EVALUATION OF GLASS FIBER/EPOX INTERFACIAL STRENGTH B THE CRUCIFORM SPECIMEN METHOD Ju KOANAGI, Hajime KATO, Akihiro KASHIMA, uichi IGARASHI, Keichi WATANABE 3, Ichiro UENO 4 ad Shiji OGIHARA 4 Istitute Space ad Astroautical Sciece, Japa Aerospace Exploratio Agecy Graduate Studet, Tokyo Uiversity of Sciece 3 Mitsubishi Rayo Co., Ltd 4 Departmet of Mechaical Egieerig, Tokyo Uiversity of Sciece ogihara@rs.oda.tus.ac.jp SUMMAR The iterfacial stregth i a glass fiber/epoxy composite is evaluated by usig the cruciform specime method. To fid the relatio betwee the tesile ad shear stresses at iterfacial debodig, the agle betwee the fiber ad the loadig directios are chaged. Based o the experimetal data, the procedure to determie the iterfacial failure criterio is discussed. Keywords: iterfacial stregth, glass fiber, epoxy, cruciform specime, debodig, iterfacial failure criterio INTRODUCTION I fiber reiforced composite materials, the iterface betwee the fiber ad the matrix plays a key role i mechaical properties of composite materials. Therefore, a more accurate evaluatio method of the iterface is ecessary to develop better fiber reiforced composite materials. The fragmetatio test ad the microbod test, etc. exist as a techique for evaluatig the iterfacial properties []. These are used to ivestigate the iterfacial shear stregth maily ad methods for ivestigatig the iterfacial tesile stregth are ot well established. The simplest way to evaluate the iterfacial tesile stregth may be to use a tesile specime with parallel straight edges i which a through-the-width embedded fiber whose directio is perpedicular to the loadig directio. However, if the fiber ed appears o the free surface, stress sigularity arises because the bimaterial iterface is o the free surface. Eve if the fiber is embedded i the matrix, the fiber ed serves as the corer bimaterial iterface which results i stress sigularity. Therefore, it may be very difficult to evaluate the iterfacial tesile stregth accurately usig this type of specime cofiguratio because debodig iitiatio is iflueced by the stress sigularity. Recetly, a experimetal method of evaluatig iterfacial tesile stregth that uses a cruciform specime is proposed from such a viewpoit [-5]. I the cruciform specime, a sigle fiber whose directio is perpedicular to the loadig directio is embedded i the specime cetral regio where the specime width is elarged. This method ca avoid the ifluece of iterfacial stress sigularity at the specime edge o the debodig iitiatio. Aother advatage of this method may be that it ca be used to fid the relatio betwee the
tesile ad shear stresses at iterfacial debodig by chagig the agle betwee the fiber ad loadig directios. This may result i experimetal developmet of the iterfacial failure criterio. I the preset study, the cruciform specime method with some differet agles betwee the fiber ad loadig directios is applied o a glass fiber/epoxy composite to fid the relatio betwee the tesile ad shear stresses at iterfacial debodig. The procedure to determie the iterfacial failure criterio is also discussed. EXPERIMENTAL PROCEDURE A glass fiber (7mm i the diameter) was used as the reiforcemet. Epoxy resi (jer 88) was used as the matrix material with TETA (Triethyleetetramie) as a hardeer. Cruciform specimes with fibers whose agles betwee the loadig directio were 9, 67.5, 45, 35 ad.5 are used. I this work, each specime is referred to as cruciform-α specime, where α is the agle betwee the fiber ad loadig directios, which we refer to as cruciform agle. Fig. shows the specime geometry. I each specime, tesio test was coducted with a small loadig machie istalled o the stage of a optical microscope. Durig loadig, iterfacial debodig iitiatio ad the progress was observed. The crosshead speed was.5mm/mi. t=. Uit : mm (a) (b) (c) (d) (e) Fig. Schematic of cruciform specimes. (a) cruciform-9, (b) crucifrom-67.5, (c) cruciform-45, (d) cruciform-35 ad (e) cruciform-.5 Fiite elemets aalysis ANALTICAL PROCEDURE The stress distributio i the specime geometry used i the experimet was examied by fiite elemet aalysis (MSC.Marc). Effective specime geometry was discussed for the material system used. Fig. shows the model of the cruiform-9 specime. As show i the figure, the directio of the specime thickess was set to be the x-directio,
ad the loadig directio y-directio, ad the directio of the specime width z-directio, respectively. Due to symmetry about the three mutually perpedicular plaes, oe eighth of the model was cosidered for the cruciform-9 specime. For the cruciform- 67.5, crciform-45, cruciform-35 ad cruciform-.5 specimes, half of the model was cosidered due to symmetry about the midplae. I each model, eight-ode solid elemets were used. The aalysis was coducted as a lier elasticity problem. The material properties used i the aalysis are show i Table. y y x z z x Fig. Schematic of a fiite elemet aalysis model (cruciform-9 specime) Table Material properties used i the aalysis oug s modulus [GPa] Poisso s ratio Glass fiber 7. Epoxy 4.8.4 Iterfacial stresses We cosidered the stress state at a poit i the fiber/matrix iterface. To describe the iterfacial tesile ad shear stresses, we defie aother three-dimesioal Cartesia coordiate system, x -y -z coordiate system, as show i Fig.3. We take the tagetial directio of the iterface as x -directio ad the ormal directio to the iterface as y -directio at a poit i the iterface as also show i Fig.3. z -directio coicides with z-directio. We also defie the agle θ which the lie from the fiber ceter ad a poit i the iterface forms from the specime thickess directio (xdirectio) to specify the stress evaluatio site. The ormal stress i y -directio at a iterface poit, σ y y is the iterfacial ormal stress. The iterfacial shear stress ca be writte by τx' y' + τ y' z'. Because the stress we ca measure is the average specime stress, we are iterested i the relatio betwee the average specime stress ad the iterfacial stresses. We defied the ormalized iterfacial ormal ad shear stresses, S ad S s, respectively, as σ y'y' S = () σ
τ x' y' + τ y' z' S = () σ which are the ratio of the iterfacial stresses to the average specime stress, σ, which ca be derived by the applied load ad the specime cross sectioal area where the specime width is ot elarged. Fig.3 Stress evaluatio site INTERFACIAL FAILURE CRITERION Although we coducted both the cruciform specime test by varyig the cruciform agles to observe the iterfacial debodig iitiatio ad FEM aalysis to obtai the stress distributio to examie the relatioship betwee the iterfacial ormal ad shear stresses at debodig, it is very difficult to determie the poit where the iterfacial failure iitiates because the diameter of the fiber is very small. Therefore we cosidered two iterfacial failure criteria to discuss the poit where the iterfacial failure iitiates, ad we cosider the procedure to determie the iterfacial failure criterio based o the experimetal results. Fig.4 shows schematics of (a) the quadratic failure criterio ad (b) parabolic failure criterio which are described by τ t t + = s s σ τ t + s = s σ t (a) Quadratic failure criterio (b) Parabolic failure criterio Fig.4 Schematic of iterfacial failure criteria. (a) Quadratic failure criterio ad (b) parabolic failure criterio. t ts + s = (3)
t ts + s = (4) where t is iterfacial ormal stress, t s iterfaicial shear stress, the iterfacial tesile stregth, s the iterfacial shear stregth, ad is the McAuley bracket with its usual defiitio x = ( x+ x). RESULT AND DISCUSSION Experimetal results Figure 5 shows the iitiatio ad progress of the iterfacial debodig observed i (a) cruciform-9 ad (b) cruciform-67.5 specimes. Similar debodig iitiatio ad progress behavior is also observed i cruciform-45 ad cruciform-35 specimes. However, i Cruciform-.5 specimes, o debodig iitiatio was observed, that is, specime fial fracture occurred before the debodig iititatio. Table shows the averaged specime average stress at iterfacial debodig. It ca be see that as the cruciform agle gets smaller, the debodig iitiatio specime average stress gets higher. I cruciform-.5 specime, it ca be cosidered that the average specime stress at iterfacial debodig is higher tha 36. MPa. (a) Fig.5 Debodig iitiatio ad progress i (a) Cruciform-9 ad (b) Cruciform-67.5 specimes (b) Table Debodig stress i cruciform-9, 67.5, 45, 35 ad.5 Specime type Debodig stress [MPa] Cruciform-9 7.6 Cruciform-67.5. Cruciform-45 9.4 Cruiform-35 33.6 Cruciform-.5 36. (Specime Failure)
Aalytical results Figure 6 shows the chages i (a) the ormalized ormal stress ad (b) the ormalized shear stress alog the fiber i the cruciform-9 specime. I Fig.6 (a), the ormalized ormal stress is highest at θ=9, but Fig4 (b) shows that the ormalized shear stress is highest at θ=45. A similar result was obtaied i the cruciform-67.5 specime. Therefore it is ot possible determie the poit (θ) where the iterfacial debodig iitiates from the stress distributios because the iterfacial failure criterio uder mixed-mode (combied) stress state is ot developed. Normalized ormal stress (σy'y'/σ).5.5 -.5 9 degrees 75 degrees 6 degrees 45 degrees 3 degrees 5 degrees degrees.5.5 Distace from ceter (mm) Normalized shear stress (τ/σ).5.5 -.5 9 degrees 75 degrees 6 degrees 45 degrees 3 degrees 5 degrees degrees.5.5 Distace from ceter (mm) (a) Fig.6 Chage i the ormalized stresses alog the fiber directio. (a) Distributio of ormalized tesile stress ad (b) distributio of ormalized shear stress. Iterfacial failure criteria It is ecessary to determie the poit where the iterfacial debodig iitiates. I the preset study, we cosidered two iterfacial failure criteria as show i Fig.4. First, the quadratic failure criterio is cosidered. Equatio (3) ca be rearraged to t s = t + (5) α where we itroduced a parameter α which ca be defied by s α = (6) which is the ratio of the iterfacial shear stregth, s, to the iterfacial tesile stregth,. Normalized iterfacial ormal ad shear stresses ca be writte by k k ( ) ( θ ) σ spe t (b) θ = (7) ( ) ( θ ) σ spe θ = (8) s t s
where σ spe is the average specime stress, ad both the ormalized iterfacial stresses ad the iterfacial stresses are expressed explicitly as fuctios of the agle θ. Equatios (7) ad (8) are substituted ito equatio (6) which results i = { k ( θ )} k s + α where the relatio betwee the iterfacial tesile stress,, ad the experimetallyobtaied average specime stress at iterfacial debodig, σ spe. Now, we defie a fuctio F(α, θ) as ( θ ) σ spe ( θ ) k s F ( α, θ ) = { k ( θ )} + () α ad we refer to as the equivalet ormalized iterfacial stress. I the parabolic failure F α,θ ca be writte as criterio, ( ) ks k( θ ) + { k( θ )} + 4 α F ( α, θ ) = () I a specific failure criterio, it ca be cosidered that θ which gives the maximum F α,θ with give α is the iterfacial failure iitiatio locatio. ( ) Figures 7 ad 8 show F as a fuctio of θ with some assumed value of a for the cruciform-9 ad cruciform-45 specimes, respectively, for both the quadratic ad parabolic failure criteria. α is assumed to be.5, ad..5.5 ( θ ) (9) F (Quadratic).5.5 α =.5 α = α = 5 3 45 6 75 9 Degree F (Parabolic) (a) Quadratic failure criterio.5.5 α =.5 α = α = 5 3 45 6 75 9 Degree (b) Parabolic failure criterio Fig.7 Normalized equivalet iterfacial stress ( ) F as a fuctio of agle θ with assumed values of α for the crucifrom-9 specime uder (a) the quadratic failure criterio ad (b) the parabolic failure criterio.
.5 α =.5 α = α =.5 α =.5 α = α = F (Quadratic).5 F (Parabolic).5.5.5 5 3 45 6 75 9 Degree (a) Quadratic failure criterio 5 3 45 6 75 9 Degree (b) Parabolic failure criterio Fig.8 Normalized equivalet iterfacial stress ( F ) as a fuctio of agle θ with assumed values of α for the crucifrom-45 specime uder (a) the quadratic failure criterio ad (b) the parabolic failure criterio. I the cruciform-9 specime, at agle θ=9, because o iterfacial shear stress exits ad the stress state is pure tesile, the ormalized equivalet iterfacial stress F is the same value regardless of α. I both cruciform-9 ad cruciform-67.5 specimes, whe we assume small α (the iterfacial shear stregth is smaller tha the iterfacial tesile stregth), the maximam F is take by θ ragig from 45 to 6 ad the poit may be the iitiatio poit. O the other had, i the cruciform-45, cruciform-35 ad cruciform-.5 specimes, it is implied that θ=9 poit is the debodig iitiatio poit. We ca also calculate by usig the experimetally-obtaied σ spe ad by assumig the value of α. Because is the material costat, the same value should be derived regardless of the cruciform agle. If we assume a right value for α ad if we choose a proper iterfacial failure criterio, we have the same from differet cruciform agles. This procedure may be used for determiatio of, α ad selectio of the iterfacial failure criterio. Figures 9 ad show the relatio betwee ad α (assumed) by usig the experimetally-obtaied σ spe i the cases of the quadratic failure criterio ad the parabolic failure criterio, respectively.
(Quadratic) 3 5 5 Cruciform-9 Cruciform-67.5 Cruciform-45 Cruciform-35 (Quadratic) 4 35 3 5 Cruciform-9 Cruciform-67.5 Cruciform-45 Cruciform-35 5 5.5.5.5 3 α (=s/)..4.6.8 α (=s/) (a) (b) Fig.9 Normalized quivalet iterfacial stress ( ) as a fuctio of α i the case of the quadratic failure criterio. (a) Overall tedecy ad (b) magified view i the rage of <α< where the curves may itersect each other 3 4 (Parabolic) 5 5 5 Cruciform-9 Cruciform-67.5 Cruciform-45 Cruciform-35 (Parabolic) 35 3 5 5 Cruciform-9 Cruciform-67.5 Cruciform-45 Cruciform-35.5.5.5 3 α (=s/)..4.6.8 α (=s/) (a) (b) Fig.9 Normalized quivalet iterfacial stress ( ) as a fuctio of α i the case of the parabolic failure criterio. (a) Overall tedecy ad (b) magified view i the rage of <α< where the curves may itersect each other Although it is cosidered that if we choose a right iterfacial failure criterio, the -α curves from differet cruciform agles itersect each other at the right value of α, practically they do ot because of the ucertaity of the experimetally-obtaied average specime stress at iterfacial debodig σ spe. However, it seems that α=.3-.8 i the quadratic failure criterio (Fig.9(b)) ad α=.5-. i the parabolic failure criterio (Fig.(b)). Ayway, α is higher tha ad it ca be cosidered that the value of the iterfacial shear stregth is higher tha that of the iterfacial tesile stregth, ad that the debodig iitiatio poit is θ=9.
If we assume that α=.5, =6MPa i the case of the quadratic failure criterio ad 8MPa i the case of the parabolic failure criterio. Figure shows the relatio betwee the ormal ad shear stresses at debodig iitiatio. I derivig this figure, Shear stress (MPa) 5 4 3 Cruciform-9 Cruciform-67.5 Cruciform-45 Cruciform-35 Cruciform-.5 (Failure) Average Quadratic curve Parabolic curve 3 4 5 Normal stress (MPa) Fig. Iterfacial failure evelopes (criteria) with experimetal results Coclusio We coducted cruciform specime test by varyig the cruciform agles to make various iterfacial stress state for glass fiber/epoxy composite. We determied the iterfacial failure iitiatio locatio by itroducig two iterfacial failure criteria, the quadratic failure criterio ad the parabolic failure criterio, usig the experimetally-obtaied debodig iitiatio stress ad FEM results. It was implied that the value of the iterfacial shear stregth is higher tha that of the tesile stregth, ad that the iterfacial failure iitiates from θ =9 locatio for all cruciform specimes tested i this work. Refereces. J.-K.Kim ad.-w.mai, Egieered Iterfaces i Fiber Reiforced Composites, Elsevier, 998. G.P.Tado, R..Kim ad V.T.Bechel, Evaluatio of Iterfacial Normal Stregth i a SCS-/Epoxy Composite with Cruciform Specimes, Composites Sciece ad Techology, 6, 8-95, 3. S.Ogihara,.Sakamoto ad J.Koyaagi, Evaluatio of Tesile Stregth i Glass Fiber/Epoxy Resi Iterface usig the Cruciform Specime Method, Trasactios of the Japa Society of Mechaical Egieers, 75, 49-55, 9 (i Japaese) 4. J.Koyaagi, H.Kato ad S.Ogihara, Aalyses for Establishig Failure Criterio o Fiber/Matrix Iterface usig Cruciform Specime Test, Materials System, 7, 63-69, 9 (i Japaese)