Academic Journal of Science and Technology ISSN: 2771-3032 | Vol. 13, No. 2, 2024 55 Finite Element Analysis of Flexural Performance of Cut Carbon Fiber Reinforced Concrete Hollow Slab Junyang Xia1, a 1School of Civil Engineering, Henan Polytechnic University, Jiaozuo 454003, China a17634480120@163.com Abstract: As a kind of light wall material installed on the surface of the main structure, hollow hanging wall board is widely used in prefabricated buildings. Ordinary concrete hollow board can no longer meet the needs of actual engineering. In order to study the influence of the length and content of carbon fiber on the bending performance of concrete hollow board, the optimal length and content of fiber in hollow board are determined. ABAQUS finite element software is used to simulate the whole process of concrete hollow slab with different fiber length and dosage, and the load displacement curve is analyzed. The results show that the bending performance of concrete slabs increases and then decreases with the increase of fiber length and content. When the fiber length is 10mm and the content is 0.24%, the bending performance of concrete hollow slabs is the strongest, and the ultimate load is increased by 27.90%, showing better deformation resistance under the same load. Keywords: Carbon fiber, fiber reinforced concrete, external wall panels, finite element analysis. 1. Introduction As a lightweight wall material installed on the surface of the main structure, externally hung hollow wallboard is widely used in prefabricated buildings [1], generally playing a role in strengthening and protecting the main structure and increasing the seismic performance and durability of the building. It mainly bears wind loads and earthquake loads [2]. In recent years, people have paid more and more attention to the durability and flexural rigidity of externally hung hollow wall panels [3]. Adding nano-sio2 [4,5] and fiber materials [6] to concrete is a common method to improve the flexural performance and durability of concrete. Among them, there are many types of fiber materials. Carbon fiber has more excellent strength and corrosion resistance [7]. Adding carbon fiber to concrete can effectively improve the tensile strength, flexural strength, flexural strength and durability of concrete matrix [8], and can effectively inhibit the formation of cracks in concrete and greatly improve the ductility of concrete slabs [9]. In recent years, the research on carbon fiber reinforced concrete has been extensive. Kizilkanat,AB[10] studied short-cut carbon fiber with different volume fractions to improve the mechanical properties and crack resistance of concrete, and the results showed that when the volume fraction of carbon fiber was greater than 0.5%, the strengthening effect on the crack resistance of concrete was better. Y.F.Li[11] studied the compressive and impact resistance of carbon fiber reinforced concrete. Patchen,A[12] used recycled carbon fiber to produce high-performance concrete. As a substitute for steel-fiber concrete, its mechanical properties were even better than those of steel- fiber concrete. Deng Zongcai [13] studied the fracture parameters and fatigue properties of carbon fiber reinforced concrete, and the research showed that carbon fiber reinforced concrete was superior to ordinary concrete in various mechanical properties. Hou Min and Duan Xiaofang [14,15] et al studied the compressive and anti-splitting strength of carbon fiber concrete. The results show that CFRP has strong compressive and splitting strength. In addition, there have been a lot of studies on the dispersion of carbon fiber in concrete and the use of carbon fiber braided mesh to enhance the crack resistance of concrete [16]. In this paper, the finite element method is used to simulate the bending performance of concrete hollow slabs with different carbon fiber content and length, analyze the ultimate bending capacity and mid-span deflection, study the influence of different lengths and contents of carbon fiber on the bending performance of concrete hollow slabs, and then determine the optimal length and content of carbon fiber. 2. Finite Element Simulation 2.1. Fiber-reinforced concrete hollow slab model establishment A concrete model with a size of 1200mm×400mm×100mm was established using ABAQUS (set according to GB/T50152-2012 "Standard for Experimental Methods of Concrete Structures") and randomly distributed carbon fibers were generated in the concrete area to finally generate a carbon fiber reinforced concrete slab model. The carbon fiber content is 0.12%, 0.24%, 0.36%, 0.48%, and the carbon fiber length is 5mm, 10mm, 15mm, 20mm, respectively. According to the volume conversion of concrete slabs, the number of carbon fiber roots can be converted according to Formula 1- 1, and the number of concrete specimens is shown in Table 1. lr V G 2   Formula 1 Where, V is the volume of concrete test block,  is the volume fraction of carbon fiber, r is the radius of carbon fiber, and l is the length 56 Table 1. Numbers and parameters of each specimen Specimen number Carbon fiber length (mm) Carbon fiber content (%) Carbon fiber number CF-0-0 0 0 0 CF-5-24 5 0.24 49890 CF-10-24 10 0.24 24945 CF-15-24 15 0.24 16630 CF-20-24 20 0.24 12473 CF-10-12 25 0.12 12473 CF-10-36 30 0.36 37418 CF-10-48 35 0.48 49890 Note: The concrete strength grade is C30, the yield stress of the steel wire mesh is 738.5MPa, the yield stress of the carbon fiber is 3000MPa, and the diameter of the carbon fiber is7 m . Figure 1. Random distribution of chopped carbon fibers Figure 2. The carbon fiber is randomly distributed in a concrete slab 2.2. Model parameter setting 2.2.1. Model selection This paper mainly studies the nonlinear analysis of concrete hollow slab in plane, using ABAQUS finite element software for nonlinear analysis, using Newton-raphson iterative method as a solution. This method is solved by gradually applying incremental loads and repeating the equilibrium iterative process. The details are as follows: (1) concrete material, choose the plastic damage (ConcreteDamagedPlasticity, CDP) model. This model is a damage model based on plasticity and continuity, which describes the inelastic behavior of concrete by combining the plastic damage elasticity under isotropy with the tensile and compressive elasticity first, and is suitable for analyzing the mechanical behavior of concrete under various loading conditions. (2) The stress state of the rebar can be assumed as the uniaxial stress state, and the model is simulated by a double- broken line model, which is expressed in the form of a double- broken line, in which two broken lines respectively represent the elastic constitutive and inelastic constitutive of the rebar, so as to distinguish the deformation of the material under different loads. Before reaching the yield point, the rebar maintains the ideal elastic behavior. Large plastic deformation occurs, the horizontal stress remains unchanged, and the steel bar is assumed to be the ideal elastic-plastic material. The selection of the above material models can more accurately describe the mechanical behavior of concrete structures under actual loads. 2.2.2. Material structure (1) Concrete In actual engineering, the internal cohesion of concrete materials will be gradually reduced under the influence of loading during the actual stress process, and then all mechanical properties will decline, resulting in internal or external holes or cracks. In order to address this phenomenon in the concrete damage model, scholars proposed the use of damage factors to express this phenomenon. In the Code for Design of Concrete Structures GB50010-2010 (2015 edition), Appendix C gives the damage evolution parameters of 57 concrete below C80, the evolution parameters of concrete compression damage are shown in the following equations 1- 2, 1-3, 1-4, 1-5, and the evolution parameters of tensile damage are shown in the following equations 1-6, 1-7,1-8.              )1( )1( 1 )1( 1 1 2 c x xx x xn n d c n c c    Formula 2 rcC rc c E f , ,    Formula 3 rcrcc rcc fE E n ,, ,     Formula 4 rc x ,   Formula 5 Formula: rcf , is the representative value of uniaxial compressive strength of concrete; rc, is the peak compressive strain corresponding to the uniaxial compressive strength; cd is the evolution parameter of concrete uniaxial compression damage; c are the parameters of the descending section of the stress-strain curve of concrete under uniaxial compression, as shown in Table 1-2 below: Table 2. C20-C60 Parameter Values of concrete uniaxial compression rcf , （N/mm2） 20 25 30 35 40 45 50 55 60 rc, （10-5） 147 156 164 172 179 185 192 198 203 c 0.74 1.06 1.36 1.65 1.94 2.21 2.48 2.74 3.00 rccu ,/ 3.0 2.6 2.3 2.1 2.0 1.9 1.9 1.8 1.8 In the table: cu is the compressive strain of concrete when the stress in the descending section of the stress-strain curve is equal to rcf ,5.0 .              )1( )1( 1 12.02.11 7.1 5 x xx xx d t t t t    Formula 6 rt x ,   Formula 7 rtc rt t E f , ,    Formula 8 Where, rtf , is the representative value of uniaxial tensile strength of concrete; rt , is the peak compressive strain corresponding to the uniaxial tensile strength; td is the evolution parameter of concrete uniaxial tensile damage; t are the parameters of the descending section of the uniaxial tensile stress-strain curve of concrete, as shown in Table 1-3 below Table 3. Parameter values of concrete uniaxial tensile stress-strain curve )/( 2 , mmNf rt 1.0 1.5 2.0 2.5 3.0 3.5 4.0 )10( 6 ,  rt 65 81 95 107 118 128 137 t 0.31 0.70 1.25 1.95 2.81 3.82 5.00 The calculation formulas of damage factors and damage evolution parameters are shown in Equation 1-9: Dd  11 Formula 9 Generally speaking, when the cumulative amount of plastic damage of concrete reaches 0.9, the material is considered to have reached the failure state. Therefore, in this model, the damage factor d value of concrete is set to about 0.9, and the corresponding inelastic strain value is also matched with it. The specific attribute damage parameters of concrete are shown in Table 1-4: Table 4. Plastic damage parameters of concrete  e 00 / cb  cK v cw tw 30° 0.1 1.16 0.667 0.001 1 0 (2) Steel reinforcement In this model, steel wire mesh is used as the stressed steel bar of concrete hollow slab. In order to describe this behavior of steel bars more accurately and facilitate calculation, the 58 double-fold line model suggested in the specification is adopted in this paper. The specific expression is shown in Formula 1-10, and the constitutive relationship of the fold line is shown in Figure 1-1.        usry ysss s f E    y, 0 Formula 10 Formula, s is reinforcement stress; sE is the elastic modulus of reinforcement; s is reinforcement strain; y is the yield strain of the steel bar; ryf , represents the yield strength of the steel bar. Figure 3. Double line constitutive relationship diagram of steel reinforcement 2.3. Grid division and calculation In this model, a three-dimensional octagonal linear hexahedron element (C3D8R) is used to simulate concrete and rigid loading pad and support. The concrete unit size is 30mm×30mm×30mm regular hexahedron first-order solid element, and the rigid loading pad and support unit size is 50mm×25mm×25mm. A two-node linear three-dimensional truss element (T3D2) was used to simulate the wire mesh and cut carbon fiber, and the length of the wire mesh element was 10mm. According to the fiber length, each carbon fiber acts as a unit, and each unit has two nodes. The final finite element model and mesh division are shown in Figure 4 below. (a) Wire mesh division (b) Meshing of hollow concrete slabs (c) Grid division of rigid loading pad and support (d) Overall meshing 3. Simulation Results of Bending Strength and Analysis 3.1. Effect of fiber content on ultimate bearing capacity and deflection enhancement of concrete hollow slab Figure 4. Load-displacement curve of concrete slab with different fiber content It can be seen from Figure 2-1 that the short-cut carbon fiber has a great enhancement effect on the ultimate bending capacity of concrete. Meanwhile, the short-cut carbon fiber with different content (0.12%, 0.24%, 0.36%, 0.48%) has different enhancement effect on the concrete slab. The detailed comparison data of the ultimate bearing capacity are shown in Table 5. 59 Table 5. Ultimate bearing capacity of concrete slabs with different fiber content Component number CF-0-0 CF-10-12 CF-10-24 CF-10-36 CF-10-48 Ultimate bearing capacity (KN) 18.183 19.574 23.256 22.126 21.792 Enhancement effect 0 7.65% 27.90% 21.69% 19.85% It can be seen from Table 2-1 that with the increase of fiber content in the case of the same fiber length, the ultimate bending capacity of the concrete slab increases first and then decreases. Among them, the 0.24% cut carbon fiber content has a more obvious effect on the bending strength reduction of the concrete slab, and the ultimate bending capacity of the concrete slab increases by 27.9% compared with the concrete slab without carbon fiber. It can be seen from Figure 2-1 that under the same load, the deflection of the short-cut carbon fiber concrete slab with 0.24% content is the smallest. 3.2. Influence of fiber length on ultimate bearing capacity and deflection of concrete hollow slab It is known that different fiber content has different effects on the flexural performance of concrete hollow slabs, and 0.24% cut carbon fiber has the largest effect on the flexural performance of concrete hollow slabs. The effects of different lengths of chopped carbon fiber (5mm, 10mm, 15mm, 20mm) on the ultimate flexural capacity of concrete hollow slabs were studied with 0.24% chopped carbon fiber as the object. It can be seen from Figure 2-2 that under the same concrete content, different fiber lengths have different strengthening effects on the ultimate flexural capacity of concrete slabs. The detailed comparison of ultimate bearing capacity is shown in Table 6. Table 6. Ultimate bearing capacity of concrete slabs with different fiber lengths Component number CF-0-0 CF-5-24 CF-10-24 CF-15-24 CF-20-24 Ultimate bearing capacity (KN) 18.183 21.453 23.256 22.460 21.254 Enhancement effect 0 17.98% 27.90% 23.52% 16.89% According to Table 3-2, under the same carbon fiber content, different fiber lengths have different reinforcement effects on concrete slabs, With the increase of fiber length, the ultimate bearing capacity of concrete slabs first increases and then decreases. Among them, 10mm carbon fiber has the most obvious effect on the ultimate bending capacity of concrete slabs, which increases by 27.9% compared with the ultimate bending capacity without carbon fiber. Meanwhile, it can be seen from Figure 2-2 that the mid-span deflection of 10mm short-cut carbon fiber concrete slab is the smallest. Figure 5. Different load displacement curves of concrete slabs with different fiber contents 3.3. Cause Analysis (1) Generally, after 24 hours of concrete pouring, the concrete matrix rapidly loses water, resulting in plastic shrinkage of the concrete matrix, resulting in a large number of cracks. The addition of short-cut carbon fiber can effectively resist the tensile stress caused by plastic shrinkage of concrete. At the same time, the short-cut carbon fiber is small in weight and light in volume, and is disorganized in the concrete slab. Not only the friction resistance between itself and the concrete matrix is closely connected between the aggregate and the aggregate, but also because of its small volume, it can fill the pores generated in the concrete matrix, so that the aggregate is more dense, thus improving the ultimate bearing capacity of concrete. (2) After adding short-cut carbon fiber into the concrete hollow slab, when the concrete slab is subjected to external load, the initial defects inside the slab will slowly expand into cracks. When the cracks are large, the carbon fiber will build a bridge between the cracks to effectively transfer part of the tensile stress through the action of fiber. Due to the good tensile properties of carbon fiber, the concrete cracks will be expanded under the action of external forces. It is necessary to overcome the bonding force between the concrete matrix and carbon fiber, improve the deformation ability of concrete, and reduce the deflection of concrete slab. (3) Excessive volume of carbon fiber will lead to poor concrete fluidity and fiber concentration, which will affect the enhancement effect of carbon fiber on concrete performance. Excessive length of carbon fiber may reduce the dispersion of fiber and increase the bending degree of fiber in concrete, resulting in the phenomenon of fiber knotting and clumping. As a result, the performance enhancement effect of fiber on concrete decreases. 4. Conclusions (1) Short-cut carbon fiber can effectively improve the flexural performance of concrete. With the increase of fiber content and length, the ultimate flexural capacity of fiber reinforced concrete slab increases first and then decreases; (2) When the volume fraction of carbon fiber is 0.24%, the 60 ultimate flexural capacity of the fiber reinforced concrete slab increases the most, which is about 27.9% higher than that of the concrete slab without carbon fiber; (3) In the case of the same volume fraction, the carbon fiber with a length of 10mm has the most obvious strengthening effect on the concrete slab; (4) The addition of carbon fiber can also effectively improve the deformation resistance of concrete slabs. Under the same load, fiber-reinforced concrete slabs exhibit smaller mid span deflection compared to concrete slabs without fibers. 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