Polymer-Based Composite Materials: Characterizations

Abstract

Various types of composite materials are becoming an inevitable part of our day-to-day life since these are used for a variety of applications. A better understanding on the various properties of the composites is very helpful in their targeted applications, and hence characterizing the composite materials by different techniques play a major role in the development of long-life, high-quality composite products. The polymer-based composite materials provide large amount of flexibility and lightweight to the final product. The selection of various reinforcements and polymer matrices is very critical in designing a desired product. In this chapter, various techniques used for characterizing the polymer-based composite materials in order to examine their mechanical, thermal, electrical, magnetic, piezoelectric, tribological, rheological, and biological properties are discussed.

Introduction

Composite materials have been in use for thousands of years. For example, mud bricks, which are composed of mud (matrix) and straw (reinforcing fiber), can resist both tensile and compressive loads, thus resulting in an excellent building material. It is a combination of at least two materials, one being a binding material (or matrix) and the other one is a reinforcing material. The matrix holds the reinforcing materials together. However, many composite products are made with more than two raw materials, but those materials are not miscible together and have different nature. Composites exist in nature and can be made by humans also. A good example for a natural composite is wood. It consists of long fibers of cellulose bound together by a much weaker substance called lignin. There are several kinds of man-made composites like structural beam, which is an inhomogeneous mixture of cement (matrix), stone (reinforcing particle), and steel rod (reinforcing fiber). The selection of materials for the matrix and reinforcement, the form of reinforcement, and the manufacturing process are very critical for obtaining a composite product with desired properties. The matrix material can be a metal, ceramic, glass, polymer, or organic material in solid (plate or powder) or semisolid forms. The reinforcing material can be a metal, ceramic, glass, textile, polymer, or organic material in the form of lamina, fiber (short and long), particle, whisker, etc. The main advantage of composite material is their high strength and stiffness combined with lightweight feature. The composites have major applications in the advanced fields such as structure, thermal engine and blade, automobile, aerospace, rocket, missile, satellite, military, biomedical, electronics, packaging, etc. The characterization of a composite is one of the essential tasks for developing the desired composite products for particular applications. The major characterization studies used for composites for the evaluation of performance in the targeted areas are mechanical, thermal, electrical, magnetic, piezoelectric, tribological, rheological, and biological.

Volume Fraction

In a composite material, the parameter “volume fraction” plays a major role in characterizing its various properties such as mechanical, thermal, electrical, etc. The evaluation of this parameter is of great importance for material scientists. For example, in a fiber-reinforced composite, the fiber volume fraction significantly determines its properties. A composite can’t be prepared with 100 % of fibers. There is a maximum limit of fiber content in a composite structure. And this maximum volume fraction is able to achieve only when the unidirectional fibers are hexagonally close packed. For a composite material, let the total volume be “V” and masses of its constituent materials be M₁, M₂, M₃, etc. Then the composite density (ρ_com) can be expressed (Eq. 2.1) as

$$ {\uprho}_{\mathrm{com}}=\frac{{\mathrm{M}}_1}{\mathrm{V}}+\frac{{\mathrm{M}}_2}{\mathrm{V}}+\frac{{\mathrm{M}}_3}{\mathrm{V}}+\dots $$

(2.1)

In terms of the densities and volumes of the constituents, Eq. 2.1 can be written as Eq. 2.2 based on the rule of mixtures.

$$ {\uprho}_{\mathrm{com}}=\frac{{\mathrm{V}}_1\;{\uprho}_1}{\mathrm{V}}+\frac{{\mathrm{V}}_2\;{\uprho}_2}{\mathrm{V}}+\frac{{\mathrm{V}}_3\;{\uprho}_3}{\mathrm{V}}+\dots $$

(2.2)

where V_i and ρ_i are the volume fractions and densities of the i^th phase, respectively.

The fiber volume fraction (V_f) can be written in terms of fiber weight fraction (W_f) [1] as

$$ {\mathrm{V}}_{\mathrm{f}}=\frac{{\mathrm{W}}_{\mathrm{f}}\;{\uprho}_{\mathrm{m}}}{{\mathrm{W}}_{\mathrm{f}}\;{\uprho}_{\mathrm{m}}+{\mathrm{W}}_{\mathrm{m}}\;{\uprho}_{\mathrm{f}}} $$

(2.3)

where ρ_m, ρ_f, W_f, and W_m are the density of the matrix, the density of the fiber, the weight fraction of the fiber, and the weight fraction of the matrix, respectively. Correspondingly, the fiber weight fraction (W_f) can be expressed in terms of fiber volume fraction (V_f) [1] as

$$ {\mathrm{W}}_{\mathrm{f}}=\frac{{\mathrm{V}}_{\mathrm{f}}\;{\uprho}_{\mathrm{f}}}{{\mathrm{V}}_{\mathrm{f}}\;{\uprho}_{\mathrm{f}}+{\mathrm{V}}_{\mathrm{m}}\;{\uprho}_{\mathrm{m}}} $$

(2.4)

The fiber volume fraction determines the strength of the composites. Ravi et al. have studied the effect of fiber volume percent on the dynamic damage behavior of woven glass fiber-reinforced polymer (FRP) composites [2]. Delamination is the major damage noticed for specimens with higher fiber volume percent, while the matrix cracking and interface debonding occurs for materials with low fiber volume percent. Fiber volume percent in combination with fiber distribution is the main parameter affecting the interlaminar fracture toughness (ILFT) [3]. It has a significant influence on the longitudinal tensile and compressive strengths and the in-plane shear strength of FRPs. The strength parameters vary in direct proportion to the fiber volume percent up to 50 % [4]. The fiber volume percent of a composite are determined by chemical matrix digestion method as described in ASTM D3171 [5], the burn test as described in ASTM standard D2584 [6], or by photomicrographic techniques. For glass fiber composites, burn test is used because the glass shows good oxidation resistance (500–600 °C), which is much more than the complete burning of matrix.

Voids

Voids form at the interface of composite structures. These are generally formed as gas bubbles trapped inside the cured composite materials. The main sources of voids include the material constituents and the synthesis processes. The presence of voids in a composite structure is found to affect its structural and mechanical properties. It has been predicted that the interlayer and intra-layer reactions caused by the stress and chemically driven diffusion are responsible for the usual void behavior in composites. Voids present in the composite material can be evaluated by matrix digestion and matrix burn-off techniques [1].

The volume fraction of void (V_void) can be calculated if the composite density and the density of the matrix and fibers are known. The equation for determining the volume fraction of void is given by Eq. 2.5 [1] as

$$ {\mathrm{V}}_{\mathrm{void}}=1-{\uprho}_{\mathrm{com}}^{\exp}\left(\frac{{\mathrm{W}}_{\mathrm{m}}}{\uprho_{\mathrm{m}}}+\frac{{\mathrm{W}}_{\mathrm{f}}}{\uprho_{\mathrm{f}}}\right) $$

(2.5)

where ρ ^exp_com is the experimentally determined composite density. Void is undesirable and has adverse effect on the mechanical properties of composites. Wu et al. have developed an analytical model to estimate the elastic properties of polymer composites with voids of various sizes and locations [7]. These voids have significant influence on the interlaminar shear strength (ILSS) of the composite materials [8]. Bowles and Frimpong have studied the influence of voids on the ILSS of graphite fiber-reinforced PMR-15 composites [9]. As the void content increases, an increase in scatter in the strength data is observed. The role of voids in the initiation and propagation of cracks in composites reinforced with unidirectional carbon fiber (CF) has been investigated by Chambers et al. [10]. Void area greater than 0.03 mm² results in deterioration of mechanical properties. Voids assist in the propagation of crack in the resin-rich interply regions. An increased void content increases composite’s susceptibility to water penetration and weathering. The procedure of measuring the voids in composites, required for the calculation of density, is given in ASTM D 1505 [11] and ASTM D 3800 [12].

Surface Roughness

Surface roughness is an important parameter for ascertaining the surface quality and aesthetic value. The average surface roughness (Ra value) is one of the most frequently used parameters for surface roughness, which describes the height of irregularities and gives an indirect indication of the sharpness and depth of surface notches [13]. It is an absolute average roughness over one sampling length [14]. Researchers have used this Ra value for studying the impacts of various process parameters on the surface quality of FRP composites. Davim and Reis have analyzed the effects of machining parameters on the surface quality of plastics reinforced with CFs [15].

Surface Topography

Scanning electron microscope (SEM) is also used for studying the topography of solids [16]. In the field of FRPs, it is used to reveal the actual distribution of fibers and matrix in the composite. It is also used for the analysis of fractured surfaces [17] and helps to examine the crack propagation in fibrous composite materials in order to gain an insight about composite strength, the adhesion between the phases, and the mode of failure [18]. It serves as an effective means to confirm the uniformity of fiber distribution across the cross section and presence of internal flaws (like voids, broken fibers, foreign inclusions, etc.) at microscopic level, which explain the physical and mechanical behavior of composites and the discrepancies associated with their properties.

Mechanical

Measurement of mechanical properties of composites involves testing on the suitably designed specimens. The interpretation of material response over the entire range of loads is necessary, if the advanced design procedures are to be used for the efficient material utilization. The macromechanical properties of composites may be computed through micromechanical analysis, and the design of composite materials may be started with constituent material properties. However, the validity of micromechanical analysis is to be checked through experiments. Another purpose of mechanical characterization is to check the adequacy of new fabrication procedure and to assure the material uniformity. The mechanical properties of composites include (i) strain and yield strength in tension, compression, shear, and torsion, (ii) ILSS between the matrix and fiber, (iii) flexural fatigue strength, (iv) impact strength, (v) stress relaxation, and (vi) creep.

Strength

A high strength-to-weight ratio is required for a composite in its applications. Hence, it is very important to determine its strength. Thus, characterizing the strength of a composite is very critical before its application. This section briefly discusses about the various mechanical characterization tools used for finding out the strength of the composite materials.

Tensile Strength

The ASTM standard D-3552-96 defines the test method for determining the tensile properties of a fiber-reinforced metal matrix composite (MMC). However, the tensile properties of advanced composite materials and polymer matrix composites can be tested by ASTM standard D-3039, and the tensile properties of MMCs can be characterized by ASTM standard D-3518 specimen. Strength characteristics of composite materials generally follow the mixture rules. These are mathematical expressions giving the property of the composite in terms of the quantity and arrangement of its constituting materials. Let us assume a part of the unidirectional composite material having unit dimensions with the fibers having volume fraction, V_f. Then, the volume fraction of the matrix, V_m (Eq. 2.6), is given [19] as

$$ {\mathrm{V}}_{\mathrm{m}}=1-{\mathrm{V}}_{\mathrm{f}} $$

(2.6)

The slab model is shown in Fig. 2.1.

Fig. 2.1

Schematic of slab model showing transverse stiffness of a unidirectional composite

If a stress σ₁ is applied in a direction of the fiber orientation, then both the fiber and matrix act parallel to resist the load. In this case, strain in both fiber (ε_f) and matrix (ε_m) must be the same (let it be ε₁) in fiber direction and can be written (Eq. 2.7) as

$$ {\upvarepsilon}_{\mathrm{f}}= {\upvarepsilon}_{\mathrm{m}} = {\upvarepsilon}_1 $$

(2.7)

It is clear that the load on the composite must be equal to the sum of the total load of the fiber phase and the matrix phase. Load on each phase is the phase area times the stress in each phase, but phase area is numerically equal to its own volume fraction. Hence, the composite strength (σ_com, Eq. 2.8) can be written [19] as

$$ {\upsigma}_{\mathrm{com}} = {\upsigma}_{\mathrm{f}}{\mathrm{V}}_{\mathrm{f}} + {\upsigma}_{\mathrm{m}}{\mathrm{V}}_{\mathrm{m}} $$

(2.8)

where, σ_f, σ_m, V_f, and V_m are the total stress on the fiber phase, the total stress on the matrix phase, the volume fraction of the fiber phase, and the volume fraction of the matrix phase, respectively.

Consider the ultimate strained condition of the fibers in the unidirectional composite at which the fiber begins to break. The breaking strength of the composite (σ_b) can be written from the rule of mixtures [19] as

$$ {\upsigma}_{\mathrm{b}} = {\upsigma}_{\mathrm{f}\mathrm{b}}{\mathrm{V}}_{\mathrm{f}} + {\upsigma}_{\mathrm{mb}}\left(1-{\mathrm{V}}_{\mathrm{f}}\right) $$

(2.9)

where σ_fb and σ_mb are the breaking strength of the fiber and the breaking strength of the matrix, respectively. At the breaking strain of the fiber, the load carried by the fiber becomes zero, which results in transferring the entire load to the matrix. The breaking strength of the composite is now reduced according to the fiber fraction as

$$ {\upsigma}_{\mathrm{b}} = {\upsigma}_{\mathrm{mb}}\left(1-{\mathrm{V}}_{\mathrm{f}}\right) $$

(2.10)

The maximum of these two strengths gives the breaking strength of the whole composite. For a certain range of fiber fraction in the composite, the strength actually reduces on the addition of fibers. These relations are presented in Fig. 2.2.

Fig. 2.2

Schematic showing the strength of a unidirectional composite in fiber direction

The tensile properties of the composites can also be determined by bending a sandwich beam specimen containing a thin layer of composite material, which is bonded to the top and bottom of a thick substrate such as an Al honeycomb [20, 21]. This method can also be used for determining off-axis properties and transverse properties as reported by Lantz [21]. Richards et al. have showed that the satisfactory results can be achieved for 45⁰ specimens having a value of 12 for the ratio of the specimen length between the grips to its width [22]. Pagano and Halpin have found that a uniform state of strain and stress exists at the center of an off-axis tensile coupon if the length-to-width ratio is sufficiently large [23]. A standard test method to determine the tensile properties of polymer matrix composite materials has been described in ASTM D3039 [24].

The strength and toughness are the properties that are strongly enhanced by the addition of nanoparticles in the matrix. This is not only observed in the polymer matrix composites but also in other composites. For example, certain nanoconstituents like silicon carbide (SiC), silicon nitride (Si₃N₄), etc. are added into the non-polymer matrix like alumina to form Al₂O₃/SiC, Al₂O₃/Si₃N₄, MgO/SiC, and SiN₄/SiC nanocomposites. The strength of alumina is almost three times augmented with the help of the dispersion of 5 vol.% SiC nanoparticles in the alumina matrix. It has been observed that the annealing also helps to improve the fracture strength by the development of sub-grain boundaries. For example, in the case of MgO/SiC nanocomposite, the annealing enhances its fracture strength over a wide temperature range [25]. A significant improvement of high-temperature strengths for Al₂O₃/SiC and MgO/SiC nanocomposites with respect to Al₂O₃ and MgO matrices is shown in Fig. 2.3.

Fig. 2.3

Temperature dependence fracture strength for ceramic oxides and ceramic nanocomposites [25]

Flexural Strength

In a bend test of a specimen, bending strength of the outermost fiber at the instant of failure is defined as flexural strength. The nominal flexural strength (σ_N, Eq. 2.11) can be written [26] as:

$$ {\upsigma}_{\mathrm{N}} = {f}_{\mathrm{r}}^{\mathrm{o}}{\left(1-\frac{{\mathrm{D}}_{\mathrm{b}}}{\mathrm{D}}\right)}^{-1} $$

(2.11)

where f ^o_r is the average tensile strength of the boundary layer and is given by

$$ {f}_r^o=\frac{{\mathrm{M}}_{\mathrm{o}}\left(\mathrm{D}-{\mathrm{D}}_{\mathrm{B}}\right)}{2\mathrm{I}} $$

(2.12)

where M_o, D, D_b, and I are the bending moment, the beam depth, the half value of boundary layer thickness, and the moment of inertia of cross section, respectively. The expression for moment of inertia (I) can be written as

$$ \mathrm{I} = \frac{{\mathrm{D}}^3}{12} $$

(2.13)

Plastics have higher flexural strength as compared to their straight tensile. The breaking force required for a specimen of specified width and thickness is known as “modulus of rupture.”

Interlaminar Shear Strength

Evaluation of ILSS can be done by a similar test procedure adopted for the flexural strength. The experimental setup is shown in Fig. 2.4. The composite specimen dimensions and geometry are recommended in ASTM D-3039-79 and ASTM D-3410 in tension and compression mode, respectively, and ASTM D-695 for advanced composite materials in compression mode. The ILSS (τ, Eq. 2.14) can be expressed [27] as follows:

Fig. 2.4

Experimental setup to measure the interlaminar shear strength

$$ \tau =\frac{3\mathrm{F}}{4\mathrm{b}\mathrm{d}} $$

(2.14)

where F, b, and d are the load at the moment of break, the width of the specimen, and the thickness of the specimen, respectively. A representative curve of load versus displacement for a specimen under testing is shown in Fig. 2.5.

Fig. 2.5

Load versus displacement curve during a test for determining ILSS

Hsu and Herakovich have examined the problem by separating each layer into an outer and an inner region [28]. The inner region is analyzed using classical laminate theory, while the region near the free edge is analyzed by employing the perturbation technique and concluded that their analysis renders better results than the finite difference solution by Pipes and Pagano [29]. Wang and Dickson have developed a method to calculate the interlaminar stresses in symmetric composite laminates [30]. They have used the extended Galerkin method with the interlaminar stresses, and the displacements are represented by complete sets of Legendre polynomials. This method provides systematic steps for direct computation of interlaminar stresses. A substantial study has been reported on the ILSS of composite materials at room temperature. ILSS depends on the resin formulation [31–35]. A group of researchers has altered the resin to improve the ILSS of composites [36–41]. Another group of researchers has altered the fiber surface using elastomer [42], silane [43, 44], styrene [45], styrene–isoprene [46], polybutadiene [47], methacryloxypropyltrimethoxysilane [46], methacryloxypropyltrimethoxysilane-modified polybutadiene [46], and oxidation to improve the ILSS of composites made of epoxy [42, 45], phenolic [43], nylon 6 [44], and vinyl ester [47]. The dependence of ILSS on fiber orientations of the neighboring plies around the interfaces has been studied extensively by Zhang et al. [48], Okada and Nishijima [49], Vishwanath et al. [50], and Costa et al. [51]. Ray has studied the ILSS of epoxy composites having glass fiber loading of 55, 60 and 65 % by weight [52, 53]. A rapid decrease in ILSS with increasing void content in FRP composites is reported by Costa et al. [51] and Mouritz [54]. Ray [52, 53] has studied the impact of strain on ILSS.

Impact Strength

The impact strength of a composite is a very important design parameter in most of the applications, e.g., aeronautics (bird impact on the engine), and personal vehicle armors. An analytical solution of the transversal impact on a yarn has been developed by Smith in 1958. In a yarn point impact for an elastic material, the transverse and longitudinal waves propagate with respective velocity (U, Eq. 2.15) written [55] as

$$ \mathrm{U}=\mathrm{C}\ \left[\sqrt{\upvarepsilon \left(1 + \upvarepsilon \right)}-\upvarepsilon \right] $$

(2.15)

where C and ε are the strain–wave velocity and strain of the yarn, respectively. The strain–wave velocity (C) can be determined from Eq. 2.16 [55]:

$$ \mathrm{C} = \frac{{2\mathrm{L}\left(1 + 3\upvarepsilon \right) + \mathrm{d}}_2}{{\mathrm{t}}_2\left(1 + 2\upvarepsilon \right)} $$

(2.16)

where L, d₂ and t₂ are the strain–wave front traveling distance after reflection at the clamp, the distance traveled by the transverse wave after reflection, and the transverse wave overtaking time after reflection.

Chocron-Benloulo et al. have shown the trend of residual velocity with striking velocity analytically, for 8 ply Kevlar 29 panel shot by a 64 grain (4.147 g) fragment simulating projectile, where the striking velocity was 300–1500 m/s [56]. This analytical model is shown in Fig. 2.6.

Fig. 2.6

Analytical model of residual velocity versus striking velocity for 8 ply Kevlar 29 panel [56]

An experiment has been conducted on a mechanically needle-punched nonwoven fabric, which is made of natural fiber [57]. Polypropylene is used as a polymer binder fiber, and the natural fibers used are flax, hemp, and kenaf. The blending ratios of natural/polymeric fiber are varied from 50/50 to 70/30. The fiber or polypropylene mats are used as a reference material. The prepregs weight ranges from 1600 to 2400 g/m². The objective of this experiment is to measure the dynamic stress using a reflection polariscope with single-flash technique. The impact test apparatus consists of a loading apparatus and a photoelastic element setup as illustrated in Fig. 2.7. In this process, pressurized air is used to accelerate the steel projectile and an anvil is used to transmit the impulse. It uses a piezoelectric force sensor and avoids damaging the composite at the contact point. The boundary conditions are different for various specimens like disk, beams, or plates, which are in the loading apparatus. Now, the wave propagation can be very easily detected in its early stages (provided that the reflection should occur at the point of interest of the specimen). It is possible to investigate the effect of superposition and reflection of propagating waves at different profile and/or boundary conditions. It also helps in understanding the fracture nature of FRP composites after the impact loading. The applications of the test are (i) locating the artificial cracks by analyzing impact strains in the specimen, (ii) determining the viscoelastic properties of composites and photoelastic coating material due to high strain rates, (iii) analyzing the strain–wave propagation in FRP composite disks, (iv) having the ability to trace stress concentration in the impact-loaded orthotropic composites, etc.

Fig. 2.7

Schematic of impact testing device [57]

Another procedure to determine the impact toughness is notched Izod test. The hammer has been dropped from a height of 0.6 m with a velocity of 3.4 m/s. This test is used to determine the impact behavior of composites with end-shaped fibers. The impact toughness depends on the various parameters like behavior of the matrix, fiber end, and fiber length.

Notch Strength

Geometry effects, locally concentrated damages, and notches influence the local stress concentration. The presence of notch is the main reason for the failure of composite materials. This is due to the square planar array of broken fibers. The extents of fiber pullout and the stress concentration around the notch lead to failure. The extent of fiber pullout mainly depends on the Weibull modulus. Normalized notch strength (σ, Eq. 2.17) can be written as follows [58]:

$$ \upsigma = \frac{\upmu *}{{\mathrm{c}}_{\mathrm{i}}} + {\upsigma}_{\mathrm{p}} $$

(2.17)

where μ*, c_i, and σ_p are the strength of the critical link at the notch, the notch size, and the normalized pullout stress, respectively. The expression for normalized pullout stress (σ_p) is given by Eq. 2.18 [58].

$$ {\upsigma}_{\mathrm{p}}={\left(\frac{1}{\mathrm{m} + 1}\right)}^{\frac{\mathrm{m}}{\mathrm{m} + 1}}\Gamma \left(\frac{\mathrm{m} + 2}{\mathrm{m} + 1}\right) $$

(2.18)

where m is the Weibull modulus.

The notch strength of composite (${\sigma _f^{\ast}}$) is given by Eq. 2.19 [58].

$$ {\upsigma}_{\mathrm{f}}^{*}={\left[\frac{\left({\mathrm{c}}_{{\mathrm{i}}_{\mathrm{n}}}-1\right)\left(\mathrm{m} + 1\right)}{{\mathrm{n}}_{{\mathrm{i}}_{\mathrm{n}}}\left({\mathrm{c}}_{{\mathrm{i}}_{\mathrm{n}}}^{\mathrm{m}+1}-1\right)}\right]}^{\frac{1}{\mathrm{m} + 1}} $$

(2.19)

where i_n and n_i are the initial notch size and the number of nearest neighbors, respectively.

The normalized notch strength predicted by an analytical local load-sharing model and by the Batdorf-type model is compared for better understanding. The normalized fiber bundle notch strength (σ_f ^* /σ_c) versus initial notch size (i_n) for fiber Weibull moduli (m) of 5 and 10 predicted by the above models are shown in Fig. 2.8. The notch strength predicted by both the models are nearly parallel for m = 10, but there is a huge difference in the notch strength obtained by two methods for m = 5. According to the Batdorf model, the fibers with m = 5 are weaker than m = 10, which is in contradiction to the local load-sharing analytical model.

Fig. 2.8

Graph showing notch strength of Ti MMCs [58]

Fracture Toughness

Fracture toughness is the energy absorbed by the composite during loading or impact in order to propagate a crack up to the failure. Actual fracture toughness is predicted by a single pullout fiber testing. Fiber properties such as fiber end shape, fiber length, friction at interface, and matrix properties have an influence on the fracture and impact toughness. ASTM D-5528:01 defines the standard test method to determine the mode-I interlaminar fracture toughness of unidirectional FRP matrix composite. However, for the mixed mode-I and mode-II, it is based on the standard number ASTM D-6671/D 6671 M-04e1. Estimation of the fracture load of notched plates is a tedious job but it has been established more or less. The influence of parameters like the notch geometry, notch root radius, notch angle, notch depth, and relative width and thickness of the specimen have been extensively studied. Dash et al. have studied how the critical stress intensity factor K_C is affected by the crack size and environmental effects on fracture toughness [59]. These new experimental procedures are more reliable and have been used for studying the fracture toughness. The total fracture toughness (R_t) is given by Eqs. 2.20, 2.21, and 2.22 [59, 60]:

$$ {\mathrm{R}}_{\mathrm{t}}={\mathrm{R}}_{\mathrm{r}}+{\mathrm{R}}_{\mathrm{po}}+{\mathrm{R}}_{\mathrm{s}} $$

(2.20)

$$\approx \frac{{V_f \sigma _f^{\ast} }}{{\tau _f }}\left[ {\frac{{\sigma _f^ {\ast} \cdot d}}{6}\left( {\frac{1}{4} + \frac{{\sigma _f^{\ast} }}{{E_f }}} \right) + \frac{{R_m }}{2}} \right] + \left( {1 - V_f } \right)R_m $$

(2.21)

$$R_s = V_f R_f + \left( {1 - V_f } \right)R_m + V_f \frac{{l_d }}{d}R_i \approx V_f \left( {\frac{{l_d }}{d} - 1} \right)R_m $$

(2.22)

where R_r, R_po, R_s, R_f, R_m, R_i, d, τ_f, l_d, V_f, and E_f are the toughness due to stress redistribution, toughness due to the fiber pullout, toughness due to a creation of new surface in the fiber, matrix and interface, toughness at the fiber, toughness at the matrix, toughness at the interface, fiber diameter, frictional shear stress, de-bond length, volume fraction of the fiber, and Young’s modulus of the fiber, respectively. For most of the fiber composites with thermoset matrices, particularly with CFs, fiber pullout is the primary source of fracture toughness and is represented by Eq. 2.23 [60].

$$R_{po} = \frac{{2V_{f^\tau f} l_{po}^2 }}{d}$$

(2.23)

where l_po = pullout distance. When the critical transfer length (l_c) is more than the fiber length (l), all the fibers are pulled out assuming l_po varies from 0 to 0.5 within the mean value of 0.25; the R_po is given by Eq. 2.24 [60].

$$R_{po} = \frac{{V_{f^\tau f} l^2 }}{{6d}}l \le lc$$

(2.24)

R_po is maximum for l = l_c.

For the composite having fiber length (l) greater than the critical fiber length (l_c), the fraction of fiber can be pulled out up to $\frac{{l_{c}}}{l}$ and the l_po varies from 0 to 0.5.

Therefore, R_po is written by Eq. 2.25 [60].

$$R_{po} = \frac{{V_{f^\tau f} l^3 }}{{6dl}}l \le lc$$

(2.25)

Recently, Dash et al. have used an epoxy resin (Araldite–LY5052 and a hardener–HY5052) reinforced by a plain-woven carbon fabric (INDCARF–30 of 3 K-filament counts: a product of IPCL) [59]. A specimen fabricated of CF-reinforced composite with ASTM standard D-3039 dimensions is shown in Fig. 2.9. A thick diamond-edged wheel with thickness 0.03 mm has been used to cut a sharp notch of varying sizes in different specimens.

Fig. 2.9

A specimen with ASTM standard D-3039 [59]

For a fracture toughness test, a specimen with single-edge sharp notch is used. This specimen is then subjected to a tensile loading on a servo-hydraulic tensile testing machine. It has been clamped initially by using pin-loaded grips. The specimen experiences a monotonic uniaxial tension at a certain displacement rate. Ample precaution has to be taken to maintain a uniform temperature around the test jig. Rate of crack displacement is closely monitored, and the critical load is calculated at the complete fracture load. The fracture equation is given by Eq. 2.26 [61].

$$ {\mathrm{K}}_{\mathrm{c}}=\upalpha\;{\upsigma}_{\mathrm{nc}}\sqrt{\uppi\;\mathrm{a}} $$

(2.26)

where K_C, α, σ_nc, and a are the notch toughness, the boundary modification factor, the critical nominal stress, and the crack length, respectively.

The delamination results in complete fracture and also reduction in stiffness, which is a very important parameter for designers. The current challenge is to increase the lifetime and load-bearing capacity of the composites by controlling the delamination behavior. The crack plane due to delamination in composites is well defined, and the elasticity of the material is retained in the vicinity of the crack tip except in the very thin layer of interface. Hence, examining the energy release rate assists in analyzing the crack formed. Wilkins et al. have found the critical strain energy release rate for mode-I and mode-II delamination [62]. Han and Koutsky have found the interlaminar fracture energy of polyester composites reinforced with glass using width-tapered double-cantilever beam (WTDCB) specimens [63]. A nonlinear theory for the energy release rate using double-cantilever beam (DCB) has been developed by Devitt et al. [64]. Mall et al. have used the DCB specimen to investigate the effect of loading rate on ILFT [65]. A substantial study of ILFT has been reported at room temperature on composite materials comprising glass fiber and polyester resin [66–73]. The ILFT of composite is influenced by the sizing agent [66, 67], materials used as matrix [68, 69], loading of particles [70], geometry of the fabric [71], fiber volume percent [74], fiber orientation of the fiber [72, 75], processing pressure [76], aging condition [68], humidity [69], and temperature [77]. It is clear from the literatures that for structural application of composite materials, ILFT is an important material property.

Modulus or Stiffness

The reinforcements such as fibers in a matrix material may have random or preferred orientations. If the fibers are aligned in the same direction, then they suffer with high stress. Hence, random orientation of material (known as anisotropic, which means that it is having different properties in different directions) is preferred. The most important factor of controlling the anisotropy is the optimization of properties for specific applications. At a microscopic level, properties of composites depend on the individual properties of the fiber and matrix as well as the orientation of the fiber in the matrix. The unidirectional fibers are the simplest arrangement of fibers in a fiber-reinforced composite and are shown in Fig. 2.10. In these composites, minimum properties are given along the transverse direction, whereas the maximum properties are given along the fiber-oriented direction.

Fig. 2.10

Longitudinal and transverse direction of fiber-reinforced composite

Unidirectional Fiber–Matrix Composites

Unidirectional composites possess different tensile moduli in various directions and are presented in Fig. 2.11a-b.

Fig. 2.11

Different tensile moduli labeled (a) in various ways and (b) in different directions

Longitudinal Tensile Modulus

The following assumptions have been used for determining the longitudinal tensile modulus:

• (i) Longitudinal load produces equal strain in fiber and matrix.

• (ii) Fibers are uniform, parallel, and continuous.

• (iii) Perfect bonding between fiber and matrix.

The net load applied (F_l) on the oriented direction of the fibers is shared by fibers (F_f) and matrix (F_m), which can be written by Eq. 2.27.

$$ {\mathrm{F}}_1={\mathrm{F}}_{\mathrm{f}}+{\mathrm{F}}_{\mathrm{m}} $$

(2.27)

The stresses depend on the cross-sectional area of fiber (A_f) and matrix (A_m). Then, Eq. 2.27 is written as Eq. 2.28.

$$ {\upsigma}_1\mathrm{A} = {\upsigma}_{\mathrm{f}}{\mathrm{A}}_{\mathrm{f}}+{\upsigma}_{\mathrm{m}}{\mathrm{A}}_{\mathrm{m}} $$

(2.28)

where A, σ_f, and σ_m are the total cross-sectional area of the composite, the fiber stress, and the matrix stress, respectively. The total cross-sectional area of the composite is given by

$$ \mathrm{A}={\mathrm{A}}_{\mathrm{f}}+{\mathrm{A}}_{\mathrm{m}} $$

(2.29)

From Hooke’s law, Eq. 2.28 is written as Eq. 2.30

$$ {\mathrm{E}}_1{\upvarepsilon}_1\;\mathrm{A}={\mathrm{E}}_{\mathrm{f}}{\upvarepsilon}_{\mathrm{f}}\ {\mathrm{A}}_{\mathrm{f}}+{\mathrm{E}}_{\mathrm{m}}{\upvarepsilon}_{\mathrm{m}}\;{\mathrm{A}}_{\mathrm{m}} $$

(2.30)

where E₁, E_f, E_m, ε₁, ε_m, and ε_f are the axial Young’s modulus of the composite, the axial modulus of the fiber, the axial modulus of the matrix, the strain on the composite, the strain on the fiber, and the strain on the matrix, respectively.

However, the strain is same on the fibers (ε_f), the matrix (ε_m), and the composite (ε₁) and can be written as

$$ {\upvarepsilon}_1={\upvarepsilon}_{\mathrm{f}}={\upvarepsilon}_{\mathrm{m}} $$

(2.31)

Then the Eq. 2.30 is reduced to Eq. 2.32.

$$ {\mathrm{E}}_1\mathrm{A}={\mathrm{E}}_{\mathrm{f}}{\mathrm{A}}_{\mathrm{f}}+{\mathrm{E}}_{\mathrm{m}}{\mathrm{A}}_{\mathrm{m}} $$

(2.32)

Dividing both sides by the area “A,” then Eq. 2.32 changes to Eq. 2.33.

$$ {\mathrm{E}}_1={\mathrm{E}}_{\mathrm{f}}\frac{{\mathrm{A}}_{\mathrm{f}}}{\mathrm{A}}+{\mathrm{E}}_{\mathrm{m}}\frac{{\mathrm{A}}_{\mathrm{m}}}{\mathrm{A}} $$

(2.33)

For a unidirectional composite,

$$ \frac{{\mathrm{A}}_{\mathrm{f}}}{\mathrm{A}}={\mathrm{V}}_{\mathrm{f}} $$

(2.34)

$$ \frac{{\mathrm{A}}_{\mathrm{m}}}{\mathrm{A}}={\mathrm{V}}_{\mathrm{m}} $$

(2.35)

where V_f and V_m are the volume fraction of the fiber and volume fraction of the matrix, respectively. Then the tensile modulus of the composite in the longitudinal direction can be represented by Eq. 2.36 [78].

$$ {\mathrm{E}}_1={\mathrm{E}}_{\mathrm{f}}{\mathrm{V}}_{\mathrm{f}} + {\mathrm{E}}_{\mathrm{m}}{\mathrm{V}}_{\mathrm{m}} $$

(2.36)

For density, this is similar to the rule of mixtures. For polymer composites, E_f>> E_m. Therefore, E₁ ≈ E_fV_f.

Transverse Tensile Modulus

For predicting the transverse tensile property, plenty of mechanical models have been used. One of such a simple model is Jones model [79]. In this model, a load, which is applied in a direction normal to the fibers, contributes for the transverse stiffness. The fibers are stacked together and the model is being simplified. It is assumed that the stresses are equal in each of the components [i.e., composite stress in the transverse direction (σ₂) = fiber stress (σ_f) = matrix stress (σ_m)], and also the Poisson contraction effects are ignored. A model showing transverse stiffness of a unidirectional composite is depicted in Fig. 2.12.

Fig. 2.12

Model showing transverse stiffness of a unidirectional composite

The total extension (δ₂) = δ_f + δ_m. If the total elongation in the load direction is L₂, and the elongation on the fibers and matrix are L_f and L_m, respectively, then length and strains are written by Eqs. 2.37 and 2.38, respectively.

$$ {\upvarepsilon}_2{\mathrm{L}}_2={\upvarepsilon}_{\mathrm{f}}{\mathrm{L}}_{\mathrm{f}} + {\upvarepsilon}_{\mathrm{m}}{\mathrm{L}}_{\mathrm{m}} $$

(2.37)

where ε₂, ε_f, and ε_m are the composite strain, fiber strain, and matrix strain, respectively.

Dividing Eq. 2.37 both sides by L₂, then

$$ {\upvarepsilon}_2={\upvarepsilon}_{\mathrm{f}}\frac{{\mathrm{L}}_{\mathrm{f}}}{{\mathrm{L}}_2} + {\upvarepsilon}_{\mathrm{m}}\frac{{\mathrm{L}}_{\mathrm{m}}}{{\mathrm{L}}_2} $$

(2.38)

However, L_f/L₂ = V_f and L_m/L₂ = V_m = (1–V_f). Therefore, strain becomes (Eq. 2.39),

$$ {\upvarepsilon}_2={\upvarepsilon}_{\mathrm{f}}{\mathrm{V}}_{\mathrm{f}} + {\upvarepsilon}_{\mathrm{m}}\left(1\hbox{--} {\mathrm{V}}_{\mathrm{f}}\right) $$

(2.39)

where V_f and V_m are the volume fraction of the fiber and volume fraction of the matrix, respectively.

By using Hooke’s law, Eq. 2.39 can be written as Eq. 2.40:

$$ \frac{\upsigma_2\;}{{\mathrm{E}}_2}=\frac{\upsigma_{\mathrm{f}}{\mathrm{V}}_{\mathrm{f}}}{\;{\mathrm{E}}_{\mathrm{f}}}+\frac{\upsigma_{\mathrm{m}}\left(1-{\mathrm{V}}_{\mathrm{f}}\right)}{{\mathrm{E}}_{\mathrm{m}}} $$

(2.40)

However, σ₂ = σ_f = σ_m; hence, Eq. 2.40 becomes Eq. 2.41 [79].

$$ {\mathrm{E}}_2= \frac{{\mathrm{E}}_{\mathrm{m}}{\mathrm{E}}_{\mathrm{f}}}{{\mathrm{E}}_{\mathrm{m}}{\mathrm{V}}_{\mathrm{f}} + {\mathrm{E}}_{\mathrm{f}}\left(1-{\mathrm{V}}_{\mathrm{f}}\right)} $$

(2.41)

where E₂, E_m, and E_f are the modulus of composite in the transverse direction, modulus of the matrix, and modulus of the fiber, respectively. It is observed that E₂ is not particularly sensitive to V_f. If E_f >> E_m, E₂ becomes independent of the property of the fiber. The matrix dominates the transverse modulus and is virtually independent of the reinforcement. Jones model is not relevant to most of the practical situations. Hence, improved mechanical models have been developed by using the theoretical studies such as Halpin–Tsai model [80]. The semiempirical Halpin–Tsai equations [81, 82] correct the Eq. 2.41 as

$$ {\mathrm{E}}_2=\frac{{\mathrm{E}}_{\mathrm{m}}^{\prime }{\mathrm{E}}_{\mathrm{f}}}{{\mathrm{E}}_{\mathrm{m}}^{\prime }{\mathrm{V}}_{\mathrm{f}}+ {\mathrm{E}}_{\mathrm{f}}\left(1-{\mathrm{V}}_{\mathrm{f}}\right)} $$

(2.42)

where $\mathrm{E}{\prime}_{\mathrm{m}}=\left[{\mathrm{E}}_{\mathrm{m}}/\left(1-{\nu^2}_{\mathrm{m}}\right)\right]$ and ν_m is the Poisson’s ratio of the matrix.

Hull et al. in 1996 have predicted the rule of mixtures for longitudinal (E₁) and transverse (E₂) modulus of glass/polyester composite (E_f = 73.7 MPa, E_m = 4GPa) as shown in Fig. 2.13 [83].

Fig. 2.13

Schematic showing rule of mixture prediction for longitudinal (E₁) and transverse (E₂) modulus [83]

Stiffness of Short Fiber Composites

For short fiber (aligned) composites, which are usually not found in polymers, the rule of mixtures for modulus [84] in the fiber direction is given as:

$$ {\mathrm{E}}_{\mathrm{c}}={\upeta}_{\mathrm{L}}{\mathrm{E}}_{\mathrm{f}}{\mathrm{V}}_{\mathrm{f}}+ {\mathrm{E}}_{\mathrm{m}}\left(1-{\mathrm{V}}_{\mathrm{f}}\right) $$

(2.43)

where E_c, η_L, E_f, E_m, and V_f are the modulus of the short fiber composite in the fiber direction, the length correction factor, the modulus of the fiber, the modulus of the matrix, and the volume fraction of the fiber, respectively. The length correction factor (η_L) is obtained theoretically (for L > 1 mm, η_L > 0.9).

The rule of mixture expression is brought into picture for composites in which fibers are not perfectly aligned by incorporating both η_L and η_o, where “η_o” is the correction for the non-unidirectional reinforcement. It is 1.0 for unidirectional, 0.5 for biaxial, 0.25 for biaxial at 45°, 0.375 for random in plane, and 0.2 for random in three dimensions.

In short fiber-reinforced thermoset polymer composites, the fibers are much longer than their critical length, and orientation effects determine the elastic properties. For the randomly oriented fiber, the following equations (Eqs. 2.44, 2.45, and 2.46) give sufficiently accurate estimates [85].

$$ {\mathrm{E}}_{\mathrm{r}}=\frac{3}{8}{\mathrm{E}}_{11}+ \frac{5}{8}\;{\mathrm{E}}_{22} $$

(2.44)

$$ {\mathrm{G}}_{\mathrm{r}}= \frac{1}{8}{\mathrm{E}}_{11}+ \frac{1}{4}\;{\mathrm{E}}_{22} $$

(2.45)

$$ {\upnu}_{\mathrm{r}}=\frac{{\mathrm{E}}_{\mathrm{r}}}{{2\mathrm{G}}_{\mathrm{r}}}-1 $$

(2.46)

where E_r, E₁₁, E₂₂, G_r, and ν_r are the modulus of randomly oriented fiber composite, longitudinal modulus of the composite, transverse modulus of the composite, shear modulus of the randomly oriented fiber composite, and Poisson’s ratio of the randomly oriented fiber composite, respectively.

Fatigue

Fiber-reinforced composites have a good rating regarding fatigue life, which can be evaluated by S-N curve. Tension–tension fatigue of advanced composites can be tested with ASTM standard D-3479 specimen. Most of the composite materials are inhomogeneous and anisotropic, and the fatigue behavior of inhomogeneous composites is much more complicated. A model proposed by Epparachchi et al. [86] is applicable to the fatigue data for glass/epoxy and glass/polypropylene specimens. The empirical fatigue law used is given below.

$$ \frac{\mathrm{d}\upsigma}{\mathrm{d}\mathrm{t}}=-{\mathrm{a}\upsigma}_{\max }{\left(1-\mathrm{R}\right)}^{\upgamma}{\mathrm{t}}^{-\mathrm{k}} $$

(2.47)

where σ, t, σ_max, R, and γ are the applied stress, time, maximum stress applied, stress ratio, and the set fixed to 1.6 (derived from assumption on fatigue crack propagation rate), respectively, and a and k are constants.

The above model can be arranged as follows [86]:

$$ \left(\frac{\upsigma_{\mathrm{ult}}}{\upsigma_{\max }}-1\right)\frac{1}{{\left(1-\mathrm{R}\right)}^{\upgamma}}{\mathrm{f}}^{\upbeta}=\upalpha \left({\mathrm{N}}^{\upbeta}-1\right) $$

(2.48)

where σ_ult, σ_max, f, and N are the ultimate stress, the maximum stress applied, the loading frequency, and the number of loading and unloading cycles till failure, respectively, and α and β are constants (can be determined experimentally).

A model has also been developed for the fatigue testing of E-glass fiber/epoxy composite, and the model equations [87] are given as follows:

$$ \frac{\mathrm{d}\upsigma}{\mathrm{d}\mathrm{t}}=-{\mathrm{C}}_2{\mathrm{t}}^{-{\mathrm{m}}_1} $$

(2.49)

$$ {\mathrm{C}}_2=\mathrm{A}.\ f\left(\mathrm{R},{\upsigma}_{\mathrm{u}},{\upsigma}_{\max}\right) $$

(2.50)

where σ, t, m₁, A, R, σ_u, and σ_max are the residual strength after n cycles, time, a material constant, a constant, stress ratio, the initial residual strength, and the maximum applied stress, respectively.

Creep

Creep can be defined as high-temperature progressive deformation at constant stress. It is a performance-based behavior since it is not an intrinsic material response. It is highly dependent on environmental conditions such as temperature. A creep test involves a tensile specimen under a constant load maintained at a constant temperature, and strain measurements are recorded over a period of time. A standard method of testing the creep and creep rupture of a continuous fiber-reinforced ceramic composites subjected to tensile loading at elevated temperature is according to ASTM C-1337:96. The creep resistance of MgO/SiC nanocomposite is found to be 2–3 times greater than that of pure MgO matrix at a temperature of 1300 °C and for the Al₂O₃/SiC nanocomposite, it is about 3–4 times greater than that of a pure Al₂O₃ matrix at a temperature of 1400 °C. In these two cases, a tremendous improvement in creep resistance is observed. This is attributed to the suppression of grain boundary slidings by the reinforced intergranular nano-sized SiC particles.

Stress Relaxation

Glass fiber-reinforced polymer (GFRP) composites used for structural applications require good, long-term mechanical properties. This behavior can be predicted by accelerated mechanical testing such as creep and stress relaxation. The dimensional stability of load-bearing structures and the retention of clamping force for bolts fastened to composites are determined by stress relaxation behavior. The stress relaxation studies of pineapple leaf fiber-reinforced polyethylene composites and banana fiber-reinforced polyester composites have been studied [88, 89]. Barpanda and Mantena have studied the effects of hybridization on the stress relaxation and creep characteristics of pultruded glass–epoxy–graphite hybrid composites [90]. The dynamic mechanical analysis is used for the stimulated stress relaxation and creep testing. Geethamma et al. have analyzed the tensile stress relaxation of natural rubber composites reinforced with short-coir fiber [91]. The strain rate, fiber orientation, and loading affect the relaxation mechanisms of both filled and unfilled composite. Kawai et al. have studied stress relaxation of unidirectional T800H/3631 epoxy/carbon composite at comparatively high tensile strain levels and at elevated temperature [92]. This test has been carried out at 100 °C on plain coupon samples having different fiber orientations, θ = 0, 10, 30, 45, and 90°. After maintaining the constant strain, relaxation of the axial stress with time takes place in a short period. In composite materials, the stress relaxation rate inclines to become zero, regardless of the orientation of the fiber. The relaxation modulus associated with stress relaxation depends on the strain level. The creep and stress relaxation studies to determine the time-dependent longitudinal strength of epoxy and polyester composites reinforced with unidirectional glass fiber have been reported by Lifshitz and Rotem [93]. The risk of delayed fracture can be avoided for stress values lower than 0.4 and 0.65 times the ultimate failure stress for the glass–polyester and glass–epoxy composites, respectively. Gutman and Soncino have analyzed the stress relaxation in polyester–fiber–glass composite under different temperature and chemical environments [94]. Wortmann and Schulz have studied the stress relaxation properties of polypropylene fibers at different temperatures (−50 to 30 °C) [95]. The moduli and relaxation time show noticeable temperature dependencies. Ikeda has assessed the chemical resistance of fiber-reinforced plastics using stress relaxation analysis [96].

Performance Under Adverse Conditions

Polymer matrix composites are sensitive to the changes in environmental conditions such as extreme temperatures, moisture, etc. The effects of temperature and moisture on the parameters such as tensile strength, ILFT, ILSS, elastic modulus, fatigue, etc. have to be examined for better understanding. Hashemi et al. have determined the influence of temperature and geometry on the mode-I, mode-II, and mixed mode-I/mode-II ILFT of the CF/PEEK composites [97]. The study is done within the temperature range 20–130 °C. An increase in ILFT with increase in temperature is observed. However, the ILFT at sub-zero temperatures has not been determined. Sloan and Seymour have investigated the impact on mode-I interlaminar fracture and crack growth in graphite/epoxy as a result of exposing to seawater [98]. Takeda et al. have studied the ILFT of epoxy matrix CFRP and GFRP composites irradiated by high-energy electrons [99]. In case of GFRP, a significant decrease in the fracture toughness is noticed. The effect of moisture on the ILFT of particle-filled glass fiber-reinforced polyester resin composites has been investigated by Srivastava and Hogg [70]. The samples are exposed to water at 20 and 40 °C. Mode-I and mode-II ILFT are measured at an interval of 2 months. It is reported that mode-I toughness is increased for all composites with an increasing moisture uptake. Watt et al. have studied the changes to the mode-I ILFT of stitched fiberglass/vinyl ester composites after exposure to elevated temperatures between 100 and 300 °C [100]. The ILFT of the stitched composites degrades significantly by heating. Pavlidou and Papaspyrides have analyzed the effect of hygrothermal history on the ILSS of glass/polyester composites [101]. The experimentation is carried out at a temperature of 35 °C. Davies et al. have studied the effect of seawater aging on the shear behavior of glass-reinforced composites at 20 and 50 °C [102]. Apicella et al. have studied polyesters and their glass mat-reinforced composites at 20 °C and 90 °C for 50 days [103]. Choqueuse et al. have done a detailed research in a 2-year period on distilled water aging at temperatures 5, 20, 40, and 60 °C [104].

Thermal

Thermal characterization is very important to achieve precise measurement before the application. The thermal behavior of composite materials is evaluated based on the coefficient of thermal expansions (CTEs). Since CTEs vary from material to material, the thermal properties of the composite may be altered. The CTEs are given by Eqs. 2.51 and 2.52 [1].

$$ {\upalpha}_{\mathrm{l}}=\frac{{\mathrm{V}}_{\mathrm{f}}{\upalpha}_{\mathrm{f}\mathrm{l}}{\mathrm{E}}_{\mathrm{f}\mathrm{l}}+{\mathrm{V}}_{\mathrm{m}}{\upalpha}_{\mathrm{m}}{\mathrm{E}}_{\mathrm{m}}}{{\mathrm{V}}_{\mathrm{f}}{\mathrm{E}}_{\mathrm{f}\mathrm{l}}+{\mathrm{V}}_{\mathrm{m}}{\mathrm{E}}_{\mathrm{m}}} $$

(2.51)

$$ {\upalpha}_{\mathrm{t}}={\mathrm{V}}_{\mathrm{f}}{\upalpha}_{\mathrm{f}\mathrm{t}}\left(1 + {\upnu}_{\mathrm{f}\mathrm{l}\mathrm{t}}\frac{\upalpha_{\mathrm{f}\mathrm{l}}}{\upalpha_{\mathrm{f}\mathrm{t}}}\right)+{\mathrm{V}}_{\mathrm{m}}{\upalpha}_{\mathrm{m}}\;\left(1 + {\upnu}_{\mathrm{m}}\right)-\left({\mathrm{V}}_{\mathrm{f}}{\upnu}_{\mathrm{f}\mathrm{l}\mathrm{t}}+{\mathrm{V}}_{\mathrm{m}}{\upnu}_{\mathrm{m}}\right){\upalpha}_{\mathrm{l}} $$

(2.52)

where α_l, α_t, α_fl, α_ft, E_fl, α_m, E_m, ν_flt, and ν_m are the coefficient of thermal expansion in the longitudinal direction, coefficient of thermal expansion in the transverse direction, coefficient of thermal expansion of fibers in the longitudinal direction, coefficient of thermal expansion of the fibers in the transverse direction, the modulus of fibers in the longitudinal direction, coefficient of thermal expansion of the matrix, the modulus of matrix, the in-plane Poisson’s ratio of fibers, and Poisson’s ratio of the matrix, respectively, and the other variables are as discussed above.

Similarly, the longitudinal (Eq. 2.53) and transverse (Eq. 2.54) thermal conductivities of the composite can be written [1] as

$$ {\mathrm{K}}_{\mathrm{l}}={\mathrm{V}}_{\mathrm{f}}{\mathrm{K}}_{\mathrm{f}\mathrm{l}}+{\mathrm{V}}_{\mathrm{m}}{\mathrm{K}}_{\mathrm{m}} $$

(2.53)

$$ {\mathrm{K}}_{\mathrm{t}}=\frac{{\mathrm{K}}_{\mathrm{f}\mathrm{l}}{\mathrm{K}}_{\mathrm{m}}}{{\mathrm{V}}_{\mathrm{f}}{\mathrm{K}}_{\mathrm{m}}+{\mathrm{V}}_{\mathrm{m}}{\mathrm{K}}_{\mathrm{f}\mathrm{t}}} $$

(2.54)

where K_l, K_fl, K_m, K_t, and K_ft are the thermal conductivity of the composite in the longitudinal direction, the thermal conductivity of fibers in the longitudinal direction, the thermal conductivity of the matrix, the thermal conductivity of the composite in the transverse direction, and the thermal conductivity of fibers in the transverse direction, respectively, and the other variables are as discussed above.

Ceramic matrix composites are the materials for high-temperature applications. Various composites have been prepared with SiC matrices, SiC fibers, and boron nitride (BN) fiber coatings [105]. High deposition temperature CVD is the most desirable technique for BN fiber coatings; however, it may lead to problems in the composite fabrication. In this composite, there appears to be three important mechanisms for BN oxidation corrosion: (i) borosilicate glass formation, (ii) gettering (is the process of removing device-degrading impurities from the active regions) of oxygen by SiC, and (iii) volatilization [105]. Rochais et al. have performed initial tests on known materials and a carbon–carbon composite with the help of different analysis methods [106]. These methods explain the modifications in the experimental setup as indicated in Fig. 2.14, a procedure used to determine the temperature diffusivity. The experimental setup has three main parts: (i) an optical setup for positioning and focusing the probe beams and the pump used, (ii) device used for measuring the intensity of the probe beam, and (iii) various electronic devices, which are used for detecting the signal and carrying out the experiment. Maximum power of the pump beam, which is a continuous Ar laser, is 2 W. Its frequency is modulated by a frequency generator-driven acousto-optic modulator operated at frequencies up to 2 MHz. Then, the pump beam is directed with the help of dichroic mirror, which is finally focused with the help of microscope onto the sample surface in the heating stage. The probe beam, which is a laser diode (wavelength 780 nm, power 20 mW), passes through a quarter-wave plate and the dichroic mirror, which is then focused with the same microscope on to the sample surface. After reflecting back, it retracts through the quarter-wave plate again, and from there it is sent to the photodiode by a beam splitter cube. A pump beam photon is protected from reaching the detector by using an optical filter. The amplitude and phase of the periodic signal collected by the photodiode is extracted by a lock-in amplifier. The dichroic mirror orientation is controlled by a PC controller, which governs the distance “r” between the probe and pump beam locations. Heating stage window, which is made of fused silica, transmits 93 % of the intensity of the two beams. Specifically designed objective (40 × magnification) with a large working distance, which is capable of correcting the spherical aberrations produced due to the heating stage window, has been used. Heating stage could attain a highest temperature of 1500 °C under a vacuum level better than 10⁻³mbar. Sample polishing is necessary in order to ensure good reflection. The sample has a diameter less than 7 mm and thickness c.a. 1 mm. Homogeneous temperature gradient is maintained by keeping the thickness of sample as small as possible.

Fig. 2.14

Schematic of a thermal microscope setup [106]

Glass Transition Temperature

Glass transition temperature (denoted by “Tg”) is the temperature at which a material experiences a significant change in properties from hard and brittle to soft and pliable. Typically, Young’s modulus changes sharply. At glass transition temperature, the polymeric structure turns “rubbery” upon heating and “glassy” upon cooling. The glass transition temperature of composites can be determined with the help of differential scanning calorimetry (DSC) technique. It is to be noted that in the case of low Tg materials, in order to achieve the benefit of orientation enhancement effect, the Tg should be in the vicinity of or lower than the measuring temperature.

Electrical

The uses of electrically conductive polymers (ECPs) have been limited in the past due to their drawbacks such as poor mechanical properties, poor environmental and thermal stabilities, etc. It has been shown that the composite structure using an insulating polymer as the host matrix improves the physical and chemical properties of ECPs. These composites can have practical advantages over the homogeneous materials. In the high-temperature region, the electrical conductivity (σ) of the films is found to follow the equation given below [107]:

$$ \upsigma ={\upsigma}_0\\exp \left(-\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{kT}}\right) $$

(2.55)

where E_a, T, and k are the activation energy, absolute temperature, and Boltzmann constant, respectively. It has been reported that the mechanical properties of the conductive composites can be improved with a decrement in the electrical conductivity [107]. Lee and Chen have proposed an idea for improving the mechanical strength of conventional ceramic superconductors, where they have found applications in magnetic levitation and shielding [108]. A series of composites have been prepared, which are flexible even at high temperatures (e.g., (Bi,Pb)₂Sr₂Ca₂Cu₃O_x (2223)). A low-melting-point thermoplastic polymer, nylon-6,6, is used as structural matrix for the composite preparation. The superconducting (Bi,Pb)₂Sr₂Ca₂Cu₃O_x, (2223) powder with critical temperature T_c ~ 104 K has been prepared by conventional solid state reactions having a nominal composition of Bi_1.6Pb_0.4Sr₂Ca₂Cu₃O_y [108].

Magnetic

Magnetic materials in the field of micromachining have been an area of interest for applications such as electromagnetic interference shielding, integrated inductive components, and magnetic microactuators and sensors. However, those materials possessing desirable hard magnetic properties might not be compatible with that of the standard microelectronic processes. For example, in preparation of magnets demanding high temperature, sintering, and pressing, such as in neodymium–iron–boron and samarium–cobalt magnets [109]. Magnetic polymer composites are made of strontium ferrite powder embedded in the polyimide organic matrix. These are considered to be compatible with the micromachining and microelectronic processes and they exhibited good magnetic properties, such as a high coercivity (c.a. 320 kA/m), square magnetization curve, a residual induction approaching 0.3 T, and a maximum energy product of 11,900 T (A/m) and are comparable to the bulk ferrite [109]. Nanostructured magnetic materials exhibit properties stemming from the intrinsic character of the particles and interactions between the particles. These magnetic properties often differ from both the individual constituent atoms and bulk crystalline counterparts. For soft magnetic properties, exchange coupling between the magnetic nanocrystalline grains is required. Therefore, freestanding nanoparticles must be consolidated to allow for this exchange coupling. A ferromagnetic nanocomposite having magnetic nanocrystalline particles in the polymeric matrix can replace conventional ferrites for various applications such as chokes, high-frequency inductors, filters, sensors, core-shaped planar transformers, etc. The increase in resistivity leads to a major reduction in the eddy-current losses in the magnetic/polymeric nanocomposite solid, while the coupling between adjacent magnetic nanoparticles produces remarkably better soft magnetic properties at larger frequencies compared with ferrites or conventional bulk materials.

Piezoelectric

Piezoelectric and electrostrictive materials are found applications in transducers and sensors. Their role in a sensing device is to detect displacement, acceleration, force, and sound. Hence, they are widely used in applications, such as strain and vibration measurement; medical, structural, and health monitoring; underwater imaging; etc. In the last two decades, the ceramics (e.g., lead titanate), polymers (e.g., polyvinylidene difluoride and its copolymers), and ceramic polymer composites (e.g., piezoelectric ceramic particles LaRC Si polyamide binder matrix composite) have been used as piezoelectric materials. Some of the electrostrictive materials have been found to produce a relatively high strain (e.g., lead magnesium niobate) with less hysteresis than that of piezoelectric materials. The piezoelectricity is commonly defined by the following equations [110]:

$$ {\upvarepsilon}_{\mathrm{i}}={\mathrm{S}}_{\mathrm{i}\mathrm{j}}^{\mathrm{E}}{\upsigma}_{\mathrm{j}}+{\mathrm{d}}_{\mathrm{m}\mathrm{i}}{\mathrm{E}}_{\mathrm{m}} $$

(2.56)

$$ {\mathrm{D}}_{\mathrm{m}}={\mathrm{d}}_{\mathrm{m}\mathrm{i}}{\upsigma}_{\mathrm{i}}+{\upzeta}_{\mathrm{i}\mathrm{j}}^{\upsigma}{\mathrm{E}}_{\mathrm{k}} $$

(2.57)

where ε, S, σ, d, E, D, and ζ are the strain vector (in m/m), matrix of compliance coefficients (in m²/N), stress vector (in N/m²), matrix of piezoelectric strain constants (in m/V), vector of applied electric field (in V/m), vector of electric displacement (in C/m²), and permittivity (in F/m), respectively. Here, i and j varies from 1 to 6, and m and k varies from 1 to 3. Also, the superscripts E and σ represent that the measurements are taken at constant electric field and constant stress, respectively.

In polycrystalline ceramics, the poled axis is usually denoted as the 3-axis, and with the ceramic having C_α symmetry, the number of nonzero matrix elements is 10 (like ${S^{E}_{11}}$, ${S^{E}_{12}}$, ${S^{E}_{13}}$, ${S^{E}_{33}}$, ${S^{E}_{44}}$, d₃₁, d₃₃, d₁₅, ${\varepsilon ^{T}_{11}}$, and ${\varepsilon ^{T}_{33}}$). Piezoelectric materials exhibit dispersion and the various material constants are function of frequencies. Most of the constants can be calculated by using resonance measurements. The resonance measurements are carried out by using small signals on the specimens. A test methodology has been developed to characterize the piezoelectric fiber composite for structural actuations as an alternative to monolithic piezoceramic wafers. By using interdigitated electrode pattern, the performance of the abovementioned actuator system has been improved, which helps in the orientation of the electric field’s primary component in the plane of the structure, thus permitting the use of piezoelectric effect along the active fibers. This technology can be applied in an integral twist actuation of helicopter rotor blades for large harmonic control. The actuators required in this application must be able to counter the effect of harsh operating conditions for rotor blades of the helicopter. Thus, actuators that can withstand a huge number of electrical and mechanical cycles with appreciable centripetal and bending loads are desired. The performance of several actuators including S2 glass-reinforced and E-glass-laminated actuators have been studied. It has been observed that the abovementioned interdigitated electrode piezoelectric fiber composite actuator has a wide range of ability for the heavy loading requirements. The micromechanical piezoelectric composites consisting of LaRC Si polyamide binder and piezoelectric ceramic particles, to serve as sensors and actuators for space applications, have been developed. A schematic of this composite is shown in Fig. 2.15. In this schematic, piezoelectric ceramic particles (reinforcement) are indicated by lighter in color, and the darker region is an indicative of LaRC Si polyamide binder (matrix).

Fig. 2.15

Schematic of piezoelectric ceramic particles reinforced LaRC Si polyamide composite

It has been shown that the ceramic particles are bound together in a conglomerate configuration. This typical feature plays a significant role to determine the thermomechanical response of the composite. It is known that a combination of negative coefficient of thermal expansion for ceramic phase and a positive coefficient of thermal expansion for LaRC Si phase results in a nonzero coefficient of thermal expansion for a piezoelectric composite. An application of thermal loading will result in internal stresses due to the thermomechanical and the piezoelectric response. The theoretical models have been developed for studying the piezoelectric behavior of lead titanate (up to 70 vol.%) and polyvinylidene difluoride composites. It has been observed that the data are matched with the experimental results. The piezoelectric polymer (PEP) composites have shown different piezoelectric relaxations. The dispersion has been prepared by adding 3–0 PEP composite piezoelectric spheres in a continuous polymer medium. When an electric field is applied to such a composite, each piezoelectric spheres experiences polarization and can be represented as a dipole. The dipole moment locally modifies the applied field and the surrounding medium. When only a small volume fraction of piezoelectric spheres are present, the influence of this dipole field on the neighboring field will be negligible.

Tribological

Tribological properties of composites are highly significant in long-term application point of views. The erosive wear behavior of Al₂O₃-fiber MMCs has been widely studied [111]. The erosion testing apparatus consists of a stainless steel T-tube in the slurry tank above an erodent reservoir, as shown in Fig. 2.16. The T-tube acts as a vacuum pump by circulation mechanism of water via. a loop arrangement, and the SiC particles (size ~ 600–800 μm) are driven up for impinging the slurry jet onto the specimen. The system gives a certain concentration (e.g., 5.6 wt%) of SiC particles, a jet velocity (e.g., 7.3 m/s) with a flow rate of water (e.g., 4.6 lit/min). The impact angle can be easily adjusted in this arrangement. The distance between the targets can be altered as per our requirements, and the ejector nozzle as well as their relative positions can be easily shuffled and can be monitored. The samples of dimension 25 mm × 25 mm × 5 mm are cut from an Al-MMC cast in two directions – one parallel to the fiber (Al-MMC-P) and the other vertical to the fiber (Al-MMC-V). An Al-alloy (K8510) matrix blank sample without fiber has been used. It has been observed that in the initial stages, the erosion rate (E) rises with the impact angle to the maximum and decreased very lethargically then after, with further increase in the erosion angle (α).

Fig. 2.16

Schematic of erosion test apparatus of sand/water slurry [111]

Bearing Strength

For an aircraft, bearing strength greatly influences the composite component designs. When applied through a cylindrical fastener surface, the maximum stress that a composite can withstand is known as the bearing strength. The bearing stress is an applied comprehensive load on an interface divided by the bearing area. Bearing strength of composite materials can be tested with standard specimen ASTM.00008.10. Furthermore, bearing strength of advanced composite materials can be tested with standard specimen SACMA SRM 9–88. Due to high dependence of notch sensitivity on laminate configuration and a lower shear and bearing strength, having a satisfactory efficiency for a structural coupling with mechanical fastening is very difficult for the composite materials when compared with metals. These properties actually restrict the structural performance of the composite structure and require special reinforcement techniques. Fink and Kolesnikov have observed a high bearing strength for CFRP/Ti hybrid composites while performing bearing tests with specimens having different Ti content unidirectional prepreg plies [112]. In this study, carbon specimens with different laminate configurations have also been tested for comparison. A 6 mm diameter bolt is used and has given a clearance fit with the clamping torque of 0–0.6 mm. The tested specimens featured an edge distance to diameter ratio of 3 and a width to diameter ratio of 4 and 5. The characteristics of static tests conducted up to the failure in on-axis and 90°-off-axis loading directions are illustrated in Fig. 2.17.

Fig. 2.17

Dependency of bearing strength of a hybrid material on Ti content [112]

Here, the maximum specific on-axis bearing strength of the hybrid material is noticed at a Ti content of 55 %, which is slightly lower in comparison to that of 50/40/10 carbon laminate, while 90°-off-axis bearing strength is about 40 % higher. However, the laminate-specific strength doesn’t reflect the absolute weight efficiency of the joint, since the laminate represents only a fraction of the whole local joint design of the structure. The realization of high absolute joint strengths contributes to the reduced complexity and weight of secondary joint components such as bolts, fittings, and connecting parts to a high extent, thus reducing the overall joint weight. The test results have shown the advantage of Ti-reinforced composite material, which offers an increase in strength about 80 % under on-axis loading and 180 % under 90°-off-axis loading compared to the bearing properties of a 50/40/10 CF laminate and is shown in Fig. 2.18. Higher strength increase rates result when comparing with laminates having a higher degree of anisotropy. Hybrid material containing 54 % Ti offers a bearing strength similar to that of a Ti-alloy.

Fig. 2.18

Bearing strength of various CFRP-Ti composites [112]

A bearing test apparatus for an aerospace grade unidirectional CF prepreg tape is shown in Fig. 2.19. The materials such as standard moduli CFs and 180 °C cure modified, toughened epoxy resin have been used for the bearing test experiment [113]. In this experiment, the fasteners with free running nut, 6.35 mm diameter steel hex head bolts, and plain steel washers having 12.7 mm diameter are used. The experimental matrix is comprised of six coupons with the following local constraint conditions: (i) a torque of 0.6, 1.3, 2.4, 3.5, or 7.0 Nm is given to the fastener and (ii) 0.5 or 0.1 mm gap is given on each side of the composite coupon. A mode of failure has been observed and is concluded that the level of local constraints (applied torque or gap size) affects the bearing strength. The gap values between 0.5 and 1.0 mm do not influence the initial failure load. Although, if failure is initiated, debris filling the gap will increase that leads the bearing strength values that do not actually shows the pin-bearing behavior. For an increase in torque values above 1.3 Nm, there is a slight increase in bearing strength, which is steady in nature, and with the increase in values of torque between 0 and 1.3 Nm, the bearing strength increases rapidly. A typical bearing stress–strain for each constraint condition is shown in Fig. 2.20.

Fig. 2.19

Bearing test apparatus for aerospace grade unidirectional carbon fiber prepreg tape [113]

Fig. 2.20

A typical bearing stress–strain for each constraint condition [113]

Rheological

Rheology is the study of the flow of liquids but also solids under conditions in which they flow rather than deform elastically. It is applicable to substances, which have a complex structure, including muds, sludges, suspensions, polymers, many foods, bodily fluids, biological materials, and composites. The rheological performance of long fiber-reinforced thermoplastic composite has been developed, and its relation to structural aspects, which stem from different processing routes used, and correlation of observed facts with available theories have been focused by Cervenka and Alan [114]. The materials for the study are selected in such a way that the role of all important variables known to control the composite performance can be assessed. The important variables are as follows:

• 1. The type of matrix: polypropylene and polyamide

• 2. The nature of the fiber: glass, carbon, and Kevlar

• 3. Processing methods: classical injection molding and multiple life-feed techniques

• 4. Initial fiber length: 5 and 10 mm long pellets used as the feedstock for both the processing methods.

In this study, measurements of rheological parameters and quantification of relevant structural features together with generation of data for composites have been conducted simultaneously. The different structures of thermoplastic matrix/fiber constituents of different mechanical properties are related to the rheological behavior of heterogeneous melts and the interfacial behavior between the matrix and the reinforcement. Shi et al. have studied the rheological properties with good amount of dispersion of single-walled nanotubes (SWNTs) at low concentrations (0.05 wt%) in uncross-linked poly(propylene fumarate) [115]. It has been observed that the SWNTs aggregate at higher concentrations. This aggregation ratifying the mechanical and rheological properties has been revealed with the help of scanning electron microscopic study of fractured nanocomposite surfaces. The oscillatory shear viscoelastic (dynamic and linear) response for an uncross-linked nanocomposite and an uncross-linked polymer with varying concentrations of SWNTs, which are made compatible with the polymer using 12-aminododecanoic acid surfactant, is shown in Fig. 2.21 [115]. The complex viscosity magnitude (|η*|) and the elastic modulus (G′) both transforms abruptly from liquid-like behavior of the matrix polymer (G′ ∝ ω², |η*| ∝ ω⁰) to solid-like behavior of the nanocomposites having 0.05 wt% and higher SWNT (G′ ∝ ω⁰, |η*| ∝ ω⁻¹).

Fig. 2.21

Schematic showing dependency of (a) elastic modulus and (b) complex viscosity magnitude on frequency [115]

Biological

Biological characterizations of composite materials include toxicity and degradation testing procedures, which are most important in biological applications [116–119]. The interphases of such composites are particularly important in the case of bio-related applications; hence, their properties in terms of biocompatibility, biodegradability, and bioactivity have to be well understood before practical applications [120, 121]. For example, the dental patients have routinely demanded high aesthetic restorations since a long time ago. The major problems related to the use of resin composites for large restorations in posterior teeth are the side effects and environmental issues related with dental amalgams. The current developments in dental researches have evoked the interest on the use of ceramic composite materials for restoration application [122]. Research on novel biodegradable, biocompatible, and bioactive composite materials for various biological applications such as bone replacement [123–127], tissue replacements [128–132], etc., are on the way to success.

Concluding Remarks

In this chapter, the various experimental characterizations of composites are discussed briefly. Since these characterizations are not adequate for determining complete properties of the composite systems, advanced techniques have to be developed in order to obtain a broad picture. The need of highly performing advanced composites is increasing day by day due to the developments on their processability, designing flexibility, etc. The advanced composites are often presenting greatest challenges in their experimental characterizations. Among these, biological characterization is also very important since the toxicity of composites will directly influence the human life. Hence, characterizing composite materials for the better understanding of their real behaviors, in all possible directions, is very critical for their practical applicability and acceptance.