The glass fiber reinforced composite (GFRP) studied is composed of polyacrylonitrile derived glass fibers in a resin matrix. A plain weave was used as a basic single-layer element design for one-layer fabric because due to its excellent performance. GFRP having fiber packing possesses a higher density which results in a higher strength, meanwhile GFRP possesses long floats and thus a lower crimp. The diameter of an E-glass fiber is approximately 9 μm, and it has less than 1% alkali chemically. The E-glass fiber has tensile strength 3448 MPa, elastic modulus 72.4 GPa, elongation 4.8%. The E-glass plain weaves were prepared by interlacing warp thread and fill thread as shown in Fig. (1). The E-glass plain weave woven with reinforcement adopted has a specific mass of 600 g/m² with approximately 6 warp ends per cm, 4.5 weft picks per cm, in another word it has a density of 2.54 g/cm³. The matrix resin has Polyester mixed up with catalyst hardener ensuring a density of 1.21 g/cm³. The basic structural element is a laminated plate containing cross-woven E-glass cloth consisting of continuous glass filaments. Panel of thirteen element layers of E-glass woven fabrics was laminated to a thickness of 8 mm under the pressure of 100 MPa on a vulcanizing machine for forty-eight hours. Fig. (2) shows the homogeneity of the structure obtained by mixture of E-glass cloth with the resin. In the material, the overall fiber volume fraction is approximately 40%, and the resin volume fraction is approximately 60%.

Fig. (1) Schematic drawing of plain weave E-glass fabric.

Fig. (2) Structure of the laminated composite material tested.

Specimen is important for a tensile test as it determines the measuring results of stress-strain relationships. The specimen must conform to exact physical dimensions and must be no wrinkles, precision cutting and free of burrs and nicks. Here a precision milling machine and hand finishing were adopted, then the required configurations were achieved. Laminated composite samples with thirteen element layers of E-glass woven fabrics were prepared in panel form for cutting into the appropriate pattern, or pattern plating of the appropriate form. Epoxy resin was used as the material matrix. Laminated composite samples were prepared through a hand lay-up process. The lay-up chosen of the laminate was [0°/90°] S which provided a fully symmetric arrangement. A [0°/90°] lay-up for the glass plies ensured that uncured epoxy resin and hardener were respectively infiltrated into the 0° and 90° plies.

The tensile samples may be in the form of “dog-bone” samples as described in Chinese Standard GB/T1446-2005, Type-1, and their plane geometry and dimensions are illustrated as Fig. (3a). Fig. (3b) shows the specimen dimensions for testing Poisson’s ratio with aluminum sheets adhered to its two ends as described in Chinese Standard GB/T1447-2005. The aluminum sheet strengthens the ends of composite specimen, and ensures the first crack to appear in the middle of specimen.

Fig. (3) Geometry and dimensions of (a) tensile specimen; (b) rectangular poison’s ratio specimen.

The setup of the dynamic tensile testing is presented in Fig. (4). Tensile testing aims to evaluate the ability of a material to sustain pulling forces and the stretching extent before breaking. In a tensile testing process, one end of the sample is clamped while another one is pulled at a constant velocity of 2 mm/min until the sample is broken. Strain represents the length change resulted from pulling per unit of beginning length. The output of such a tensile test is a load versus elongation curve as shown in Fig. (5a) which will be converted into a curve about engineering stress versus engineering strain as shown in Fig. (5b). The engineering stress and the engineering strain data can be obtained by dividing the load and elongation by some constant values such as geometry informations). Fig. (5b) represents a typical engineering stress versus engineering strain curve, from which it can be seen that stress increases continuously along with strain and linearly up to a sudden drop (i.e. fracture).

Fig. (4) Test set-up for high speed tensile testing.

In addition, during a tensile test for Poisson’s ratio, the elastic lateral strains need to be measured accurately, while their values of laminated composite samples reinforced with E-glass woven fabrics in a tensile test are usually very small. Therefore, in order to perform the reasonably accurate measurement of Poisson’s ratio, a very sensitive extensometer (strain gages) is always used for lateral strains. Fig. (6) represents the lateral strain versus longitudinal strain curve which indicates a linear relationship.

Fig. (5b) shows that the engineering stress increases linearly and then exits when the engineering strain passes the maximum value, 0.018. Meanwhile, from Fig. (6), it can be seen that the lateral compressive strain increases linearly along with the longitudinal strain increasing up to 0.018. The linear elasticity is valid due to the fact that stress states do not produce yielding. In Fig. (7a) the observation by optical microscope reveal that the fracture of the laminated composite reinforced with E-glass woven fabrics is smooth, which indicates that the material has negligible ductility. Fig. (7b) shows that the E-glass woven fabrics in the laminated composite have been pulled out from their matrix, and the curved E-glass fibers have become straight under large pullout energy. The observations reveal that the laminated composite reinforced with E-glass woven fabrics is also a kind of linear elastic material.

Fig. (5) Tensile property in principal direction: (a) load versus elongation curve; (b) engineering stress versus engineering strain curve.

Fig. (6) Lateral strain versus longitudinal strain curve.

Fig. (7) Failure of specimen (a) fracture; (b) failure fiber.

In the coordinate system of 2D woven reinforced composite layer plate shown in Fig. (8), x₁ and x₂ indicate the direction of laying fiber longitudinal and transverse directions while x₃ represents the thickness direction.

Fig. (8) The coordinate system of woven reinforced composite layer plate.

When the main direction x₁ subjects to tensile effect, the global and local coordinate systems coincide. According to axial conversion formula, the following forms can be obtained.

(1)

According to tensile test results, the elastic modulus and Poisson's ratio of the composite material can be expressed as:

(2)

The elastic constant in z direction (perpendicular to the layer) is approximately equal to the resin matrix. The elastic modulus and Poisson's ratio of this resin can be expressed as E₃= 907.42MPa, v₂₃= 0.072. Main direction strength is calculated using the following equation:

Main direction strength σ₁₁ is about 670 MPa. Interlaminar shear modulus parameters are not independent and Eq. (4) shows the relationship of three projects elastic constants, E, G and V.

(4)

Substituing Eq. (2) into Eq. (4), thus, interlaminar shear modulus can be expressed as G₁₂ = G₁₃ = 1325.892MPa, G₂₃ = 423.237MPa.

According to the mechanical properties of the elastic plate, stress-strain relationship during loading conforms to the generalized Hooke's law and can be expressed as

(5)

In the theory of elasticity, the majority of anisotropic materials have symmetrical internal structure. Suppose there are two orthogonal symmetric elastic material, taking X₁-X₃ plane as symmetry plane, flexibility matrix can be expressed as

(6)

Where E₁, E₂, E₃ are Young's modulus, and G₁₂, G₁₃, G₂₃ are shear modulus.

According to the flexibility coefficient and the relationships between the elastic constants of engineering, the flexibility matrix is solved.

Eq. (7) is obtained by substituting the experimental results of tensile test.

(7)

Stiffness coefficient C_ij Eq. (8) is obtained by the flexibility matrix inversion.

(8)

in which,

Substituting the above results into Eq.6, it can obtain the elastic constitutive model of glass fiber reinforced composite.

(9)

The failure criteria based on failure mechanisms was established by Hashin who in 1973 proposed two failure criteria considering the quadratic interaction between tractions acting on failure plane based on his own experimental observations of tensile specimen failures, one related to fiber failure and another one related to matrix failure. After that, in 1980, he furthermore deduced the fiber and matrix failure criteria distinguished by tension and compression statuses. In the failure modes of lamina, the method of Hashin is best suited for determining failure criteria. The coefficients in the quadratic polynomials are related to a series of strength parameters Xt, Xc, Yt, S₁₂, and S₂₃, which can be obtained from simple uniaxial compressions and tensions. In a practical application, the transverse and axial shear strength parameters are proposed to be equal. As the plane stress assumptions have been conducted, the following four failure criteria are constructed as follows:

(10)

Material parameters of the glass-epoxy laminae are expressed as Table 1. The damaging effect resulting from the shear stresses and normal stresses in matrix and fibers frequently occurs on matrix or fiber-matrix interface, which often leads to debonding. In common the bonding strength of fiber-matrix interface is the lower in comparison with the strength of single constituents. The cracks in matrix soon transmit into fiber-matrix interface and propagate along fibers without crossing into fiber material. In common, yield and longitudinal shear failure are the main two causes inducing longitudinal compressive failure of composite. In further the compressive strength can be characterized by two models, and the first one is tension or compression damage model, meanwhile the second one is shear damage. They are written as

Table 1
Material parameters of composites.

(11)

The longitudinal compressive strength of composite selects the smaller one, then X_c =666.59MPa can be obtained. Substituting Eq.7, Table 1 and X_c into the Eq. 10, the Failure criteria finally becomes

(12)

The established failure criteria are usually inserted into finite element method to predict and describe failure behaviors in composite materials. The developed constitutive equation is incorporated into a finite element code. It can simulate the actual production and the results can provide a theoretical reference. The simulations of trial impact with damage/delamination model in ABAQUS/Explicit solver on ideal GFRP laminates are modeled. The plates consist of 6 plies of E-glass fabric/epoxy, and their nominal dimensions are 80×80×4 mm. In the trial impact a steel sphere impactor with a diameter of 50 mm and an added density of 7.8 g/cm³ shown in Fig. (9) is often adopted. The dimension data of the composite is imported, and then the surfaces are meshed. As the material thickness is small, shell element is suite. The parameters of impactor are shown in Table 2.

Fig. (9) The projectile and laminated composite plate model.

Table 2
Material parameters of projectile.

Orthotropic elastic constitutive model and Hashin failure criteria are used in 2D woven E-glass laminate and the parameters of them are shown in Tables 3 and 4 respectively. The composite plate is impacted at its center with a rigid impactor, meanwhile it is supported over the frame. The simulation results corresponding to an impact velocity of 55 m/s are shown in Fig. (10). These figures show that with the increase of deformation time deformation gradually increases until rupture of composite panels. From the deformation process under the impact effect in Fig. (10), it can be seen that the deformation of plate is small in the initial stage. With the increasing of the impact load, the deformation of plate gradually increases. When the impact load reaches a critical material damage value (732N), the plate begins to break. After about 24 μs, material deformation reaches the maximum and reallocation occurs subsequently.

Table 3
Material properties for orthotropic model.

Table 4
Material properties for failure criterion.

Fig. (10) Deformation process under the impact effect.

Fig. (11) shows the typical deformation plots and stress contours during this impact event at an impact velocity of 55 m/s. In the initial stage of the impact, the stress (as shown in Fig. (11a)) is “cross-petal-shaped” distribution, which is because that transverse and longitudinal of composite laminates are the main fiber direction and suffer the most of the tensile stress. As shown in Fig. (11a)~d, material damage area increases with the prolonging of time. From Fig. (11b), it can be seen that stress gradually spreads to the surrounding from 619.6 MPa to 0 MPa. Fig. (11d) shows that at the maximal deformation during the impact process stress gradually increases outwards and it can be seen that the stress value of composite with 0 MPa becomes greater to 254.9 MPa, 509.8 MPa respectively after 24 μs corresponding to three points of 1, 2, and 3. Throughout the entire process, the material damage decrease radially from the center to the edges. As shown in Fig. (11), for a fixed time, material damage gradually increases from the edges to the center and reaches a constant value of 1, which means that the rupture of the damage process.

Fig. (11) Stress distribution rule under the impact effect.