Analysis of stress intensity factor along semi-elliptical surface crack reinforced by composite patching

Abstract

Semi-elliptical surface cracks are one of the most frequent cracks found in many structures in service, such as off-shore structures and aircraft components. The expense of replacement and time out of service have made repairing policy more attractive. Use of bonded composite patches is widely regarded as favorite reinforcement methods for repairing cracked structures. It is the main aim of present work to investigate the effect of the single-sided composite patch on residual strength of a semi-elliptical surface crack. Computer code ANSYS is used to calculate numerically the stress intensity factor of rehabilitated cracks. The influence of geometrical and mechanical parameters has been studied and it is found that the presence of composite patch leads to a massive reduction of stress intensity factor along crack front. Moreover, the stress intensity factors remain almost unchanged for different crack width and depth when rehabilitated with composite patches.

Keywords

Finite element solution stress intensity factor semi-elliptical surface crack composite patch

1. Introduction

Structures can be damaged by overloading, environmental events or human errors in the design and fabrication process. Cracks and corrosion are two widely occurring defects observed in aged structural components. Composite patches are increasingly used to repair cracked and corroded structures, or to rehabilitate structures that must bear increasing loads beyond the structure’s rated capacity at significantly low cost.

Many research works have conducted worldwide to investigate the effect of composite rehabilitation on residual strength of cracked or corroded structures. Ramji and Srilakshmi [1,2], Bouiadjra et al. [3], and Ayatollahi and Hashemi [4,5] have used Finite Element Method (FEM) to study the impact of composite patching on Stress Intensity Factor (SIF) along the crack front which is known as necessarily a true measure of assessing the performance of composite reinforcement technique. According to the geometry of composite patching, bonded repairs have generally divided into double-sided and one-sided. Okafor et al. [6] have obtained stress distributions at the various parts of the aluminum-adhesive-patch assembly to predict the increase in strength and durability of the one-sided repaired crack using FEM and experiment. Fracture mechanics is frequently performed to estimate fatigue crack growth in one-sided repaired panels [7–10]. Seo and Lee [10] have determined the fatigue crack growth behavior of thick panel repaired cracks with bonded composite patches using the SIF range and fatigue crack growth rate.

In spite of the fact that engineering components commonly experience semi-elliptical surface cracks during service life [11–13], most of the previous studies are limited to repaired panels having the through-thickness edge or center cracks. There are only a few investigations which have studied the behavior of semi-elliptical surface crack rehabilitated with composite patches. Chuanyu et al. [14] have numerically calculated the SIF along a three-dimensional surface crack in steel tension specimen rehabilitated with carbon fiber laminate (CFL). However, Kumar et al. made a distinction between the efficient of the composite patch and laminated fiber at the load bearing capacity [15] so that it seems essential to assess the effect of both on the fracture. It is the main aim of present work to investigate the influence of composite reinforcement on the fracture strength of semi-elliptical cracks. A three-dimensional FEM of surface cracked plate reinforced by bonding a graphite/epoxy composite patch at one side is used. SIF along crack fronts are calculated for the various dimension of semi-elliptical crack, patching size, the thickness of plate and thickness of film adhesive.

2. Numerical analysis

A typical model for the single-sided reinforced crack specimen is shown in Fig. 1. The panel is made of aluminum alloy 2024 T3 with dimensions of 39 × 160 × 3.175 mm and a center semi-elliptical surface crack. The maximum depth of crack, a, is 2 mm and half-width of crack, c, is 5 mm (Fig. 2). The specimen is subjected to the uniaxial uniform tensile stress of 𝜎 = 121.11 MPa, taken arbitrarily as a reference value. The graphite/epoxy composite patch was bonded on one side of the plate, using a thin layer of adhesive. The dimensions of the composite patch are considered as 25 × 25 × 1.5 mm. The general material properties of the aluminum panel, composite patch and adhesive are depicted in Table 1 [1].

Computer code ANSYS (version 14.5) is used to calculate SIF along the semi-elliptical surface crack. A three-dimensional FE model is built using SOLID186, the 20-node brick element to mesh crack front, the patch and film adhesive, SOLID187 is used to mesh the rest of the plate (Fig. 3). Since the patch and adhesive meshes have the same size and shape as the meshes of the panel, so they can easily be coupled at common nodes. In the thickness direction, the panel and adhesive mesh with two elements, and patch with four elements.

The SIF is calculated at the crack front at the different points around the crack front, shown by angular parameter $\frac{2{\phi}}{{\pi}}$ (Fig. 3) using CINT command of ANSYS. To investigate the accuracy of calculated SIF, an overall comparison is made with Lin and Smith [16] (Table 2 and Fig. 4). Due to the symmetrical distribution of SIF along crack front, only half of crack front are shown in the rest of the paper.

Since all errors of the normalized SIF calculated by the present method are about 2% against Lin and Smith [15], it can be concluded that present method has good accuracy and can be used for further analysis.

3. Parametric analyses and discussion

3.1. Basic study: Comparison between patched and un-patched specimens

The variation of SIF along the crack front for a patched and unpatched cracked plate with different layup orientations such as [−45]₄ and [90]₄ is depicted in Table 3 for crack with maximum depth and half-width of 2 mm and 5 mm, respectively. It is remarked that due to composite patch, distribution of SIF undergoes significant changes and the SIF reduces sharply, about 97% and 98% for [−45]₄ and [90]₄ layup orientation, respectively. The reason is that a transfer of stresses through the adhesive towards the composite laminate leads to this considerable reduction. As can be seen, though the SIF for both layups in Table 3 and Fig. 4 have reduced significantly, however, SIF’s for [−45]₄ layup is about 16% higher than [90]₄ layup at the deepest point and 29% higher at the inner surface points. It should be added that the symmetrical pattern of SIF along the crack front changes but not significantly.

Based on the results shown in Fig. 5, one can conclude that there is no difference between [−30]₄ and [30]₄, [−45]₄ and [45]₄ or [−60]₄ and [60]₄ layups. Also, by increasing the angle of fiber layups with respect of the loading, the effect of the composite patch reduces.

To study the effect of geometrical parameters on the influence of composite patch on the reduction of SIF, five different cases have been studied (Table 4). In case (i) crack parameters, in cases (ii) and (iii) composite parameters, and in case (iv) adhesive parameters are changed. There are a number of different likely failure modes in the composite patching (Ayatollahi and R. Hashemi [4]), however, in this research only the impact of composite patching on the brittle fracture of rehabilitated cracked plates have been studied.

3.2. Impact of crack configuration

Two non-dimensional parameters, $\frac{a}{c}$ and $\frac{a}{t}$ , are defined to study the influence of crack geometry. Figure 6 shows the variation of SIF’s along the crack front for different crack depth ratio in rehabilitated cracks with [90]₄ layup.

It is observed that the trend of SIF’s is the same regardless of the value of crack depth ratio. Moreover, Table 5 is provided to show SIF for different dimensionless parameters $\frac{a}{t}$ in the patched and un-patched crack plates. To study the effect of the composite patch on the reduction of SIF, a reduction parameter called the impact factor is defined as follows (Ayatollahi and R. Hashemi [4]), $\begin{eqnarray}\displaystyle F_{i}=1-\frac{K_{p}}{K_{u}} & & \displaystyle\end{eqnarray}$ (1) where K _p is SIF in patched cracked plate and K _u is SIF in the un-patched cracked plate. As can be seen from Table 5, the impact factor of the composite patch is independent of the dimensionless parameter $\frac{a}{t}$ and is about 98%.

Figure 7 shows the distribution of the SIF’s along the crack front for different dimensionless parameters $\frac{a}{c}$ for plate with layup orientation [90]₄ and Table 6 is provided to show SIF’s for different dimensionless parameters $\frac{a}{c}$ in patched and un-patched plate. It can be concluded that there is no change in the value of impact factor along the crack front.

3.3. Comparison the effect of composite patch and fiber laminate

The effect of composite patch and CFL on strength of rehabilitated cracked body are compared when material properties of reinforcements and the dimensions of plate and reinforcement, and the material of plate are the same (Table 6). CFL is modeled as isotropic material whose Young modulus and Poisson’s ratio are considered as 208.3 GPa and 0.3, respectively [14]. In modeling CFL, there is no need to consider adhesive component. As can be seen, composite patch reduces considerably SIF along crack front by 98% while CFL reduces it nearly by 35%. Moreover, the effect of CFL on SIF at the deepest points of crack front is not as large as near the surface plate. At deepest point of crack is 33% while near the surface is 49%.

3.4. Impact of composite laminate width

Figure 8 is plotted to show SIF’s along the crack front for different composite patch width for a plate with layup orientation [−45]₄. It is observed that increasing composite laminate width reduces slightly SIF value along crack front. Besides, inner surface points feel the impact of composite patch much greater than deepest surface points. It is interesting to note that maximum reduction in SIF accounts for about 14% and minimum reduction presents about 6% when composite patch width changes from 6 mm to 12.5 mm.

3.5. Impact of composite laminate thickness

In this section, the impact of composite laminate thickness on SIF is investigated. The thickness of each layer is assumed as constant and equal to 0.375 mm and a different number of the layer are considered 0.75, 1.5, 2.25, 3, 3.75 mm. Figure 9 is provided to illustrate the distribution of the SIF’s along the crack front for different composite laminate thickness (four layers) for plates with layup orientation [90]₄. As can be seen, the number of layers or thickness of composite patch has no significant effect on the reduction of SIF’s along the crack front. An increase of composite patch thickness from 1.5 mm to 3.75 mm reduces SIF from 7 MPa $\sqrt{\text{mm}}$ to 6.7 MPa $\sqrt{\text{mm}}$ at the deepest point and this fact is also similar for inner surface points.

3.6. Impact of adhesive thickness

The objective of bonding a composite patch on the cracked plate is to transmit part of the stresses to the adhesive layer and consequently to the patch, so as to restore the fracture strength of crack specimens [1]. Figure 10 shows SIF’s distribution along the crack front for different values of adhesive thickness on a plate with layup [−45]₄. It is observed that the increase in adhesive thickness increases gradually SIF along crack front. Moreover, the increasing of this parameter reduces the performance of composite patch. However, the rate of this increase in SIF calculated is not similar along crack front. It should be added that the increasing SIF at inner surface points is much greater than compared to that at the deepest point.

4. Conclusions

A series of three-dimensional FE investigations were conducted to investigate the impact of the single-sided composite patch on SIF along semi-elliptical crack under tensile load condition. The following conclusions can be drawn from the obtained results:

Due to composite patch, the SIF along surface crack experiences a massive reduction (about 97%) compared to the un-patched plate and its distribution remains symmetrical along the semi-elliptical crack front. However, it cannot completely keep the surface crack from propagation.

Layup orientation of composite patch contributes to decrease in SIF or increase in the impact of the composite patch. By increasing the angle of fiber layups with respect to loading, the effect of the composite patch reduces. It is interesting to note that changes in layup orientation have a greater impact on points where they are near to the plate surface (inner surface points).

The impact of the composite patch is independent of dimensionless parameters of semi-elliptical surface crack ( $\frac{a}{t}$ and $\frac{a}{c}$ ). Moreover, there is no change in the impact of the composite patch on SIF value along the surface crack front with increasing of the half-width of crack and crack depth.

The effect of composite patch on SIF vastly exceeds the effect of laminated fiber.

Increasing composite laminate width reduces slightly SIF value along crack front. Like Layup orientation, inner surface points feel the impact of composite patch much greater than the deepest surface points.

Increasing of composite laminate thickness has no impact on SIF values along the crack front.

Adhesive thickness performs a negative role in the performance of composite patch. This is because it increases SIF along crack front. Besides, the rate of this increase in SIF calculated is not similar along crack front. The increasing SIF at inner surface points is much greater than compared to the deepest point.

Footnotes

Conflict of interest

None to report.

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