences the final properties of the composite. Indeed, one of the modes of damage in composites is rupture at the interface. The best interface depends not only on the properties of the components but also on its formation.

Chaboche considers a damaged solid in which a finite volume element of a sufficiently large notch with respect to heterogeneities is defined as follows [79]:

S: representative elementary volume area identified by its norm

Se: the effective resistance zone

Si : damage area

The mechanical measurement of the local damage compared to the direction

is then given by:

From where

If D = 0: the material is in undamaged state;

If D = 1: the volume element is broken into two parts according to the normal plane ;

If 0 < D < 1: D characterizes the defined state of damage.

Interface shear analytical model of Cox

For a representative elementary volume, many analytical models have been proposed. Cox model [80] gives the shape of the shear stress along the length of the fiber, expressed by the formula in (5): the interface shear stress (IFSS-interfacial shear strength) can be expressed as follows (see Fig. 1 [80]:

Fig. 1

Representative elemental volume (R.E.V.) [80]

With:

(): shear modulus of the matrix;

(): Young’s modulus of the fiber;

(): deformation;

(a): radius of the fiber;

(): distance between fibers;

(): shear stress of the interface;

(): the distance between fiber and the matrix.

Materials used

Polyether ether ketone (PEEK) has high mechanical properties which, due to its thermostable nature, are preserved over a wide temperature range. This makes PEEK an ideal matrix for a structurally applied composite. In addition, PEEK can be obtained in semi-crystalline form or in amorphous form depending on its thermal history, offering a potential worthy of interest for its implementation. PEEK is a copolymer, the order of appearance of the monomers in the macromolecular chain may differ but the ratio of the number of ether/ketone units will always remain equal to 2 [81]. For crystallization at low temperature, the impact on the microstructure is manifested by smaller spherolites and thinner lamellae (Fig. 2). By the size of the spherulites smaller, the amorphous phase is more constrained.

Fig. 2

Micrograph of crystallized PEEK a from the molten state and b from the amorphous state [81, 82]

The mechanical properties of PEEK have the advantage of being similar to those encountered on thermosetting polymers, such as epoxies, while retaining a resilient and ductile character typical of thermoplastic polymers. With its glass transition temperature of 143 °C, its mechanical properties are preserved over a wide range of temperatures [82]. Even after exceeding the Tg, its properties remain high up to 250 °C (see Table 1).

Table 1

Mechanical properties of Victrex Grade 450G PEEK at 23 °C

Elongation at break in tension (%)	Tensile strength (MPa)	Young’s modulus in tension (GPa)	Simple shear modulus (GPa)	Poisson’s ratio	References
45%	100	3.7	1.3	0.4	[81, 82]

The different POF fibers, namely PMMA, Topas, Zeonex, and PC, were obtained by dynamic mechanical analysis (DMA) of mPOFs made from the aforementioned materials. DMA is also performed on a step index single-mode POF with Topas core and Zeonex sheath made by Leal et al. [83]. DMA involves the application of an oscillatory load with a predefined frequency and stress to the polymer samples. The tests presented by the study conducted by Leal et al. are carried out with different strains, frequencies, temperatures, and relative humidity to obtain a broader understanding of the Young’s modulus variation of each POF with respect to these parameters.

In this study, we have used the values of Young’s modulus of Topas, PMMA, and Topas-Zeonex fibers found by Leal et al. in their experimental work [83, 84]. The values are mentioned in Fig. 3 and Table 2.

Fig. 3

Stress–strain cycles and Young’s modulus for the PMMA (blue), Topas (red), Topas-Zeonex (black), Zeonex (purple), and polycarbonate (green) POF [83]

Table 2

Different values of the Young’s modulus found by Leal et al. [83]

Materials	Young’s modulus(GPa)
PMMA	4.16 ± 0.42
TOPAS	3.43 ± 0.43
TOPAS-ZEONEX	2.54 ± 0.21

Results and discussion

The results of this study were obtained by a genetic simulation based on the damage of the fiber (Eq. 1) and the matrix (Eq. 2) determined by the probabilistic law of Weibull. The interface damage was calculated by the genetic operator crossing the two aforementioned damages, using a mutation probability of 0.29. An initial population of 3200 individuals was randomly generated. The genes of the chromosomes represent the variables defined by the analytical shear interface model of the Cox: Young’s modulus of the fibers, shear modulus of the matrix, fibers radius, and fibers length. Individuals found are ranked and positioned to get the best out of them; these genetic variables are inserted in the first line, and during the construction of a new generation, the process is repeated until convergence (Max = 1600) [85-91].

Calculations were performed on the three types of composite materials PMMA/PEEK, Topas/PEEK, and Topas-Zeonex/PEEK. The resistance of aforesaid studied materials are compared and examined under the effect of different values of the applied tensile stress (σ = 1600 N/m2, 1750 N/m2, 1900 N/m2, 2050 N/m2, and 2200 N/m2) that will make possible to calculate the fiber-matrix interface shear damage with respect to the length of the fiber. Figures 4, 5, and 6 show the level of damage to the interface for the studied materials.

Fig. 4

Fiber-matrix interface shear damage of PMMA/PEEK

Fig. 5

Fiber-matrix interface shear damage of TOPA//PEEK

Fig. 6

Fiber-matrix interface shear damage of Topas-Zeonex/PEEK

Figure 4 (PMMA/PEEK) shows that the level of shear damage begins for a damage value D = 0.08 when σ = 1600 N/m2, and that it reaches a maximum value D = 0.29 for a maximum constrained value of σ = 2200 N/m2. A damage symmetry is observed in the middle of the fiber, since the random variables represented graphically by the blue points or the cloud in blue explain that the interface shear damage is very strong at the ends of the fiber compared to the middle, as it has been already demonstrated by the micromechanical model of Cox, (see Fig. 7) [83]. Figure 5 (Topas/PEEK) shows that the shear damage level begins for a damage value D = 0.19 when σ = 1600 N/m2, and that it reaches a maximum value D = 0.37 for a maximum constrained value of σ = 2200 N/m2. A presence of a symmetry in the caused damage at the middle of the fiber is observed, since the random variables represented graphically by the blue points or the cloud in blue color explain that the interface shear damage is much higher at the fiber ends compared to the middle, as it has already demonstrated by the micromechanical model of Cox. Figure 6 (Topas-Zeonex/PEEK) shows that the shear damage level begins for a damage value D = 0.35 when σ = 1600 N/m2, and that it reaches a maximum value D = 0, 57 for a maximum stress value of σ = 2200 N/m2. We observe the presence of symmetry of the damage at the middle of the fiber, since the random variables represented graphically by the blue points or the cloud in blue explain that the interface shear damage is very strong at the ends compared to the middle of the fiber, as it has already demonstrated by Cox’s micromechanical model. The gained genetic results obviously showed the real behavior of the three materials according to their mechanical properties, in particular the values of the three Youngs modulus found by Leal et al. [83]. As a conclusion, the fiber with the greatest Young’s modulus value represents the strong mechanical interface efficiency.

Fig. 7

Stress profiles at the interface (τi) by the Cox model [80]

Conclusion

The shear strength of the interface largely influences the final properties of the composite material. Indeed, one of the damage modes of composites is the interface damage. The best interface depends not only on the properties of the fiber and the matrix but also on the point of contact between the two constituents. In this work, we have investigated the effect of shear damage on the fiber-matrix interface of PMMA/PEEK, Topas/PEEK, and Topas-Zeonex/PEEK composite materials. The objective sought is to study the reliability and the resistance of each composite material among the three presented materials, where a uniaxial tensile stress on the representative elementary volume (REV) is applied. The obtained results by genetic modeling showed that the PMMA/PEEK composite material is the most resistant to the different values of the mechanical stresses applied compared to the two other materials. These results were confirmed by the level of damage at the interface observed for the three materials studied. The numerical calculations are in very good agreement with the analytical results found by Cox where he demonstrated that the Young’s modulus of the fibers has an important influence on the shear strength of the interface. The PMMA and Zeonex POFs essentially based on PEEK polymers present the key interest of various new researches, since they are chosen as prime candidates for various sensing applications and telecoms aims.