Investigation of mechanical properties of composite materials reinforced with carbon fibers

. Theoretical and experimental methods for obtaining and investigating effective thermomechanical characteristics - residual stresses and deformation in panels made of nanomodified materials with asymmetrical reinforcement scheme have been developed in this paper. The study of the residual stress-strain state of structural elements made of carbon plastic using the values of thermoelastic characteristics of composite monolayers identified on the basis of the developed methods meade it possible to reveal the possibility of reducing the residual stress-strain state in structures with asymmetric reinforcement schemes


Introduction
When creating nanocomposites, the key challenges are the development of mass-produced, reliable, and efficient production technologies that allow the production of materials with stable characteristics . Hand lay-up technology, also called wet lay-up, is the simplest and most widely used process for the production of flat reinforced composites. The process consists of laying layers of carbon fibre-reinforced plastic in a sequential layout using an epoxy resin matrix. Wet lay-up is a moulding process that combines layers of reinforced carbon fibre with epoxy resin to create a high-quality laminate. Before starting the laying process, an appropriate mould must be prepared. This preparation consists of cleaning the table and applying an anti-adhesive to the surface. The hand laying process can be divided into four basic steps: mould preparation, epoxy resin coating, laying and curing. Form preparation is one of the most important steps in the paving process. This process requires dry reinforcement layers and the application of a wet epoxy resin, the matrix. They are combined together -the carbon fibre (reinforcing) material, impregnated with the matrixepoxy resin.
Examples of a composite using unidirectional layers and lay-up designation are shown in Figure 1.

Characteristics of the obtained composites
We use the spherical inclusion model to simulate the properties of the filled matrix [27][28][29][30][31][32][33][34][35][36]. Assuming that the reinforcing particles of fullerene carbon black are spheres. We assume that the particles are absolutely solid and do not collapse (top estimate). The volume content is 0.6%. We use the Digimat module -MF, averaging method -Mori -Tanaka. The strength criterion is based on the maximum principal stresses acting in the matrix.
If we set the initial bulk content of inclusions to 0.6%, the model predicts that the properties of the matrix will not change as the inclusions are too low. It is necessary to consider the influence of the interfacial layer. For this purpose, we consider the calculation with given effective volume content (volume content of the filler + volume content of the interfacial layer, assuming their properties are equal). Let's choose the effective volume content which allows to describe the experimental data received in relation to the modulus and ultimate strength [37][38][39][40][41][42][43][44][45][46][47][48].
If we choose the ultimate strength, the effective volume content of inclusions should be 50% and the modulus of the composite should be 6 GPa. If it is matched by modulus, the effective inclusion volume content should be 11% and the modulus of the composite should be 23 MPa.
To describe the experiment it may be assumed that the effective volume content of inclusions is 11 % (we obtain the coincidence of the calculation and modulus experiment) and the matrix strength increases when the filler is added up to 30 MPa (we obtain the coincidence of the calculation and strength experiment). For the found volume content of inclusions we determine by selection what should be the volume content of inclusions so that the calculation and the experiment of measuring the KTR of the composite coincide. For 11%, we obtain that the KTR of the filler (and the surrounding interfacial layer) should be 85 10 -6 C -1 . The obtained high value of FTR of the filler and the experimentally established phenomenon of increasing FTR of composites with nanomodified matrix may be related to a change in the structure of the polymer matrix or may be a consequence of ongoing chemical reactions between the filler and the matrix.
The input data for the simulation of the degradation process of mechanical properties of the tested specimens are the characteristics of the monolayer. In the test, we use a fibre of NTA 40 grade and a matrix of EDT 10 grade, whose properties are given in Tables 2 and 3.  Table 3. Properties of EDT 10 matrix.

Features
Unit The task of determining the properties of a monolayer based on the properties of the NTA 40 fibre and the EDT 10 matrix is solved using the "DIGIMAT" software. "DIGIMAT" is designed for fast and highly accurate prediction of nonlinear behaviour of multicomponent materials such as plastics, polymers, carbon and glass plastics, nanomaterials, etc., for accurate evaluation of local and global behaviour of multicomponent structures using the finite element method, for preparation, storage and confidential exchange of material models, for easy and highly efficient design of cellular sandwich panels. Also "DIGIMAT" presents to user a number of interfaces for finite-element software systems of computer engineering ("ANSYS", "LS DYNA", "SIMULIA/Abaqus" etc.), intended for computer simulation and research problems of deformable solid body mechanics, mechanics of structures and software systems of finite-element modelling of plastic moulding processes ("MOLDEX3D", "MOLDFLOW" etc.). Fig. 3 shows σ-ε diagrams obtained as a result of finite element analysis in conjunction with "DIGIMAT". Two analyses were given: a unidirectional sample and a longitudinally cross-stacked sample. These diagrams coincided exactly with the diagrams obtained when testing these two types of samples. Based on the results of the property simulation, we obtain the stiffness matrix of the packet, which is presented in Table 4.
Find the average modulus using the formula: 23 22 The obtained value of the average Young's modulus of the package differs from the test. It is known that when using test data for a unidirectional material, inaccuracies can occur in the calculation of the properties of a laminated package, so it is usually necessary to use stiffness data for several variants of packages with different stacking of layers. If modulus values are used, it is not possible to describe the test data. In this study, we will use an overestimated transverse modulus value of 28 GPa for monolayer properties, which is higher than the experimental data obtained from unidirectional samples (6.5 GPa). In this case it is possible to reliably describe the experimental data obtained for the Young's modulus of composite specimens with symmetrical stacking.

Conclusions
The research carried out made it possible: to investigate the residual deformations in panels with asymmetrical reinforcement scheme on the basis of the obtained analytical solution as well as numerical simulation. Comparison of results of analytical and numerical solutions with obtained experimental data confirms reliability and validity of developed mathematical models and methods of investigation of effective thermomechanical characteristics and residual stress-strain state of panels made of layered nanomodified materials.