The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced Polymer Composites

*Huseyin Ersen Balcioglu and Hayri Baytan Ozmen*

## **Abstract**

Due to the high synergistic effects of the components, hybrid composite materials are more advantageous than nonhybrid composite materials for advanced engineering applications. Additionally, knitted fabrics may have a different behavior than woven ones. Although the nonhybrid composites have only one reinforcing fiber type, the hybrid composites have multiple reinforcing fibers. In this chapter, fracture characterizations of laminated composites reinforced with intraply pure and hybrid knitted fabrics are experimentally and numerically investigated under different loading conditions. For this purpose, pure (100%) and hybrid fabrics (50–50%), which have 1 1 rib-knitted structure, were knitted by using glass and carbon fibers. Also, hybrid fabrics were knitted in three different widths in order to investigate the effect of knitting pattern width on the fracture toughness. Fracture toughness and energy strain release rates of pure and hybrid Arcan test specimens were determined under mode I (0o ), mixed-mode I/II (30o , 45o , and 60o ), and mode II (90o ) loading conditions. Also, the J-integral method was used to determine the fracture toughness. Experimental and numerical results were found to be consistent. When the results obtained from pure and hybrid fabrics are compared, it is seen that hybridization had positive effects on the fracture strength of composite material compared to pure glass/epoxy material. Additionally, as the width of the pattern decreased, the fracture strength of the hybrid composites increased. In this respect, the hybridization processing should be done in the narrowest pattern width for higher resistance to fracture.

**Keywords:** fracture toughness, strain energy release rate, Arcan fracture test, pure and hybrid laminated composite, knitted fabric, J-integral method

## **1. Introduction**

High strength to low weight ratio is a sought-after feature in the materials used in the structural elements of today's world. With the technological advances in recent years, composite materials are used in many industries, where durability and lightness are at the forefront, especially from the aerospace to automotive sectors. Polymeric composites have been used in many engineering applications due to their high strength in proportion to their weight, high stability, rigidity, superior corrosion, and fatigue resistance [1–3]. Woven or knitted fabrics of durable synthetic fibers such as glass, carbon, or aramid are used to reinforce polymer matrix

composite. Woven reinforcement exhibits good stability in the warp and weft directions and offers the highest cover or yarn packing density in relation to fabric thickness [4]. Knitting is another technique of fabric formation for reinforcing. The fabric is formed by the inter-looping of yarn. The inter-looping of yarn can be done in two ways, namely, warp and weft knitting [5]. Complex lattice structures can be produced by local deformation of the loop in knitted structures. The loop that oriented through-thickness direction improves the out-of-plane mechanical properties of the structure. In addition, thanks to the perfectible geometry of the loop, high impact resistance and damage tolerance can be achieved. Textile-reinforced composites consist of a textile form as the reinforcement phase and usually a polymer for the matrix phase. 2D or 3D woven fabrics, knitted fabrics, stitched fabrics, braids, nonwovens, and multiaxial fabrics can be used as textile materials. Each of these textile forms has its own fiber architecture and combination of properties such as strength, stiffness, flexibility, and toughness, which are reflected on the composite performance to a certain extent [6]. A number of researchers have studied the damage strength of knitted fabric-reinforced composite structures under loading of tensile, compressive, fracture, and impact [7–10].

growth of defects that occur during the service that leads to destruction, is vital to the safety of the composite structures. The value of fracture toughness of composite materials strongly depends on three loading states at the end of the crack tip as the tensile opening mode (mode I), the in-plane shear mode (mode II), and the out-of-plane shear mode (mode III). However, fracture state does not form in pure mode I or mode II in the fiber-reinforced composite materials due to combined loading or anisotropy of composite structures [17]. For this reason, the study of the mixed-mode interlaminar fracture toughness is very important. Zhao et al. [18] have studied interlaminar fracture toughness of hybrid woven carbon-Dyneema composites with different hybridization schemes. The results showed that hybridization improves both mode I and mode II fracture toughness of carbon-Dyneema interfaces. Bienias et al. [19] have investigated interlaminar fracture toughness of woven glass and carbon-reinforced multidirectional fiber metal laminates under mixed-mode (mode I/II) loading. Jung and Kim [20] have investigated the fracture toughness of carbon-glass/epoxy interply hybrid composite under mode I loading condition. Saidane et al. [21] have investigated mode-I interlaminar fracture toughness of flax; glass and hybrid flax-glass fiber are woven composites by using a double cantilever beam test method. Swolf et al. [22] have studied translaminar fracture toughness of woven carbon/glass hybrid composites

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced…*

*DOI: http://dx.doi.org/10.5772/intechopen.89478*

Hybridizing two or more reinforcement materials within a matrix seeks to enhance the advantages of the reinforcing constituents and lessen the effect of the less desirable characteristics. In this study, the fracture toughness of pure and intraply hybrid knitted fabric-reinforced laminated composite plates have been investigated, experimentally and numerically. For this purposes, hybrid fabrics were knitted in a 1 1 rib-knitted structure by using glass and carbon fibers with equal weight carbon/glass fibers (50–50%). In order to investigate the effect of the knitting pattern width on the fracture behavior, the reinforcing hybrid fabrics were knitted at three different widths, such as 50, 25, and 12.5 mm. Arcan test apparatus was used to define mode I (opening mode), mode II (shearing mode), and mode I/II (mixed-mode) fracture toughness of test specimens. Also, fracture toughness for all composite samples was numerically determined in finite element analysis by using

Knitting is primarily classified as weft knitting and warp knitting. This classification is based on the direction of movement of yarn with respect to the direction of fabric formation. If the yarns run in the width or crosswise direction with reference to the direction of fabric formation during knitting, then the process of knitting is called weft knitting. The yarns in the knitted structure are just like weft yarns in woven fabrics. The weft-knitted fabrics made with one set of needles arranged in the grooves on one needle bed are called single jersey fabrics or plain knitted fabrics. In the experimental study, intraply hybrid reinforcement fabrics, which have 11 rib knitting structure, were knitted in a V-bed semi-automatic knitting machine. For this aim, 2400tex E-glass fibers and 3K carbon fibers were used as a knitting

A loop is called a face loop or back loop according to the direction of the passing of one loop through another one during inter-looping (**Figure 1a**). A course is a horizontal row of loops produced by all the adjacent needles during the same knitting cycle. A wale is a vertical column of loops made by the same needle in

under impact loading.

the J-integral method.

reinforcement element.

**67**

**2. Materials and methods**

**2.1 Knitting process of hybrid fabric**

Lower cost, lower density, comparable specific strength, and better deformation capacity are the advantages of glass fibers as compared to carbon fibers. However, types of glass fibers have worse mechanical properties than carbon fibers, which is a limitation to the applications, especially when these materials are exposed to more severe stresses. One way to overcome this problem is hybridization, i.e., the combination of glass and carbon fibers, using a matrix compatible with both fibers, to obtain a composite material with satisfactory properties and lower cost. Hybridization with different fiber types within laminated composites increases the design space and opens up possible new engineering applications with optimized mechanical and functional properties. In addition, in the classical composites, the hybridization of carbon and glass fibers may cause a positive hybrid effect, which relies on the increase of carbon fibers failure strain, when compared to the pure carbonbased composites [11]. Generally, as far as the strength of the carbon/glass hybrid is concerned, the higher the volume percentage of carbon fibers is, the stronger the hybrid laminate becomes. The reason is that the carbon fibers are very tough and stiff, while the glass fibers are less stiff and less durable. In carbon/glass fiberreinforced composites, an advantageous hybrid effect is also observed, which consists in increasing the carbon fiber failure strain when compared to the pure carbon fiber. In the literature, there are studies investigating the effects of carbon/glass hybridization on mechanical behavior. Tabrizi et al. [12] have investigated damage evolution in carbon/glass fiber hybrid composites with various stacking sequences under pure bending and tensile loading conditions. Swolfs et al. [13] concluded that the effect for tensile failure strain is well established, with a typical range of 10–50% for traditional hybrid composites such as carbon/glass. Wisnon et al. [14] have investigated hybrid effects on thin ply carbon/glass unidirectional laminates. Test results showed that the magnitude of the hybrid effect depends on the ply thickness. Dong and Davies [15] have studied the mechanical properties of the hybrid composites reinforced with the glass and carbon fibers. Naito and Oguma [16] have investigated tensile properties and fracture behavior of carbon/glass hybrid thermoplastic composite rods consisting of unidirectional PAN-based carbon fiber, braids of E-glass glass fibers, and thermoplastic epoxy matrix.

Composite materials used for structural purposes can be damaged during manufacturing, assembly, and usage of them. These damages can cause breaking of the materials under environmental effects and external loadings. One of these damages is crack onset and fracture, which depends on crack formation. Fracture, which is precarious for composite structures, can cause loss of life and property. Thus, the fracture analysis of the composite materials, especially focusing on the

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.89478*

growth of defects that occur during the service that leads to destruction, is vital to the safety of the composite structures. The value of fracture toughness of composite materials strongly depends on three loading states at the end of the crack tip as the tensile opening mode (mode I), the in-plane shear mode (mode II), and the out-of-plane shear mode (mode III). However, fracture state does not form in pure mode I or mode II in the fiber-reinforced composite materials due to combined loading or anisotropy of composite structures [17]. For this reason, the study of the mixed-mode interlaminar fracture toughness is very important. Zhao et al. [18] have studied interlaminar fracture toughness of hybrid woven carbon-Dyneema composites with different hybridization schemes. The results showed that hybridization improves both mode I and mode II fracture toughness of carbon-Dyneema interfaces. Bienias et al. [19] have investigated interlaminar fracture toughness of woven glass and carbon-reinforced multidirectional fiber metal laminates under mixed-mode (mode I/II) loading. Jung and Kim [20] have investigated the fracture toughness of carbon-glass/epoxy interply hybrid composite under mode I loading condition. Saidane et al. [21] have investigated mode-I interlaminar fracture toughness of flax; glass and hybrid flax-glass fiber are woven composites by using a double cantilever beam test method. Swolf et al. [22] have studied translaminar fracture toughness of woven carbon/glass hybrid composites under impact loading.

Hybridizing two or more reinforcement materials within a matrix seeks to enhance the advantages of the reinforcing constituents and lessen the effect of the less desirable characteristics. In this study, the fracture toughness of pure and intraply hybrid knitted fabric-reinforced laminated composite plates have been investigated, experimentally and numerically. For this purposes, hybrid fabrics were knitted in a 1 1 rib-knitted structure by using glass and carbon fibers with equal weight carbon/glass fibers (50–50%). In order to investigate the effect of the knitting pattern width on the fracture behavior, the reinforcing hybrid fabrics were knitted at three different widths, such as 50, 25, and 12.5 mm. Arcan test apparatus was used to define mode I (opening mode), mode II (shearing mode), and mode I/II (mixed-mode) fracture toughness of test specimens. Also, fracture toughness for all composite samples was numerically determined in finite element analysis by using the J-integral method.

## **2. Materials and methods**

#### **2.1 Knitting process of hybrid fabric**

Knitting is primarily classified as weft knitting and warp knitting. This classification is based on the direction of movement of yarn with respect to the direction of fabric formation. If the yarns run in the width or crosswise direction with reference to the direction of fabric formation during knitting, then the process of knitting is called weft knitting. The yarns in the knitted structure are just like weft yarns in woven fabrics. The weft-knitted fabrics made with one set of needles arranged in the grooves on one needle bed are called single jersey fabrics or plain knitted fabrics. In the experimental study, intraply hybrid reinforcement fabrics, which have 11 rib knitting structure, were knitted in a V-bed semi-automatic knitting machine. For this aim, 2400tex E-glass fibers and 3K carbon fibers were used as a knitting reinforcement element.

A loop is called a face loop or back loop according to the direction of the passing of one loop through another one during inter-looping (**Figure 1a**). A course is a horizontal row of loops produced by all the adjacent needles during the same knitting cycle. A wale is a vertical column of loops made by the same needle in

composite. Woven reinforcement exhibits good stability in the warp and weft directions and offers the highest cover or yarn packing density in relation to fabric thickness [4]. Knitting is another technique of fabric formation for reinforcing. The fabric is formed by the inter-looping of yarn. The inter-looping of yarn can be done in two ways, namely, warp and weft knitting [5]. Complex lattice structures can be produced by local deformation of the loop in knitted structures. The loop that oriented through-thickness direction improves the out-of-plane mechanical properties of the structure. In addition, thanks to the perfectible geometry of the loop, high impact resistance and damage tolerance can be achieved. Textile-reinforced composites consist of a textile form as the reinforcement phase and usually a polymer for the matrix phase. 2D or 3D woven fabrics, knitted fabrics, stitched fabrics, braids, nonwovens, and multiaxial fabrics can be used as textile materials. Each of these textile forms has its own fiber architecture and combination of properties such as strength, stiffness, flexibility, and toughness, which are reflected on the composite performance to a certain extent [6]. A number of researchers have studied the damage strength of knitted fabric-reinforced composite structures

*Fracture Mechanics Applications*

under loading of tensile, compressive, fracture, and impact [7–10].

braids of E-glass glass fibers, and thermoplastic epoxy matrix.

**66**

Composite materials used for structural purposes can be damaged during manufacturing, assembly, and usage of them. These damages can cause breaking of the materials under environmental effects and external loadings. One of these damages is crack onset and fracture, which depends on crack formation. Fracture, which is precarious for composite structures, can cause loss of life and property. Thus, the fracture analysis of the composite materials, especially focusing on the

Lower cost, lower density, comparable specific strength, and better deformation capacity are the advantages of glass fibers as compared to carbon fibers. However, types of glass fibers have worse mechanical properties than carbon fibers, which is a limitation to the applications, especially when these materials are exposed to more severe stresses. One way to overcome this problem is hybridization, i.e., the combination of glass and carbon fibers, using a matrix compatible with both fibers, to obtain a composite material with satisfactory properties and lower cost. Hybridization with different fiber types within laminated composites increases the design space and opens up possible new engineering applications with optimized mechanical and functional properties. In addition, in the classical composites, the hybridization of carbon and glass fibers may cause a positive hybrid effect, which relies on the increase of carbon fibers failure strain, when compared to the pure carbonbased composites [11]. Generally, as far as the strength of the carbon/glass hybrid is concerned, the higher the volume percentage of carbon fibers is, the stronger the hybrid laminate becomes. The reason is that the carbon fibers are very tough and stiff, while the glass fibers are less stiff and less durable. In carbon/glass fiberreinforced composites, an advantageous hybrid effect is also observed, which consists in increasing the carbon fiber failure strain when compared to the pure carbon fiber. In the literature, there are studies investigating the effects of carbon/glass hybridization on mechanical behavior. Tabrizi et al. [12] have investigated damage evolution in carbon/glass fiber hybrid composites with various stacking sequences under pure bending and tensile loading conditions. Swolfs et al. [13] concluded that the effect for tensile failure strain is well established, with a typical range of 10–50% for traditional hybrid composites such as carbon/glass. Wisnon et al. [14] have investigated hybrid effects on thin ply carbon/glass unidirectional laminates. Test results showed that the magnitude of the hybrid effect depends on the ply thickness. Dong and Davies [15] have studied the mechanical properties of the hybrid composites reinforced with the glass and carbon fibers. Naito and Oguma [16] have investigated tensile properties and fracture behavior of carbon/glass hybrid thermoplastic composite rods consisting of unidirectional PAN-based carbon fiber,

carbon-glass/epoxy laminated composites were determined as 55% approximately. In this study, the hybridization process is carried out using reinforcing fabrics knitted with different types of fibers on the same layer [23–25]. During stacking of layers, the same type of fibers was brought one on the top of another. The photographic representation of produced knitted hybrid composites is shown in **Figure 2**.

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced…*

The fracture toughness of pure and hybrid knitted laminated composites was determined for mode I (0°), mode I–II (30°, 45°, and 60°), and mode II (90°) by using modified Arcan test apparatus. In this context, Arcan test samples were cut with a CNC router machine by using 3 mm cutter blade (**Figure 3**). After cutting, crack having 4 mm was created on the Arcan test sample by using a jigsaw, which had 0.6 mm diameter. Hybrid composite specimens had two different reinforcement materials like glass and carbon fibers in the same layer. Therefore, crack onset in a different reinforcement material may occur in a different shape under load. Crack in the Arcan test sample having the same knitting pattern width was varied in two different forms to investigate crack onset mechanism in glass and carbon fibers. In the first form, the crack was opened to glass fiber side and made to move toward the carbon fiber side. In the other form, the crack was opened to carbon fiber side and made to move toward the glass fiber side (**Figure 3c**, **d**). Linear elastic

*Arcan test specimen (a) pure carbon/epoxy, (b) pure glass/epoxy, and hybrid carbon-glass/epoxy having*

**3. Experimental study**

**Figure 3.**

**69**

*(c) carbon side crack and (d) glass side crack.*

**3.1 Determination of fracture toughness**

*DOI: http://dx.doi.org/10.5772/intechopen.89478*

#### **Figure 1.**

*(a) A knitted loop and (b) wale and course directions of loops.*


#### **Table 1.**

*The row numbers of glass and carbon fibers for desired pattern widths.*

successive knitting cycles. The direction of course and wale in weft-knitted fabric is shown in **Figure 1b**.

The row numbers of glass and carbon corresponding to the considered width are shown in **Table 1**. The average width of a single row is around 2.8–3.3 mm in the scope of this study. The average weight of hybrid and non-hybrid reinforcement fabrics was 730 g/m2 . The thickness of knitted fabric is approximately 2.7 mm.

## **2.2 Manufacturing of hybrid laminated composites**

The matrix material was procured from Duratek Epoxy and Polyurethane Systems in Turkey. Hybrid laminated composite materials having four laminas were produced by hand lay-up methods. After all, laminas were saturated with epoxy resin; semi-product laminated composites were cured at 100<sup>o</sup> C under pressure of 8 MPa for 100 min, by using temperature-time-pressure-controlled hydraulic press.

After this process, the composite plates were cooled to room temperature under the same pressure to avoid warping effects. The fiber volume fractions for hybrid

#### **Figure 2.**

*Manufactured knitted fabric laminated composites (a) pure carbon/epoxy and (b) pure glass/epoxy fabric, and hybrid carbon-glass/epoxy composites with (c) 12.5, (d) 25, and (e) 50 mm pattern widths.*

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.89478*

carbon-glass/epoxy laminated composites were determined as 55% approximately. In this study, the hybridization process is carried out using reinforcing fabrics knitted with different types of fibers on the same layer [23–25]. During stacking of layers, the same type of fibers was brought one on the top of another. The photographic representation of produced knitted hybrid composites is shown in **Figure 2**.

## **3. Experimental study**

## **3.1 Determination of fracture toughness**

The fracture toughness of pure and hybrid knitted laminated composites was determined for mode I (0°), mode I–II (30°, 45°, and 60°), and mode II (90°) by using modified Arcan test apparatus. In this context, Arcan test samples were cut with a CNC router machine by using 3 mm cutter blade (**Figure 3**). After cutting, crack having 4 mm was created on the Arcan test sample by using a jigsaw, which had 0.6 mm diameter. Hybrid composite specimens had two different reinforcement materials like glass and carbon fibers in the same layer. Therefore, crack onset in a different reinforcement material may occur in a different shape under load. Crack in the Arcan test sample having the same knitting pattern width was varied in two different forms to investigate crack onset mechanism in glass and carbon fibers.

In the first form, the crack was opened to glass fiber side and made to move toward the carbon fiber side. In the other form, the crack was opened to carbon fiber side and made to move toward the glass fiber side (**Figure 3c**, **d**). Linear elastic

**Figure 3.**

*Arcan test specimen (a) pure carbon/epoxy, (b) pure glass/epoxy, and hybrid carbon-glass/epoxy having (c) carbon side crack and (d) glass side crack.*

successive knitting cycles. The direction of course and wale in weft-knitted fabric is

Glass 4 8 15 Carbon 4 9 17

The row numbers of glass and carbon corresponding to the considered width are shown in **Table 1**. The average width of a single row is around 2.8–3.3 mm in the scope of this study. The average weight of hybrid and non-hybrid reinforcement

The matrix material was procured from Duratek Epoxy and Polyurethane Systems in Turkey. Hybrid laminated composite materials having four laminas were produced by hand lay-up methods. After all, laminas were saturated with epoxy

8 MPa for 100 min, by using temperature-time-pressure-controlled hydraulic press. After this process, the composite plates were cooled to room temperature under the same pressure to avoid warping effects. The fiber volume fractions for hybrid

*Manufactured knitted fabric laminated composites (a) pure carbon/epoxy and (b) pure glass/epoxy fabric, and hybrid carbon-glass/epoxy composites with (c) 12.5, (d) 25, and (e) 50 mm pattern widths.*

. The thickness of knitted fabric is approximately 2.7 mm.

**12.5 25 50**

C under pressure of

shown in **Figure 1b**.

**Figure 1.**

**Table 1.**

**Figure 2.**

**68**

fabrics was 730 g/m2

**2.2 Manufacturing of hybrid laminated composites**

*The row numbers of glass and carbon fibers for desired pattern widths.*

*(a) A knitted loop and (b) wale and course directions of loops.*

*Fracture Mechanics Applications*

**Fiber type Pattern width (mm)**

resin; semi-product laminated composites were cured at 100<sup>o</sup>

fracture mechanics (LEFM) has been found as a useful tool for the investigation of cracks in composite materials. The purpose of fracture toughness testing is to determine the value of the critical stress intensity factor or plane strain fracture toughness K*C*. The values of fracture toughness for the opening mode (mode I), tension/shearing mode (mixed-mode I/II), and shearing mode (mode II) were found using the following formulas. The stress intensity factor, *KC*, at the tip of the crack for the Arcan test tension specimens is given by Eq. (1):

$$K\_C = \frac{P\_c \sqrt{\pi a}}{wt} f\left(\frac{a}{w}\right) \tag{1}$$

release rates for orthotropic material with the crack line parallel to the principal orthotropic direction which coincides with the fiber orientation can be calculated by

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced…*

Mode I strain energy release rate Mode II strain energy release rate

where *EI* and *EII* are effective moduli for orthotropic materials. In order to apply the linear elastic fracture mechanics, the test sample must have some conditions. One of these is a load-displacement curve of the cracked test sample, which must show the linear elastic material behavior. Another requirement is that the strain state in the crack tip is known. When a material with a crack is loaded in tension, the materials develop plastic strains as the yield stress is exceeded in the region near the crack tip. Material within the crack tip stress field, situated close to a free surface, can deform laterally because there can be no stresses normal to the free surface. The state of stress tends to biaxial, and the material fractures in a characteristic ductile manner, with a 45<sup>o</sup> shear lip being formed at each free surface. This condition is called "plane stress," and it occurs in relatively thin bodies where the stress through the thickness cannot vary appreciably due to the thin section. Knitted fabric-reinforced composite materials conform to the conditions of thin plates. Therefore, the plane stress state occurs at the crack tip. *EI* and *EII* according to the

*GII* <sup>¼</sup> *<sup>K</sup>*<sup>2</sup> *II EII*

ffiffi 2 <sup>p</sup> *Ew* ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffi *Ew Ec* q

<sup>þ</sup> <sup>2</sup>*ϑGwc*þ*Ew*

*GC* ¼ *GI* þ *GII* (8)

� �*d*Γ*<sup>ε</sup>* (9)

<sup>2</sup>*Gwc* <sup>r</sup> (7)

(6)

Eq. (6):

*GI* <sup>¼</sup> *<sup>K</sup>*<sup>2</sup> *I EI*

*DOI: http://dx.doi.org/10.5772/intechopen.89478*

plane stress state are expressed in Eq. (7) [32, 37]:

ffiffiffiffiffiffiffiffiffiffiffiffiffi 2*EwEc* p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffi *Ew Ec* q

<sup>þ</sup> <sup>2</sup>*ϑGwc*þ*Ew* <sup>2</sup>*Gwc* <sup>r</sup> , *EII* <sup>¼</sup>

G*II* represent the energy release values in mode I and mode II directions.

where *Ew* is elasticity modulus in the wale direction and *Ec* is elasticity modulus in the course direction. In order to determine the mixed-mode strain energy release

where similar to the effective fracture toughness formula, the values of G*<sup>I</sup>* and

In fracture analysis of composite materials, J-integral method expresses the stress energy release rate or work (energy) per unit fracture surface area. The Jintegral defines the plastic stress and strain intensity in a manner similar to the fracture toughness (K) parameter, which represents the stress intensity of the surrounding elastic field, in the crack vicinity. The J-integral depends on stress, strain, crack size, and the geometry of the crack and body. The expression of J in the

2D form can be given by Eq. (9). It assumes that the crack lies in the global

*Wn<sup>ε</sup> <sup>i</sup>* � *<sup>n</sup><sup>ε</sup> <sup>i</sup> σij ∂uj ∂x*<sup>1</sup>

*J* ¼ ð 1

Γ

*EI* ¼

rate value, Eq. (8) is utilized [32]:

**4. Finite element analysis**

Cartesian x(u)–y(v) plane:

**71**

where P*<sup>c</sup>* is the fracture load, a is the crack length, w is specimen width, t is the specimen thickness, and *f <sup>a</sup> w* � � is a geometrical factor. ASTM D5045 gives some guidance for plane strain fracture toughness and strain energy release rate [26]. ASTM D5045 is a reference in the literature for the studies, which are about the fracture behavior of fiber-reinforced polymer composites [27–29]. K*<sup>I</sup>* (opening mode stress intensity factor) and K*II* (shearing mode stress intensity factor) state the severity of the crack tip environment, and it is logical to characterize resistance to fracture by a critical value, that is, K*IC* and K*IIC* (Eq. 2). When the applied normal stress reaches the failure stress, the stress intensity factors K*<sup>I</sup>* and K*II* become the critical stress intensity factor (K*IC* and K*IIC*), which is taken as the fracture toughness of the composite specimens [30, 31]. The stress intensity factors ahead of the crack tip for Arcan test sample are calculated by using Eq. (2) [32–34]:

Mode I fracture toughness Mode II fracture toughness

$$\mathbf{K\_{IC}} = \frac{\mathbf{P\_{max}}\sqrt{\pi \mathbf{a}}}{\mathbf{w}\mathbf{t}} \mathbf{f\_{l}} \left(\frac{\mathbf{a}}{\mathbf{w}}\right) \qquad \qquad \mathbf{K\_{IC}} = \frac{\mathbf{P\_{max}}\sqrt{\pi \mathbf{a}}}{\mathbf{w}\mathbf{t}} \mathbf{f\_{ll}} \left(\frac{\mathbf{a}}{\mathbf{w}}\right) \tag{2}$$

The geometric factor formulas *f <sup>I</sup> <sup>a</sup> w* � � and *<sup>f</sup> II <sup>a</sup> w* � � used to calculate the K*<sup>I</sup>* and K*II* were provided by Eqs. (3–4) [32]:

$$f\_I\left(\frac{a}{w}\right) = 182.12\left(\frac{a}{w}\right)^4 - 293.81\left(\frac{a}{w}\right)^3 + 187.87\left(\frac{a}{w}\right)^2 - 51.492\left(\frac{a}{w}\right) + 6.1137\tag{3}$$

$$f\_{II} \left(\frac{a}{w}\right) = -18.622 \left(\frac{a}{w}\right)^4 + 36.753 \left(\frac{a}{w}\right)^3 - 25.182 \left(\frac{a}{w}\right)^2 + 7.759 \left(\frac{a}{w}\right) + 0.0944 \tag{4}$$

For the mixed-mode loading effective fracture toughness, *Keff* is calculated by Eq. (5) [35, 36]:

$$K\_{\rm eff} = \sqrt{K\_I^2 + K\_{II}^2} \tag{5}$$

where *KI* and *KII* are components of the fracture toughness in mode I and mode II directions. To calculate the values of mode I and mode II and total mixed-mode components of knitted fabric-reinforced composites, the material anisotropy should be taken into account.

#### **3.2 Determination of strain energy release rate**

The energy release rate (G) is defined as the amount of energy released per unit of the new fractured area formed due to cracking. The energy release rate is also defined as the crack extension force. A simple procedure using energy concepts is utilized to develop an analytical description of the crack extension force. The energy *The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.89478*

release rates for orthotropic material with the crack line parallel to the principal orthotropic direction which coincides with the fiber orientation can be calculated by Eq. (6):

Mode I strain energy release rate Mode II strain energy release rate

$$\mathbf{G}\_{I} = \frac{\mathbf{K}\_{I}^{2}}{\mathbf{E}\_{I}} \tag{6}$$

where *EI* and *EII* are effective moduli for orthotropic materials. In order to apply the linear elastic fracture mechanics, the test sample must have some conditions. One of these is a load-displacement curve of the cracked test sample, which must show the linear elastic material behavior. Another requirement is that the strain state in the crack tip is known. When a material with a crack is loaded in tension, the materials develop plastic strains as the yield stress is exceeded in the region near the crack tip. Material within the crack tip stress field, situated close to a free surface, can deform laterally because there can be no stresses normal to the free surface. The state of stress tends to biaxial, and the material fractures in a characteristic ductile manner, with a 45<sup>o</sup> shear lip being formed at each free surface. This condition is called "plane stress," and it occurs in relatively thin bodies where the stress through the thickness cannot vary appreciably due to the thin section. Knitted fabric-reinforced composite materials conform to the conditions of thin plates. Therefore, the plane stress state occurs at the crack tip. *EI* and *EII* according to the plane stress state are expressed in Eq. (7) [32, 37]:

$$E\_I = \frac{\sqrt{2E\_w E\_c}}{\sqrt{\sqrt{\frac{E\_v}{E\_c}} + \frac{2\theta G\_{\text{av}} + E\_w}{2G\_{\text{av}}}}},\\ E\_{II} = \frac{\sqrt{2}E\_w}{\sqrt{\sqrt{\frac{E\_w}{E\_c}} + \frac{2\theta G\_{\text{av}} + E\_w}{2G\_{\text{av}}}}} \tag{7}$$

where *Ew* is elasticity modulus in the wale direction and *Ec* is elasticity modulus in the course direction. In order to determine the mixed-mode strain energy release rate value, Eq. (8) is utilized [32]:

$$\mathbf{G}\_{\rm C} = \mathbf{G}\_{I} + \mathbf{G}\_{\rm II} \tag{8}$$

where similar to the effective fracture toughness formula, the values of G*<sup>I</sup>* and G*II* represent the energy release values in mode I and mode II directions.

## **4. Finite element analysis**

In fracture analysis of composite materials, J-integral method expresses the stress energy release rate or work (energy) per unit fracture surface area. The Jintegral defines the plastic stress and strain intensity in a manner similar to the fracture toughness (K) parameter, which represents the stress intensity of the surrounding elastic field, in the crack vicinity. The J-integral depends on stress, strain, crack size, and the geometry of the crack and body. The expression of J in the 2D form can be given by Eq. (9). It assumes that the crack lies in the global Cartesian x(u)–y(v) plane:

$$J = \prod\_{\Gamma}^{1} (Wn\_i^{\varepsilon} - n\_i^{\varepsilon}\sigma\_{ij}\frac{\partial u\_j}{\partial \mathbf{x}\_1})d\Gamma\_{\varepsilon} \tag{9}$$

fracture mechanics (LEFM) has been found as a useful tool for the investigation of cracks in composite materials. The purpose of fracture toughness testing is to determine the value of the critical stress intensity factor or plane strain fracture toughness K*C*. The values of fracture toughness for the opening mode (mode I), tension/shearing mode (mixed-mode I/II), and shearing mode (mode II) were found using the following formulas. The stress intensity factor, *KC*, at the tip of the

> ffiffiffiffiffi *πa* p *wt <sup>f</sup> <sup>a</sup> w* � �

where P*<sup>c</sup>* is the fracture load, a is the crack length, w is specimen width, t is the

guidance for plane strain fracture toughness and strain energy release rate [26]. ASTM D5045 is a reference in the literature for the studies, which are about the fracture behavior of fiber-reinforced polymer composites [27–29]. K*<sup>I</sup>* (opening mode stress intensity factor) and K*II* (shearing mode stress intensity factor) state the severity of the crack tip environment, and it is logical to characterize resistance to fracture by a critical value, that is, K*IC* and K*IIC* (Eq. 2). When the applied normal stress reaches the failure stress, the stress intensity factors K*<sup>I</sup>* and K*II* become the critical stress intensity factor (K*IC* and K*IIC*), which is taken as the fracture toughness of the composite specimens [30, 31]. The stress intensity factors ahead of the

� � is a geometrical factor. ASTM D5045 gives some

KIIC <sup>¼</sup> Pmax

*w*

*w* � �<sup>2</sup>

> *w* � �<sup>2</sup>

ffiffiffiffiffi <sup>π</sup><sup>a</sup> <sup>p</sup> wt

� <sup>51</sup>*:*<sup>492</sup> *<sup>a</sup>*

<sup>þ</sup> <sup>7</sup>*:*<sup>759</sup> *<sup>a</sup>*

fII a w

� � used to calculate the K*<sup>I</sup>* and K*II*

*w* � �

*w* � �

� � (2)

þ 6*:*1137 (3)

þ 0*:*0944 (4)

(5)

(1)

crack for the Arcan test tension specimens is given by Eq. (1):

*w*

KIC <sup>¼</sup> Pmax

The geometric factor formulas *f <sup>I</sup> <sup>a</sup>*

*w* � �<sup>4</sup>

> *w* � �<sup>4</sup>

**3.2 Determination of strain energy release rate**

were provided by Eqs. (3–4) [32]:

<sup>¼</sup> <sup>182</sup>*:*<sup>12</sup> *<sup>a</sup>*

¼ �18*:*<sup>622</sup> *<sup>a</sup>*

*f I a w* � �

*f II a w* � �

**70**

Eq. (5) [35, 36]:

be taken into account.

specimen thickness, and *f <sup>a</sup>*

*Fracture Mechanics Applications*

*KC* <sup>¼</sup> *Pc*

crack tip for Arcan test sample are calculated by using Eq. (2) [32–34]:

*w*

*w* � �<sup>3</sup>

> *w* � �<sup>3</sup>

*Keff* ¼

ffiffiffiffiffi <sup>π</sup><sup>a</sup> <sup>p</sup> wt

� <sup>293</sup>*:*<sup>81</sup> *<sup>a</sup>*

<sup>þ</sup> <sup>36</sup>*:*<sup>753</sup> *<sup>a</sup>*

fI a w � �

Mode I fracture toughness Mode II fracture toughness

� � and *<sup>f</sup> II <sup>a</sup>*

For the mixed-mode loading effective fracture toughness, *Keff* is calculated by

q

where *KI* and *KII* are components of the fracture toughness in mode I and mode II directions. To calculate the values of mode I and mode II and total mixed-mode components of knitted fabric-reinforced composites, the material anisotropy should

The energy release rate (G) is defined as the amount of energy released per unit of the new fractured area formed due to cracking. The energy release rate is also defined as the crack extension force. A simple procedure using energy concepts is utilized to develop an analytical description of the crack extension force. The energy

<sup>þ</sup> <sup>187</sup>*:*<sup>87</sup> *<sup>a</sup>*

� <sup>25</sup>*:*<sup>182</sup> *<sup>a</sup>*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *K*2 *<sup>I</sup>* <sup>þ</sup> *<sup>K</sup>*<sup>2</sup> *II*

#### *Fracture Mechanics Applications*

where Γ is a contour around the crack in the Cartesian coordinate system, W is stress field energy density, and *xi*, *ui*, and *σij* are the spatial coordinates, the displacements, and the Cauchy stresses, respectively. *n<sup>ε</sup> <sup>i</sup>* are the components of the unit outward normal vector on Γ*ε*. The coordinate system and typical J-integral paths were illustrated in **Figure 4**. For a linearly elastic solid, the strain energy density is expressed in Eq. 10:

$$W = W(\mathbf{x}, \varepsilon) = \frac{1}{2} \sigma\_{\vec{\eta}} \varepsilon\_{\vec{\eta}} = \frac{1}{2} E\_{\vec{\eta}kl}(\mathbf{x}) \varepsilon\_{\vec{\eta}} \varepsilon\_{kl} \tag{10}$$

where *Eijkl*ð Þ *x* are the Cartesian components of the fourth-order tensor expressing the generalized Hooke's law, ε is the strain tensor, and *εij* are its Cartesian components [38]. Notice that the line integral shown in **Figure 4** is evaluated in a counterclockwise direction beginning on the lower crack surface and ending on the upper crack surface. The J-integral approach is a measure of the energy release rate associated with crack onset. One of the advantages of using J-integral is that under quasi-static conditions, it is equal to the energy release rate G for linear elastic materials [39]. Assuming linear elastic conditions prevailing along the integration path Γ, the numerical value of the J-integral can be related to the fracture toughness in plane stress condition as in Eq. (11) [40]:

$$J = \frac{K\_C^2}{E} \tag{11}$$

family of fracture criteria that measures the resistance of a material to growing a crack. In this context, CTOD failure criteria were employed for the crack onset in finite element analysis. There are two elastic-plastic parameters widely accepted by the fractured community; J-integral and CTOD [42, 43]. In case of LEFM, the

CTOD <sup>¼</sup> <sup>4</sup>

π *K* Eσ*ys*

where *K* is the stress intensity factor, *E* is the effective modulus, and *σys* is the

The connection between the fixture and specimen is idealized by a rigid and continuous joint, based on the fact that the fixture and pins used in Arcan tests are relatively rigid compared to the specimen. Thus in the finite element analysis, the specimen-fixture system was treated as one continuous solid with two regions of different thickness and material properties. The fixed boundary condition was used, and distributed loads were assigned for the numerical model. **Figure 5** shows the

The fracture tests were carried out using the Arcan test apparatus for 0°, 30°, 45°, 60°, and 90° loading angles. **Figure 6** has presented the load-displacement curve of pure glass/epoxy and pure carbon/epoxy at different loading angles. Loaddisplacement graphs of hybrid composites are not given because they behave similarly to others. When the loading angle changes from mode I to mode II plane, the maximum damage load (P*C*) has increased. In addition, when the loading angle increased, specimens showed more deformation under load due to the increasing shear tendency of the test specimens. The fracture test was repeated five times for

The average P*<sup>C</sup>* values of critical fracture loads were used to determine the fracture toughness (K) and strain energy release rates (G) for all fracture modes. Calculated fracture toughness *KI*, *KII*, and *Keff* according to the crack side was given

), and all mixed-mode (30<sup>o</sup>

, 45<sup>o</sup>

, and 60o

), and

(12)

elastic calculation for the CTOD can be expressed in Eq. (12):

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced…*

uniaxial yield stress of the composite material.

*The state of the finite element model after the analysis.*

*DOI: http://dx.doi.org/10.5772/intechopen.89478*

state of the finite element model after the analysis.

**5.1 Results of Arcan fracture toughness test**

), pure mode II (90<sup>o</sup>

the obtained average PC values are given in **Table 2**.

**5. Results and discussion**

**Figure 5.**

pure mode I (0<sup>o</sup>

**73**

in **Tables 3** and **4**, respectively.

The numerical analysis was performed in the commercial finite element software ANSYS Workbench by the use of a quasi-static rate-independent J-integral method, which can be used to determine the pure mode and mixed-mode fracture toughness. Eight-node quadrilateral plane elements with two degrees of freedom per node were used to model the cracked test specimens. The element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities. The mesh was refined around the crack tip so that the smallest element size found in the crack tip elements was approximately 0.2 mm. The numerical model consists of 29,600 nodes approximately. An implicit solver was used for the finite element analysis. Implicit solutions are based on quantities calculated in the previous time step (backward Euler time scheme), which means even for large time steps the solution remains stable (unconditionally stable) [41]. In modeling fracture mechanics for laminated composite where both tensile and shear failure are common, a fracture criterion for predicting mode I, mode II, and mixed-mode I/II fracture onset is needed. Crack tip opening displacement test or CTOD is one of a

**Figure 4.** *The coordinates and typical paths to evaluate the J-integral.*

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.89478*

**Figure 5.** *The state of the finite element model after the analysis.*

where Γ is a contour around the crack in the Cartesian coordinate system, W is stress field energy density, and *xi*, *ui*, and *σij* are the spatial coordinates, the dis-

outward normal vector on Γ*ε*. The coordinate system and typical J-integral paths were illustrated in **Figure 4**. For a linearly elastic solid, the strain energy density is

2

*<sup>J</sup>* <sup>¼</sup> *<sup>K</sup>*<sup>2</sup> *C*

The numerical analysis was performed in the commercial finite element software ANSYS Workbench by the use of a quasi-static rate-independent J-integral method, which can be used to determine the pure mode and mixed-mode fracture toughness. Eight-node quadrilateral plane elements with two degrees of freedom per node were used to model the cracked test specimens. The element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities. The mesh was refined around the crack tip so that the smallest element size found in the crack tip elements was approximately 0.2 mm. The numerical model consists of 29,600 nodes approximately. An implicit solver was used for the finite element analysis. Implicit solutions are based on quantities calculated in the previous time step (backward Euler time scheme), which means even for large time steps the solution remains stable (unconditionally stable) [41]. In modeling fracture mechanics for laminated composite where both tensile and shear failure are common, a fracture criterion for predicting mode I, mode II, and mixed-mode I/II fracture onset is needed. Crack tip opening displacement test or CTOD is one of a

where *Eijkl*ð Þ *x* are the Cartesian components of the fourth-order tensor expressing the generalized Hooke's law, ε is the strain tensor, and *εij* are its Cartesian components [38]. Notice that the line integral shown in **Figure 4** is evaluated in a counterclockwise direction beginning on the lower crack surface and ending on the upper crack surface. The J-integral approach is a measure of the energy release rate associated with crack onset. One of the advantages of using J-integral is that under quasi-static conditions, it is equal to the energy release rate G for linear elastic materials [39]. Assuming linear elastic conditions prevailing along the integration path Γ, the numerical value of the J-integral can be related to the fracture toughness

*<sup>σ</sup>ijεij* <sup>¼</sup> <sup>1</sup> 2 *<sup>i</sup>* are the components of the unit

*Eijkl*ð Þ *x εijεkl* (10)

*<sup>E</sup>* (11)

placements, and the Cauchy stresses, respectively. *n<sup>ε</sup>*

in plane stress condition as in Eq. (11) [40]:

*The coordinates and typical paths to evaluate the J-integral.*

*<sup>W</sup>* <sup>¼</sup> *W x*ð Þ¼ , *<sup>ε</sup>* <sup>1</sup>

expressed in Eq. 10:

*Fracture Mechanics Applications*

**Figure 4.**

**72**

family of fracture criteria that measures the resistance of a material to growing a crack. In this context, CTOD failure criteria were employed for the crack onset in finite element analysis. There are two elastic-plastic parameters widely accepted by the fractured community; J-integral and CTOD [42, 43]. In case of LEFM, the elastic calculation for the CTOD can be expressed in Eq. (12):

$$\text{CTOD} = \frac{4}{\pi} \frac{K}{\text{E}\sigma\_{\text{ys}}} \tag{12}$$

where *K* is the stress intensity factor, *E* is the effective modulus, and *σys* is the uniaxial yield stress of the composite material.

The connection between the fixture and specimen is idealized by a rigid and continuous joint, based on the fact that the fixture and pins used in Arcan tests are relatively rigid compared to the specimen. Thus in the finite element analysis, the specimen-fixture system was treated as one continuous solid with two regions of different thickness and material properties. The fixed boundary condition was used, and distributed loads were assigned for the numerical model. **Figure 5** shows the state of the finite element model after the analysis.

## **5. Results and discussion**

#### **5.1 Results of Arcan fracture toughness test**

The fracture tests were carried out using the Arcan test apparatus for 0°, 30°, 45°, 60°, and 90° loading angles. **Figure 6** has presented the load-displacement curve of pure glass/epoxy and pure carbon/epoxy at different loading angles. Loaddisplacement graphs of hybrid composites are not given because they behave similarly to others. When the loading angle changes from mode I to mode II plane, the maximum damage load (P*C*) has increased. In addition, when the loading angle increased, specimens showed more deformation under load due to the increasing shear tendency of the test specimens. The fracture test was repeated five times for pure mode I (0<sup>o</sup> ), pure mode II (90<sup>o</sup> ), and all mixed-mode (30<sup>o</sup> , 45<sup>o</sup> , and 60o ), and the obtained average PC values are given in **Table 2**.

The average P*<sup>C</sup>* values of critical fracture loads were used to determine the fracture toughness (K) and strain energy release rates (G) for all fracture modes. Calculated fracture toughness *KI*, *KII*, and *Keff* according to the crack side was given in **Tables 3** and **4**, respectively.


case of the opening mode, the damage occurs in the form of a matrix crack and subsequent fiber breakage. Also, the breakage occurs in a fast and brittle form, due to high-stress concentrations occurring at the crack end in the opening mode. During mode II loading, the applied load progresses the crack by shearing. As a result of shear deformation, the separation between laminas named delamination occurs. Damage of the brittle matrix material holding the lamina together allows the delamination to spread easily between the laminas. Thus, the material gains more ability to deform. The loads on the sample are transferred to the reinforcing hybrid fabric with increasing deformation, and the fiber structure is subjected to shear force. Due to the anisotropic behavior of the knitting structure, it can be seen from

*Fracture toughness (MPa*√*mm) for carbon-glass/epoxy laminated composites with carbon side cracked.*

**Material type Loading angle**

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced…*

*DOI: http://dx.doi.org/10.5772/intechopen.89478*

Pure glass/epoxy *KI* 562.55 441.17 343.75 259.71 –

Carbon-glass/epoxy (12.5 mm) *KI* 629.80 500.37 438.25 336.11 –

Carbon-glass/epoxy (25 mm) *KI* 597.71 468.11 398.30 330.30 –

Carbon-glass/epoxy (50 mm) *KI* 585.46 454.56 383.10 304.46 –

*Fracture toughness (MPa*√*mm) for carbon-glass/epoxy laminated composites with glass side cracked.*

Pure carbon/epoxy *KI* 664.64 532.40 494.83 360.78 –

Carbon-glass/epoxy (12.5 mm) *KI* 635.60 523.76 467.58 352.70 –

Carbon-glass/epoxy (25 mm) *KI* 619.57 505.11 436.68 345.04 –

Carbon-glass/epoxy (50 mm) *KI* 599.85 479.02 415.84 337.96 –

**Material type Loading angle**

**Table 3.**

**Table 4.**

**75**

**0<sup>o</sup> 30o 45<sup>o</sup> 60<sup>o</sup> 90<sup>o</sup>**

*KII* – 63.46 83.40 109.18 161.30 *Keff* 562.55 445.71 353.72 281.73 161.30

*KII* – 70.28 110.97 146.10 158.59 *Keff* 629.80 505.28 452.08 366.50 158.59

*KII* – 67.03 103.33 135.53 146.70 *Keff* 597.71 472.89 411.49 357.02 146.70

*KII* – 64.14 94.61 130.11 141.90 *Keff* 585.46 459.06 394.61 331.10 141.90

**0o 30o 45<sup>o</sup> 60<sup>o</sup> 90<sup>o</sup>**

*KII* – 73.25 119.60 159.56 177.15 *Keff* 664.64 537.41 509.08 394.49 177.15

*KII* – 71.40 115.39 153.05 165.03 *Keff* 635.60 528.60 481.61 384.47 165.03

*KII* – 70.15 109.41 147.50 151.22 *Keff* 619.57 509.96 450.18 375.24 151.22

*KII* – 68.60 107.79 144.49 148.98 *Keff* 599.85 483.90 429.59 367.55 148.98

#### **Table 2.**

*Average critical fracture loads P*<sup>C</sup> *(N) for pure and hybrid knitted fabric laminated composites.*

The calculated fracture toughness results showed that the loading angle, crack position, and pattern width directly affect the fracture behavior of the composite material. As loading angle increases from mode I to mode II, fracture toughness for each material type decreases. Applied load during mode I loading case forces the crack to open. So, damage occurs in the form of fiber and matrix fracture. In the


*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.89478*

**Table 3.**

*Fracture toughness (MPa*√*mm) for carbon-glass/epoxy laminated composites with glass side cracked.*


**Table 4.**

*Fracture toughness (MPa*√*mm) for carbon-glass/epoxy laminated composites with carbon side cracked.*

case of the opening mode, the damage occurs in the form of a matrix crack and subsequent fiber breakage. Also, the breakage occurs in a fast and brittle form, due to high-stress concentrations occurring at the crack end in the opening mode. During mode II loading, the applied load progresses the crack by shearing. As a result of shear deformation, the separation between laminas named delamination occurs. Damage of the brittle matrix material holding the lamina together allows the delamination to spread easily between the laminas. Thus, the material gains more ability to deform. The loads on the sample are transferred to the reinforcing hybrid fabric with increasing deformation, and the fiber structure is subjected to shear force. Due to the anisotropic behavior of the knitting structure, it can be seen from

The calculated fracture toughness results showed that the loading angle, crack position, and pattern width directly affect the fracture behavior of the composite material. As loading angle increases from mode I to mode II, fracture toughness for each material type decreases. Applied load during mode I loading case forces the crack to open. So, damage occurs in the form of fiber and matrix fracture. In the

*Average critical fracture loads P*<sup>C</sup> *(N) for pure and hybrid knitted fabric laminated composites.*

*Load-displacement curves according to loading angles (a) pure glass/epoxy and (b) pure carbon/epoxy.*

Glass side cracked Pure glass/epoxy 6883 6902 6453 7576 8553

Carbon side cracked Pure carbon/epoxy 9358 8406 9567 10366 12510

Carbon-glass/epoxy (12.5 mm width) 8642 7970 8557 9345 9669 Carbon-glass/epoxy (25 mm width) 8531 7791 8323 8990 8917 Carbon-glass/epoxy (50 mm width) 7900 7373 7440 8405 8745

Carbon-glass/epoxy (12.5 mm width) 8771 8772 9119 9816 9943 Carbon-glass/epoxy (25 mm width) 8718 8187 9049 9453 9654 Carbon-glass/epoxy (50 mm width) 8426 8178 8491 9356 9413

**0o 30o 45<sup>o</sup> 60<sup>o</sup> 90<sup>o</sup>**

**Material type Loading angle**

**Figure 6.**

*Fracture Mechanics Applications*

**Table 2.**

**74**

fracture test results that the shear strength of reinforcement fabric was higher than the tensile strength.

When fracture toughness values of pure glass and carbon fabric-reinforced composites were compared, fracture toughness of carbon/epoxy composites was found to be up to 43% higher than glass/epoxy. If a similar comparison is made for hybrid composites that had the same pattern width, the fracture toughness of the samples with carbon side cracked is 11% higher than for samples with glass side cracked. According to the results obtained from pure and hybrid composites, the crack on the carbon side has a tougher spreading mechanism than on the glass side.

Although all hybrid fabric-reinforced composites contain equal amounts of glass and carbon fiber, different fracture toughness values were obtained for the same loading angle and crack location. Glass and carbon knitting pattern widths of hybrid fabrics have affected the fracture toughness of the material. At the combination boundary of the glass and carbon fiber knitting, a new intermediate form is occurred by the interlocking of glass fiber and carbon fiber loops. This intermediate form increased the strength of the structure due to exhibited behavior that is as flexible as the glass fiber and as strong as the carbon fiber. Accordingly, the fracture toughness value of the material has increased by decreasing pattern width or in other words increasing the number of intermediate forms. When the fracture toughness values at the same loading angle of the samples having the carbon side crack were compared with regard to the pattern width, the samples having a pattern width of 12.5 mm have more toughness value up to 9 and 12%, respectively, than the samples with 25 and 50 mm pattern width. If the similar comparison was made for the samples having a crack on the glass side, it was seen that the samples with a pattern width of 12.5 mm have more toughness value up to 10 and 15% than those with a pattern width of 25 and 50 mm, respectively.

(*Scw*) of glass and carbon knitted fabric-reinforced composites were determined according to ASTM D 5379 standard by using V-notched test samples [47]. The *Sw* and *Sc* have been found by dividing of maximum load by the cross-sectional area of the samples. All the tests for the mechanical properties were done five times for each material structure in room temperature. The average results of these five tests were accepted as mechanical property values. When **Table 5** is investigated, it can be seen that the mechanical strength of carbon/epoxy composite is higher than the glass/epoxy composite. Such that, tensile properties of pure carbon/epoxy as *Ew*, *Ec*, *Tw*, and *Tc* are 67.75, 52.34, 57.18, and 32.73% higher than glass/epoxy, respectively. The compression strength of carbon/epoxy in wale and course direction are 27.57 and 21.15% higher than glass/epoxy, respectively. For the comparison of shear modulus and shear strength, it can be seen that *Gwc*, *Swc*, and *Scw* values of carbon/

*Comparison of J-integral and strain energy release rate (*Gc*) of glass side cracked specimens.*

**Material type Loading angle**

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced…*

*DOI: http://dx.doi.org/10.5772/intechopen.89478*

Pure glass/epoxy *Jint* 17.81 8.52 3.19 2.16 1.28

Carbon-glass/epoxy (12.5 mm) *Jint* 16.97 11.61 9.63 6.65 0.95

Carbon-glass/epoxy (25 mm) *Jint* 14.93 11.13 7.93 5.53 0.90

Carbon-glass/epoxy (50 mm) *Jint* 14.34 10.02 7.93 4.82 0.67

**0<sup>o</sup> 30o 45<sup>o</sup> 60<sup>o</sup> 90<sup>o</sup>**

*Gc* 14.98 9.38 5.88 3.68 1.06

*Gc* 18.78 12.05 9.59 6.22 1.02

*Gc* 16.91 10.56 7.94 5.91 0.88

*Gc* 16.23 9.95 7.31 5.08 0.82

epoxy are 22.9, 28.78, and 27.66% higher than glass/epoxy, respectively.

experimental data in theoretical formulas.

side crack at the same loading angle.

condition [30, 37, 48]:

**77**

**Table 6.**

From the physical point of view, the energy release rate is the most appropriate physical quantity to characterize the fracture behavior. For purely elastic materials, the energy release rate G is identical to the J-integral because there is no energy stored in the crack cavity. In linear elastic fracture mechanics, the J-integral coincides with total energy release rate, *Jint* = *Gc* = *GI* + *GII* + *GIII*, where *GI*, *GII*, and *GIII* are the energy release rates associated with the mode I, mode II, and mode III stress intensity factors. In this study, the energy release rate (*G*) is obtained by using

The J-integral value is calculated by the ANSYS program with the aid of the finite element model. The comparisons of the J-integral and strain energy release rate values, which were obtained from experimental and numerical analyses, were given in **Tables 6** and **7** depending on the crack location. When the comparisons in **Tables 6** and **7** are examined, it is seen that experimental and numerical results are compatible with each other. However, for the samples having the same pattern width, the energy required to progress the carbon side crack is higher than the glass

In linear elastic fracture mechanics, Eq. (11) is valid between the fracture stress intensity factor (K*C*) and the J-integral value for plane stress and plane strain cases. During the analysis, if the thickness of the material is neglected, plane stress condition is applicable, and if it is included in the solution, the plane strain condition is applicable. Depending on the J-integral value obtained from finite element numerical analysis, fracture toughness was determined according to Eq. 13 for plane stress

## **5.2 Results of finite element analysis**

A numerical study was also performed by using ANSYS finite element program for all loading angles. Some mechanical test values, which required to create a finite element model of glass and carbon knitted fabric-reinforced composite structures, were determined experimentally, and the obtained results are given in **Table 5**. The elasticity modulus in the wale direction (*Ew*) and the course direction (*Ec*) and the tensile strength in the wale (*Tw*) and course direction (*Tc*) of laminated composites were determined according to ASTM D3039M standard [44]. Shear modulus (*Gwc*) was determined according to the ASTM D3518M-13 standard test method [45]. Compressive properties were determined according to the ASTM D3410-87 standard test method [46]. Wale and course direction compressive strength of composite specimens (*Cw* and *Cc*) were calculated by dividing the failure load to the cross-sectional area of the specimens in wale and course direction, respectively. The in-plane shear properties in the wale direction (*Swc*) and in the course direction


**Table 5.** *Mechanical properties of nonhybrid knitted fabric-reinforced composite specimens.*


*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.89478*

#### **Table 6.**

fracture test results that the shear strength of reinforcement fabric was higher than

When fracture toughness values of pure glass and carbon fabric-reinforced composites were compared, fracture toughness of carbon/epoxy composites was found to be up to 43% higher than glass/epoxy. If a similar comparison is made for hybrid composites that had the same pattern width, the fracture toughness of the samples with carbon side cracked is 11% higher than for samples with glass side cracked. According to the results obtained from pure and hybrid composites, the crack on the carbon side has a tougher spreading mechanism than on the glass side. Although all hybrid fabric-reinforced composites contain equal amounts of glass and carbon fiber, different fracture toughness values were obtained for the same loading angle and crack location. Glass and carbon knitting pattern widths of hybrid fabrics have affected the fracture toughness of the material. At the combination boundary of the glass and carbon fiber knitting, a new intermediate form is

occurred by the interlocking of glass fiber and carbon fiber loops. This intermediate form increased the strength of the structure due to exhibited behavior that is as flexible as the glass fiber and as strong as the carbon fiber. Accordingly, the fracture toughness value of the material has increased by decreasing pattern width or in other words increasing the number of intermediate forms. When the fracture toughness values at the same loading angle of the samples having the carbon side crack were compared with regard to the pattern width, the samples having a pattern width of 12.5 mm have more toughness value up to 9 and 12%, respectively, than the samples with 25 and 50 mm pattern width. If the similar comparison was made for the samples having a crack on the glass side, it was seen that the samples with a pattern width of 12.5 mm have more toughness value up to 10 and 15% than those

A numerical study was also performed by using ANSYS finite element program for all loading angles. Some mechanical test values, which required to create a finite element model of glass and carbon knitted fabric-reinforced composite structures, were determined experimentally, and the obtained results are given in **Table 5**. The elasticity modulus in the wale direction (*Ew*) and the course direction (*Ec*) and the tensile strength in the wale (*Tw*) and course direction (*Tc*) of laminated composites were determined according to ASTM D3039M standard [44]. Shear modulus (*Gwc*) was determined according to the ASTM D3518M-13 standard test method [45]. Compressive properties were determined according to the ASTM D3410-87 standard test method [46]. Wale and course direction compressive strength of composite specimens (*Cw* and *Cc*) were calculated by dividing the failure load to the cross-sectional area of the specimens in wale and course direction, respectively. The in-plane shear properties in the wale direction (*Swc*) and in the course direction

with a pattern width of 25 and 50 mm, respectively.

**5.2 Results of finite element analysis**

**Material type**

Glass/ epoxy

Carbon/ epoxy

**Table 5.**

**76**

*Ew* **(MPa)**

*Ec* **(MPa)**

*Gwc* **(MPa)**

*Mechanical properties of nonhybrid knitted fabric-reinforced composite specimens.*

*Tw* **(MPa)**

*Tc* **(MPa)**

24105.84 19621.19 4160.16 127.82 117.80 98.61 81.94 40.33 36.21

40437.71 29891.17 5112.89 200.91 156.36 125.80 99.27 51.94 46.23

*Cw* **(MPa)**

*Cc* **(MPa)**

*Swc* **(MPa)**

*Scw* **(MPa)**

the tensile strength.

*Fracture Mechanics Applications*

*Comparison of J-integral and strain energy release rate (*Gc*) of glass side cracked specimens.*

(*Scw*) of glass and carbon knitted fabric-reinforced composites were determined according to ASTM D 5379 standard by using V-notched test samples [47]. The *Sw* and *Sc* have been found by dividing of maximum load by the cross-sectional area of the samples. All the tests for the mechanical properties were done five times for each material structure in room temperature. The average results of these five tests were accepted as mechanical property values. When **Table 5** is investigated, it can be seen that the mechanical strength of carbon/epoxy composite is higher than the glass/epoxy composite. Such that, tensile properties of pure carbon/epoxy as *Ew*, *Ec*, *Tw*, and *Tc* are 67.75, 52.34, 57.18, and 32.73% higher than glass/epoxy, respectively. The compression strength of carbon/epoxy in wale and course direction are 27.57 and 21.15% higher than glass/epoxy, respectively. For the comparison of shear modulus and shear strength, it can be seen that *Gwc*, *Swc*, and *Scw* values of carbon/ epoxy are 22.9, 28.78, and 27.66% higher than glass/epoxy, respectively.

From the physical point of view, the energy release rate is the most appropriate physical quantity to characterize the fracture behavior. For purely elastic materials, the energy release rate G is identical to the J-integral because there is no energy stored in the crack cavity. In linear elastic fracture mechanics, the J-integral coincides with total energy release rate, *Jint* = *Gc* = *GI* + *GII* + *GIII*, where *GI*, *GII*, and *GIII* are the energy release rates associated with the mode I, mode II, and mode III stress intensity factors. In this study, the energy release rate (*G*) is obtained by using experimental data in theoretical formulas.

The J-integral value is calculated by the ANSYS program with the aid of the finite element model. The comparisons of the J-integral and strain energy release rate values, which were obtained from experimental and numerical analyses, were given in **Tables 6** and **7** depending on the crack location. When the comparisons in **Tables 6** and **7** are examined, it is seen that experimental and numerical results are compatible with each other. However, for the samples having the same pattern width, the energy required to progress the carbon side crack is higher than the glass side crack at the same loading angle.

In linear elastic fracture mechanics, Eq. (11) is valid between the fracture stress intensity factor (K*C*) and the J-integral value for plane stress and plane strain cases. During the analysis, if the thickness of the material is neglected, plane stress condition is applicable, and if it is included in the solution, the plane strain condition is applicable. Depending on the J-integral value obtained from finite element numerical analysis, fracture toughness was determined according to Eq. 13 for plane stress condition [30, 37, 48]:

$$K\_J = \sqrt{J.E\_{\text{effective}}} \tag{13}$$

**Material type Loading angle**

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced…*

*DOI: http://dx.doi.org/10.5772/intechopen.89478*

**Table 9.**

**Figure 7.**

**79**

*(a) glass/epoxy and (b) carbon/epoxy.*

Pure glass/epoxy (*KC*)*exp* 664.64 537.41 509.08 394.49 177.15

Carbon-glass/epoxy (12.5 mm) (*KC*)*exp* 635.60 528.60 481.61 384.47 165.03

Carbon-glass/epoxy (25 mm) (*KC*)*exp* 619.57 509.96 450.18 375.24 151.22

Carbon-glass/epoxy (50 mm) (*KC*)*exp* 599.85 483.90 429.59 367.55 148.98

*Damage and stress distributions after experimental fracture and FEM analysis of laminated composites for*

*Experimental and numerical fracture toughness values of carbon side cracked specimens.*

**0<sup>o</sup> 30<sup>o</sup> 45o 60<sup>o</sup> 90o**

(*KJ*)*num* 623.11 564.88 468.68 408.48 189.78 % error 6.25 5.11 7.94 3.55 7.13

(*KJ*)*num* 607.15 597.83 541.68 426.50 180.12 % error 4.48 13.10 12.47 10.93 9.14

(*KJ*)*num* 674.09 574.84 513.97 417.84 163.68 % error 8.80 12.72 14.17 11.35 8.24

(*KJ*)*num* 524.25 553.78 484.21 406.19 160.65 % error 12.60 14.44 12.72 10.51 7.83

A comparison of the experimentally obtained fracture toughness values ((K*C*)*exp*) and the numerical fracture toughness values obtained using J-integral ((K*J*)*num*) is given in **Tables 8** and **9** according to the crack location.

According to **Tables 8** and **9**, it can be said that the results are close to each other when numerical values are compared with experimental values. The maximum error value was 15% for the finite element analysis when the experimental values are taken as reference. This maximum error value indicates that the numerical model created for finite element analysis successfully converges to the fracture test condition.

Damage modes and stress distributions of laminated composites were given in **Figure 7** after experimental fracture damage and FEM analysis. Due to important stress concentrations around the notches in uniaxial tension, specimen fracture


**Table 7.**

*Comparison of J-integral and strain energy release rate (G*c*) of carbon side cracked specimens.*


#### **Table 8.**

*Experimental and numerical fracture toughness values of glass side cracked specimens.*


## *The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.89478*

## **Table 9.**

*KJ* ¼

((K*J*)*num*) is given in **Tables 8** and **9** according to the crack location.

**Material type Loading angle**

**Material type Loading angle**

*Comparison of J-integral and strain energy release rate (G*c*) of carbon side cracked specimens.*

Pure glass/epoxy (*KC*)*exp* 562.55 445.71 353.72 281.73 161.30

Carbon-glass/epoxy (12.5 mm) (*KC*)*exp* 629.80 505.28 452.08 366.50 158.59

Carbon-glass/epoxy (25 mm) (*KC*)*exp* 597.71 472.89 411.49 357.02 146.70

Carbon-glass/epoxy (50 mm) (*KC*)*exp* 585.46 459.06 394.61 331.10 141.90

*Experimental and numerical fracture toughness values of glass side cracked specimens.*

**0<sup>o</sup> 30o 45<sup>o</sup> 60<sup>o</sup> 90<sup>o</sup>**

**0o 30o 45o 60<sup>o</sup> 90<sup>o</sup>**

*Gc* 20.91 13.64 12.17 7.20 1.28

*Gc* 19.12 13.19 10.89 6.84 1.11

*Gc* 18.17 12.28 9.51 6.52 0.93

*Gc* 17.03 11.05 8.66 6.26 0.90

(*KJ*)*num* 516.85 417.70 317.40 261.29 145.66 % error 8.12 6.28 10.27 7.25 9.70

(*KJ*)*num* 639.68 551.30 515.75 400.53 172.45 % error 1.57 9.11 14.08 9.29 8.74

(*KJ*)*num* 549.63 536.17 462.49 371.52 159.11 % error 8.04 13.38 12.39 4.06 8.46

(*KJ*)*num* 499.28 517.96 437.08 377.01 127.37 % error 14.72 12.83 10.76 13.87 10.24

condition.

*Fracture Mechanics Applications*

**Table 8.**

**78**

**Table 7.**

q

A comparison of the experimentally obtained fracture toughness values ((K*C*)*exp*) and the numerical fracture toughness values obtained using J-integral

when numerical values are compared with experimental values. The maximum error value was 15% for the finite element analysis when the experimental values are taken as reference. This maximum error value indicates that the numerical model created for finite element analysis successfully converges to the fracture test

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *J:Eeffective*

According to **Tables 8** and **9**, it can be said that the results are close to each other

Damage modes and stress distributions of laminated composites were given in **Figure 7** after experimental fracture damage and FEM analysis. Due to important stress concentrations around the notches in uniaxial tension, specimen fracture

Pure carbon/epoxy *Jint* 18.38 11.98 9.81 6.65 1.47

Carbon-glass/epoxy (12.5 mm) *Jint* 17.45 12.96 9.82 7.09 1.09

Carbon-glass/epoxy (25 mm) *Jint* 15.20 11.05 8.84 5.84 0.95

Carbon-glass/epoxy (50 mm) *Jint* 15.62 10.26 7.82 5.52 1.05

(13)

*Experimental and numerical fracture toughness values of carbon side cracked specimens.*

#### **Figure 7.**

*Damage and stress distributions after experimental fracture and FEM analysis of laminated composites for (a) glass/epoxy and (b) carbon/epoxy.*

generally occurred in the significant crack tip. As noticed from previous tests, the fracture mechanism consisted of one unique cracked interface identical for all glass/ epoxy composite samples tested whatever the loading direction. In such a case, the crack propagated between the two loops of rows, which is in the direction of the wale, and the crack could not pass through the other loops. Although different crack onset mechanisms did not appear depending on the loading angle in the glass/epoxy specimens, FEM analyses have shown that the stress distributions in the crack region vary depending on the loading angle. Fractured carbon/epoxy composite samples presented a nearly horizontal cracked zone that was different from a plane surface for loading angle of 30o and 60<sup>o</sup> . During the experimental Arcan test, it was observed that the crack progress in the main delamination plane without any side cracking and branching. Fiber bending and breaking behind the crack tip were observed macroscopically in crack onset during the test.

crack tip due to high-stress concentration at the crack tip, and it propagates to the other side by breaking fibers and/or fiber pull out. It can be clearly said that the numerical damage forms were obtained in the similar views of the experimental damage forms as illustrated in **Figure 8**. According to the results of numerical damage, Von Mises stresses show a vertical progression in the case of mode I, while

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced…*

This paper has presented the fracture behavior of pure and hybrid knitted fabric-reinforced laminated composites based on experimental and numerical analyses. In this context, the effect of crack location, loading angle, and pattern width on fracture behavior are examined. A modified version of the Arcan test fixture was employed to conduct a mode I, mode II, and mode I/II test. The obtained fracture test results of hybrid specimens are compared with the test results of pure glass/ epoxy and pure carbon/epoxy samples. In addition, finite element models of cracked test specimens were created according to the data obtained from the mechanical tests. Fracture behaviors of hybrid composites were numerically analyzed using J-integral method. The concluding remarks in this study can be sum-

• According to the results obtained from the mechanical tests, knitted fabrics have been found to be an alternative to woven fabrics for reinforcing polymer composites. In addition, the test results show that the mechanical strength values change depending on the knitting direction and all mechanical test

• The maximum and minimum fracture toughness value for carbon-glass/epoxy hybrid laminated composites was obtained in mode I and mode II loading conditions. The highly complex structure of the knitted fabric composites induces various toughening mechanisms. Fracture toughness behaviors of pure and hybrid composites varied in terms of loading angle. When, the loading angle increased from 0 (mode I) to 90 (mode II), the critical damage load increases. On the contrary, the fracture toughness and energy release rate decreases. The results indicated that the Arcan cracked specimen is tougher in

tensile loading conditions and weaker in shear loading conditions.

• The rib-knitted fabric-reinforced composite shows different fracture

• For all fracture tests of pure fabric-reinforced composite, carbon/epoxy

specimens were much more resistant than glass/epoxy in terms of failure loads

toughness and energy release rate values for both crack progression directions despite the fact that damage images showed that the crack growth modes are different: in the wale direction, the crack followed the wavy surface of the fabric, and in the course direction, the majority of yarns is broken. In the wale direction, the major fracture mechanisms were the matrix deformations, leading to micro-cracks, which will branch in a network. In the course direction, the crack does not strictly follow the waviness of the fabrics but tends to grow through them. The main damage occurs by multiple fiber breakage. This phenomenon is supposed to be highly energy consuming because it implies events such as peel off, yarn bridging, and yarn failure.

a more horizontal progression occurs in the case of mode II.

*DOI: http://dx.doi.org/10.5772/intechopen.89478*

values are larger in the wale direction.

whatever the loading angle.

**81**

**6. Conclusion**

marized as follow:

The experimental and numerical analysis visual results of hybrid composites with 12.5 mm pattern width, which have the maximum fracture toughness values, are given in **Figure 8**. The crack propagates by the glass in **Figure 8(a)** and by carbon in **Figure 8(b)**. Von Mises stress distribution for different loading angles, which obtained from finite element analysis, is shown. The crack started from the

#### **Figure 8.**

*The experimental and numerical visual results of hybrid composites with 12.5 mm pattern width having (a) glass side crack and (b) carbon side crack.*

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.89478*

crack tip due to high-stress concentration at the crack tip, and it propagates to the other side by breaking fibers and/or fiber pull out. It can be clearly said that the numerical damage forms were obtained in the similar views of the experimental damage forms as illustrated in **Figure 8**. According to the results of numerical damage, Von Mises stresses show a vertical progression in the case of mode I, while a more horizontal progression occurs in the case of mode II.

## **6. Conclusion**

generally occurred in the significant crack tip. As noticed from previous tests, the fracture mechanism consisted of one unique cracked interface identical for all glass/ epoxy composite samples tested whatever the loading direction. In such a case, the crack propagated between the two loops of rows, which is in the direction of the wale, and the crack could not pass through the other loops. Although different crack onset mechanisms did not appear depending on the loading angle in the glass/epoxy specimens, FEM analyses have shown that the stress distributions in the crack region vary depending on the loading angle. Fractured carbon/epoxy composite samples presented a nearly horizontal cracked zone that was different from a plane

observed that the crack progress in the main delamination plane without any side cracking and branching. Fiber bending and breaking behind the crack tip were

The experimental and numerical analysis visual results of hybrid composites with 12.5 mm pattern width, which have the maximum fracture toughness values, are given in **Figure 8**. The crack propagates by the glass in **Figure 8(a)** and by carbon in **Figure 8(b)**. Von Mises stress distribution for different loading angles, which obtained from finite element analysis, is shown. The crack started from the

*The experimental and numerical visual results of hybrid composites with 12.5 mm pattern width having*

. During the experimental Arcan test, it was

surface for loading angle of 30o and 60<sup>o</sup>

*Fracture Mechanics Applications*

**Figure 8.**

**80**

*(a) glass side crack and (b) carbon side crack.*

observed macroscopically in crack onset during the test.

This paper has presented the fracture behavior of pure and hybrid knitted fabric-reinforced laminated composites based on experimental and numerical analyses. In this context, the effect of crack location, loading angle, and pattern width on fracture behavior are examined. A modified version of the Arcan test fixture was employed to conduct a mode I, mode II, and mode I/II test. The obtained fracture test results of hybrid specimens are compared with the test results of pure glass/ epoxy and pure carbon/epoxy samples. In addition, finite element models of cracked test specimens were created according to the data obtained from the mechanical tests. Fracture behaviors of hybrid composites were numerically analyzed using J-integral method. The concluding remarks in this study can be summarized as follow:


• As the width of the pattern increased, the fracture strength of the hybrid composites decreased. In this respect, the hybridization processing should be done in the narrowest pattern width for high resistance to fracture.

**References**

[1] Balcıoğlu HE, Sakin R, Gün H. The design of multi-sample flexural fatigue device and fatigue behavior of glass/ epoxy laminated composites. Research

*DOI: http://dx.doi.org/10.5772/intechopen.89478*

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced…*

[8] Pei X, Shang B, Chen L, Li J, Tang Y. Compression properties of multilayerconnected biaxial weft knitted carbon fiber fabric reinforced composites. Composites. Part B, Engineering. 2016;

**91**:296-305. DOI: 10.1016/j. compositesb.2015.12.041

compositesa.2004.12.004

compstruct.2019.03.051

[10] Falconnet D, Bourban PE, Pandita S, Månson JAE, Verpoest I. Fracture toughness of weft-knitted fabric composites. Composites. Part B, Engineering. 2002;**33**:579-588. DOI: 10.1016/S1359-8368(02)00053-7

[11] Dadej K, Bienias J, Surowska B. On the effect of glass and carbon fiber hybridization in fiber metal laminates: Analytical, numerical and experimental investigation. Composite Structures. 2019;**220**:250-260. DOI: 10.1016/j.

[12] Tabrizi IE, Kefal A, Zanjani JSM, Akalin C, Yildiz M. Experimental and numerical investigation on fracture behavior of glass/carbon fiber hybrid composites using acoustic emission method and refined zigzag theory. Composite Structures. 2019;**223**:110971. DOI: 10.1016/j.compstruct.2019.110971

[13] Swolfs Y, Gorbatikh L, Verpoest I.

Manufacturing. 2014;**67**:181-200. DOI: 10.1016/j.compositesa.2014.08.027

[14] Wisnom MR, Czél G, Swolfs Y, Jalalvand M, Gorbatikh L, Verpoest I. Hybrid effects in thin ply carbon/glass

Fibre hybridisation in polymer composites: A review. Composites. Part A, Applied Science and

[9] Kim KY, Curiskis JI, Ye L, Fu SY. Mode-I interlaminar fracture behaviour of weft-knitted fabric reinforced composites. Composites. Part A, Applied Science and Manufacturing. 2005;**36**:954-964. DOI: 10.1016/j.

[2] Atay HY. Multi-functional materials for military aircrafts; radar absorbing and flame retardant composites.

Research on Engineering Structures and Materials. 2016;**3**:45-54. DOI: 10.17515/

[4] Karakoç A. A fiber network model to understand the effects of fiber length and height on the deformation of fibrous materials. Research on

Engineering Structures and Materials.

[5] Ashraf W, Nawab Y, Umair M, Shaker K, Karahan M. Investigation of mechanical behavior of woven/knitted hybrid composites. Journal of the Textile Institute. 2017;**108**:1510-1517. DOI: 10.1080/00405000.2016.1258951

[6] Nesrin Sahbaz K, Yekta K,

[7] Muralidhar BA. Tensile and compressive behaviour of multilayer flax-rib knitted preform reinforced epoxy composites. Materials and

intechopen.68245

j.matdes.2012.12.040

**83**

Huseyin O, Gokce O. Textile reinforced structural composites for advanced applications. Textiles for Advanced Applications. 2016:13. DOI: 10.5772/

Design. 2013;**49**:400-405. DOI: 10.1016/

2016;**2**:51-57. DOI: 10.17515/

resm2015.17ma0825

[3] Costa DMS, Loja MAR. On the characterization of the free vibrations behavior of multiscale composite plates. Research on Engineering Structures and Materials. 2016;**3**:27-44. DOI: 10.17515/

on Engineering Structures and Materials. 2018;**4**:279-296. DOI: 10.17515/resm2018.67me0917

resm2016.38ma0204

resm2016.43st0602


## **Author details**

Huseyin Ersen Balcioglu<sup>1</sup> \* and Hayri Baytan Ozmen<sup>2</sup>

1 Department of Mechanical Engineering, Usak University, Usak, Turkey

2 Department of Civil Engineering, Usak University, Usak, Turkey

\*Address all correspondence to: ersen.balcioglu@usak.edu.tr

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.89478*

## **References**

• As the width of the pattern increased, the fracture strength of the hybrid composites decreased. In this respect, the hybridization processing should be

• In terms of crack locations, the progression of the crack in the glass-reinforced zone is more hazardous than the progress in the carbon reinforcing zone. During the assembly of carbon-glass hybrid composites, it is better to ensure that the bolt holes are opened on the carbon side if the bolts are to be used.

• When the fracture toughness values that were obtained experimentally and numerically are compared, it is seen that the results are consistent. In addition, in terms of fracture energy, experimentally obtained strain energy release rate (G) and numerical fracture energy (J-integral) values are similar. In this respect, the usability and validity of the J-integral method have been proven to simulate numerical fracture analysis of knitted fabric-reinforced laminated

\* and Hayri Baytan Ozmen<sup>2</sup>

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

1 Department of Mechanical Engineering, Usak University, Usak, Turkey

2 Department of Civil Engineering, Usak University, Usak, Turkey

\*Address all correspondence to: ersen.balcioglu@usak.edu.tr

provided the original work is properly cited.

composites.

*Fracture Mechanics Applications*

**Author details**

**82**

Huseyin Ersen Balcioglu<sup>1</sup>

done in the narrowest pattern width for high resistance to fracture.

[1] Balcıoğlu HE, Sakin R, Gün H. The design of multi-sample flexural fatigue device and fatigue behavior of glass/ epoxy laminated composites. Research on Engineering Structures and Materials. 2018;**4**:279-296. DOI: 10.17515/resm2018.67me0917

[2] Atay HY. Multi-functional materials for military aircrafts; radar absorbing and flame retardant composites. Research on Engineering Structures and Materials. 2016;**3**:45-54. DOI: 10.17515/ resm2016.38ma0204

[3] Costa DMS, Loja MAR. On the characterization of the free vibrations behavior of multiscale composite plates. Research on Engineering Structures and Materials. 2016;**3**:27-44. DOI: 10.17515/ resm2016.43st0602

[4] Karakoç A. A fiber network model to understand the effects of fiber length and height on the deformation of fibrous materials. Research on Engineering Structures and Materials. 2016;**2**:51-57. DOI: 10.17515/ resm2015.17ma0825

[5] Ashraf W, Nawab Y, Umair M, Shaker K, Karahan M. Investigation of mechanical behavior of woven/knitted hybrid composites. Journal of the Textile Institute. 2017;**108**:1510-1517. DOI: 10.1080/00405000.2016.1258951

[6] Nesrin Sahbaz K, Yekta K, Huseyin O, Gokce O. Textile reinforced structural composites for advanced applications. Textiles for Advanced Applications. 2016:13. DOI: 10.5772/ intechopen.68245

[7] Muralidhar BA. Tensile and compressive behaviour of multilayer flax-rib knitted preform reinforced epoxy composites. Materials and Design. 2013;**49**:400-405. DOI: 10.1016/ j.matdes.2012.12.040

[8] Pei X, Shang B, Chen L, Li J, Tang Y. Compression properties of multilayerconnected biaxial weft knitted carbon fiber fabric reinforced composites. Composites. Part B, Engineering. 2016; **91**:296-305. DOI: 10.1016/j. compositesb.2015.12.041

[9] Kim KY, Curiskis JI, Ye L, Fu SY. Mode-I interlaminar fracture behaviour of weft-knitted fabric reinforced composites. Composites. Part A, Applied Science and Manufacturing. 2005;**36**:954-964. DOI: 10.1016/j. compositesa.2004.12.004

[10] Falconnet D, Bourban PE, Pandita S, Månson JAE, Verpoest I. Fracture toughness of weft-knitted fabric composites. Composites. Part B, Engineering. 2002;**33**:579-588. DOI: 10.1016/S1359-8368(02)00053-7

[11] Dadej K, Bienias J, Surowska B. On the effect of glass and carbon fiber hybridization in fiber metal laminates: Analytical, numerical and experimental investigation. Composite Structures. 2019;**220**:250-260. DOI: 10.1016/j. compstruct.2019.03.051

[12] Tabrizi IE, Kefal A, Zanjani JSM, Akalin C, Yildiz M. Experimental and numerical investigation on fracture behavior of glass/carbon fiber hybrid composites using acoustic emission method and refined zigzag theory. Composite Structures. 2019;**223**:110971. DOI: 10.1016/j.compstruct.2019.110971

[13] Swolfs Y, Gorbatikh L, Verpoest I. Fibre hybridisation in polymer composites: A review. Composites. Part A, Applied Science and Manufacturing. 2014;**67**:181-200. DOI: 10.1016/j.compositesa.2014.08.027

[14] Wisnom MR, Czél G, Swolfs Y, Jalalvand M, Gorbatikh L, Verpoest I. Hybrid effects in thin ply carbon/glass unidirectional laminates: Accurate experimental determination and prediction. Composites. Part A, Applied Science and Manufacturing. 2016;**88**: 131-139. DOI: 10.1016/j. compositesa.2016.04.014

[15] Dong C, Davies IJ. Flexural and tensile strengths of unidirectional hybrid epoxy composites reinforced by S-2 glass and T700S carbon fibres. Materials and Design. 2014;**54**:955-966. DOI: 10.1016/j.matdes.2013.08.087

[16] Naito K, Oguma H. Tensile properties of novel carbon/glass hybrid thermoplastic composite rods. Composite Structures. 2017;**161**:23-31. DOI: 10.1016/j.compstruct.2016.11.042

[17] Greenhalgh E, Hiley CM. The influence of fibre architecture in the failure of polymer composites. In: Failure Analysis and Fractography of Polymer Composites, Woodhead Publishing Series in Composites Science and Engineering. 2009. pp. 279-355. DOI: 10.1533/9781845696818.279

[18] Zhao Y, Cao M, Lum WP, Tan VBC, Tay TE. Interlaminar fracture toughness of hybrid woven carbon-Dyneema composites. Composites. Part A, Applied Science and Manufacturing. 2018;**114**:377-387. DOI: 10.1016/j. compositesa.2018.08.035

[19] Bieniaś J, Dadej K, Surowska B. Interlaminar fracture toughness of glass and carbon reinforced multidirectional fiber metal laminates. Engineering Fracture Mechanics. 2017;**175**:127-145. DOI: 10.1016/j.engfracmech.2017. 02.007

[20] Jung H, Kim Y. Mode I fracture toughness of carbon-glass/epoxy interply hybrid composites. Journal of Mechanical Science and Technology. 2015;**29**:1955-1962. DOI: 10.1007/ s12206-015-0416-3

[21] Saidane EH, Scida D, Pac MJ, Ayad R. Mode-I interlaminar fracture toughness of flax, glass and hybrid flaxglass fibre woven composites: Failure mechanism evaluation using acoustic emission analysis. Polymer Testing. 2019;**75**:246-253. DOI: 10.1016/j. polymertesting.2019.02.022

Tarpani JR. Fracture toughness of natural fibers/castor oil polyurethane composites. Composites Science and Technology. 2006;**66**:1328-1335. DOI: 10.1016/j.compscitech.2005.10.012

*DOI: http://dx.doi.org/10.5772/intechopen.89478*

in-plane loading using the CTS test. Engineering Fracture Mechanics. 2016; **156**:83-95. DOI: 10.1016/j.engfracmech.

[36] Jamali J, Fan Y, Wood JT. The mixed-mode fracture behavior of epoxy by the compact tension shear test. International Journal of Adhesion and Adhesives. 2015;**63**:79-86. DOI: 10.1016/

j.ijadhadh.2015.08.006

[37] Nikbakht M, Choupani N.

Numerical investigation of delamination in carbon-epoxy composite using arcan specimen. International Journal of Mechanical and Mechatronics Engineering. 2008;**2**:750-757

[38] Okada H, Kadowaki S, Suzuki M, Yusa Y. J-integral computation for elastic-plastic materials with spatially varying mechanical properties.

Engineering Fracture Mechanics. 2019;

[39] Tafazzolimoghaddam B, Curiel-Sosa JL. On the calculation of energy release rates in composite laminates by finite elements , boundary elements and analytical methods. Composites:

Mechanics, Computations, Applications:

An International Journal. 2015;**6**:

CompMechComputApplIntJ.v6.i3.40

[40] Gonzáles GLG, González JAO, Castro JTP, Freire JLF. A J-integral approach using digital image correlation for evaluating stress intensity factors in fatigue cracks with closure effects. Theoretical and Applied Fracture Mechanics. 2017;**90**:14-21. DOI: 10.1016/j.tafmec.2017.02.008

[41] Crump T, Ferté G, Jivkov A, Mummery P, Tran VX. Dynamic fracture analysis by explicit solid dynamics and implicit crack

propagation. International Journal of Solids and Structures. 2017;**110–111**:

219-237. DOI: 10.1615/

**207**:181-202. DOI: 10.1016/j. engfracmech.2018.12.029

2016.01.016

*The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced…*

[29] Hanif WYW, Risby MS, Noor MM. Influence of carbon nanotube inclusion on the fracture toughness and ballistic resistance of twaron/epoxy composite panels. Procedia Engineering. 2015;**114**: 118-123. DOI: 10.1016/j.proeng.2015.

[30] Kaman MO. Effect of fiber orientation on fracture toughness of laminated composite plates [0°/θ°]s. Engineering Fracture Mechanics. 2011;

**78**:2521-2534. DOI: 10.1016/j. engfracmech.2011.06.005

10.1002/pc.23999

[31] Arasan Ş, Aktaş M, Balcıoğlu HE. Fracture toughness of woven glass and carbon reinforced hybrid and nonhybrid composite plates. Polymer Composites. 2018;**39**:783-793. DOI:

[32] Choupani N. Experimental and numerical investigation of the mixedmode delamination in Arcan laminated specimens. Materials Science and Engineering A. 2008;**478**:229-242. DOI:

[33] Hasanpour R, Choupani N. Rock fracture characterization using the modified Arcan test specimen.

International Journal of Rock Mechanics and Mining Sciences. 2009;**46**:346-354. DOI: 10.1016/j.ijrmms.2008.07.004

[34] Yoon SH, Hong CS. Interlaminar fracture toughness of graphite/epoxy composite under mixed-mode

deformations. Experimental Mechanics.

1990;**30**:234-239. DOI: 10.1007/

[35] Jamali J, Mourad AHI, Fan Y, Wood JT. Through-thickness fracture behavior of unidirectional glass fibers/ epoxy composites under various

BF02322816

**85**

10.1016/j.msea.2007.05.103

08.049

[22] Swolfs Y, Geboes Y, Gorbatikh L, Pinho ST. The importance of translaminar fracture toughness for the penetration impact behaviour of woven carbon/glass hybrid composites. Composites. Part A, Applied Science and Manufacturing. 2017;**103**:1-8. DOI: 10.1016/j.compositesa.2017.09.009

[23] Yeter E, Erkliğ A, Bulut M. Hybridization effects on the buckling behavior of laminated composite plates. Composite Structures. 2014;**118**:19-27. DOI: 10.1016/j.compstruct.2014.07.020

[24] Nisini E, Santulli C, Liverani A. Mechanical and impact characterization of hybrid composite laminates with carbon, basalt and flax fibres. Composites. Part B, Engineering. 2017; **127**:92-99. DOI: 10.1016/j. compositesb.2016.06.071

[25] Bulut M, Erklig A, Yeter E. ˇ Hybridization effects on quasi-static penetration resistance in fiber reinforced hybrid composite laminates. Composites. Part B, Engineering. 2016; **98**:9-22. DOI: 10.1016/j. compositesb.2016.05.025

[26] ASTM International. ASTM D 5054 standard test methods for plane-strain fracture toughness and strain energy release rate of plastic materials. ASTM B Stand. 2013;**99**:1-9. DOI: 10.1520/ D5045-14.priate

[27] Khan Z, Yousif BF, Islam M. Fracture behaviour of bamboo fiber reinforced epoxy composites. Composites. Part B, Engineering. 2017; **116**:186-199. DOI: 10.1016/j. compositesb.2017.02.015

[28] Silva RV, Spinelli D, Bose Filho WW, Claro Neto S, Chierice GO, *The Fracture Behavior of Pure and Hybrid Intraply Knitted Fabric-Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.89478*

Tarpani JR. Fracture toughness of natural fibers/castor oil polyurethane composites. Composites Science and Technology. 2006;**66**:1328-1335. DOI: 10.1016/j.compscitech.2005.10.012

unidirectional laminates: Accurate experimental determination and

*Fracture Mechanics Applications*

[15] Dong C, Davies IJ. Flexural and tensile strengths of unidirectional hybrid epoxy composites reinforced by S-2 glass and T700S carbon fibres. Materials and Design. 2014;**54**:955-966. DOI: 10.1016/j.matdes.2013.08.087

[16] Naito K, Oguma H. Tensile

thermoplastic composite rods.

properties of novel carbon/glass hybrid

Composite Structures. 2017;**161**:23-31. DOI: 10.1016/j.compstruct.2016.11.042

[18] Zhao Y, Cao M, Lum WP, Tan VBC, Tay TE. Interlaminar fracture toughness of hybrid woven carbon-Dyneema composites. Composites. Part A, Applied Science and Manufacturing. 2018;**114**:377-387. DOI: 10.1016/j.

compositesa.2018.08.035

02.007

**84**

s12206-015-0416-3

[19] Bieniaś J, Dadej K, Surowska B. Interlaminar fracture toughness of glass and carbon reinforced multidirectional fiber metal laminates. Engineering Fracture Mechanics. 2017;**175**:127-145. DOI: 10.1016/j.engfracmech.2017.

[20] Jung H, Kim Y. Mode I fracture toughness of carbon-glass/epoxy interply hybrid composites. Journal of Mechanical Science and Technology. 2015;**29**:1955-1962. DOI: 10.1007/

[21] Saidane EH, Scida D, Pac MJ, Ayad R. Mode-I interlaminar fracture

[17] Greenhalgh E, Hiley CM. The influence of fibre architecture in the failure of polymer composites. In: Failure Analysis and Fractography of Polymer Composites, Woodhead Publishing Series in Composites Science and Engineering. 2009. pp. 279-355. DOI: 10.1533/9781845696818.279

131-139. DOI: 10.1016/j. compositesa.2016.04.014

prediction. Composites. Part A, Applied Science and Manufacturing. 2016;**88**:

toughness of flax, glass and hybrid flaxglass fibre woven composites: Failure mechanism evaluation using acoustic emission analysis. Polymer Testing. 2019;**75**:246-253. DOI: 10.1016/j. polymertesting.2019.02.022

[22] Swolfs Y, Geboes Y, Gorbatikh L,

translaminar fracture toughness for the penetration impact behaviour of woven

Pinho ST. The importance of

carbon/glass hybrid composites. Composites. Part A, Applied Science and Manufacturing. 2017;**103**:1-8. DOI: 10.1016/j.compositesa.2017.09.009

[23] Yeter E, Erkliğ A, Bulut M. Hybridization effects on the buckling behavior of laminated composite plates. Composite Structures. 2014;**118**:19-27. DOI: 10.1016/j.compstruct.2014.07.020

[24] Nisini E, Santulli C, Liverani A. Mechanical and impact characterization of hybrid composite laminates with carbon, basalt and flax fibres.

Composites. Part B, Engineering. 2017;

reinforced hybrid composite laminates. Composites. Part B, Engineering. 2016;

[26] ASTM International. ASTM D 5054 standard test methods for plane-strain fracture toughness and strain energy release rate of plastic materials. ASTM B Stand. 2013;**99**:1-9. DOI: 10.1520/

[27] Khan Z, Yousif BF, Islam M. Fracture behaviour of bamboo fiber reinforced epoxy composites.

**116**:186-199. DOI: 10.1016/j. compositesb.2017.02.015

[28] Silva RV, Spinelli D, Bose

Composites. Part B, Engineering. 2017;

Filho WW, Claro Neto S, Chierice GO,

**127**:92-99. DOI: 10.1016/j. compositesb.2016.06.071

**98**:9-22. DOI: 10.1016/j. compositesb.2016.05.025

D5045-14.priate

[25] Bulut M, Erklig A, Yeter E. ˇ Hybridization effects on quasi-static penetration resistance in fiber

[29] Hanif WYW, Risby MS, Noor MM. Influence of carbon nanotube inclusion on the fracture toughness and ballistic resistance of twaron/epoxy composite panels. Procedia Engineering. 2015;**114**: 118-123. DOI: 10.1016/j.proeng.2015. 08.049

[30] Kaman MO. Effect of fiber orientation on fracture toughness of laminated composite plates [0°/θ°]s. Engineering Fracture Mechanics. 2011; **78**:2521-2534. DOI: 10.1016/j. engfracmech.2011.06.005

[31] Arasan Ş, Aktaş M, Balcıoğlu HE. Fracture toughness of woven glass and carbon reinforced hybrid and nonhybrid composite plates. Polymer Composites. 2018;**39**:783-793. DOI: 10.1002/pc.23999

[32] Choupani N. Experimental and numerical investigation of the mixedmode delamination in Arcan laminated specimens. Materials Science and Engineering A. 2008;**478**:229-242. DOI: 10.1016/j.msea.2007.05.103

[33] Hasanpour R, Choupani N. Rock fracture characterization using the modified Arcan test specimen. International Journal of Rock Mechanics and Mining Sciences. 2009;**46**:346-354. DOI: 10.1016/j.ijrmms.2008.07.004

[34] Yoon SH, Hong CS. Interlaminar fracture toughness of graphite/epoxy composite under mixed-mode deformations. Experimental Mechanics. 1990;**30**:234-239. DOI: 10.1007/ BF02322816

[35] Jamali J, Mourad AHI, Fan Y, Wood JT. Through-thickness fracture behavior of unidirectional glass fibers/ epoxy composites under various

in-plane loading using the CTS test. Engineering Fracture Mechanics. 2016; **156**:83-95. DOI: 10.1016/j.engfracmech. 2016.01.016

[36] Jamali J, Fan Y, Wood JT. The mixed-mode fracture behavior of epoxy by the compact tension shear test. International Journal of Adhesion and Adhesives. 2015;**63**:79-86. DOI: 10.1016/ j.ijadhadh.2015.08.006

[37] Nikbakht M, Choupani N. Numerical investigation of delamination in carbon-epoxy composite using arcan specimen. International Journal of Mechanical and Mechatronics Engineering. 2008;**2**:750-757

[38] Okada H, Kadowaki S, Suzuki M, Yusa Y. J-integral computation for elastic-plastic materials with spatially varying mechanical properties. Engineering Fracture Mechanics. 2019; **207**:181-202. DOI: 10.1016/j. engfracmech.2018.12.029

[39] Tafazzolimoghaddam B, Curiel-Sosa JL. On the calculation of energy release rates in composite laminates by finite elements , boundary elements and analytical methods. Composites: Mechanics, Computations, Applications: An International Journal. 2015;**6**: 219-237. DOI: 10.1615/ CompMechComputApplIntJ.v6.i3.40

[40] Gonzáles GLG, González JAO, Castro JTP, Freire JLF. A J-integral approach using digital image correlation for evaluating stress intensity factors in fatigue cracks with closure effects. Theoretical and Applied Fracture Mechanics. 2017;**90**:14-21. DOI: 10.1016/j.tafmec.2017.02.008

[41] Crump T, Ferté G, Jivkov A, Mummery P, Tran VX. Dynamic fracture analysis by explicit solid dynamics and implicit crack propagation. International Journal of Solids and Structures. 2017;**110–111**:

113-126. DOI: 10.1016/j.ijsolstr.2017. 01.035

[42] Chabchoub M, Bouscarrat D, Vieille B, Gautrelet C, Beyaoui M, Taktak M, et al. Investigations on the mode I translaminar failure and determination of fracture toughness in woven-ply carbon fibers thermoplastic composites at high temperatures. Applied Acoustics. 2017;**128**:55-63. DOI: 10.1016/j.apacoust.2017.01.028

[43] Castrodeza EM, Perez Ipina JE, Bastian FL. Fracture toughness evaluation of unidirectional fibre metal laminates using traditional CTOD (δ) and Schwalbe (δ5) methodologies. Engineering Fracture Mechanics. 2004; **71**:1107-1118. DOI: 10.1016/S0013-7944 (03)00138-3

[44] ASTM International. Designation: D 3039/D 3039M–00 Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials 1. 2002. p. 15. DOI: 10.1520/D3039\_ D3039M-08

[45] ASTM International. Designation: D 3518/D 3518M–94 Standard Test Method for In-Plane Shear Response of Polymer Matrix Composite Materials by Tensile Test of a 45° Laminate. 2001;**5**: 1-7. DOI: 10.1520/D 3518/D\_3518M-94

[46] ASTM International. ASTM-D3410 standard test method for compressive properties of polymer matrix composite materials with unsupported gage section by shear loading. Annual Book of ASTM Standards. 2003;**15**(03):1-16. DOI: 10.1520/D3410

[47] ASTM International. ASTM D5379: Standard Test Method for Shear Properties of Composite Materials by the V-Notched Beam Method. 1998. pp. 1-13

[48] Garcia-Manrique J, Camas D, Lopez-Crespo P, Gonzalez-Herrera A. Stress intensity factor analysis of

through thickness effects. International Journal of Fatigue. 2013;**46**:58-66. DOI: 10.1016/j.ijfatigue.2011.12.012

**Chapter 5**

**Abstract**

Construction of an Artificial

Detect Structural Damage

*and Xochicale-Rojas Hugo Alberto*

rather simple. It was carried out in four steps.

structural analysis

**1. Introduction**

**87**

Neural Network-Based Method to

*Francisco Casanova-del-Angel, Daniel Hernández-Galicia*

This chapter shows the framework used to obtain data with which the artificial neural network (ANN) was developed. It describes its geometry, properties of the material, sections of structural elements, and loads used. Then, the numerical model of the framework under study is developed in structural analysis using SAP2000® software in order to obtain its modal parameters. In addition, a program made in MATLAB® is shown, from which data with and without damage to the framework under study were obtained, and with which the ANN was developed. Data from the numerical model were used to corroborate data obtained with MATLAB®. The neural model used in this work to detect structural damage is described. Data on damage were obtained simulating a plastic hinge in various elements of a test framework, varying the position of the hinge. The above resulted in obtaining various damage conditions for the same framework, which data thus obtained were used to develop the network. Damage conditions were hierarchized based on their fundamental periods in order to know where is more damage, depending on location of the hinge within the framework. Upon completion of the research, we have concluded that the methodology implemented to detect structural damage is

**Keywords:** damage detection, neural network, failure condition, framework,

Throughout their useful life, structures accumulate gradual damage as time passes. Such damage is caused by actions and natural phenomena such as earthquakes, winds, and explosions, among others. Therefore, and taking into account the functioning and the safety of structures, it is of paramount importance to detect damage, to follow up and monitor structures in order to know their physical conditions, and to increase safety and structural reliability. If damage is detected in a structure early, its evolution may be observed regarding magnitude and size, meaning it can be treated properly. Nowadays, there are various methods used to detect structural damage, all of which have advantages and disadvantages. There is

no consensus that one method is the best. Therefore, for those who are not

## **Chapter 5**

113-126. DOI: 10.1016/j.ijsolstr.2017.

*Fracture Mechanics Applications*

through thickness effects. International Journal of Fatigue. 2013;**46**:58-66. DOI:

10.1016/j.ijfatigue.2011.12.012

[42] Chabchoub M, Bouscarrat D, Vieille B, Gautrelet C, Beyaoui M, Taktak M, et al. Investigations on the mode I translaminar failure and determination of fracture toughness in woven-ply carbon fibers thermoplastic composites at high temperatures. Applied Acoustics. 2017;**128**:55-63. DOI:

10.1016/j.apacoust.2017.01.028

[43] Castrodeza EM, Perez Ipina JE, Bastian FL. Fracture toughness

evaluation of unidirectional fibre metal laminates using traditional CTOD (δ) and Schwalbe (δ5) methodologies. Engineering Fracture Mechanics. 2004; **71**:1107-1118. DOI: 10.1016/S0013-7944

[44] ASTM International. Designation: D 3039/D 3039M–00 Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials 1. 2002. p. 15. DOI: 10.1520/D3039\_

[45] ASTM International. Designation: D

[46] ASTM International. ASTM-D3410 standard test method for compressive properties of polymer matrix composite materials with unsupported gage section by shear loading. Annual Book of ASTM Standards. 2003;**15**(03):1-16. DOI:

[47] ASTM International. ASTM D5379: Standard Test Method for Shear Properties of Composite Materials by the V-Notched Beam Method. 1998.

[48] Garcia-Manrique J, Camas D, Lopez-Crespo P, Gonzalez-Herrera A. Stress intensity factor analysis of

3518/D 3518M–94 Standard Test Method for In-Plane Shear Response of Polymer Matrix Composite Materials by Tensile Test of a 45° Laminate. 2001;**5**: 1-7. DOI: 10.1520/D 3518/D\_3518M-94

01.035

(03)00138-3

D3039M-08

10.1520/D3410

pp. 1-13

**86**
