Effect of fiber type on strength of quasi-isotropic bonded/unbonded plastic composites subjected to tension and compression loadings

1 Introduction

Plastic matrix composite materials reinforced with metallic fibers are attractive because of their high specific stiffness and strength. Advantage can be taken from the high strength of metallic fibers and the ductility of the metal matrix to produce a composite with superior combined properties. Compared with conventional materials, fiber-reinforced composite materials present such distinguished features as high stiffness-to-weight ratio and strength-to-weight ratio and the possibility of changing its stiffness characteristics while keeping its weight constant. Nowadays, they are widely used as a primary material in various industrial areas, especially in space and military applications. They offer an increased service temperature and improved specific mechanical properties over existing metal alloys. The investigation of a composite laminate containing a circular hole has been undertaken by several investigators. However, very few studies have been reported on the evaluation of strength for laminate containing circular hole with reinforcement. Kocher and Cross [1] investigated the reinforced cutouts in composite materials. These reinforcements were occurred with the composite laminate so as to form an integral part of the structure to form an integral part of the structure. Tan and Tsai [2] offered an analytic method that was able to provide stress distribution near the hole in the laminate. This analytic analysis showed that the strength of notched laminate can be increased with proper selection of reinforcement. Pickett and Sullivan [3] investigated the reinforcement of a hole for very large composite laminates. In addition, elastic-plastic and residual stresses are very important in the failure analysis of plastic matrix composite materials. When the yield strength of the composite laminate is exceeded, the residual stresses occur in the laminated plates. Lee and Mall [4] made an experimental investigation about quasi-isotropic epoxy laminate with a hole. The obtained residual stresses can be used to raise the yield strength of the laminated plates. Jeronimidis and Parkyn [5] investigated residual stresses in carbon fiber/thermoplastic matrix laminates with a hole. Bahei-El-Din and Dvorak [6] investigated the elastic-plastic behavior of symmetric metal-matrix composite laminates with holes in the case of in-plane mechanical loading. Karakuzu and Sayman [7] gave an exact solution to the elasto-plastic stress analysis of an aluminum metal-matrix composite beam reinforced by steel fibers. Residual stresses are determined in metal matrix rotating discs with holes and flat plates containing notches by using finite element method, and the Tsai-Hill criterion is used as the failure criterion [8].

An elastic-plastic stress analysis in steel fibrous aluminum-matrix composites was conducted using the finite element method, and residual stresses were also found [9, 10].

In this article, the strength and failure mechanism of composite laminates with a reinforced hole were investigated experimentally. Experimental results were compared with the results of the finite element method.

2 Mathematical formulation

The composite laminated plate of constant thickness is composed of an orthotropic layer. Notch geometry and loading configuration are illustrated in Figure 1.

Figure 1

Notch geometry and loading (compressive) configuration.

The solution of laminated plate includes transverse shear deformations. Therefore, the constitutive relations for an orthotropic composite layer can be written as

where the transformed reduced stiffness, Q̅_ij, is given in terms of engineering constants of the material. According to first-order shear deformation theory, the particles of the plate, originally on a line that is normal to the nondeformed middle surface, remain on a straight line during deformation, but this line is not necessarily normal to the deformed middle surface. Thus, the displacement components of a point of coordinates x, y, z for small deformation can be written as follows:

where u₀, v₀, and w are the displacements of a point on the middle surface and Ψ_x and Ψ_y are the rotation angles of normal to the y and x axes, respectively.

By using linear strain-displacement relations, bending strains are found to vary linearly through the plate thickness, whereas shear strains are assumed to be constant throughout the thickness as

In order to obtain the element equilibrium equations, the total energy of a laminated plate under static loading is given as follows,

where U_b is the strain energy of bending, U_s is the strain energy of shear, and V is the potential energy of external in-plane loadings (N₁, N₂, N₁₂). They are defined as

where dA=dxdy and R is the region of a rectangle excluding the hole and are the in-plane loads applied on the boundary ∂R. The resultant forces N_x, N_y, and N_xy, are not constant but are functions of x and y.

The forces (N_x, N_y, N_xy); moments M_x, M_y, and M_xy; and shearing forces Q_x and Q_y per unit length of the cross-section of the laminated plate are given as

For equilibrium, the potential energy ∏ must be stationary. It is obtained so that δ∏=0, which may be regarded as the principle of virtual displacement for the plate element [10].

3 Finite element analysis

In this work, the finite element procedure was employed to calculate the notched strength and unnotched strength of the composite laminates. Nine-node elements are used with displacement functions. The stiffness matrix of the composite plate can be obtained by using the minimum potential energy principle. Bending and shear and geometric stiffness matrices are

where

D_b, D_s, and D_g are the bending and shear and geometric parts of the material matrix, respectively. A₄₅ is negligible in comparison with A₄₄ and A₅₅. K₅₅ represents the shear correction factors for rectangular cross-sections and is given as

In order to obtain system equations, the total potential energy principle is used as follows:

where Π is given by,

where

In Eq. 10, nodal displacements {δ_j} (j=1, 2, 3,...n) have been replaced by the global nodal displacement {Δ} whose number of degrees of freedom is nd.

From Eqs. 9 and 10, the following linear algebraic equation is obtained,

The critical load N̅_cr is obtained from the smallest eigen -λ_b value, determined using the following equation [9]:

Eq. 13 is solved by using the iteration technique. In this solution, 288 nodes and 64 nine-node plate elements are used. Boundary conditions for finite element analysis are illustrated in Figure 2.

Figure 2

Boundary conditions for the finite element analysis.

4 Experiments

The aim of this experimental study was to research the effects of the following parameters on the strength of plastic composite laminate with a reinforced hole.

Type of reinforcement

• Adhesively bonded plug

• Snug-fit plug

Material of reinforcement

• Steel

• Aluminum

• E-glass

Five different diameters for hole sizes

• 2.5 mm

• 5 mm

• 7.5 mm

• 10 mm

• 12.5 mm

5 Results and discussion

The initially finite element method was used to develop the database for comparison with the results of experimental tests. Thereafter, tests with unbonded and bonded reinforcement were conducted, which are discussed separately below.

5.1 Unbonded reinforcement

5.1.1 Tension loading

For the aluminum-reinforced case, improvement in the strength for the open-hole case was good. This good improvement in strength was for the hole with a diameter greater than 5 mm. However, for the 2.5-mm hole diameter, there was no such improvement. The results of the E-glass reinforcement showed no increase. It may be that the stiffness of E-glass is very much low in comparison with that of laminated plate. For that reason, in most cases, the E-glass reinforcement fractured at the same time when the laminated plate failed. In case of steel, the results of the test showed an improvement in strength for 2.5- and 5-mm hole diameters, showing similar results as in the case of aluminum. However, for the case of the larger hole, steel showed a smaller increase than aluminum did. The stiffness of steel is much higher than that of laminated plate. That is why it did not follow the deformed shape of the laminated plate hole with the increase in the load. The results of all tension tests are shown in Figure 3. In general, the aluminum reinforcement showed little improvement relative to the open hole, while the E-glass and steel inclusion showed no increase.

Figure 3

Comparison of NSF in tension for unbonded reinforcements.

5.1.2 Compression loading

In this case, aluminum showed the largest amount of improvement, similar in the tension test. Especially when hole diameter is increased, the improvement in reinforcement was significantly high. In case of E-glass reinforcement, the improvement was relatively small. However, the case of compression was higher than the case of tension because of the compressive load, which caused more interaction between the plug and the hole. The results of all compression tests are shown in Figure 4. It can be seen from Figure 4 that the reinforcement of steel also showed a large improvement, as in the aluminum case.

Figure 4

Comparison of NSF in compression for unbonded reinforcements.

5.2 Bonded reinforcement

5.2.1 Tension tests

The results of the bonded reinforcement case are shown in Figure 5 for the case of tension loading. It can be seen from the figure that there was no improvement due to bonded reinforcement for any hole size.

Figure 5

Comparison of NSF in tension for bonded reinforcements.

5.2.2 Compression tests

The compression test with bonded reinforcement was realized with two types of reinforcement: steel and aluminum. The results of this case are shown in Figure 6 for comparison. The improvement in strength due to reinforcement in comparison with open or unreinforced hole can be seen easily, which is very similar to its counterpart with unbonded reinforcement. The increase in strength was very much seen in the in case of bonded reinforcement than in unbonded reinforcement for both aluminum and steel. However, bonded aluminum of large diameter significantly improved in strength in comparison with open hole.

Figure 6

Comparison of NSF in compression for bonded reinforcements.

6 Conclusion

In the present study, the effects of different types of fibers on the strength of quasi-isotropic silicon carbide/epoxy composite laminate with a reinforced hole were investigated experimentally. The composite laminated plate with a reinforced hole showed an improvement in ultimate strength relative to the laminate with an open hole. The largest improvement was obtained with the reinforcing material having the same stiffness as that of laminate. This improvement was also related to the size of the reinforcement. The improvement in the strength was larger in compression than in tension. This result is due to much more interaction between the hole and the reinforcing plug during loading. The case of composite with bonded reinforcement under tension showed no increase in ultimate strength. This is due to adhesive failure. As a result, it is a necessity that a strong bond between the reinforcement and the plug be obtained to achieve improvement in ultimate strength.