Optimization design, manufacturing and mechanical performance of box girder made by carbon fiber-reinforced epoxy composites

2.1 Materials

The polymer is used as a matrix is epoxy resin. This resin could be cured in the presence of a hardening agent and an accelerating agent at a specific temperature. The hardening agent is methyl ethyl ketone peroxide (MEKP) and the accelerating agent is dimethylaniline. When used, the resin is mixed with the accelerating and hardening agents at a mass ratio of 1%:1%:0.1%. The curing temperature of the epoxy resin is a stage-like temperature: first, fleetly heating the system to 180°C for 5 h and then decreasing the temperature to 150°C for 3 h. The reinforced material is woven carbon fabric (WCF) with a surface density of 300 g/m². A photograph of the used carbon fabric cloth with its dimensions is shown in Figure 1. This cloth is a two-dimensional orthogonal plain woven fabric cloth. The gap between adjacent strands in the cloth is 0.2 mm, and the strand width is 3 mm. The sand particles with an average diameter of 0.3 mm are adopted to make the sand-core mold. Polyving akohol is adopted to cohere the loose sand particles and help them maintain the designed appearance.

Figure 1:

Photograph of the adopted carbon fabric cloth with geometrical dimensions.

2.2 Fundamental mechanical properties of epoxy resin and WCF/epoxy composites

Epoxy casts were prepared by the resin casting process. During the process, epoxy resin, hardening agent and accelerating agent were mixed in a container according to their ratio. The mixture was then poured into a cuboid metal mold. The resin started curing after it had been put in an oven at 180°C. The dimensions of casts in tensile test are 13×90×7 mm³, while in the bending test are 60×13×3 mm³. The two dimensions were selected in accordance with the ASTM standard (D638, D648). WGF/epoxy composite specimens were manufactured by the carbon prepreg process, and the specimen was cut into 60×15×2 mm³ for the flexural test according to the ASTM-D7264 standard.

All the mechanical tests were finished on a Zwick-Z010 servo-electric testing machine at room temperature. The calibrating length of all the specimens was 50 mm, and the cross-head speed was 2 mm/min. Five specimens were tested at each experimental point. Figure 2 shows the typical mechanical performance of the prepared specimens. As seen in Figure 2A and B, flexural and tensile strengths of the cured epoxy cast are 93 MPa and 50 MPa with failure strains of 4.5% and 9%, respectively. Figure 2C is a typical flexural load-deformation (L-D) curve of WGF/epoxy composites in the three-point-bending test. As seen, the load increases linearly with increasing deformation until damaged at the strength of composites. As calculated from the initial stage of the L-D curve, the flexural strength of the obtained composite laminates is 211.8 MPa, and the failure strain is 6.7%. The flexural modulus is defined by the following formula:

Figure 2:

Fundamental mechanical performance of the used materials in WCF/epoxy composites: (A) flexural and (B) tensile stress-strain curves of cured epoxy resin; (C) flexural load-deformation curves of WCF/epoxy composites.

where E_f is the flexural modulus; S, the support span; m, load-deflection curve slope; and b and h, the width and thickness of the beam, respectively. The flexural modulus of epoxy cast calculated by Eq. 1 is 45 GPa, while the flexural modulus of WCF/epoxy composites is 124 GPa.

Table 1 summarizes the mechanical performance of WGF/epoxy composites that can be used as input parameters in the next simulation work. As seen, the tensile modulus in the warp and fill directions of the cloth is 140 GPa, while the compress modulus is 135 GPa. The tensile strength in both directions is 650 MPa, and the compressive strength is 750 MPa. The in-plane shear modulus is 4.6 GPa, and the shear strength is 60 MPa. The major Poisson’s ratio of the composite materials is 0.32. These parameters are adopted as input parameters in the next optimization design process of box girder in the ANSYS software.

3.1 Optimization design method

The successful design of a composite structure requires efficient and safe use of the materials [27]. In this paper, we used the classical maximum stress criterion to evaluate the element failure in composite box girder structure. In this criterion, the principal stresses in each ply are compared with their corresponding strength values such as X_c,t and Y_c,t, and S. Whenever one of the principal stress components exceeds its corresponding strength, failure of the element occurs. For example, if a laminate is subjected to tensile stress, then its failure modes could be fiber breakage, transverse matrix cracking in the plane of the laminate or inter-fiber shear failure of the matrix. In case of compressive stresses, the failure shapes could be fiber buckling which dominates the failure of the lamina along the fiber direction, and matrix crushing leads to the failure of the composite matrix. Barbero [28] defined the failure index, If, as follows:

where σ₁₁ and σ₂₂ are the true stresses that are applied on the element. τ₁₂ is the shear stress that is applied from the first direction to the second direction.

Based on the geometrical dimensions shown in Figure 3, we first used a structure that comprised anisotropic materials to help decide the fundamental thickness of the constituents. The optimization procedure was performed using APDL. During the simulation, the mesh type was shell 99. Both sides of the girder were fixed linearly in the Z-direction, and the load was applied on the 50×50 mm² region in the center of the top plate. The optimal design procedure flow chart was shown in Figure 4. As known, the design reliability was determined by the mechanical properties and structure stability. Based on the Euler-Bernoulli beam theory [29], the structure stability was highly related to Young’s modulus of the material used to fabricate the movable structures. For the pressure bar with one end fixed and the other end capable of moving lengthways, the critical force (F_cr) was determined by the following equation:

Figure 3:

Dimensions of the studied composites box girder.

Figure 4:

Optimal design procedure flow chart.

where E is the Young’s modulus of the bar; I, the moment of inertia of the cross section and l, the length of the pressure bar.

As the structural stability played an important role in the designing process of the box girder, the program first calculated the structural stability of the structure. The structural stability was judged by the natural frequency in the APDL program. If the frequency is smaller than one, the procedure will change the thickness of the plate and restart to calculate the structural stability again. If the natural frequency is greater than one, the procedure will calculate the stress component of the structure. The optimum program will then increase or decrease the corresponding girder wall’s thickness according to the stress-to-strength ratio. For composites, the thickness mainly depends on the ply number in the structure. The calculation is finished, once the stability and the stress condition are satisfied.

3.1.1 Design variables

According to the finial-optimized thickness of the girder with anisotropic materials, the first design variables in the structure are listed in Table 2. The meanings of design variables are also given in the table and shown in Figure 5. Totally, there are 17 design variables in the initial optimum procedure. h1 and h2 limit the middle and end heights of the girder, respectively, while W1–W3 determine the widths of the structure. L1–L3 are the dimensions that decide the bottom plate length, and L4–L7 are the web-geometric parameters. L8–L12 make the thickness of the top plate of box girder, which is alterable along the axial direction. It should be mentioned that the 17 design variables used in the initial stage of the parameter optimization procedure are mainly to determine the length and width of different components in the composite box girder. After they are determined, we also selected the thickness and ply mode as design variables in the above-mentioned locations for the next optimization procedure cycles. In detail, we first selected the ply mode that follows the sequence of [–45°/0°/45°/90°] in all locations. Then according to the thickness of each component obtained in the simulation of the anisotropic case, we decided the ply amount by dividing the total thickness by each layer’s thickness (0.1 mm). Once the thickness of the component is increased or decreased, we add or reduce the composite layer accordingly. It should be mentioned that –45° and 45° layers always appear in pairs in the composite plate to keep its symmetrical characteristics.

Table 2:

The initial design parameters and their meanings.

Parameter	Meaning	Parameter	Meaning
h1	Grid end height	L5	Web end length (outer)
h2	Grid middle height	L6	Middle web length (inner)
W1	Web width	L7	Middle web length (outer)
W2	Bottom plate width	L8	Middle-top plate length (inner)
W3	Top plate width	L9	First middle-top plate length
L1	End-bottom plate length (inner)	L10	Second middle-top plate length
L2	End-bottom plate length (outer)	L11	Third middle-top plate length
L3	Middle-bottom plate length	L12	Fourth end-top plate length
L4	Web end length (inner)

Figure 5:

The initial optimum design parameters and their locations.

3.2 Optimization design results

After calculation by APDL in the first and second optimum design processes, the finial structure style of the box girder is decided, as shown in Figure 6. In the figure, we give the layer mode, location and WCF amount in the box girder composite structure. Also in Tables 3 and 4, we list the ply modes of different components together with the stiffening plate location in the box girder. As seen in the table and figure, the basic thickness of arch top plate is 1.7 mm. After adding the stiffening plate, the middle thickness of the top panel is the biggest, and this thickness is decreasing progressively toward both the ends. The location of the stiffening plate in the middle is both inside and outside the top plate from 235 to 385 mm and 185 to 435 mm from the end of the girder. In terms of the web, fundamental layer number is 34, and the middle of web end has the stiffening plate in it. The thickness of the bottom plate seems the minimum one among all the components, and it merely has the stiffening plate at the end to serve as adminiculum during the flexural test. As discussed, the optimum result indicates that the web is the main structure to bear flexural load in the three-point-bending test. Another aspect is that it can also be found that the ply angle of the web is mainly composed of 0° and 90°. This optimum result matches the load transferring mechanism of a beam under flexural load well. As known, 45° fibers in a plate are mainly used to bear shear load, but the tensile and/or compress performance is not high in the 0° and 90° directions. As the flexural load in the web comprised 0° compression by the cross-head, this design result will help leave higher compressive strength of the whole girder structure. Because the contact flexural load is first applied on the middle-top surface of the girder, carbon layer in the middle-top plate is higher. As the web and the bottom plate could bear some flexural load by their deformation during the flexural load transferring process, the load that acted on the top plate end is smaller.

Figure 6:

Detailed layer mode, location and amount of carbon fabric cloth in the box girder.

Figure 7 is the stress distribution nephogram of the girder before and after optimization calculated in ANSYS. As seen, before the optimization procedure, stress in the girder is not uniform. Some stress concentration region is found in Figure 7A, and the maximum stress point is located in the middle of the girder. However, after optimization, stress in Figure 7B is uniform, and maximum and minimum stress points move to the girder end. A uniform stress distribution in the structure could avoid local failure of the structure, and this further increases the load-bear capacity of the whole composite structure.

Figure 7:

Stress distribution in composite box girder before (A) and after (B) optimization.

4.1 Manufacturing process of composite box girder

There are numerous manufacturing processes available to fabricate FRP composites, such as mold-pressing technology, injection molding, prepreg technology and resin transfer molding (RTM), etc. Considering the structural complexity of the designed box girder, we combined mold-pressing technology with prepreg technology to fabricate the WGF/epoxy box girder according to the optimal design results. Before the manufacturing process, a sand-core mold should be prepared to help obtain the inner cavity of the box girder. Another aspect is that the sand particles could break up easily during the demolding process; thus, it is possible to make a structure with a small enter port and a large inner cavity. Figure 8 shows the manufacturing details of the sand-core mold. The specific process is as follows: First, we mixed polyving akohol with water at a mass ratio of 1:10. Then, the mixture was heated at 80°C in a container for 2 h until it became clear. We mixed the mixture with sand particles in the mold as shown in Figure 8A. Second, we heated the whole system in an oven at 120°C for 20 h to evaporate the water and then polyving akohol can adhere the sand particles during the heating process. When the system cooled to room temperature, the sand core can be demolded (Figure 8B). Care should be taken to remove the sand core from the mold as the core is very sensitive to external load and can easily be broken. After demolding, the sand-core mold needs to be modified by plaster to keep its surface smooth, as shown in Figure 8C. The finished sand-core mold is shown in Figure 8D, and it will be used as a filled core to maintain the FRP shape in the next step.

Figure 8:

Manufacturing process of sand-particle core mold.

Figure 9 shows the manufacturing process of the composite box girder made by carbon fabric cloth and epoxy resin by mold-pressing technology of carbon prepregs. The details are as follows: First, we laid the carbon cloth layer by layer outside the sand core and the two aluminum molds (Figure 9A). Then, we built the top and bottom carbon layer plates of the box girder, as shown in Figure 9B and C. Pressing and heating of the whole system was performed in an oven at 180°C for 5 h and then at 150°C for 3 h after coating the top and bottom molds on the specimen (Figure 9D and E). Pressing was provided by U-type clamps, and the load magnitude that acted on different locations could be regulated. It should be noted that the curing time of the resin was 3 h, and the resin was demolded when the system naturally cooled to room temperature. The finished composite girder after demolding is shown in Figure 9F, and this composite girder needs to be cut to the required dimensions by a diamond saw according to the dimensions given in simulation results. All the layers and their ply mold are in accord with the simulation results, and the total weight of obtained WGF girder is 700.85 g.

Figure 9:

Manufacturing process of box girder by mold-pressing prepreg technology.

4.2 Three-point-bending test of composite box girder structure

Figure 10 shows the L-D curve of the box girder bridge in the three-point-bending test. As a comparison, L-D curve obtained in simulation work is also shown in the figure. As seen, the load increases linearly with increasing deformation until damaged at the strength of the structure. The critical load of the girder is 75.6 KN, while the failure displacement of the structure is 5.5 mm. The load-carrying capacity of unit mass in the girder is as high as 107.8 N/g. L-D curve in simulation is higher than that in experiment. This is mainly due to the fact that the material performance in simulation is ideal without any defects. Another reason is that the interlaminar performance between different layers is not taken into consideration, which also makes the simulating results higher than experiment. Figure 11 shows the maximum and minimum stresses in each carbon layer of the girder in different components. As seen in the figure, tensile and compressive stresses in all the layers in arch top, web and bottom plates and their stiffening plate do not exceed the strength of carbon fiber. This phenomenon further verifies the feasibility of the optimum design method adopted in this work.

Figure 10:

Load-deformation curve of the box girder in bending test.

Figure 11:

Maximum and minimum stress tendencies as a function of layer code in bottom, web and top plate and their stiffening region.