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1、Using Plane Stress Method to Simulate the interfacial bond between steel fiber and concreteAbstract interfacial bond between steel fiber and concrete impacts directly on the reinforcing and toughening for the fibers to the concrete. All along,most interfacial bond results between the two were based
2、on the test .It is difficult to simulate the destruction of the interface by the numerical finite element method due to the lack of bond stress versus slip relationship in local.This paper improves the calculating method on bond stress versus slip relationship in local of straight steel fiber pulled
3、 out from the concrete, and adopts a new modeling methodusing plane stress method to simulate the process of the shear staight steel fiber pulled out from the concrete. Finite element results and test results are in good agreement.So the calculating method in this paper on bond stress versus slip re
4、lationship in local and plane stress method are reasonable.Key words Steel fiber-reinforced concrete(SFRC);Interfacial bonding;Plane stress; Finite element1.InstructionThe destruction of steel fiber reinforced concrete(SFRC) is generally start with the concrete matrix cracking. A large number of mic
5、ro-cracks in concrete matrix continuous expansion under the force. Bridging fiber blending in concrete will play a blocking role, while the size of which will ultimately depend on interface bonding strength between SF and concrete.Therefore, interface issue has become the basis research subjects unr
6、emitting.With the development of computer technology and the modern computing methods, more and more domestic and foreign researchers use FEM to simulate the process that steel fiber pulled out from the matrix,This process usually be simplified axisymmetrical two-dimensional model 2.However, this si
7、mplification can only be simulated the process of straight fibers pulled out from the matrix with 0-degree angle rather than non 0-degree .And it Can not be simulated the process of deformed fibers pulled out from the matrix.When modeling,we need to bond stress versus slip relationship in local of i
8、nterface between SF and concrete.But due to the distribution of interface shear stress is complex and steel fiber is smaller in size, it is difficult to obtaine from the experiment directly 2,and the formula witch used to calculate is few.At the present time, the constitutive relation obtained mainl
9、y by the fowling methods that iterative computation and pilot calculation.For the former we must work out computer iterative program and for the latter it may take time and hard work.So this paper improves the computation method of the bond stress versus slip relationship for SF pulled out from the
10、concrete ,which is suitable for finite element method.At the same time, a new modelling method is adopted using plane stress method to simulate the process of the shear staight SF pullouted out from the concrete.2. Text2.1 Bond stress versus slip relationshipBond stress versus slip relationship can
11、be approximate calculated by load-displacement curve in test for the steel fiber pulled out from the concrete. According to the load - displacement curve with an evident transition before the peak load or not,bond stress versus slip relationship can be simplified Four-linear model(Fig ) or trilinear
12、 model(Fig ) . Calculation assumptions:(1)Suppose that shear stress on interface is in uniform distribution, that is average bond strength as bond strength(2) Suppose that shear stress on SF is in equivalent distributionThe value ofcan be taken the following formula to approximate calculate.1=F1 / u
13、f lf ; max=Fmax/uflf ; 2=F2/uflf ; 3=F3/uflf； where uf is circumference of SF cross-section (mm) , lf is embedment length of SFs (mm),and F1、Fmax、F2、F3 are the corresponding pullout load of the loaddisplacement cuve(N).If there are more than one steel fibers pulled out ,take the average.where Fmaxis
14、 the peak load, F1 is the load of the evident transition before Fmax, F2 is the load of the evident transition after Fmax and F3 is the load of the cuves end. 图1（a） 图2（a）For the two models above is important to define ,which can be seen as slippage per unit length.We must conder it as follow.Steel f
15、iber and concrete deform together when the pullout load is smaller.With the increasing of the pullout load, the steel fiber and the concrete debond in local. The slippage between them of the debonding segment is the deformation difference of the two,that is ,where is mean tensile strain of steel fib
16、er in l length, is mean shear strain of concrete in l length and l is the length of the debonding segment.In per unit length, the deformation difference of the debonding segment between steel fiber and concrete can be simplified approximately as .Spring elements which are simulated the interface mus
17、t be added on the coincidence nodes of steel fiber elements and Concrete elements. In theory, steel fiber and concrete deform together before debonding which equivalent of spring not stretch, but the spring elements used are not allowed to this suitation that the force incrases and the deformation d
18、oest incrase .So, can be written in the following manner:,where is the tensile strain of steel fiber with pullout load . For quadrilateral form model take and trilinear model take. 、in model and in Four-linear model take the mean vaule in per length corresponding the slippage of 、at the pullout load
19、-displacement curve.2.2 Material propertiesTaking into account the shear straight steel fiber may in large deformation or pulled off when pulled out. So the material property of it adopting perfect elastic-plastic and hardening model.Fig.2 图2Actually concrete constitutive models have declined sectio
20、n which can lead to unconvergence when used to calculate. Sometimes，we should avoid the decline3 . In this paper,the model of concrete constitutive proposed by Rsch is adopted. Cube crushing strength of concrete obtained in test come from 4.They are: the matrix 1:28.59 MPa; the matrix 2:41.04 MPa. T
21、ensile strength is caculated by.2.3 Uing plane stress method to simulate the process of the shear staight SF pullouted out Along the axis from the concrete.2.3.1The finite element modelElement Plane82 is adopted to Simulate steel fiber and concrete and element Combin39 which is nonlinear spring to S
22、imulate the interface of the two. Springs are added on the intermediate coincidence nodes of steel fiber element and concrete element.Interfacial bonding strength is considered only along the fiber axis.As the pulled out model in test has symmetry, therefore, the pulled out process of only one steel
23、 fiber is simulated by plane stress method. The dimensions of the fibers cross section in finite element model can be converted by Eq.(2) (2)where is the original cross-sectional area of fiber, is the width of the fibers cross section in model and is the height. Eq.(3) also needed to satisfied , (3)
24、Where is Circumference of the steel fiber. The finite element model established as shown Fig.3 图32.3.2 Selection of the model parametersInthis paper, =0.54mm, =1.6956mm and =16.74mm,where is the embedded lengths in one concrete block. The size of the concrete block is 50.76mm22.14mm1.6956mm. Because
25、 the model is in plane ,so 1.6956 which is not directly involved in the Geometric Modelling is used as Real Constants of Thickness. Four-linear model is used as bond stress versus slip relationship (是否用复数？)in this paper and value calculated by the above method as shown in Table 1表1取值表Table. 1 Table
26、of valulationTypeParameter/mm/MPa/ mm/ MPa/ mm/ MPa/ mm/ MPaJ1J20.0008090.0008422.5662.8301.2500.9002.7303.2303.0002.1800.7011.5755.7006.0000.3710.437J1：shear staight steel fiber pulled out from the the matrix 1; J2：shear staight steel fiber pulled out from the the matrix 2The forces of spring eleme
27、nt along the fibers axis can be written in the following manner (4)Where is the meshing length of the elements ,taking 0.54mm.As the value of the bond strength is smaller and shorter between the fiber ends and thematrix,taking 0.79MPa .supposing the Stiffness of the spring 260N/mm,so the forces of t
28、he spring elements are shown as =0.5420.79=0.723N,where Rf is the equivalent radius of the fiber.Thus the elongation of the springs is shown as =0.003mm and after then it becomes 0.2.3.3The numerical results compared with the experimental resultsFig. 4 presents that an excellent concordance has been
29、 obtained between the two curves of the experimental results and the numerical results, but the change in displament of the numerical curves are not very clear before debonding completely. The curves of small displacement forJ-1、J -2 are illustrated in Fig. 5. 图4 图5As can be seen from Fig. 5 the loa
30、d-displacement curves before debonding completely are divided into two stages,that is elastic stage and local debonding stage. At the former stage, the load and the Displacement are almost by Linear growth. When the two curves reach the stage of debonding completely ,The loads Comply with the law th
31、at increase at first, then decrease with a narrow range and then increase again. This is entirely consistent with the conditions from the stage of debonding completely to of the peak load.The numerical results compared with the experimental results of the interfacial bond of SFRC shown in Table 2.Ta
32、ble2 Bond shear strength of numberial results and experimental results of the interface between the steel fiber and the concretResults categoryType specimensLoad of local starting debonding /NShear stress of local starting debonding /MPaLoad of starting debonding completely /NShear stress of startin
33、g debonding completely/MPaPeak load/NShear stress of peak load /MPaMaximum shear stress of SF/MPaMeanNode valueTest J1139.52.441148.52.598161.41J2155.02.710178.23.118 202.54Plane StressJ155.372.291133.522.296141.22.455148.56163.56J260.72.44148.22.444167.92.814181.54193.46Mean. 3.Conclusion The follo
34、wing conclusions are drawn from this study.1. Bond stress versus slip relationship improved in this paper is applicable to finite element analysis and four-linear mode can accurately reflect the interfacial bond between steel fiber and concrete in the numerical simulation.2. It is a good Numerical Modeling Method to adopte plane stress method Combined with combin 39 element to simulate the axial pulled out of straight steel fiber from concrete that provides a new thought for the straight fiber and the deformed fiber pulled out for All directions .