**1. Introduction**

Composite structures have found widespread applications in aerospace and other major industries where weight reduction and directional properties are the main criteria. Circular cutouts are unavoidable in these structures to satisfy the design requirements. However, these cutouts change the mechanical behavior of these structures and produce a high undesirable stress concentration located at the vicinity of these notches. If the material strength is not high enough, failure will undoubtedly occur, usually from the region near the cutout. Therefore, it is mandatory to well identify the stress-strain distributions around the cutout.

Many studies have been done during the past two decades to determine the stress-strain distributions at the circumferential of notches in isotropic and anisotropic structures. A variety of methods have been used to estimate the stress concentration factor (SCF) values, such as exact and approximate analytical analysis. A brief review on current analytical methods for the determination of stress distribution around holes has been given by Sevenois [1].

In structural design field, engineers try to optimize various objectives, such as strength and structural weight, depending upon some requirements. Within the context of optimization, the weight or the strength is the objective function. The structural dimensions such as the thickness, length, or width are the design variables that can be controlled to achieve the best configuration [2]. In the case of composite laminated plates with cutouts, various response mechanisms of these structures are not fully understood and are still topics for continuing research.

Based on Sevenois [1] work, most of the research works to solve the stress concentration problem focus on the stress distributions in orthotropic plates subjected to different loads with different material properties. However, these investigations do not address the problem of whether the stress concentration degree is acceptable for a certain material strength and how one can improve the stress-strain distributions and the strength for these types of structures.

From a design point of view, if there is more than one cutout, the stress concentration at the vicinity of the original notch can be reduced, if one determines the optimum locations of other corresponding holes. This is known as the defense hole theory (DHT). It relies on the following rationale. By introducing small notches (auxiliary holes) on both sides of the main hole, it is possible to smooth the flow of the principal stress paths past the main notch, and this will reduce the SCF around the main notch [3].

This idea is very powerful for reducing the stress concentration. In this context, Erickson and Riley [4] were one of the first investigators to reduce the stress concentration around circular notch in isotropic plates under uniaxial loading. Durelli et al. [5] tried to obtain an ideal boundary of a discontinuity in perforated rectangular plate. They defined this boundary as that boundary along which there is no stress concentration. The ideal design of the boundary of the hole in the rectangular plate reduces the maximum stresses by 26%. On the other hand, the response of orthotropic laminated plates with circular notches has been also studied by Jain [6]. In this study, a FE study was made for reduction of SCF around circular notch in infinite isotropic and orthotropic laminates subjected to uniaxial tension. The SCF was reduced up to 24.4% in isotropic plates and 31% in orthotropic laminates by introducing four auxiliary notches on both sides of the original cutout.

Here, the current investigation addresses the research in the domain of optimization of composites for stress concentration and strength. The main goal of the present experimental and numerical studies is to obtain the best optimal size and position of defense holes for perforated laminates when they are subjected to uniaxial loading condition. For practical industrial applications, the most important characteristic to improve is the strength of the particular structure. Thereby, one of the aims of this study is to contribute to the minimization of the stress concentration and know if there can be a significant improvement in the strength of particular perforated composite laminates. Experimental studies investigated using E-glass/epoxy laminates to validate the improvement of the behavior of perforated laminates with auxiliary holes. Material and specimen preparation steps and different material characterization tests are dealt in detail.

### **2. Materials and sample preparation**

During the present work, samples with different opening diameters were fabricated by the hand lay-up method. A mold release agent is first applied to the mold for getting a high-quality surface finish and facilitates the release of the laminated plates from the metallic mold. When the release agent has cured sufficiently, the UD E-glass fibers are manually placed on the metallic mold. After putting the

**173**

**Figure 1.**

*Strength Improvement and Stress Analysis of E-Glass Laminated Plates with Circular Notches…*

fibers properly, the resin is applied by brushing. A paint roller is used, in order to distribute the resin uniformly on the metallic mold surface and also to consolidate the lamina, thoroughly wetting the reinforcement and removing the entrapped air. Subsequent layers of the UD glass fibers are added to build the required laminate thickness. The samples were made of four-ply UD E-glass/epoxy lamina. The thickness of each layer is 0.5 mm. The initial materials, E-glass fiber 400 g/m2

The completed specimens have been checked to ensure that the final laminates

In order to create circular notches at the center of samples, different sizes of drills were used. On the other hand, to limit the delamination effects at the vicinity of the holes, caused by the drilling process, wooden plates under the samples and a drill machine with a speed of 2300 rad/min were used. Various diameters of drill (2.5, 5, 7.5, and 10 mm) were used in order to obtain various diameter-towidth (*D*/*W*) ratios. The main notch is machined by drilling initially a hole of a small diameter and then carefully enlarging it to its final dimension by incremen-

In addition, the following procedure is followed to create different diameters of auxiliary holes in various locations at the vicinity of the main one. The first step is to make transparent papers and fix them onto the laminates using adhesive tape. These papers show the centers of the auxiliary holes. A needle is used in order to mark the center locations of the auxiliary holes on the laminates. Initially, 1 mm diameter drill is used for creating the initial holes. Starting with a small size of a drill improves the accuracy of the locations of the notches. Then, using a drill of

Before the testing, the DIC samples were cleaned to remove dirt, and then they were prepared and covered using a black paint and sprayed with a white aerosol to create a random speckle pattern. The samples tested for the present experimental

are in good quality without defects and then cut into samples with a length of *L* = 250 mm and a width of *W* = 25 mm. These specimens have been cut using a dedicated cutting machine with a diamond-coated blade. Four-layered laminated plates, all in the same direction [0]4, were fabricated in this experimental investiga-

and

and a hardener with a density of

*DOI: http://dx.doi.org/10.5772/intechopen.87089*

1.02 g/cm3

tal drill size.

tion as perforated specimens.

investigation are shown in **Figure 1**.

*UD laminated plates with various DHS configurations.*

clear 1070 resin epoxy with a density of 1.15 g/cm3

, were purchased from SF Composites (France).

sufficient size, a bigger hole centered at the initial hole is created.

#### *Strength Improvement and Stress Analysis of E-Glass Laminated Plates with Circular Notches… DOI: http://dx.doi.org/10.5772/intechopen.87089*

fibers properly, the resin is applied by brushing. A paint roller is used, in order to distribute the resin uniformly on the metallic mold surface and also to consolidate the lamina, thoroughly wetting the reinforcement and removing the entrapped air. Subsequent layers of the UD glass fibers are added to build the required laminate thickness. The samples were made of four-ply UD E-glass/epoxy lamina. The thickness of each layer is 0.5 mm. The initial materials, E-glass fiber 400 g/m2 and clear 1070 resin epoxy with a density of 1.15 g/cm3 and a hardener with a density of 1.02 g/cm3 , were purchased from SF Composites (France).

The completed specimens have been checked to ensure that the final laminates are in good quality without defects and then cut into samples with a length of *L* = 250 mm and a width of *W* = 25 mm. These specimens have been cut using a dedicated cutting machine with a diamond-coated blade. Four-layered laminated plates, all in the same direction [0]4, were fabricated in this experimental investigation as perforated specimens.

In order to create circular notches at the center of samples, different sizes of drills were used. On the other hand, to limit the delamination effects at the vicinity of the holes, caused by the drilling process, wooden plates under the samples and a drill machine with a speed of 2300 rad/min were used. Various diameters of drill (2.5, 5, 7.5, and 10 mm) were used in order to obtain various diameter-towidth (*D*/*W*) ratios. The main notch is machined by drilling initially a hole of a small diameter and then carefully enlarging it to its final dimension by incremental drill size.

In addition, the following procedure is followed to create different diameters of auxiliary holes in various locations at the vicinity of the main one. The first step is to make transparent papers and fix them onto the laminates using adhesive tape. These papers show the centers of the auxiliary holes. A needle is used in order to mark the center locations of the auxiliary holes on the laminates. Initially, 1 mm diameter drill is used for creating the initial holes. Starting with a small size of a drill improves the accuracy of the locations of the notches. Then, using a drill of sufficient size, a bigger hole centered at the initial hole is created.

Before the testing, the DIC samples were cleaned to remove dirt, and then they were prepared and covered using a black paint and sprayed with a white aerosol to create a random speckle pattern. The samples tested for the present experimental investigation are shown in **Figure 1**.

**Figure 1.** *UD laminated plates with various DHS configurations.*

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

tions and the strength for these types of structures.

the main notch [3].

In structural design field, engineers try to optimize various objectives, such as strength and structural weight, depending upon some requirements. Within the context of optimization, the weight or the strength is the objective function. The structural dimensions such as the thickness, length, or width are the design variables that can be controlled to achieve the best configuration [2]. In the case of composite laminated plates with cutouts, various response mechanisms of these structures are not fully understood and are still topics for continuing research. Based on Sevenois [1] work, most of the research works to solve the stress concentration problem focus on the stress distributions in orthotropic plates subjected to different loads with different material properties. However, these investigations do not address the problem of whether the stress concentration degree is acceptable for a certain material strength and how one can improve the stress-strain distribu-

From a design point of view, if there is more than one cutout, the stress concentration at the vicinity of the original notch can be reduced, if one determines the optimum locations of other corresponding holes. This is known as the defense hole theory (DHT). It relies on the following rationale. By introducing small notches (auxiliary holes) on both sides of the main hole, it is possible to smooth the flow of the principal stress paths past the main notch, and this will reduce the SCF around

This idea is very powerful for reducing the stress concentration. In this context, Erickson and Riley [4] were one of the first investigators to reduce the stress concentration around circular notch in isotropic plates under uniaxial loading. Durelli et al. [5] tried to obtain an ideal boundary of a discontinuity in perforated rectangular plate. They defined this boundary as that boundary along which there is no stress concentration. The ideal design of the boundary of the hole in the rectangular plate reduces the maximum stresses by 26%. On the other hand, the response of orthotropic laminated plates with circular notches has been also studied by Jain [6]. In this study, a FE study was made for reduction of SCF around circular notch in infinite isotropic and orthotropic laminates subjected to uniaxial tension. The SCF was reduced up to 24.4% in isotropic plates and 31% in orthotropic laminates

by introducing four auxiliary notches on both sides of the original cutout.

ent material characterization tests are dealt in detail.

**2. Materials and sample preparation**

Here, the current investigation addresses the research in the domain of optimization of composites for stress concentration and strength. The main goal of the present experimental and numerical studies is to obtain the best optimal size and position of defense holes for perforated laminates when they are subjected to uniaxial loading condition. For practical industrial applications, the most important characteristic to improve is the strength of the particular structure. Thereby, one of the aims of this study is to contribute to the minimization of the stress concentration and know if there can be a significant improvement in the strength of particular perforated composite laminates. Experimental studies investigated using E-glass/epoxy laminates to validate the improvement of the behavior of perforated laminates with auxiliary holes. Material and specimen preparation steps and differ-

During the present work, samples with different opening diameters were fabricated by the hand lay-up method. A mold release agent is first applied to the mold for getting a high-quality surface finish and facilitates the release of the laminated plates from the metallic mold. When the release agent has cured sufficiently, the UD E-glass fibers are manually placed on the metallic mold. After putting the

**172**

**Figure 2.** *Experimental setup for the DIC analysis.*

In order to obtain the in-plane mechanical properties of the present material, the following ASTM D3039 [7] and ASTM D3518 [8] for tensile and shear properties, respectively, have been used.

The tensile properties of the unnotched samples, such as the laminate Young's modulus *E*1 and *E*2, Poisson's ratio *v*12, and ultimate strength, were measured by static tension testing of longitudinal [0]4 and transverse [90]4 UD samples. The shear modulus of the samples was measured by loading the specimens whose principal axes are on 45°. Four samples were used in the characterization tests.

The INSTRON-5969 testing machine was used in the present study in order to conduct the experimental tests on laminated samples (see **Figure 2**).

The testing machine is connected with a computer in order to record the stressstrain curves during the tensile tests. As shown in **Figure 2**, the samples were illuminated by ordinary white light during the experiments. During the loading process, high-resolution images were taken using a digital camera. The experimental results obtained in the present study were processed with a 2D-DIC MATLAB code [9]. In order to perform the DIC tests, we replicate three experiments for each sample, and the results are averaged. This procedure was repeated for all samples to obtain correct stress distributions and reduce the errors that can be related to the speckle pattern.

**Remark**: The DHS technique is based on the idea of introducing smaller holes (auxiliary holes) on both sides of the main notch, in order to smooth the flow of the principal stress paths past the main notch, and this will reduce the stress concentration developed around the original notch. This process is similar to the topology optimization technique which is based on logic of "material should be removed from the regions that are less essential for carrying the loads."

**Remark**: The DIC is one of the powerful noncontact techniques used for measuring the deformations. The DIC technique uses images in order to track the relative displacements of a random speckle pattern point. These displacements are calculated between an undeformed image (reference image) and the current one (the deformed image). In the present work, the authors obtained the full-field strain distributions using a 2D-DIC MATLAB code [9].

**175**

**Figure 3.**

*(b) a plate with DHS.*

*Strength Improvement and Stress Analysis of E-Glass Laminated Plates with Circular Notches…*

2D finite element models were developed using the open-source FE software FreeFem++ [10]. The models were developed using a linear triangular element (three nodes with 2 degrees of freedom per node), because these elements are more adaptable for meshing plates with circular notches. In order to validate the experimental results, the dimensions and the mechanical properties of the numerical models are chosen to be the same as the experimental specimens (a total length of *L* = 250 mm and a width of *W* = 25 mm). In addition, various sizes of hole diameters (2.5, 5, 7.5, and 10 mm) are used in order to obtain different diameterto-width (*D*/*W*) ratios. The length and width of the plates are divided into 70 and

The FE models of all groups of samples are created, and the stress-strain distributions at the vicinity of notches are obtained. Furthermore, in view of the rapid change in the stress-strain fields around the holes, a higher mesh density with smaller finite elements is adopted and a coarse mesh far from the hole region. A convergence study is carried out to obtain initial appropriate fine mesh in the open hole zone (the initial mesh size was 30 elements around a hole diameter of 2.5 mm), and then automatic parametric program was developed in order to change the notch size and the mesh refinement automatically, because if one keeps the same element number at the vicinity of the notch boundary, the stress-strain distributions will be affected by changing the notch diameter (see **Figure 3a**). All

On the other hand, the introduction of the DHS is dependent on the logic of adding auxiliary holes in the areas of low stress near the main cutout. The number of the auxiliary holes in this study is two circular holes (see **Figure 3b**). Various finite element models are also developed for different DHS configurations.

*Finite element models of laminated plates under a tensile loading. (a) A plate with a single hole and* 

*DOI: http://dx.doi.org/10.5772/intechopen.87089*

the numerical models are subjected to a tensile load.

**3. Finite element modeling**

5 elements, respectively.

*Strength Improvement and Stress Analysis of E-Glass Laminated Plates with Circular Notches… DOI: http://dx.doi.org/10.5772/intechopen.87089*
