**4. Aramid fiber-matrix interfaces and tests**

To understand the influence and nature of a modification on adhesion, the interface between fibers and matrix must be probed. Because most of the interest in surface modifications is founded on the targets by mechanical performance, the mechanical testing of the fiber-matrix bond is surveyed in the following.

Whenever a single filament or a bundle of fibers is analyzed, the samples or test specimens are small. Consequently, the load introduction and sensor configuration must be arranged in a highly sophisticated way. Currently, there are several test methods to study fiber-matrix interfaces:


The mechanical testing of fiber-matrix interfaces is not standardized, and therefore, the methodology among the current literature is not in harmony. The devices, specimen preparation, statistical significance, and the theory of data analysis vary in different reports and publications.

**43**

**Figure 1.**

*Advanced Treatments of Aramid Fibers for Composite Laminates*

*IFSS* = \_

Due to the challenges of surfaces of aramid fibers, the tests of fiber-matrix interfaces are much used. The main presumption behind different test methods of interfaces is that the breakage of the interfacial bond occurs in a brittle manner. Also, it is typical to estimate that only shear load is subjected to the interface during testing. Then, the basic form of "interfacial strength" is denoted by interfacial shear

> *Fcrit Aemb*

where *Fcrit* represents the peak value of the shear force observed during a test, and *Aemb* is the area carrying the load, i.e., the embedded fiber area. Eq. (1) is rather useful when the microdroplet method is used because the embedded area is relatively easy to determine. However, several corrections to the calculation of IFSS have been formulated when testing droplets bonded on carbon, aramid, glass, and natural fibers. Synthetic fibers, especially aramid fibers, are typically considered smooth or nearly smooth with only minor roughness that could result in sheer mechanical interlocking. Thus, the presumption of brittle failure of the interface

The main deficiency related to interface tests is the lack of statistical significance

A specific note related to aramid fibers is the role of friction between individual fibers and bundles in a fabric or preform structure. For certain ballistic applications, the amount of resin in the final product is low or entirely omitted, and then, the behavior of the aramid fiber-based reinforcement is governed by friction [26].

and, consequently, reliability. For example, many of the works done using the microdroplet method are covering a low number of fiber-droplet samples and a low amount of variation in the droplet configuration per aramid fiber sample [25]. Also, the localized plastic deformation occurring in the droplet has an effect on the interfacial loading but is seldomly accounted for yet it can be detected easily in the

microscopy images of the tested droplets, as shown in **Figure 1**.

*An example of fiber-matrix droplets that have been tested using the microdroplet method [18].*

(1)

*DOI: http://dx.doi.org/10.5772/intechopen.90816*

strength (IFSS):

ought to be justified.

#### *Advanced Treatments of Aramid Fibers for Composite Laminates DOI: http://dx.doi.org/10.5772/intechopen.90816*

*Composite and Nanocomposite Materials - From Knowledge to Industrial Applications*

Only few works reported the potential of covalent bonds [7, 17].

remain acceptable [18, 19].

high interfacial loads [4].

**4. Aramid fiber-matrix interfaces and tests**

methods to study fiber-matrix interfaces:

• the pull-out method, e.g., [23];

in different reports and publications.

• the micro-droplet method, e.g., [21];

• the fiber push-out method, e.g., [24]; and

• the fiber bundle pull-out method, e.g., [10].

• the single-fiber fragmentation method, e.g., [22];

Many of the studies of surface treatments anticipated that the treatments did not result in covalent bonds between the fiber surface and the matrix polymers [15, 16].

The optimization of surface treatments is important to gain the desired macroscopic behavior in specific composite laminates. Naturally, the recipe of an optimum treatment depends on the targeted laminate behavior. Due to the typical applications of aramid fibers and their reinforcements, impact tests are frequently used in the evaluation of the interface performance on a laminate scale. Impact resistance and impact damage are complex phenomena. Good interfacial adhesion does not necessarily lead to desired impact performance [8, 17]. Within impact, frictional sliding along layer and fiber (inter)faces plays a role in energy absorption and might be hindered by a high level of adhesion. When a surface treatment is tailored for a macroscopic performance, it is advantageous that secondary properties remain unchanged, while the primary properties are improved [18]. Moreover, the performance under effects of harsh operation environments should

It was mentioned that high enough adhesion can lead to shattering of the aramid surfaces upon loading due to the internal structure of aramid fibers. Kanerva et al. [18] applied a diamond-like carbon (DLC) coating to form a nanoscale protective surface structure and also to gain high adhesion between the fibers and an epoxy matrix. The high adhesion related to DLC-coated aramid fibers and matrix polymers was also established by Devlin et al. (US Patent 6432537) [20] for short fibers. The latest research of modifying aramid fibers has been targeted to improve the internal structure of aramid fibers in order to prevent the fiber's cohesive damage at

To understand the influence and nature of a modification on adhesion, the interface between fibers and matrix must be probed. Because most of the interest in surface modifications is founded on the targets by mechanical performance, the

Whenever a single filament or a bundle of fibers is analyzed, the samples or test specimens are small. Consequently, the load introduction and sensor configuration must be arranged in a highly sophisticated way. Currently, there are several test

The mechanical testing of fiber-matrix interfaces is not standardized, and therefore, the methodology among the current literature is not in harmony. The devices, specimen preparation, statistical significance, and the theory of data analysis vary

mechanical testing of the fiber-matrix bond is surveyed in the following.

**42**

Due to the challenges of surfaces of aramid fibers, the tests of fiber-matrix interfaces are much used. The main presumption behind different test methods of interfaces is that the breakage of the interfacial bond occurs in a brittle manner. Also, it is typical to estimate that only shear load is subjected to the interface during testing. Then, the basic form of "interfacial strength" is denoted by interfacial shear strength (IFSS): *IFSS* = \_

$$IFSS = \frac{F\_{crit}}{A\_{cub}} \tag{1}$$

where *Fcrit* represents the peak value of the shear force observed during a test, and *Aemb* is the area carrying the load, i.e., the embedded fiber area. Eq. (1) is rather useful when the microdroplet method is used because the embedded area is relatively easy to determine. However, several corrections to the calculation of IFSS have been formulated when testing droplets bonded on carbon, aramid, glass, and natural fibers. Synthetic fibers, especially aramid fibers, are typically considered smooth or nearly smooth with only minor roughness that could result in sheer mechanical interlocking. Thus, the presumption of brittle failure of the interface ought to be justified.

The main deficiency related to interface tests is the lack of statistical significance and, consequently, reliability. For example, many of the works done using the microdroplet method are covering a low number of fiber-droplet samples and a low amount of variation in the droplet configuration per aramid fiber sample [25]. Also, the localized plastic deformation occurring in the droplet has an effect on the interfacial loading but is seldomly accounted for yet it can be detected easily in the microscopy images of the tested droplets, as shown in **Figure 1**.

A specific note related to aramid fibers is the role of friction between individual fibers and bundles in a fabric or preform structure. For certain ballistic applications, the amount of resin in the final product is low or entirely omitted, and then, the behavior of the aramid fiber-based reinforcement is governed by friction [26].

#### **Figure 1.**

*An example of fiber-matrix droplets that have been tested using the microdroplet method [18].*

In the end, the macroscopic behavior of a fibrous composite system is important. This means that the role of the interface and its strength should be known on the laminate level of length scales. Unfortunately, the exact relationship extending up from the single-filament behavior and up to the homogenized laminate level is lacking in the scientific literature. Several models exist to input interfacial effects while modeling bulk elasticity or strength [27]. To envisage the way that the combination of aramid fibers and matrix works, the well-known Halpin-Tsai model can be used as an example. For fibers, the model distinguishes between the effects of a particulate ("Greek symbol capital Phi" volume fraction) in its longitudinal direction and the effects in the transverse direction; these two directions are noted, by subindices *L* and *T*, here. Then, for the longitudinal direction, the model reads: *r* \_

$$\frac{E\_L}{E\_m} = \frac{\mathbf{1} + \frac{l}{l^\*} \boldsymbol{\eta}\_L \,\mathrm{q}}{\mathbf{1} - \boldsymbol{\eta}\_L \,\mathrm{q}} \tag{2}$$

where

$$\mathbf{\eta}\_{L} = \frac{\frac{E\_f}{E\_m} - \mathbf{1}}{\frac{E\_f}{E\_m} + \frac{I}{Y}} \tag{3}$$

and where *l* is the fibrous particles' length, *r* is the diameter, and *E* refers to Young's modulus of the individual components. The individual components are the matrix (*m*) polymer and the fibers (*f*). For the transverse direction, the model reads: = \_

$$\frac{E\_T}{E\_m} = \frac{\mathbf{1} + 2\,\eta\_T\,\mathrm{q}}{\mathbf{1} - \eta\_T\,\mathrm{q}}\tag{4}$$

where

$$
\begin{aligned}
\mathbf{u} &= \mathbf{u} + \mathbf{u} \\
&= \frac{E\_f}{E\_m} - \mathbf{1} \\
&= \frac{\frac{E\_f}{E\_m} - \mathbf{1}}{\frac{E\_f}{E\_m} + \mathbf{2}}
\end{aligned}
\tag{5}
$$

By combining the longitudinal and transverse effects, the model yields the composite's stiffness (modulus) in a system of randomly oriented fibers:

$$E\_c = a \, E\_L + \left(\mathbf{1} - a\right) E\_T \tag{6}$$

**45**

(see, e.g., [33]).

*Advanced Treatments of Aramid Fibers for Composite Laminates*

or bundle-bundle cross-over point. However, the numerical simulations can be harnessed with models on different length scales. Models of a single-length scale as well as multiscale routines are excellent tools to survey various effects on composite

To model an interface, its volume in finite element (FE) models is commonly estimated to be zero, i.e., interface is a two-dimensional object or contact formulation. As a first estimate, this type of an interface can be estimated to behave in a brittle manner for aramid fibers, so that linear elastic fracture mechanics (LEFMs) are applicable in addition to sheer stress analysis. The power in the LEFM for interfaces is that a fracture toughness (*Gi*) in terms of a strain energy release rate can be used to describe the "strength" of an interface. With this type of a fracture parameter, the simulation results are somewhat less element mesh-dependent. As noted, the plastic deformation of matrix around fibers affects interfacial breakage. To allow research of these effects, the models must be analyzed beyond LEFM. FE analysis with a homogenized interface model has been applied for models

When plastic deformation at the interfacial region is considered, the fracture

*Gp* = \_ *d Wp d Aemb*

*Ge* = \_ *d W*<sup>e</sup> *d Aemb*

where the subindex *p* refers to plastic energy dissipation at interface, and the subindex *e* refers to the elastic strain energy release rate (ERR). In detail, the fracture toughness values can be related to the critical levels of energy release rate of damage onset (e.g., *Gc*) or propagation. In the applications of plastic dissipation at an interface, the common interface modeling method is the cohesive zone model (CZM). CZM refers to a mechanical model where the traction (*τ*) at the interface is defined as a function of the separation (*δ*) between the originally bonded bodies, i.e., fiber and matrix. As an example, a bilinear traction-separation law can be

(7)

(8)

(9)

*<sup>K</sup>* (10)

. (11)

energy over the fiber surface (*Aemb*) divides into two parts upon fracture:

⎧ ⎪ ⎨ ⎪ ⎩

*K*δ \_ *a*<sup>1</sup> − δ *a*<sup>1</sup> − *a*<sup>0</sup> τ<sup>0</sup> 0

*for*

*<sup>a</sup>*0 = \_ τ0

*<sup>a</sup>*1 = \_ 2 *Gc τ*0

It can be seen that the simple bilinear formulation leads to two strength-related parameters: fracture toughness (*Gc*) and the critical traction (*τ0*) related to the onset criterion of damage. Additionally, the numerical computation requires a definite value for the interfacial stiffness (*K*). Due to the strong relation to the computational procedures, the definition of *K* is vague from the point of view of material interfaces—several theories for CZM applications have been presented

δ ≤ *a*<sup>0</sup> *a*0 ≤ δ ≤ *a*<sup>1</sup> δ ≥ *a*<sup>1</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.90816*

properties.

and

with a single fiber [30–32].

formulated as follows:

and

τ =

In Eq. (9), the below notations are used:

where *a* is a parameter that could be considered a function of the interface, orientation, or a shape factor. The *a*-parameter can be a constant value or a function of other external factors [28]. However, there is no universal model to implement interfacial effects specific to aramid fibers by the parameter.

For advanced composites, where the fibers are continuous, the above format of Halpin-Tsai equations cannot be used (*l* goes toward infinity in Eqs. 2 and 3). In this case, the bulk composite properties are entirely anisotropic, and the elastic constants, for example, must be determined for each of the three directions individually [2]. In these formulations, the so-called Halpin-Tsai parameters can be thought to represent the interfacial effects on the laminate's transverse and shear properties. Various studies have applied these equations to account for multiscale interfacial effects in composites (see, e.g., [29]).

### **5. Numerical predictions and finite element modeling**

The experimental analysis of advanced composites is lacking the length scale of a representative bundle level. This is probably due to the practical challenges by small scale and due to the large variation, in size, of a representative bundle

or bundle-bundle cross-over point. However, the numerical simulations can be harnessed with models on different length scales. Models of a single-length scale as well as multiscale routines are excellent tools to survey various effects on composite properties.

To model an interface, its volume in finite element (FE) models is commonly estimated to be zero, i.e., interface is a two-dimensional object or contact formulation. As a first estimate, this type of an interface can be estimated to behave in a brittle manner for aramid fibers, so that linear elastic fracture mechanics (LEFMs) are applicable in addition to sheer stress analysis. The power in the LEFM for interfaces is that a fracture toughness (*Gi*) in terms of a strain energy release rate can be used to describe the "strength" of an interface. With this type of a fracture parameter, the simulation results are somewhat less element mesh-dependent.

As noted, the plastic deformation of matrix around fibers affects interfacial breakage. To allow research of these effects, the models must be analyzed beyond LEFM. FE analysis with a homogenized interface model has been applied for models with a single fiber [30–32].

When plastic deformation at the interfacial region is considered, the fracture energy over the fiber surface (*Aemb*) divides into two parts upon fracture:

$$\begin{array}{c} \text{---} \quad \text{g-} \quad \text{---} \quad \text{---} \quad \text{---} \quad \text{---} \quad \text{---} \\ \text{ divides into two parts upon fracture:} \\\\ G\_p = \frac{d \, W\_p}{dA\_{cub}} \end{array} \tag{7}$$

and

*Composite and Nanocomposite Materials - From Knowledge to Industrial Applications*

*L* and *T*, here. Then, for the longitudinal direction, the model reads:

\_ *EL Em* <sup>=</sup><sup>1</sup> <sup>+</sup> \_*l r* \_ η*L*φ

\_ *Ef Em* \_ − 1 \_ *Ef Em* + \_*l r*

η*L* =

and where *l* is the fibrous particles' length, *r* is the diameter, and *E* refers to Young's modulus of the individual components. The individual components are the matrix (*m*) polymer and the fibers (*f*). For the transverse direction, the model reads:

= \_ 1 + 2 η*<sup>T</sup>* φ

\_ *Ef Em* \_ − 1 \_ *Ef Em* + 2

\_ *ET Em*

composite's stiffness (modulus) in a system of randomly oriented fibers:

interfacial effects specific to aramid fibers by the parameter.

**5. Numerical predictions and finite element modeling**

effects in composites (see, e.g., [29]).

η*T* =

By combining the longitudinal and transverse effects, the model yields the

where *a* is a parameter that could be considered a function of the interface, orientation, or a shape factor. The *a*-parameter can be a constant value or a function of other external factors [28]. However, there is no universal model to implement

For advanced composites, where the fibers are continuous, the above format of Halpin-Tsai equations cannot be used (*l* goes toward infinity in Eqs. 2 and 3). In this case, the bulk composite properties are entirely anisotropic, and the elastic constants, for example, must be determined for each of the three directions individually [2]. In these formulations, the so-called Halpin-Tsai parameters can be thought to represent the interfacial effects on the laminate's transverse and shear properties. Various studies have applied these equations to account for multiscale interfacial

The experimental analysis of advanced composites is lacking the length scale of a representative bundle level. This is probably due to the practical challenges by small scale and due to the large variation, in size, of a representative bundle

<sup>1</sup> <sup>−</sup>η*L*<sup>φ</sup> (2)

<sup>1</sup> <sup>−</sup>η*<sup>T</sup>* <sup>φ</sup> (4)

*Ec* = *a EL* + (1 − *a*) *ET* (6)

(5)

(3)

In the end, the macroscopic behavior of a fibrous composite system is important. This means that the role of the interface and its strength should be known on the laminate level of length scales. Unfortunately, the exact relationship extending up from the single-filament behavior and up to the homogenized laminate level is lacking in the scientific literature. Several models exist to input interfacial effects while modeling bulk elasticity or strength [27]. To envisage the way that the combination of aramid fibers and matrix works, the well-known Halpin-Tsai model can be used as an example. For fibers, the model distinguishes between the effects of a particulate ("Greek symbol capital Phi" volume fraction) in its longitudinal direction and the effects in the transverse direction; these two directions are noted, by subindices

**44**

where

where

$$\mathbf{G}\_{\varepsilon} = \frac{d \, W\_{\varepsilon}}{d \, A\_{comb}} \tag{8}$$

where the subindex *p* refers to plastic energy dissipation at interface, and the subindex *e* refers to the elastic strain energy release rate (ERR). In detail, the fracture toughness values can be related to the critical levels of energy release rate of damage onset (e.g., *Gc*) or propagation. In the applications of plastic dissipation at an interface, the common interface modeling method is the cohesive zone model (CZM). CZM refers to a mechanical model where the traction (*τ*) at the interface is defined as a function of the separation (*δ*) between the originally bonded bodies, i.e., fiber and matrix. As an example, a bilinear traction-separation law can be formulated as follows:

1.e., inder auhu maturx. As an exampie, a numéar \*\*narrow-separation\*\* Law can be multiplied as follows: 
$$\mathsf{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\texttt{\beta}}}}}}}}}}}}}}}}}}}{\texttt{\texttt{\texttt{\texttt{\texttt{\cdot}}}}}}{\texttt{\texttt{\texttt{\cdot}}}} $$

In Eq. (9), the below notations are used:

$$\mathcal{A}\_0 = \frac{\mathbf{r}\_0}{K} \tag{10}$$

and

$$\mathcal{A}\_1 = \frac{2\,G\_c}{\tau\_0}.\tag{11}$$

It can be seen that the simple bilinear formulation leads to two strength-related parameters: fracture toughness (*Gc*) and the critical traction (*τ0*) related to the onset criterion of damage. Additionally, the numerical computation requires a definite value for the interfacial stiffness (*K*). Due to the strong relation to the computational procedures, the definition of *K* is vague from the point of view of material interfaces—several theories for CZM applications have been presented (see, e.g., [33]).

**Figure 2.** *An example of a 3D model simulating the microdroplet testing.*

The power of numerical procedures allows to expand the analysis and consider exact three-dimensional models. Evidently, the parameters of the interface will have to defined in the three-dimensional system. For example, the damage onset will require a fracture criterion, and the fracture toughness will have to be applied via an interaction function.

For aramid fiber composites, an FE analysis was reported by Kanerva et al. [18] with a full 3D representation (see **Figure 2**). For the DLC-coated aramid fibers, values of 22.2 MPa and 500 J/m2 were determined for the case-specific critical traction and interfacial fracture toughness, respectively.

It is clear that the current numerical modeling techniques and computational capacities can offer efficient tools to study fiber-matrix interactions in composites with aramid fibers. However, the multiplicity of parameters currently leads to overlapping fitting procedures. Thus, the solutions are not typically unitary to the simulation case in question. There is an urgent need to improve the microtest methods in order to gain more experimental output and data to validate the numerical models. There are very recent works in the current literature that target to improvements in the test systems to enhance statistical significance, data rate, and accurate output from the microtests [34, 35].

In future, it will be possible to accurately account for plastic deformation, residual stresses, and a multistage fracture process in the simulations of fibermatrix interfaces. This will be an important step toward analyses of fatigue and environmental effects on interfaces in composites with aramid fibers.
