1. Introduction

Studies and analyses of mechanical properties of long fiber-reinforced composites provide important information for future lightweight constructions. First of all, it is important to approach the issues and specifics of long fiber-reinforced composite structures to increase the strength and toughness of the resulting structure. The long fiber-reinforced composite structure is typically formed from two dominant components: carrier fiber reinforcement and a

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

matrix. Ideal arrangement of the final composite (fiber-matrix connection), due to synergy, the high specific properties (high strength, stiffness, and toughness) can be achieved, where none of input components reached. It is that the optimal synergistic effect is characterized by a known "illogical" rule 2 + 3 = 7, which characterizes the sum of the properties of the individual input components (fibers + matrix) achieves a higher value of the specific properties of the newly created structure. In general, the highest specific properties can be achieved if the fibers are stressed up to the strength limit σ<sup>f</sup> M F f !max with stress transferred with matrix. The matrix transforms the stress into the fibers, and it also has a significant effect on the bonding with the fibers. Thus, the matrix is the binder component of the composite, creating the final geometry of the composite and at the same time protecting the fibers from wear and damage, which would lead to loss of stability and strength of the resulting composite. The description of the properties of composite structures reinforced with long fibers due to their potential and specific characteristics was given by the authors namely Agarwal et al. [1], Guedes [2], Gay and Gambelin [3], Reifsnider [4], Teply and Reddy [5], Berthelot [6], Gibson [7], or Soden et al. [8]. The authors agree that long fiber-reinforced composite structures are unique materials whose mechanical properties cannot be generally described in an analytical or experimental manner. Theories also differ in mathematical relationships derived for unidirectional composite structures, let alone complete synthesis of mechanical properties for geometrically complex structures of frames with multidirectional fibrous arrangement. This is due to the fact that their properties vary significantly with the type of fibers and a matrix (e.g., physical and mechanical properties, surface treatment, chemical compositions, binding agents, density, thermal expansion, etc.) because only a slight change forms various combinations with significantly different properties in mechanical behavior.<sup>1</sup> Generally, long fiber-reinforced composite structures can be considered as inhomogeneous and heterogeneous structures with anisotropic properties in terms of physical and mechanical behavior. Their heterogeneity is manifested by a large number of combinations of different variants of the resulting structural materials suitable or unsuitable for the specific design requirements and load.<sup>2</sup> If the strength of the composite has to be maximized, the specific surface of the fiber-matrix interface must be high and free of defects. The selection of fiber reinforcement is possible to use a wide range of fibers, whereas their offer is developed and expanded. For structural applications such as frames for machine parts and equipment may be used virtually any organic natural fibers (e.g., coconut, cotton, cellulose fibers, etc.) from a variety of polycrystalline ceramic materials, polymeric fibers, glass, or carbon fibers. The production technology of these fibers is well described by Bareš [9]. Carbon fibers are industrially manufactured with a diameter of 5–12 μm by various methods such as carbonization of organic fibers or pyrolysis. It is generally known that carbon can exist in nature in three forms: diamond, graphite, and glassy (amorphous). Carbon fibers can be

considered as fibers produced at 800–1600C, and graphite fibers are produced at >2200C. However, only fibers obtained from the crystalline form of carbon arranged in a certain direction (production under tension) have a high elastic modulus and other specific design parameters such as a lower density, higher surface area, lower thermal conductivity, higher electrical resistance, and so forth compared to graphite fibers. Glass fibers with diameter of 3.5–20 μm are produced by fast drawing from the melts (the speed reaches up to 400 m min<sup>1</sup>

FEM Analysis of Mechanical and Structural Properties of Long Fiber-Reinforced Composites

http://dx.doi.org/10.5772/intechopen.71881

The spinning speed is also influenced by the viscosity (50–100 Pa s), the melting temperature,

Figure 1. Example: Low strength of the fiber composite structure due to the poor joint of the fiber with matrix.

Figure 2. Cross section of composite sample with long fibers (upper), detail: fiber-matrix (bottom left), detail: phase

interface (bottom right).

).

3

<sup>1</sup> This can be mentioned in the example given by Bareš [9]. A simple combination of three homogeneous isotropic light metals to form ternary cast iron is obtained 82,160 possible variants of alloys, if more six metals are combined, more than 300 million different alloy variants could be obtained. (The composite structure reinforced with long fibers has a similar behavior, where the change of the matrix, directional arrangement, and type of fiber significantly affect resulting mechanical properties because it leads to qualitatively different structure [10]).

<sup>2</sup> Transmission of static stress applied to the composite and transferred with fibers is required excellent consistency of fibers and matrix; on the contrary, a dynamic impact requires energy absorption by the crack propagation along fibers.

considered as fibers produced at 800–1600C, and graphite fibers are produced at >2200C. However, only fibers obtained from the crystalline form of carbon arranged in a certain direction (production under tension) have a high elastic modulus and other specific design parameters such as a lower density, higher surface area, lower thermal conductivity, higher electrical resistance, and so forth compared to graphite fibers. Glass fibers with diameter of 3.5–20 μm are produced by fast drawing from the melts (the speed reaches up to 400 m min<sup>1</sup> ). The spinning speed is also influenced by the viscosity (50–100 Pa s), the melting temperature,

matrix. Ideal arrangement of the final composite (fiber-matrix connection), due to synergy, the high specific properties (high strength, stiffness, and toughness) can be achieved, where none of input components reached. It is that the optimal synergistic effect is characterized by a known "illogical" rule 2 + 3 = 7, which characterizes the sum of the properties of the individual input components (fibers + matrix) achieves a higher value of the specific properties of the newly created structure. In general, the highest specific properties can be achieved if the fibers

transforms the stress into the fibers, and it also has a significant effect on the bonding with the fibers. Thus, the matrix is the binder component of the composite, creating the final geometry of the composite and at the same time protecting the fibers from wear and damage, which would lead to loss of stability and strength of the resulting composite. The description of the properties of composite structures reinforced with long fibers due to their potential and specific characteristics was given by the authors namely Agarwal et al. [1], Guedes [2], Gay and Gambelin [3], Reifsnider [4], Teply and Reddy [5], Berthelot [6], Gibson [7], or Soden et al. [8]. The authors agree that long fiber-reinforced composite structures are unique materials whose mechanical properties cannot be generally described in an analytical or experimental manner. Theories also differ in mathematical relationships derived for unidirectional composite structures, let alone complete synthesis of mechanical properties for geometrically complex structures of frames with multidirectional fibrous arrangement. This is due to the fact that their properties vary significantly with the type of fibers and a matrix (e.g., physical and mechanical properties, surface treatment, chemical compositions, binding agents, density, thermal expansion, etc.) because only a slight change forms various combinations with significantly different properties in mechanical behavior.<sup>1</sup> Generally, long fiber-reinforced composite structures can be considered as inhomogeneous and heterogeneous structures with anisotropic properties in terms of physical and mechanical behavior. Their heterogeneity is manifested by a large number of combinations of different variants of the resulting structural materials suitable or unsuitable for the specific design requirements and load.<sup>2</sup> If the strength of the composite has to be maximized, the specific surface of the fiber-matrix interface must be high and free of defects. The selection of fiber reinforcement is possible to use a wide range of fibers, whereas their offer is developed and expanded. For structural applications such as frames for machine parts and equipment may be used virtually any organic natural fibers (e.g., coconut, cotton, cellulose fibers, etc.) from a variety of polycrystalline ceramic materials, polymeric fibers, glass, or carbon fibers. The production technology of these fibers is well described by Bareš [9]. Carbon fibers are industrially manufactured with a diameter of 5–12 μm by various methods such as carbonization of organic fibers or pyrolysis. It is generally known that carbon can exist in nature in three forms: diamond, graphite, and glassy (amorphous). Carbon fibers can be

This can be mentioned in the example given by Bareš [9]. A simple combination of three homogeneous isotropic light metals to form ternary cast iron is obtained 82,160 possible variants of alloys, if more six metals are combined, more than 300 million different alloy variants could be obtained. (The composite structure reinforced with long fibers has a similar behavior, where the change of the matrix, directional arrangement, and type of fiber significantly affect resulting mechan-

Transmission of static stress applied to the composite and transferred with fibers is required excellent consistency of fibers and matrix; on the contrary, a dynamic impact requires energy absorption by the crack propagation along fibers.

ical properties because it leads to qualitatively different structure [10]).

!max with stress transferred with matrix. The matrix

M F f

2 Finite Element Method - Simulation, Numerical Analysis and Solution Techniques

are stressed up to the strength limit σ<sup>f</sup>

1

2

Figure 1. Example: Low strength of the fiber composite structure due to the poor joint of the fiber with matrix.

Figure 2. Cross section of composite sample with long fibers (upper), detail: fiber-matrix (bottom left), detail: phase interface (bottom right).

and, of course, the chemical composition of the glass. The matrix, which affects the properties and usability of the resulting composite, has been epoxy used for both the testing sample and design of the developed composite construction. The composite production may result in imperfect bonding of the matrix fibers (e.g., low wettability of the fiber reinforcement in the matrix, bubble formation, etc.), which leads in mechanical defects in the composite structure, which often over grow into critical defects with a significant reduction in strength (Figure 1). The resulting strength of the composite structure affects mechanical properties of the selected fiber reinforcement and matrix, which are characterized by mechanical parameters, for example, the elastic modulus, Poisson number, or other parameters such as the creep and fracture properties of the individual components. In terms of strength, a significant role (if not most) plays the interfaces among the fibers and the matrix, which is shown in Figure 2. This is due to the fact that the characteristic properties of the interface create a mechanism that apparently causes the synergistic effect that provides their unique mechanical properties to composite structures. Although a number of theories have been compiled, the synergistic mechanism of the phase interface is not yet clear.
