Numerical Analysis of Finger-Point Beams Reinforced with CFRP Strips*

XUE Meihui,WANG Jianxing,WEI Changxi

(School of Civil Engineering，North China University of Technology，Beijing 100144，China)

Abstract：Based on finite element analysis (FEA) in Ansys software,a numerical simulation is proposed to accurately describe the damage behavior and mechanical performance of the model.The results show that the ultimate bearing capacity is increased by CFRP.The stress is mainly concentrated on the CFRP material.

Key words：component model;finger joint;timber beams;carbon fiber reinforced polymer

For about a century,the use of the structural connectors for the assembly industry has become increasingly important.Connection is the weak link in the structure.Using finger-point process could meet the requirements of straightness,size requirements of the higher stiffness and strength of the components.The infinite advantage of edge length and interchangeability with unattached wood makes it a common component in the wood industry.The finger jointing process of wood is developed empirically[1].Wood can hardly be effectively identified as wood due to the load-deformation behavior of the connection compared with other materials such as construction steel and concrete.Its maximum intensity parallel to the grain affects the overall stress distribution.Therefore,the knowledge of connection behavior is the basis of a proper structural modeling[1-8].Pine serves sereved as an important raw materials for civil wood due to its high density and mechanical strength.In addition,CFRP materials have high strength and are lighter than steel.In the literature,the properties of different types of finger joint have been extensively studied,which has shown the dependence on many factors related to the strength of the gluing process,i.e.,the rate of spreading the adhesive,the assembly time and pressure.[9]In addition,the specific gravity,planning and thickness of the wood affect the resistance of the finger joints.[9-11]Other studies have focused on the bondline formation and stability.M Stehr et al.[11-13]have studied the effects of surface roughness and weak boundary layer formation.Besides,the adhesive penetrating into the cell cavity and diffusing into the cell wall of the wood have found the significant affect on the strength of the finger joint[8].

Cheng E et al.[14]have reported that the lower viscosity adhesives penetrate the more into the substrate,resulting lower adhesive strength in poor adhesive-substrate interfaces.The mechanical strength plays a principal role.When timber and CFRP are worked by loading processes,they undergo large plastic deformation,resulting in the occurrence of microdefects.[1,4]Existing structures have been retrofitted with epoxy composites[15-23].Then,the initial damage must be considered before it is reinforced with externally bonded CFRP.Finger joints that adhere to different types of adhesives have also attracted attention[5-8，24-25].In the case of fire,modeling of wood connections has been extensively studied[26-27].In addition,the effect of calculating the load-rate-time curve on an operator is very small[22].To better understand the mechanical behavior of the wooden beams,nonlinear numerical analysis is required.The purpose of this study is to provide accurate results for single-finger joints.

1 FE Model

The experimental work was performed on pine without any apparent defect.The test is based on timber finger-jointed beam including relation between displacement of beam and its loading.All beams were subjected to four-point bending carried out until failure.Using a testing machine,the experimental tests were gradual loaded at a speed of 1 mm/min,and the range of loading step equipped with a load cell was from 4 to 150 kN.The joint profiles is shown in Fig. 1.The corresponding geometry is shown in Table 1,while part of the finger joint is shown in Fig. 2.Adhesion is directly attached to the underside of the wood with CFRP material.Engaging portion is directly connected to the lower surface in order to obtain detailed fracture mode in Fig. 3.In Table 1,the use of the geometric parameters of the finger joint profile is pressented.

Item Joint UsedThickness of CFRP material/mm0.064Finger pitch/mm6.18Finger slope/(°)4.2Finger depth/mm42

Fig. 2 Joint Parameters

Fig. 3 Four-Point Bending Analysis

The post-softening elasto-plastic model describes the closure of the crack under loading.The compression behavior is based on Hill's isotropic hardening yield criterion,which is related to the flow rule and correctly describes the one-way flow.The fourth-order symmetry elastic property tensor can be written as:

whereD1111=E1(1-ν23ν32)γ,D2222=E2(1-ν13ν31)γ,D3333=E3(1-ν12ν21)γ,D1122=E1(ν21+ν31ν23)γ,D1133=E3(ν13+ν12ν23)γ,D2233=E2(ν32+ν12ν31)γ,D1212=2G12,D1313=2G31,D2323=2G23,γ=(1 -ν12ν21-ν23ν32-ν31ν13-2ν21ν32ν13)-1,ε12=γ12/2,ε23=γ23/2,ε31=γ31/2,E1,E2andE3are the three-way elastic modulus of woodL,RandT,respectively,G12,G23andG31are the shear modulus in theL-R,R-TandT-Lplanes,νijis the Poisson' ratio,σijandεijare the stress and strain components.Yield criterion is given as

where "∶" represents a two-point multiplication operation,σis the Cauchy stress component,εerepresents the elastic strain component,Λis the fourth-order symmetry elastic property tensor,Ris the scalar variable,ris the parameter,andQis the isotropic hardening modulus.

With only one potential of dissipationF,the mechanical dissipation is described as

whereQandbare the material parameters which characterize the isotropic hardening,Sandscharacterise the ductile densification evolution.Hdefines the Hill's forth order,namely

wherea1111=G+C,a2222=F+C,a3333=F+C,a1122=a2211=-C,a2233=a3322=-F,a1133=a3311=-G,a1212=2N,a2323=2M,a1313=2L,F,G,C,L,MandNare parameters of the initial plastic anisotropy function based on the Hill's law.The damage and crack propagation across the glue-lines within the finger-joint linear elastic behavior can be written as the bi-linear traction-separation law

The number of fingers is 8,and the length is 22 mm.Tip thickness and length are 1 mm and 22 mm.The tip gap is 0.22 mm.Other geometrics are shown in Table 1.Table 2 shows the constants of wood material,Table 3 shows the constants of the CFRP material.The adhesive material properties areE(E=12.8 GPa) and tensilestrength (tensilestrength is 32.7 MPa).Each local modulus of elasticity is obtained by a nondestructive penetration test.

Table 2 Constants of Wood Material

Table 3 Constants of CFRP Material

2 FE Model Results

The input file of the finite element model is the length of the segment and the local elastic modulus.The maximum principal stress before failure increases from 8.81e7to 1.34e8Pa,and the uniform maximum load level of all the beams and the different loadings are detected.This uniform loading level is 4 kN for each of the two forces in a true bend test.

Fig. 4 Comparison of Load-Midspan Deflection Curves

The comparison of the solid beam with the finite element model results in a half-span displacement.As can be seen from the Fig. 4,the specimen failes initially due to finger bonding.Cracks in the beam line near the sample side of the binding corresponding to the maximum tensile and compression region,propagate toward the upper surface,causing the knuckles gradually open.As shown in Fig.5,the bending behavior of CFRP beams is better than that of unreinforced beams.The stress of CFRP beams is mainly concentrated on the CFRP material.

a Stress in Unreinforced Structure

b Stress in Reinforced StructureFig. 5 Stress Distributions in Reinforced and Unreinforced Beams

3 Comparison of FE Model Results and Test Results

Fig. 6 Comparisons of Load-Bend Curves

Numerical test and experimental load-span comparison of deflection curves are shown in Fig. 6.It can be seen that there is good agreement between the predicted beam and the actual beam.The specimen moves linearly until the average load value and the average deviation value of FE model can correctly predict the beam bending performance.Beyond this peak (average load value is 10 kN and average bend value is 20 mm),the load-bend curve decreases rapidly.The reason is that brittle fracture occurs.Fracture occurs at the bond line in the vicinity of the lower surface of the sample,corresponding to the maximum tension zone,and spreads results on the surface,which resulting the finger-joint elements opened.In each case,the difference between the maximum limit load calculations and experiments is about 5%.Thus,the finite element model can correctly predict the bending behavior of reinforced concrete beams.Therefore,it can be concluded that brittle failure of the finger can hinder the entire sample until reaching its carrying capacity.It can be seen that a similar failure mode and experimental values indicated a significant increase of load-bearing capacity,since the sample is completely broken bond failure.

4 Conclusions

In order to correctly predict the behavior of CFRP-reinforced finger-point beams,a nonlinear finite element method is proposed.The conclusion is that the initial crack is brittle failure which is different from the solid pine beam due to the ultimate load on the loose fingers and the initial bending stiffness.Compared with unreinforced samples,CFRP strengthened specimens flexural capacity increased.Numerical analysis shows that the carbon fiber composite material is effective to reinforce the fingertip.