Mechanical Properties of Steel-FRP Composite Bars under...

Research ArticleMechanical Properties of Steel-FRP Composite Bars underTensile and Compressive Loading

Zeyang Sun1 Yu Tang2 Yunbiao Luo3 Gang Wu12 and Xiaoyuan He2

1Southeast University Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of EducationNanjing 210096 China2School of Civil Engineering Southeast University Nanjing 210096 China3Department of Civil Engineering Tianjin University Tianjin 300072 China

Correspondence should be addressed to Gang Wu gwuseueducn

Received 20 October 2016 Accepted 4 December 2016 Published 3 January 2017

Academic Editor Jun Deng

Copyright copy 2017 Zeyang Sun et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The factory-produced steel-fiber reinforced polymer composite bar (SFCB) is a new kind of reinforcement for concrete structuresThemanufacturing technology of SFCB is presented based on a large number of handmade specimensThe calculated stress-straincurves of ordinary steel bar and SFCB under repeated tensile loading agree well with the corresponding experimental results Theenergy-dissipation capacity and residual strain of both steel bar and SFCB were analyzed Based on the good simulation resultsof ordinary steel bar and FRP bar under compressive loading the compressive behavior of SFCB under monotonic loading wasstudied using the principle of equivalent flexural rigidity There are three failure modes of SFCB under compressive loading elasticbuckling postyield buckling and no buckling (ultimate compressive strength is reached) The increase in the postyield stiffnessof SFCB (119903sf ) can delay the postyield buckling of SFCB with a large length-to-diameter ratio and an empirical equation for therelationship between the postbuckling stress and 119903sf is suggested which can be used for the design of concrete structures reinforcedby SFCB to consider the effect of reinforcement buckling

1 Introduction

Fiber Reinforced Composites (FRP) have been widely usedin the aerospace shipbuilding automobile and mechanicalindustries since the 1940s In recent years FRP has becomea new type of reinforcement for civil engineering with highstrength light weight and anticorrosion performance [12] The design guidelines for the FRP bar for prestressingconcrete structures were proposed by an ACI committee[3] With the development of research and application theshortcomings of different types of FRP include the following(1) the ultimate tensile strain of FRP is generally not morethan 3 which cannot meet the ductility demand for con-crete structures located in a region of high seismic hazard(2) the price of carbon FRP (CFRP) cannot meet the low-cost requirements for use in civil engineering (3) the shearstrength of FRP is approximately 5 of its tensile strengthand the brittle FRP may be broken during the constructionprocess (concrete vibration anchoring or bending) (4) the

elastic modulus of glass FRP (GFRP) or basalt FRP (BFRP) islow which cannot guarantee the stiffness of the correspond-ing concrete structures Studies on concrete beams reinforcedby hybrid FRP were conducted to enhance the stiffness orductility [4] however the ductility was achieved as a resultof the partial fracture of fibers with low elongation ratesSteel bar has the characteristics of low strength high elasticmodulus high ductility poor durability and large densitywhile FRP has the opposite characteristics By combiningsteel and FRP a composite bar with optimized performancecan be obtained and the hybrid reinforced concrete beamswere studied by research from the perspective of corrosioncontrol and improvement in stiffness [5 6]

As shown in Figure 1 the stable postyield stiffness (1198642)of a steel-FRP composite bar (SFCB) [7] can be achievedby combining the linear elastic FRP and the elastic-plasticsteel bar Compared with steel bars the weight of SFCB iscomparatively reduced and the anticorrosion performanceis enhanced Compared with a pure FRP bar the stiffness of

HindawiInternational Journal of Polymer ScienceVolume 2017 Article ID 5691278 11 pageshttpsdoiorg10115520175691278

2 International Journal of Polymer Science

f

Steel barFRP

0 0

SFCB

0

+ =

FRP rupturef f

fy

Es

120576 120576 120576

Ef

fsfE2

E1

Figure 1 Schematic view of the mechanical property of an SFCB

(a) Resin brushing (b) Handmade SFCB specimens

Figure 2 Exploratory handmade SFCB specimens

the composite bar is greatly improved especially for a GFRPor BFRP bar [8] and the cost is much lower Compared to aGFRP bar a BFRP bar can have a relatively higher stiffnessand strength with the same cost [9] and the fatigue behaviorand the degradation mechanism of BFRP under differentstress levels of cyclic loadings were conducted [10] by Zhaoet al in Southeast University BFRP was adopted to producethe composite bar (steel-BFRP composite bar) in this study

Themechanical behavior of SFCB [11] the static behaviorof concrete beams reinforced by SFCB [12] and concretebeams strengthened by near-surface-mounted (NSM) SFCB[13] were conducted by our research group These studiesdemonstrated that the effective postyield stiffness of SFCBcan improve the corresponding reinforced concrete struc-tures To improve the seismic performance of concrete struc-tures SFCB can be used as the longitudinal reinforcement toform a controllable postyield stiffness [14 15] In addition thebond strength between SFCB and concrete can be optimizedto enhance the seismic performance of the structure [16]Thispaper mainly introduces the technology of factory-producedSFCB and its mechanical properties under tensilerepeatedtensile loading Based on the experimental results for ordi-nary steel bars and FRP bar under compressive loadingthe effects of postyield stiffness and equivalent length-to-diameter ratio (ELDR) of the SFCB on compressive behaviorwere analyzed

2 Factory Production of SFCB

SFCB has several key interfaces that include the fiberresinmatrix steelFRP and SFCBenvironmentalmediaThe shear

performance of the interfaces directly reflects the mechanicalproperty of SFCB The debonding of FRP at the interfacebetween the fiber and resin matrix can effectively adjust thestress distribution inside the FRP and the ultimate strengthof fiber can be fully utilized The key production technologyand the basic mechanical properties of the SFCBwere carriedout based on numerous exploratory trials (Figure 2) usingparameters including inner steel type (roundor ribbed rebar)inner steel bar diameter FRP sheet type steelFRP interfacetreatment and so on

When using a round bar as the inner core a uniformdistribution of the outer longitudinal fiber can be ensuredIn such a case the strength of the FRP can be fully utilizedHowever the tensile test of the corresponding SFCB showsthat the relative slip between the round inner steel bar andouter FRP happened The anchorage test demonstrated thatthe bonding performance between round steel bar and theouter FRP was difficult to guarantee As a result ribbedrebar with winding roving was selected as the inner coreof the SFCB (Figure 3(a)) The winding roving could fill inthe gaps between the ribs of the steel bar to protect thelongitudinal FRP from being hurt Meanwhile an enhancedinterface was achieved between steel bar and FRPThe factoryproduction of SFCB was proposed by modifying the currentFRP pultrusion equipment (Figure 3(b)) and the surfacerib was formed by winding a plastic tape with a specificwidth during the pultrusion processThemodified pultrusionequipment can also be used to produce steel wire-FRPcomposite bar or steel-hybrid FRP composite bar for differentstructural needs

International Journal of Polymer Science 3

(a) Ribbed rebar with winding rov-ing

Longitudinal wrapped outer FRP

Inner steel bar

(b) Factory-produced SFCB

Figure 3 Factory-produced SFCB and its interface treatment

Table 1 Mechanical properties of steel bar basalt fibers and SFCBs

Material type Elastic modulusGPa

Yield strengthMPa

Ultimate strengthMPa

Elongation rate()

Steel bar (HRB400) 200 420 580 15S10-B20 14003 3096 5418 25S10-B30 13810 30235 57345 2320 bundles of basalt fiber 60 mdash 1670 2530 bundles of basalt fiber 60 mdash 1500 23

3 Mechanical Properties of SFCB underTensile and Repeated Tensile Loading

The mechanical properties of SFCB can be expressed basedon the composite law [11] and the tensile postyield stiffnessratio of SFCB (119903sf ) can be calculated by

119903sf = 119864f119860 f(119864s119860 s + 119864f119860 f) (1)

where 119864f and 119860 f are the elastic modulus and cross-sectionalarea of the outer FRP of the SFCB respectively and119864s and119860 sare the elastic modulus and cross-sectional area of the innersteel bar respectively

The mechanical properties of the steel bar basalt fiberand SFCBs obtained experimentally are shown in Table 1 inwhich S10-B20 represents the SFCBmade of 10mm diameterinner steel bar longitudinally wrapped by 20 bundles of 2400tex basalt fiber The unit ldquotexrdquo represents the weight in gramsof each bundle fiber 1000 meters long It can be seen fromTable 1 that the strength of the basalt fiber with 20 bundlesin S10-B20 was approximately 657 of the original fiberstrength Moreover the effective strength of the basalt fiberwill be further decreased by the increasing amount of basaltfiber For example the average strength of 30 bundles of basaltfiber in S10-B30 was approximately 573 of the original fiberThe reason for this strength reduction could be due to thefact of the inevitable nonuniformity of the outer fiber duringthe SFCB pultrusion process which would result in an initialbending and partial fracture of the outer fiber

Thenumericalmodels for the inner steel bar and the outerFRP of the SFCB were separately established in OpenSees([17]) and ReinforcingSteel was adopted for the steel bar bydefining the yield point (119891y 120576y) hardening point (119891sh 120576sh)tangent at initial strain hardening (1198642) and the peak stress-strain point (119891u 120576u)Themechanical behavior of FRP in SFCBwas set according to the test results the interface of steelFRPwas assumed to be perfect bonding The load-strain curvesof inner steel bar and S10-B20 under repeated tensile loadingare presented in Figure 4 It can be found that the calculatedvalues were basically in agreement with the experimentalcurves Compared with an ordinary steel bar an SFCB canachieve less residual strain under the same unloading strainand therefore reduce the unloading residual strain of anSFCB reinforced concrete structureThere are two reasons forthis advantage (1) the unloading stress level of an SFCB ishigher than an ordinary steel bar with the same unloadingstrain and unloading stiffness (2) when the inner steel barof an SFCB reaches ldquo0rdquo stress with the plastic residual strainthe corresponding FRP still remains in ldquotensionrdquo due to theresidual tensile strain of inner steel bar Therefore the FRPwill further compress the inner steel bar and then decrease theresidual strain of the SFCB After S10-B20 reached a relativelylarge strain (gt13500 120583120576) the tested residual strain was slightlylarger than the calculated value which indicated that thecompression effect of the linear elastic FRP on the inner steelbar was reduced

The energy-dissipation capacity of a steel bar and anSFCB that achieve the same unloading strain was shown inFigure 5(a) which can be calculated by the integration of the


0 5000 10000 15000 20000 250000

10

20

30

40

50Lo

ad (k

N)

Steel hardeningSteel yielding

Residual strain

Unloading strain

Calculated (S10)Tested curve (S10)

Strain (120583120576)

(a) Steel bar (10mm)

Load

(kN

)

0 10000 20000 300000

20

40

60

80

Calculated (S10-B20)Tested curve (S10-B20)

Steel hardening

FRP rupture

Strain (120583120576)

(b) SFCB (S10-B20)

Figure 4 Typical performance of a steel bar and an SFCB under repeated tensile loading

The sameunloading strain

SFCBSteel bar

0 SFCBResidual strain

Residual strain (steel bar)

Fsf

Fsfy(Fy)

k1

k2

ku_SFCB

Δfsf

ku_steel

120576

120576y

120576u

(a) Comparison of energy dissipation between SFCB and steel bar

5000 10000 15000 20000 250000

5000

10000

15000

20000 Residual strain decreased by 1267

Residual strain decreased by 1075

S10 tested valueS10-B20 tested valueS10-B20 calculated value

Resid

ual s

trai

n(120583

120576)

Unloading strain (120583120576)

(b) Residual strain of SFCB and steel bar

Figure 5 Energy-dissipation capacity and residual strain of SFCB and steel bar

load-strain curveThe hardening of the steel bar is very smallbefore the FRP fractures therefore the ratio of the dissipatedenergy of the inner steel bar (119878steel) to the SFCB (119878SFCB) canbe calculated as follows

119878SFCB119878steel =119903sf (120576u minus 120576y)22120576y120576u minus 120576y2 (2)

where 120576y and 120576u are the yield strain and ultimate strainrespectively It can be seen that with the increase of 119903sf theSFCB has a larger energy-dissipation capacity at the samepeak strain

The experimental and calculated residual strains of S10-B20 are shown in Figure 5(b) Only the experimental valuesof the steel bar (S10) were listed because the calculated valueswere basically consistent with the experimental values It canbe found that the residual strain of S10-B20 was reduced byapproximately 10 compared with the corresponding steelbar and the reduction of the residual strain slightly increasedwhen the strain approached the ultimate stage (Figure 5(b))The tested residual strain of S10-B20 was slightly larger thanthat of the calculated value The reasons for this are mainlyas follows (1) FRP is assumed to be completely straight inthe calculation and the steel bar had no initial bending whilein the experiment the surface of the SFCB was formed by


The strain distribution atthe right side

0

Compressivestrain

Tensile strain

Theinitial

positionof therebar

ΔL

Lu

(a) Schematic view of rebar under compression

0

2

4

6

8

10

12

14

minus1 0 1 2 3 4 5 6 7

The lateral displacement increase with the increase of compressive loading

Lateral displacement (mm)

Nod

e num

ber

The initial node

position


Figure 6 The mechanics of a steel bar under compressive loading

a plastic band that is the longitudinal fibers were partiallycurved resulting in an FRP strain slightly behind that of theinner steel bar (2) the inner steel bar was assumed to worktogether with the outer FRP while in reality a relative slipoccurred at the steelFRP interface after the inner steel baryielded

4 The Compressive Behavior of SFCB

41 The Compressive Behavior of Ordinary Steel Bar Whenpartial spalling of the concrete cover of a concrete columnoccurs the longitudinal rebar would be exposed to theenvironment with the stirrup [18] and the mechanical modelin the laboratory can be regarded as having both ends fixed(Figure 6(a)) With the development of the compressionforce the left side of the middle part was in compressionwhile the right side was in tension The lateral deformationof the middle section increased with the development ofcompressive loading (Figure 6(b))

A great amount of experimental and theoretical researchon the compressive behavior of steel bars has been conducted[19ndash21]Themain parameters were the geometric shape of therebar yield strength (ordinary steel bar high-strength steelbar) hardening degree and loading pattern (unidirectionalcompression cyclic tensile and compressive loading) Theratio between the tested length and diameter of the steel bar(119903119871119863) was defined as follows

119903119871119863 = 119871u119889b (3)

where 119871u and 119889b are the calculated length of longitudinalreinforcement and rebar diameter respectively

An experimental study on the hysteretic behavior of thesteel bars subjected to tensile repeated tensile and cyclictensile and compressive loading was conducted by Zheng[22] The comparison between the test results and the corre-sponding calculated curves is shown in Figure 7 in which theelastic modulus of the rebar was 119864s = 200GPa yield strength119891y = 568MPa hardening strain 120576sh = 01505 and ultimate

strength 119891u = 1286 119891y It is found that the tensile skeletoncurve agrees well with the experimental results (Figure 7(a))Figures 7(b)ndash7(d) illustrated the simulation results of thecompressive behavior of the rebar with 119903119871119863 of 10 and 20 Theinitial lateral drift of the middle node was set to be 11000of the diameter to achieve a uniform buckling mode It wasfound that the calculated backbone curves under compressiveloadingwith 119903119871119863 of 10 and 20 agreewell with the experimentaldata

The comparison of the stress-strain relationships of thesteel bar under cyclic loading (119903119871119863 = 20) is presentedin Figure 7(d) The calculated curve cannot exactly agreewith the tested result due to the convergence problem Toavoid the influence of the effect of the loading path on thecompressive behavior of SFCB the performance of SFCBunder monotonous compressive loading is presented

42 The Compressive Behavior of SFCB FRP is wrapped onthe outside of the SFCB so it is necessary to analyze thecompressive behavior of an FRPbarThere is a large differencebetween the tensile and compressive behavior of an FRPbar [23] The difference can be caused by the fiber typefiber volume fraction and resin type The failure modes ofan FRP bar under compression include horizontal tensilefailure local fiber buckling or shear failure The compressivestrength values of GFRP bar CFRP bar and AFRP bar aregenerally considered to be 55 78 and 20 of their tensilestrengths respectively [24]

The stress-strain relationship of SFCB under compressiveloading (see (4)) can be obtained according to the constitutiverelation under tensile loading [7]119891sfminus

=

120576sfminus (119864s119860 s + 119864fminus119860 f)119860 0 lt 1003816100381610038161003816120576sfminus1003816100381610038161003816 le 10038161003816100381610038161003816120576sfyminus10038161003816100381610038161003816119891sfyminus + (120576sf

minus minus 120576sfyminus) 119864fminus119860 f119860 10038161003816100381610038161003816120576sfyminus10038161003816100381610038161003816 lt 1003816100381610038161003816120576sfminus1003816100381610038161003816 le 1003816100381610038161003816120576sfuminus1003816100381610038161003816119891yminus119860 s119860 1003816100381610038161003816120576sfuminus1003816100381610038161003816 lt 1003816100381610038161003816120576sfminus1003816100381610038161003816 (4)


000 005 010 0150

200

400

600

800

Tested curveCalculated

Stre

ss (M

Pa)

Strain (120576)

(a) Tensile behavior of the steel bar

minus005 000 005

minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)

Tested curve (LD = 10)Calculated (LD = 10)

(b) 119871119863 = 10

minus005 000 005

minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)


(c) 119871119863 = 20 (compressive loading)

minus005 000 005

minus600

minus400

minus200

0

200

400

600St

ress

(MPa

)

Strain (120576)


(d) 119871119863 = 20 (cyclic loading)

Figure 7 Comparison of the tested and calculated results of a steel bar

where ldquominusrdquomeans that the SFCB is under compressive loadingThe corresponding postyield stiffness ratio of SFCB undercompressive loading (119903sfminus) can be calculated as follows

119903sfminus = 119903sf 119864fminus (119864s119860 s + 119864f119860 f)119864f (119864s119860 s + 119864fminus119860 f) (5)

It can be found that 119903sfminus of an SFCB is 0 when the tensilepostyield stiffness ratio 119903sf is 0 and the 119903sfminus of a pure FRP baris 1 when the corresponding 119903sf is 1

Since there is a large difference between the compressivemodulus of a steel bar and an FRP bar the equivalentflexural rigidity of an SFCB is defined as 119864s119868sf Is

e = 119864s119868s +119864f119868f (Figure 8) and the corresponding equivalent diameter

(119889sf Ise) and equivalent compressive strength (119891sf Is

e) of SFCBcan be calculated using (6) and (7) respectively

119889sf Ise = 4radic119864f119864s (119889sf 4 minus 119889s4) + 119889s4 (6)

119891sf Ise = 119875sfminusradic(119864f119864s) (119860 f 2 + 2119860 s119860 f) + 119860 s2 (7)

where 119889s and 119889sf are the diameter of the inner steel bar andthe diameter of the SFCB respectively119875sfminus is the compressiveload The critical load 119875cr sf of SFCB with two fixed ends canbe calculated based on

119875cr sf = 1205872 (119864s119868s + 119864f119868f)(120583b119871u)2 (8)


Inner steel barOuter FRP

Equivalent flexuralrigidity (EI)

dSFCB dsf_Ise

Figure 8 Equivalent diameter of SFCB based on equivalent flexural rigidity

minus0015 minus0010 minus0005 0000 0005 0010 0015minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 25

Rsf_Ise = 50

Rsf_Ise = 20

Rsf_Ise = 8

(a) BFRP bar under tensile and compressive loading

00 02 04 0600

02

04

06

08

Theo

retic

al re

sults

(ff_

crminusf

fu+)

Calculated by OpenSees (ffminusffu

+)

(b) The comparison between the calculated results and the theoreticalresults

Figure 9 The simulation results of a BFRP bar under cyclic loading

where 119868s and 119868f are the area moments of inertia of steel barand FRP respectively 120583b is the coefficient considering the endconstraints The corresponding ELDR of SFCB is defined as119877sf Is

e = 119871u119889sf Ise

43 Parametric Analysis of SFCB The experimental studyof the compressive behavior of BFRP bar under monotoniccompressive loading has been conducted by Zhou [25]who found that the compressive elastic modulus of a BFRPbar is approximately 80 of the tensile elastic modulusand the compressive strength is approximately 50 of thetensile strength Based on the test results the stress-strainbehavior of the BFRP bar under tensile and compressiveloading was illustrated in Figure 9(a) With an increase in119877sf Is

e the maximum average stress of FRP bar graduallydecreases due to bar buckling The comparison between the

calculated dimensionless critical compressive load and thecorresponding theoretical value is presented in Figure 9(b)and the former was approximately 142 less than the latterwhich was caused by the initial offset (11000 of the diameter)in the OpenSees model The development trends of criticalstress with the increase in 119877sf Is

e are still in good agreementwith each other therefore this calculation method can beused to analyze the compressive properties of SFCB

The load-strain curves and equivalent stress-strain curvesof SFCB with the same 119871u119889sf Is

e and different postyieldstiffness ratios are shown in Figure 10 The load-straincurve shows that the initial compressive stiffness of SFCBis kept constant (Figure 10(a)) while the initial compressiveelastic modulus of SFCB decreases with the increase of 119903sfminus(Figure 10(b)) The equation of initial compressive elasticmodulus (119864minus) of SFCB could be presented as follows

119864minus = 119864sfminus119860 sfradic(119864s119864fminus) (119860 s (119903sfminus (1 minus 119903sfminus)))2 + 2119860 s (119903sfminus (1 minus 119903sfminus)) + 119860 s2

(9)


minus003 minus002 minus001 000minus400

minus300

minus200

minus100

0

Load

(kN

)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 02

rsfminus = 05

rsfminus = 09

(a) Load-strain (119871u119889sf Ise= 4)

minus003 minus002 minus001 000

minus2500

minus2000

minus1500

minus1000

minus500

0

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09

(b) Stress-strain (119871u119889sf Ise= 4)


minus2500

minus2000

minus1500

minus1000

minus500

0

The ultimate strain before buckling increased with the increase

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 15

of rsfminus

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09

(c) Stress-strain (119871u119889sf Ise= 15)


minus2500

minus2000

minus1500

minus1000

minus500

0St

ress

(MPa

)

Strain (120576)

Rsf_Ise = 45

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09

Compressive strain = minus0016

(d) Stress-strain (119871u119889sf Ise= 45)

Figure 10 The compressive behavior of SFCB

When 119903sfminus is relatively small the stiffness degradationincreases significantly with the increase of 119871u119889sf Is

e after theaverage stress reaches the peak stress When the value of119871u119889sf Is

e is between 4 and 15 the yield occurred first andthen a stable postyield stiffness was obtained (Figure 10(b))which is similar to the tension behavior With an increase in119871u119889sf Is

e the SFCB with a lower 119903sf value buckled earlier Incontrast the SFCB with a higher 119903sfminus shows a better com-pression postyield stiffness After the compressive yield ofSFCB occurred the ultimate stable strain increased with theincrease of 119903sfminus (Figure 10(c)) For example when the values of119871u119889sf Is

e for SFCBwere 15 20 and 25 the corresponding 119903sfminusto maintain a stable compressive postyield stiffness were 015035 and 050 respectively When the 119871u119889sf Is

e is between

30 and 45 elastic buckling occurred in all of the SFCBsHowever the slope of the compressive postbuckling curvesvaries from negative stiffness to zero stiffness as the 119903sfminusvalue increases (Figure 10(d)) For example the postbucklingstress of an ordinary steel bar decreased dramatically withthe development of compressive loading while for SFCBwhen 119903sfminus = 035 the postbuckling stress-strain curvecould maintain a horizontal line which indicates a stablepostbuckling capacity can be realized This phenomenon issimilar to that of the elastic FRP bars after elastic buckling

The relationship between the compressive postyield stiff-ness ratio and tensile postyield stiffness ratio is illustrated inFigure 11 where the compression postyield stiffness ratio isfitted by using compressive strain values between minus00054


00 02 04 06 08 10minus02

00

02

04

06

08

10

Com

pres

siver

sfminus

Tensile rsf

Ludsf_Ise = 4

Ludsf_Ise = 10

Ludsf_Ise = 15

Ludsf_Ise = 20

Ludsf_Ise = 25

Figure 11 The relationship between the values of tensile 119903sf andcompressive 119903sf

and minus00064 It can be found that with an increase in119871u119889sf Ise the demands on 119903sfminus to maintain a stable compres-

sive postyield stiffness increaseWith an increase of 119903sf the buckling loads of SFCBs with

the same initial stiffness gradually increase while the equiva-lent stresses remained constant The stress in the descendingpart of elastic buckling also increases with an increase of119903sfminus until the buckling stress is reached By comparing thestress values of the two sets of elastic buckling specimens(119871u119889sf Is

e equal to 45 and 50) the average compression stresswas a function of 119903sfminus (when the compressive strain wasminus0016) and basically independent of 119871u119889sf Is

e When 119903sfminuswas between 0 and 08 (10) can be obtained with a coefficientof determination1198772 equal to 0998 (Figure 12) After the valueof 119903sfminus reached 08 for the SFCB the compressive stress wasapproximately equal to the peak buckling stress

119891cr minus0016e119891cr sf e = minus1437 (119903sfminus)2 + 2004 (119903sfminus) + 03024

119903sf le 08(10)

44 Compression Failure Modes of SFCB Based on the aboveparametric analysis it can be found that there are threecompression failure modes of SFCB (Figure 13) (a) elasticbuckling before the yield of the inner steel bar (b) bucklingfailure after the yield of the inner steel of the SFCB and (c)the SFCB reaching its ultimate strength When the failuremode is elastic buckling the postpeak stress carrying capacityincreases with the increase in 119903sfminus until it reaches the peakbuckling stress

The determinationmethods of different failuremodes areas follows

(1) When 119875cr lt 119875sfy elastic buckling occurred the peakbuckling stress can be calculated using (8) and thepostpeak stress is expressed by (10)

00 02 04 06 08 1002

04

06

08

10

Average

SFCB rsfminus

Ludsf_Ise = 45

Ludsf_Ise = 50

Postb

uckl

ing

stres

s rat

iof

cr_minus001

6e f

cr_

sfe

Figure 12 The postpeak stress of SFCB with elastic buckling

(2) When the critical load is between the yield load of theSFCB (119875sfy le 119875cr) and the ultimate load the elasticbuckling equation is no longer applicable In this casethe load increase after yield is defined as 119875cr sf part2 =119875cr sf f minus 119875sfy f This is a load equal to the criticalbuckling load of the FRPminus the yield load carriedby the FRP (119875cr sf part2 +119875sfy lt 119875sfu) The failure modeis SFCB buckling after the yield of the inner steel bar

(3) When the critical load reaches the ultimate compres-sive strength of the SFCB no buckling occurred

5 Conclusions

Based on the factory-produced SFCB themechanical proper-ties of SFCB under tensile repeated tensile and compressiveloading are analyzed and the following conclusions can bedrawn

(1) The interface of an SFCB manufactured by roundrebar and FRP cannot be guaranteed and rovingshould be placed between the inner ribbed steel barand outer longitudinal fibers to ensure the interfaceperformance

(2) The mechanical behavior of SFCB under repeatedtensile loading can be well simulated in OpenSeesSimilar to a pure FRP bar the ultimate strengthof SFCB slightly decreases with an increase in FRPcontent Due to the elastic property of FRP theresidual strain of SFCB (S10-B20) can be reduced bymore than 10 after the unloading strain reached13500 120583120576

(3) The elastic buckling stress of SFCB with differentpostyield stiffness ratios can be unified by the corre-sponding equivalent length-to-diameter ratio of theSFCB based on the equivalent flexural rigidity Whenthe buckling of SFCB occurred after yield of theinner steel bar the postyield buckling load of SFCB


0

fsf_Ise

120576sf

(a) Elastic buckling before yield

0

fsf_Ise

120576sf

(b) Buckling failure after yield

0

fsf_Ise

fsfu_Ise

120576sf120576sfu

(c) Strength failure

Figure 13 Schematic compression failure modes of SFCB

increases with the increase in the postyield stiffnessand the contribution of the FRP bar to the bucklingload should be considered An empirical equation forthe postbuckling stress considering the effect of 119903sfminuswas proposed

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge the financial support from theNational Key Technology Support Program of China(2014BAK11B04) the National Natural Science Foundationof China (nos 51408126 51528802) the Natural ScienceFoundation of Jiangsu Province China (no BK20140631)and the project funding from the Priority Academic ProgramDevelopment of Jiangsu Higher Education Institutions(CE01-2-3)

References

[1] L Lam and J G Teng ldquoStrength models for fiber-reinforcedplastic-confined concreterdquo Journal of Structural Engineeringvol 128 no 5 pp 612ndash623 2002

[2] J Deng T Liu W Xie and W Lu ldquoStudy on repaired earth-quake-damaged bridge piers under seismic loadrdquo Advances inMaterials Science and Engineering vol 2015 Article ID 29539210 pages 2015

[3] ldquoPrestressing concrete structures with FRP tendonsrdquo ACI4404R-04 2004

[4] D Lau and H J Pam ldquoExperimental study of hybrid FRPreinforced concrete beamsrdquo Engineering Structures vol 32 no12 pp 3857ndash3865 2010

[5] A Nanni M J Henneke and T Okamoto ldquoTensile propertiesof hybrid rods for concrete reinforcementrdquo Construction andBuilding Materials vol 8 no 1 pp 27ndash34 1994

[6] B Saikia J Thomas A Ramaswamy and K S N RaoldquoPerformance of hybrid rebars as longitudinal reinforcement innormal strength concreterdquoMaterials and Structures vol 38 no10 pp 857ndash864 2005

[7] GWu Z SWu Y B Luo andH CWei ldquoA new reinforcementmaterial of steel fiber composite bar (SFCB) and its mechanics

propertiesrdquo in Proceedings of the 9th International Symposiumon ldquoFiber Reinforced Polymer (FRP) Reinforcement for ConcreteStructuresrdquo (FRPRCS-9) University of Adelaide Adelaide Aus-tralia July 2009

[8] J Sim C Park and D Y Moon ldquoCharacteristics of basalt fiberas a strengthening material for concrete structuresrdquo CompositesPart B Engineering vol 36 no 6-7 pp 504ndash512 2005

[9] X Wang Z Wu G Wu H Zhu and F Zen ldquoEnhancement ofbasalt FRP by hybridization for long-span cable-stayed bridgerdquoComposites Part B Engineering vol 44 no 1 pp 184ndash192 2013

[10] X Zhao X Wang Z Wu and Z Zhu ldquoFatigue behavior andfailure mechanism of basalt FRP composites under long-termcyclic loadsrdquo International Journal of Fatigue vol 88 pp 58ndash672016

[11] G Wu Z-S Wu Y-B Luo Z-Y Sun and X-Q Hu ldquoMechan-ical properties of steel-frp composite bar under uniaxial andcyclic tensile loadsrdquo Journal of Materials in Civil Engineeringvol 22 no 10 pp 1056ndash1066 2010

[12] Z Y Sun Y Yang W H Qin S T Ren and G WuldquoExperimental study on flexural behavior of concrete beamsreinforced by steel-fiber reinforced polymer composite barsrdquoJournal of Reinforced Plastics and Composites vol 31 no 24 pp1737ndash1745 2012

[13] Z Y Sun G Wu Z S Wu and Y B Luo ldquoFlexural strength-ening of concrete beams with near-surface mounted steel-fiber-reinforced polymer composite barsrdquo Journal of ReinforcedPlastics and Composites vol 30 no 18 pp 1529ndash1537 2011

[14] A I Ibrahim G Wu and Z Sun ldquoExperimental study of cyclicbehavior of concrete bridge columns reinforced by steel basalt-fiber composite bars and hybrid stirrupsrdquo Journal of Compositesfor Construction 2016

[15] Z-Y Sun G Wu Z-S Wu and M Zhang ldquoSeismic behaviorof concrete columns reinforced by steel-FRP composite barsrdquoJournal of Composites for Construction ASCE vol 15 no 5 pp696ndash706 2011

[16] G R Pandey H Mutsuyoshi and T Maki ldquoSeismic perfor-mance of bond controlled RC columnsrdquo Engineering Structuresvol 30 no 9 pp 2538ndash2547 2008

[17] S Mazzoni F McKenne M H Scott and G L Fenves OpenSystem for Earthquake Engineering Simulation User ManualVersion 20 Pacific Earthquake Engineering Center Univer-sity of California Berkeley Calif USA 2009 httpopenseesberkeleyeduOpenSeesmanualsusermanualindexhtml

[18] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013


[19] S Bae A M Mieses and O Bayrak ldquoInelastic buckling ofreinforcing barsrdquo Journal of Structural Engineering vol 131 no2 pp 314ndash321 2005

[20] J B Mander F D Panthaki and A Kasalanati ldquoLow-cyclefatigue behavior of reinforcing steelrdquo Journal of Materials inCivil Engineering vol 6 no 4 pp 453ndash468 1994

[21] R Hawileh A Rahman and H Tabatabai ldquoEvaluation of thelow-cycle fatigue life in ASTM A706 and A615 grade 60 steelreinforcing barsrdquo Journal of Materials in Civil Engineering vol22 no 1 pp 65ndash76 2010

[22] J Zheng Experimental studies on cyclic behavior of reinforcingbars including buckling [MS thesis] ChongqingUniversity 2012(Chinese)

[23] ldquoGuide for the design and construction of concrete reinforcedwith FRP barsrdquo ACI 4401R-06 2006

[24] W P Wu Thermomechanical properties of Fiber ReinforcedPlastic (FRP) bars [PhD dissertation]West Virginia UniversityMorgantown WVa USA 1992

[25] S Zhou Study on the basic mechanical performance of concretemembers with BFRP bars [MS thesis] Southeast University2012 (Chinese)

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


f

Steel barFRP

0 0

SFCB

0

+ =

FRP rupturef f

fy

Es

120576 120576 120576

Ef

fsfE2

E1

Figure 1 Schematic view of the mechanical property of an SFCB

(a) Resin brushing (b) Handmade SFCB specimens

Figure 2 Exploratory handmade SFCB specimens

the composite bar is greatly improved especially for a GFRPor BFRP bar [8] and the cost is much lower Compared to aGFRP bar a BFRP bar can have a relatively higher stiffnessand strength with the same cost [9] and the fatigue behaviorand the degradation mechanism of BFRP under differentstress levels of cyclic loadings were conducted [10] by Zhaoet al in Southeast University BFRP was adopted to producethe composite bar (steel-BFRP composite bar) in this study

Themechanical behavior of SFCB [11] the static behaviorof concrete beams reinforced by SFCB [12] and concretebeams strengthened by near-surface-mounted (NSM) SFCB[13] were conducted by our research group These studiesdemonstrated that the effective postyield stiffness of SFCBcan improve the corresponding reinforced concrete struc-tures To improve the seismic performance of concrete struc-tures SFCB can be used as the longitudinal reinforcement toform a controllable postyield stiffness [14 15] In addition thebond strength between SFCB and concrete can be optimizedto enhance the seismic performance of the structure [16]Thispaper mainly introduces the technology of factory-producedSFCB and its mechanical properties under tensilerepeatedtensile loading Based on the experimental results for ordi-nary steel bars and FRP bar under compressive loadingthe effects of postyield stiffness and equivalent length-to-diameter ratio (ELDR) of the SFCB on compressive behaviorwere analyzed

2 Factory Production of SFCB

SFCB has several key interfaces that include the fiberresinmatrix steelFRP and SFCBenvironmentalmediaThe shear

performance of the interfaces directly reflects the mechanicalproperty of SFCB The debonding of FRP at the interfacebetween the fiber and resin matrix can effectively adjust thestress distribution inside the FRP and the ultimate strengthof fiber can be fully utilized The key production technologyand the basic mechanical properties of the SFCBwere carriedout based on numerous exploratory trials (Figure 2) usingparameters including inner steel type (roundor ribbed rebar)inner steel bar diameter FRP sheet type steelFRP interfacetreatment and so on

When using a round bar as the inner core a uniformdistribution of the outer longitudinal fiber can be ensuredIn such a case the strength of the FRP can be fully utilizedHowever the tensile test of the corresponding SFCB showsthat the relative slip between the round inner steel bar andouter FRP happened The anchorage test demonstrated thatthe bonding performance between round steel bar and theouter FRP was difficult to guarantee As a result ribbedrebar with winding roving was selected as the inner coreof the SFCB (Figure 3(a)) The winding roving could fill inthe gaps between the ribs of the steel bar to protect thelongitudinal FRP from being hurt Meanwhile an enhancedinterface was achieved between steel bar and FRPThe factoryproduction of SFCB was proposed by modifying the currentFRP pultrusion equipment (Figure 3(b)) and the surfacerib was formed by winding a plastic tape with a specificwidth during the pultrusion processThemodified pultrusionequipment can also be used to produce steel wire-FRPcomposite bar or steel-hybrid FRP composite bar for differentstructural needs




Inner steel bar





Yield strengthMPa


Elongation rate()




119903sf = 119864f119860 f(119864s119860 s + 119864f119860 f) (1)






0 5000 10000 15000 20000 250000

10

20

30

40

50Lo

ad (k

N)


Residual strain

Unloading strain


Strain (120583120576)


Load

(kN

)

0 10000 20000 300000

20

40

60

80


Steel hardening

FRP rupture

Strain (120583120576)

(b) SFCB (S10-B20)



SFCBSteel bar



Fsf

Fsfy(Fy)

k1

k2

ku_SFCB

Δfsf

ku_steel

120576

120576y

120576u


5000 10000 15000 20000 250000

5000

10000

15000




Resid

ual s

trai

n(120583

120576)










0

Compressivestrain

Tensile strain

Theinitial

positionof therebar

ΔL

Lu


0

2

4

6

8

10

12

14

minus1 0 1 2 3 4 5 6 7



Nod

e num

ber

The initial node

position







119903119871119863 = 119871u119889b (3)







=




000 005 010 0150

200

400

600

800


Stre

ss (M

Pa)

Strain (120576)


minus005 000 005

minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)


(b) 119871119863 = 10

minus005 000 005

minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)



minus005 000 005

minus600

minus400

minus200

0

200

400

600St

ress

(MPa

)

Strain (120576)


(d) 119871119863 = 20 (cyclic loading)












119875cr sf = 1205872 (119864s119868s + 119864f119868f)(120583b119871u)2 (8)




dSFCB dsf_Ise



minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 25

Rsf_Ise = 50

Rsf_Ise = 20

Rsf_Ise = 8


00 02 04 0600

02

04

06

08

Theo

retic

al re

sults

(ff_

crminusf

fu+)


+)




e = 119871u119889sf Ise








(9)



minus300

minus200

minus100

0

Load

(kN

)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 02

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0


Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 15

of rsfminus

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0St

ress

(MPa

)

Strain (120576)

Rsf_Ise = 45

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09









e is between




00 02 04 06 08 10minus02

00

02

04

06

08

10

Com

pres

siver

sfminus

Tensile rsf

Ludsf_Ise = 4

Ludsf_Ise = 10

Ludsf_Ise = 15

Ludsf_Ise = 20

Ludsf_Ise = 25








119903sf le 08(10)




00 02 04 06 08 1002

04

06

08

10

Average

SFCB rsfminus

Ludsf_Ise = 45

Ludsf_Ise = 50

Postb

uckl

ing

stres

s rat

iof

cr_minus001

6e f

cr_

sfe




5 Conclusions






0

fsf_Ise

120576sf


0

fsf_Ise

120576sf


0

fsf_Ise

fsfu_Ise

120576sf120576sfu




Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






Inner steel bar





Yield strengthMPa


Elongation rate()




119903sf = 119864f119860 f(119864s119860 s + 119864f119860 f) (1)






0 5000 10000 15000 20000 250000

10

20

30

40

50Lo

ad (k

N)


Residual strain

Unloading strain


Strain (120583120576)


Load

(kN

)

0 10000 20000 300000

20

40

60

80


Steel hardening

FRP rupture

Strain (120583120576)

(b) SFCB (S10-B20)



SFCBSteel bar



Fsf

Fsfy(Fy)

k1

k2

ku_SFCB

Δfsf

ku_steel

120576

120576y

120576u


5000 10000 15000 20000 250000

5000

10000

15000




Resid

ual s

trai

n(120583

120576)










0

Compressivestrain

Tensile strain

Theinitial

positionof therebar

ΔL

Lu


0

2

4

6

8

10

12

14

minus1 0 1 2 3 4 5 6 7



Nod

e num

ber

The initial node

position







119903119871119863 = 119871u119889b (3)







=




000 005 010 0150

200

400

600

800


Stre

ss (M

Pa)

Strain (120576)


minus005 000 005

minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)


(b) 119871119863 = 10

minus005 000 005

minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)



minus005 000 005

minus600

minus400

minus200

0

200

400

600St

ress

(MPa

)

Strain (120576)


(d) 119871119863 = 20 (cyclic loading)












119875cr sf = 1205872 (119864s119868s + 119864f119868f)(120583b119871u)2 (8)




dSFCB dsf_Ise



minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 25

Rsf_Ise = 50

Rsf_Ise = 20

Rsf_Ise = 8


00 02 04 0600

02

04

06

08

Theo

retic

al re

sults

(ff_

crminusf

fu+)


+)




e = 119871u119889sf Ise








(9)



minus300

minus200

minus100

0

Load

(kN

)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 02

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0


Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 15

of rsfminus

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0St

ress

(MPa

)

Strain (120576)

Rsf_Ise = 45

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09









e is between




00 02 04 06 08 10minus02

00

02

04

06

08

10

Com

pres

siver

sfminus

Tensile rsf

Ludsf_Ise = 4

Ludsf_Ise = 10

Ludsf_Ise = 15

Ludsf_Ise = 20

Ludsf_Ise = 25








119903sf le 08(10)




00 02 04 06 08 1002

04

06

08

10

Average

SFCB rsfminus

Ludsf_Ise = 45

Ludsf_Ise = 50

Postb

uckl

ing

stres

s rat

iof

cr_minus001

6e f

cr_

sfe




5 Conclusions






0

fsf_Ise

120576sf


0

fsf_Ise

120576sf


0

fsf_Ise

fsfu_Ise

120576sf120576sfu




Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0 5000 10000 15000 20000 250000

10

20

30

40

50Lo

ad (k

N)


Residual strain

Unloading strain


Strain (120583120576)


Load

(kN

)

0 10000 20000 300000

20

40

60

80


Steel hardening

FRP rupture

Strain (120583120576)

(b) SFCB (S10-B20)



SFCBSteel bar



Fsf

Fsfy(Fy)

k1

k2

ku_SFCB

Δfsf

ku_steel

120576

120576y

120576u


5000 10000 15000 20000 250000

5000

10000

15000




Resid

ual s

trai

n(120583

120576)










0

Compressivestrain

Tensile strain

Theinitial

positionof therebar

ΔL

Lu


0

2

4

6

8

10

12

14

minus1 0 1 2 3 4 5 6 7



Nod

e num

ber

The initial node

position







119903119871119863 = 119871u119889b (3)







=




000 005 010 0150

200

400

600

800


Stre

ss (M

Pa)

Strain (120576)


minus005 000 005

minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)


(b) 119871119863 = 10

minus005 000 005

minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)



minus005 000 005

minus600

minus400

minus200

0

200

400

600St

ress

(MPa

)

Strain (120576)


(d) 119871119863 = 20 (cyclic loading)












119875cr sf = 1205872 (119864s119868s + 119864f119868f)(120583b119871u)2 (8)




dSFCB dsf_Ise



minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 25

Rsf_Ise = 50

Rsf_Ise = 20

Rsf_Ise = 8


00 02 04 0600

02

04

06

08

Theo

retic

al re

sults

(ff_

crminusf

fu+)


+)




e = 119871u119889sf Ise








(9)



minus300

minus200

minus100

0

Load

(kN

)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 02

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0


Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 15

of rsfminus

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0St

ress

(MPa

)

Strain (120576)

Rsf_Ise = 45

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09









e is between




00 02 04 06 08 10minus02

00

02

04

06

08

10

Com

pres

siver

sfminus

Tensile rsf

Ludsf_Ise = 4

Ludsf_Ise = 10

Ludsf_Ise = 15

Ludsf_Ise = 20

Ludsf_Ise = 25








119903sf le 08(10)




00 02 04 06 08 1002

04

06

08

10

Average

SFCB rsfminus

Ludsf_Ise = 45

Ludsf_Ise = 50

Postb

uckl

ing

stres

s rat

iof

cr_minus001

6e f

cr_

sfe




5 Conclusions






0

fsf_Ise

120576sf


0

fsf_Ise

120576sf


0

fsf_Ise

fsfu_Ise

120576sf120576sfu




Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





0

Compressivestrain

Tensile strain

Theinitial

positionof therebar

ΔL

Lu


0

2

4

6

8

10

12

14

minus1 0 1 2 3 4 5 6 7



Nod

e num

ber

The initial node

position







119903119871119863 = 119871u119889b (3)







=




000 005 010 0150

200

400

600

800


Stre

ss (M

Pa)

Strain (120576)


minus005 000 005

minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)


(b) 119871119863 = 10

minus005 000 005

minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)



minus005 000 005

minus600

minus400

minus200

0

200

400

600St

ress

(MPa

)

Strain (120576)


(d) 119871119863 = 20 (cyclic loading)












119875cr sf = 1205872 (119864s119868s + 119864f119868f)(120583b119871u)2 (8)




dSFCB dsf_Ise



minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 25

Rsf_Ise = 50

Rsf_Ise = 20

Rsf_Ise = 8


00 02 04 0600

02

04

06

08

Theo

retic

al re

sults

(ff_

crminusf

fu+)


+)




e = 119871u119889sf Ise








(9)



minus300

minus200

minus100

0

Load

(kN

)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 02

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0


Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 15

of rsfminus

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0St

ress

(MPa

)

Strain (120576)

Rsf_Ise = 45

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09









e is between




00 02 04 06 08 10minus02

00

02

04

06

08

10

Com

pres

siver

sfminus

Tensile rsf

Ludsf_Ise = 4

Ludsf_Ise = 10

Ludsf_Ise = 15

Ludsf_Ise = 20

Ludsf_Ise = 25








119903sf le 08(10)




00 02 04 06 08 1002

04

06

08

10

Average

SFCB rsfminus

Ludsf_Ise = 45

Ludsf_Ise = 50

Postb

uckl

ing

stres

s rat

iof

cr_minus001

6e f

cr_

sfe




5 Conclusions






0

fsf_Ise

120576sf


0

fsf_Ise

120576sf


0

fsf_Ise

fsfu_Ise

120576sf120576sfu




Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




000 005 010 0150

200

400

600

800


Stre

ss (M

Pa)

Strain (120576)


minus005 000 005

minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)


(b) 119871119863 = 10

minus005 000 005

minus600

minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)



minus005 000 005

minus600

minus400

minus200

0

200

400

600St

ress

(MPa

)

Strain (120576)


(d) 119871119863 = 20 (cyclic loading)












119875cr sf = 1205872 (119864s119868s + 119864f119868f)(120583b119871u)2 (8)




dSFCB dsf_Ise



minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 25

Rsf_Ise = 50

Rsf_Ise = 20

Rsf_Ise = 8


00 02 04 0600

02

04

06

08

Theo

retic

al re

sults

(ff_

crminusf

fu+)


+)




e = 119871u119889sf Ise








(9)



minus300

minus200

minus100

0

Load

(kN

)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 02

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0


Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 15

of rsfminus

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0St

ress

(MPa

)

Strain (120576)

Rsf_Ise = 45

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09









e is between




00 02 04 06 08 10minus02

00

02

04

06

08

10

Com

pres

siver

sfminus

Tensile rsf

Ludsf_Ise = 4

Ludsf_Ise = 10

Ludsf_Ise = 15

Ludsf_Ise = 20

Ludsf_Ise = 25








119903sf le 08(10)




00 02 04 06 08 1002

04

06

08

10

Average

SFCB rsfminus

Ludsf_Ise = 45

Ludsf_Ise = 50

Postb

uckl

ing

stres

s rat

iof

cr_minus001

6e f

cr_

sfe




5 Conclusions






0

fsf_Ise

120576sf


0

fsf_Ise

120576sf


0

fsf_Ise

fsfu_Ise

120576sf120576sfu




Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






dSFCB dsf_Ise



minus400

minus200

0

200

400

600

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 25

Rsf_Ise = 50

Rsf_Ise = 20

Rsf_Ise = 8


00 02 04 0600

02

04

06

08

Theo

retic

al re

sults

(ff_

crminusf

fu+)


+)




e = 119871u119889sf Ise








(9)



minus300

minus200

minus100

0

Load

(kN

)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 02

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0


Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 15

of rsfminus

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0St

ress

(MPa

)

Strain (120576)

Rsf_Ise = 45

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09









e is between




00 02 04 06 08 10minus02

00

02

04

06

08

10

Com

pres

siver

sfminus

Tensile rsf

Ludsf_Ise = 4

Ludsf_Ise = 10

Ludsf_Ise = 15

Ludsf_Ise = 20

Ludsf_Ise = 25








119903sf le 08(10)




00 02 04 06 08 1002

04

06

08

10

Average

SFCB rsfminus

Ludsf_Ise = 45

Ludsf_Ise = 50

Postb

uckl

ing

stres

s rat

iof

cr_minus001

6e f

cr_

sfe




5 Conclusions






0

fsf_Ise

120576sf


0

fsf_Ise

120576sf


0

fsf_Ise

fsfu_Ise

120576sf120576sfu




Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





minus300

minus200

minus100

0

Load

(kN

)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 02

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0

Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 4

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0


Stre

ss (M

Pa)

Strain (120576)

Rsf_Ise = 15

of rsfminus

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09



minus2500

minus2000

minus1500

minus1000

minus500

0St

ress

(MPa

)

Strain (120576)

Rsf_Ise = 45

rsfminus = 001

rsfminus = 015

rsfminus = 035

rsfminus = 05

rsfminus = 09









e is between




00 02 04 06 08 10minus02

00

02

04

06

08

10

Com

pres

siver

sfminus

Tensile rsf

Ludsf_Ise = 4

Ludsf_Ise = 10

Ludsf_Ise = 15

Ludsf_Ise = 20

Ludsf_Ise = 25








119903sf le 08(10)




00 02 04 06 08 1002

04

06

08

10

Average

SFCB rsfminus

Ludsf_Ise = 45

Ludsf_Ise = 50

Postb

uckl

ing

stres

s rat

iof

cr_minus001

6e f

cr_

sfe




5 Conclusions






0

fsf_Ise

120576sf


0

fsf_Ise

120576sf


0

fsf_Ise

fsfu_Ise

120576sf120576sfu




Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




00 02 04 06 08 10minus02

00

02

04

06

08

10

Com

pres

siver

sfminus

Tensile rsf

Ludsf_Ise = 4

Ludsf_Ise = 10

Ludsf_Ise = 15

Ludsf_Ise = 20

Ludsf_Ise = 25








119903sf le 08(10)




00 02 04 06 08 1002

04

06

08

10

Average

SFCB rsfminus

Ludsf_Ise = 45

Ludsf_Ise = 50

Postb

uckl

ing

stres

s rat

iof

cr_minus001

6e f

cr_

sfe




5 Conclusions






0

fsf_Ise

120576sf


0

fsf_Ise

120576sf


0

fsf_Ise

fsfu_Ise

120576sf120576sfu




Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

fsf_Ise

120576sf


0

fsf_Ise

120576sf


0

fsf_Ise

fsfu_Ise

120576sf120576sfu




Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



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