Experimental determination of the adhesive characteristics of the “elementary fiber -epoxy matrix” system

. The paper considers the method of testing the elementary fiber-polymer matrix system. Results of determining the following adhesive characteristics are provided: apparent and local adhesive strength, start and end in the adhesive destruction of the fiber-matrix joint under study. Basalt fiber and epoxy matrix based on the epoxy resin and amine hardener are considered as the study objects. Influence of the samples geometric characteristics on their adhesive characteristics is established. The paper shows that at the depth of the elementary fiber emersion in the polymer matrix equal to 200 µm, the scatter of all determined adhesive characteristics is significantly reduced.


Introduction
Basalt plastics belong to the group of reinforced polymer composite materials (PCM), which operation scope is constantly increasing [1][2][3][4]. Basalt fibers are comparable to the glass fibers according to their deformation-strength and thermophysical characteristics; however, if the properties of PCM based on the glass reinforcing fillers are well studied [5][6][7][8][9][10][11][12], technical literature contains only a very limited number of works devoted to studying basalt fibers and composites on their basis.
The authors of works [1][2][3]13] show the prospects of using vacuum infusion technology in the PCM production based on the basalt fibers. This molding technology is widely used in manufacturing parts made of fiberglass, because it allows significantly reducing the cost of finished parts made of the composite materials.
Many standard methods are used to evaluate the PCM mechanical characteristics making it possible to determine their values under static and dynamic conditions at tension, compression, bending, etc. Researchers pay much less attention to experimental evaluation of the adhesive strength, although it is known [4,14] that exactly the composite structure durability depends on it.
The authors of [14,15] are using the pull-out method to evaluate adhesive strength in the polymer matrix-fiber system. Essence of the method is to experimentally determine the force, at which the elementary fiber is being pulled out (without destruction) of the cured matrix. Based on the results of these tests, a certain average value of the adhesive strength is determined, but the influence of residual stresses, friction forces and other factors that have a significant effect on the adhesive characteristics is not taken into account.
Objective of this work is a comprehensive evaluation of the adhesive strength characteristics of the elementary basalt fiber-epoxy matrix system.

Research objects
Research objects included elementary basalt fibers (Table 1) and epoxy binder ( Table 2).  Polyethylenepolyamine was used as the curing agent, and the ED-20 epoxy oligomer -as the resin. This material cures at the room temperature for 24 hours, and it was cured at the high temperature in order to reduce duration of the sample preparation.

Methods for experimental evaluation of the adhesive characteristics of the elementary fiber-epoxy matrix system
Samples were prepared and tested using the Textechno equipment consisted of two modules: Favimat+ and Fimabond (Table 3) [15]. Technique used in manufacturing the samples for their pull-out testing consisted of the following main operations: -binder manufacture, pouring it into the cup and installing the cup with the binder into the Fimabond module; -elementary fiber extension from the multifilament thread, which was used to produce the fabric, its capture in the device, installation of the device with elementary fiber in the Fimabond module, fiber immersion in the binding agent and curing the binding agent.
The finished sample was put into the Favimat+ module, where a load was applied to the fiber, and the force was determined at the room temperature, at which the elementary fiber was extracted (without destruction) from the cured polymer. As a result of experimental research, dependence of force on displacement was obtained, it is shown in Fig. 1. The following notations are used in Fig. 1: • Fd is the force applied to the adhesive joint initiating the crack growth and leading in turn to the adhesive failure.
• Fmax is the maximum force, at which the adhesive joint is being completely destroyed (Fd = Fmax value in Table 4). • Fb is the minimum frictional force between the polymer matrix and the fiber appearing during destruction of the adhesive joint. As the adhesive connection initial characteristics, the following notations are used: -df -individual fiber diameters; -le -depth of elementary fiber immersion in the polymer matrix [mcm].

Methods for theoretical evaluation of the adhesive characteristics of the elementary fiber-epoxy matrix system
Based on the results of experimental studies, for each adhesive joint and in accordance with the procedure [16,17], the following is determined: • Wde adhesive destruction operation, which is assessed by the area under the curve (Fig.) in the OB section. • Wfric work spent on overcoming the friction forces, which is determined by the area under the curve (Fig.) in the CD section.

= ∫ • (2)
• τapp apparent adhesive strength (MPa), which is characterized by the average shear stress at the interface at the maximum load.
• τf interfacial friction stress (MPa), which characterizes the stress resulting from the fiber surface friction against the matrix and corresponding to the CD section on the forcedisplacement curve.
• τd local adhesive strength (MPa), which represents the shear stress average value at the matrix-fiber interface under a load corresponding to the adhesive joint complete destruction.
where: τT are the residual thermal stresses; rf is the fiber radius; β is the coefficient, which the authors of this works [16,17] called the shift delay parameter.  Table 4 presents the results obtained in determining adhesive characteristics for two types of samples, which differed from each other in immersion depth of the elementary fiber in the polymer matrix. Results of the research demonstrated that the elementary fiber immersion depth in the matrix equal to 100 µm was not sufficient, because of a large data scatter. Thus, the τd local adhesive strength values were varying from 44,728.4 kPa to 80,610.7 kPa, i.e. by 1.8 times. It should be noted that for the same materials at the immersion depth equal to 200 μm, error in the local adhesion strength was not exceeding 12% (the τd local adhesion strength values varied from 64,565.2 kPa to 72,571.4 kPa).

Results and discussion
It was established that for all the studied samples, the apparent adhesive strength value was significantly higher than the friction stresses arising after the adhesive joint destruction due to fiber extension from the polymer matrix. The local adhesive strength value, also for all the samples under study, was higher than the apparent adhesive strength value. Thus, the local adhesive strength value actually reflected the true adhesive strength value of the elementary fiber-polymer matrix system.
For specimens No. 6 and No. 8 (see Table 4), the value of work spent on the adhesive joint destruction was equal to the work of the friction forces occurring already after the adhesive joint destruction. For the sample No. 4, its value even exceeded the work expended on destructing the adhesive joint. That was probably due to high roughness of the samples No. 4, No. 6 and No. 8. However, higher roughness values of those samples were not leading to a similar increase in the local adhesive strength values.

Conclusion
The pull-out method used in this work makes it possible to determine the adhesive strength values with a high degree of accuracy.
As the research results, the following adhesive characteristic values were experimentally determined: work that should be performed for adhesive destruction, work associated with overcoming the friction forces after the adhesive destruction, as well the apparent and local values of the adhesive strength. It was established that the work value that should be performed on the adhesive joint destruction could be equal to similar work occurring after destruction of the matrix-fiber interface.
It was also found that in order to reduce the spread in all the determined values of the adhesive characteristics, it was necessary that the fiber immersion depth in the matrix should be 200 μm.
The proposed method could be widely used in design and development of new coupling agents and technologies for their application to fiber, since it would allow evaluating the coupling agent material contribution to the adhesive strength value in the elementary fiberpolymer matrix system.