27ƒ 5A Á 2007 9œ pp. 735 ~ 743 gj p ª w š p w { ³ p Flexural Behavior and Cracking Characteristics of High Performance Fiber Reinforced Cementitious Composites according to Fine Aggregate Contents *Á ³x** Shin, Kyung-JoonÁJang, Kyu-Hyoun Abstract Various methods have been used to reinforce the cementitious material such as mortar and concrete that have weak tensile strength. Major reinforcing method is to mix matrix with fibers which have strong tensile strength. Recently, High Performance Fiber Reinforced Cementitious Composites (HPFRCC) has been developed which shows multiple cracking behavior, that is different from conventional FRC. Related studies mainly have focusing on the mechanical behaviors according to fiber types and mixture proportions such as W/C and binder contents. However, study related to fine aggregate type and contents are insufficient. Therefore, this paper examines the fracture characteristics related to fine aggregate and contents, and reports the cracking behavior as well as mechanical behavior for various mixtures which have different fiber type and mixture proportions. From the results, it was useful to use silica sand as a fine aggregate for reducing fracture toughness as maintaining compressive strength and elastic modulus. It is showed that optimal silica-cement ratio was 0.8~1.0 to maximize flexural toughness and number of crack. Keywords : HPFRCC, fiber reinforced mortar, cracking characteristic, flexural behavior w ƒ š p yw k gj p w» w w š, w wƒ w gj p y w gj pƒ ã. w w w w ³ g ƒƒ ³ s y j w x ƒ j š p w (HPFRCC) w ƒ y w š. w wp - p w w w, w p w w., š HPFRCC w» w p ww š, w k HPFRCC ³ p w ww. x, ³ w k w q û w, { ƒ z ³ w w (³ )- p ƒ 0.8~1.0 ù kû. w : š p w, k, ³ p, { 1. p w k gj p», ƒ û» ³ w» p. w gj p ³ ü w ƒ w wƒ» ³ w» w w š. w w gj p y w gj p(frc, Fiber Reinforced Concrete)ƒ ã (Balaguru et al. 1992; Bentur et al. 1990). w gj p(frc) ³ z w j z ù, ³ w» w». wr, FRC w w» w š p w ( w z w y œw z (E-mail : kj12@snu.ac.kr) ( ) (E-mail : addio0024@hanmail.net) 27ƒ 5A 2007 9œ 735
t 1. e p Fiber ID Diameter Length Tensile Strength Elastic Modulus Remark PVA04 0.04 mm 12 mm 1.6 GPa 40 GPa Resin-bundled type PVA10 0.10 mm 12 mm 1.1 Gpa 25 GPa Resin-bundled type msteel 0.20 mm 12 mm 2.0 Gpa 200 GPa Straight, Brass Coating HPFRCC, High Performance Fiber Reinforced Cementitious Composites) w ƒ y w š (Fischer et al. 2006; Naaman et al. 1995, 2003). HPFRCC š ( 2005) š (½ 2005) w, š t w (Fischer et al. 2006)ƒ ww š. š HPFRCC gj p w w» FRC w w ³ g ƒƒ ³ s y j w x ƒ g, y j ³ (Smeard multiple cracking) ƒ š (Li et al. 1995). w š HPFRCC w ³ w š q û» w w ³ wš j yww p ƒ š (½ w 2005; ½ 2005; 2004). j k, p HPFRCC p p q p w r ³» z w w w w ƒ v. ù, w p y w (½ w 2005) - p ù w w (½ 2005; Song et al. 2004) w ù, p w, w (Guerrero 1999; Wu 2001) š š. Li (Li et al. 1995) ³ w p p w tw ù, y w yw w. w š HPFRCC w» w w p w ww š, w k y HPFRCC { ³ p w ww. ¼ 12 mm 0.2 mm w, sww gj p j p j t»w. 2. x 2.1 x z w š p w w ³ ƒ (Crack Bridging) w»³ q š, w ƒw ³ w, w ƒw ³ w j x ý. w ³ k p (Matrix) q p w, k p q w w x ww. q yw w ³ w w k p q w ù(li et al. 1995) yw w., š HPFRCC w w p w w ³ w x w w p q w x ww. p w p w. x p w x m w HPFRCC w w wš, - p (S/C) x w HPFRCC w p ³ p w x ww. w A 1 m sp p s e š ƒ, 2 PVA 1 ƒ. 0.2 mm ¼ 12 mm š ƒ, PVA ¼ 12 mm š 0.04 mm 0.1 mm ƒ. ƒ p t 1 ùkü. gj p w (F.M.) 2.5 s³ 0.43 mm š 2.65 ( w ) (F.M.) 0.3 š s³ 0.125 mm 2.65 ³ ( w ³ )ƒ ƒ s 1 ùkü. 2.2 p w p x 2.2.1 q (Matrix fracture toughness) w x 1. s x 736
x p x HPFRCC { x W/C t 2. e x S/C C (kg/m 3 ) W (kg/m 3 ) S (kg/m 3 ) sp (kg/m 3 ) 0.46 0.5 1036 477 518 5.18 0.46 1.0 866 398 866 4.33 0.46 1.5 745 343 1117 3.72 0.46 0.4 1077 495 431 5.30 0.46 0.6 996 458 598 4.98 0.46 0.8 926 426 741 4.63 0.46 1.0 866 398 866 4.33 a f ---- W a a 2 + ---- W 0.886 4.64 W a 2 W + ---- 13.32 ---- + 14.72 ---- a 32 1 ---- W a 3 a 4 5.6 ---- W W = ------------------------------------------------------------------------------------------------------------------------------------------------», a= e ¼, P Q = d w, B= r s, W= r ¾ (2) 2. CT(Compact Tension)xk q x r x w w k p (Matrix) q p sƒw» w k p q w w w q x ww. - p (W/C) 0.46 w - p (S/C) 0.5, 1.0, 1.5 y g ³ w r w t 2 x w ùkü. r 2 ASTM E 399 ³ šw CT(Compact Tension) x w xk w x ww. LEFM(Linear Elastic Fracture Mechanics; xk q w) w d q zw» w q w (fracture process zone) j»ƒ r j» w w, gj p FRC x ³ r LEFM w w, w size effect w r j» d q w š (Bazant and Planas 1998). ù, 1 mm w w k pt LEFM zw (Li et al. 1995)š š, x q q š., sww š ³ w x LEFM w q zw. Closed Loop System ƒ ƒ w MTS 810»» w x ww. w w 0.1 mm/min w, w q (K Q ) w (Sanford 2003). P K Q a Q = -------------- f ---- BW 1 2 W (1) 2.2.2 k w x k d w» w 100 mm š 200 mm mx œ w, KS F 2405 KS F 2438 w w w. 2.3 HPFRCC { w x q w x mw HPFRCC w w q y k w w, w j p w { r w x ww. x w Ì 25 mm, s 60 mm, ¼ 250 mm r w. - p (W/C) 0.46 y 2% w š w, p p x w mw - p (S/C) 0.4~1.0 y g r w t 2 x wt ùkü. r kxz w 28 ù z x ww. r ̃» JCI-SF4(1983) wš r ü d» w»ƒ» 3 r d» š» w w 3. 4 w w k { x 27ƒ 5A 2007 9œ 737
d w. ³ w ³ j» w { 4 w w { x w. x Closed Loop System ƒ ƒ w MTS 810»» w, w w 0.002 mm/sec w. 3. x 3.1 p p w x 3.1.1 x 4 t 3 w ùkü. ³ w ƒ ƒw w ù, w S/Cƒ 1.5 w. S/Cƒ 0.5 w r ƒ ³ w r 15%j ùkû ù, S/Cƒ 1.0 1.5 ³ w r ƒ 5% 20% j ùkû. Guerrero(1999) W/C 0.5 š S/C 1.0 w ³ (silica sand) w ƒ w 8~47% j š ew w š. 3.1.2 k x 5 t 3 w k ùkü. k (S/C)ƒ ƒw f, S/Cƒ 0.5 k ƒ j ùkû ù S/Cƒ 1.0 ƒ w. 5. w k 6. w q 3.1.3 q x S/C q (fracture toughness) x w 6 t 3 ùkü. ³ w S/C q (K) 0.167~0.284 MPaÁm 1/2, w 0.428~0.724 MPaÁm 1/2. x S/C ƒ q f ùkû, w r ³ w r 2.55~3.45 q y w. w, w r ƒ û q ³ w r ƒ q ùkû. 3.1.4 x 4. w w p y w» w t 3. w p w p S/C ratio Elastic modulus(gpa) Compressive strength(mpa) Fracture toughness(mpam 1/2 ) SilicaSand PlainSand E plain /E silica SilicaSand PlainSand f ck,plain /f ck,silica SilicaSand PlainSand K Plain /K Silica 0.5 15.6 21.1 1.35 48.1 55.3 1.15 0.167 0.428 2.56 1.0 21.1 22.2 1.05 61.4 58.5 0.95 0.192 0.660 3.45 1.5 28.5 28.1 0.99 64.5 53.8 0.83 0.284 0.724 2.55 738
f w. w š HPFRCC ³ w t wš, ³ w» w w ƒ q û w. p q 0.3 MPaÁm 1/2 w û» w ³ kwš y w w. ³ - p 7. ³ w» w w e ³ w w e w w e y w 7 ùkü. x ³ w w w 40% w q ù, w k ù 74%., q yƒ ù k y j ùkû, ³ w k w q j k ùkû. š p w ³ p ƒ j k»³ z ³ s ƒw ³ ƒ w» e ³ w x p, w ùkù» w w. w ƒ»³»³ z w w ƒ x ww w.,»³ ûš ƒ w. w,»³ z w» e ³ w w w p q w, ƒ w»¾ ƒ ƒ w ³ s, ƒ w w ³ ³ w w j ƒ w. j w w (½ 2005; Li et al. 1995) ³ ƒ j š, ù k ³ j» w w w ³ ³ (Complementary energy, J b )ƒ p ³ q (J tip ) f w š š. ƒ j» w y ƒ j y w ñ ü» w w š, j» w p q û w, j» w ƒ ³ s 8. yw { x w s³ w - š 27ƒ 5A 2007 9œ 739
(S/C)ƒ 1.5 w w, š y ƒ v w», S/ C=0.4~1.0 w { x w S/C HPFRCC { ³ p w. š w p w š w w, k w ww w. 3.2 HPFRCC { w x 3.2.1 { p p w x w ³ w - p (S/C) 0.4, 0.6, 0.8, 1.0 w PVA04, PVA10, msteel 3 y w { x ww š, 8 ùkü. x 3 r xw s³ t»w. PVA04, PVA10 r ³» x ³ y w ùkû, ³ z»³ z { ƒw - y(displacement hardening effect) x. ù ³ z ƒ PVA04 ƒ j ùkû. msteel r PVA r w 1.2~2.7 { k ƒ PVA w j». w ³ s ƒw ƒ q x w» z w w w w. p w ³ w» p ƒ y ( k ) k, r ³ k w. ù, ³ w z ³ w w ƒ w p š ƒ ³ z w, w w w w w ³ ƒ (crack bridging relation) ùkü (Lin et al. 1999). yw w š ƒ w, w ƒ ƒ j w» w ¼ x k, ƒ w w» w j» w w. ƒ w z (Snubbing effect) w ƒ w w w ƒ w j» q. ³ ƒ 9(a) ùkü. q» ƒw ³ ww j» f. 8 x r ƒ ƒw ƒ ƒw w ùkü.»³ z ƒ w. msteel r p ƒ ƒwš, ³ ƒ (Crack Bridging-Stress) ƒw, q w» r { ƒ f. 9(b) PVA w r ³ ƒ ù kü. PVA ƒ ƒw ƒ ƒ.» (Redon et al. 2001) PVA ƒ û š yw j ƒw x - y(slip-hardening)x» q» p. ƒ ƒw ƒ f, q» ƒ ƒ w ùk P = σa = τs (3)», τ σ w š, L d ¼, A S t πd 2 /4 πd L/2 tx.» (Li and Stang 1997) w 2.35~7.0MPa x ƒ w w» w τ=(σd)/ (2L)=15.38 MPa 1/2., w w, 9. PVA w ³ ƒ (Crack bridging relation) š 740
ù. 8 PVA w r ƒ ƒw ƒ ƒw, ƒ { y w j ùkû. 9(a) ³ ƒ y w ƒ ƒw ƒ f, q» { w w ùkù.» (Li et al. 1997) w w p (S/ C,,, s ) p ùkù š wš, x (Balaguru et al. 1992) ùkû. Guerrero(1999) x w j w ƒ w w 80% ƒw š šwš. w p š j» ³ w w w (interlocking) ƒw j»ƒ ƒw ù, y w x ƒ w, mw w v w.» k ƒ j» r ƒ w q, PVA ƒz x- y(slip-hardening)x ³ ƒ ƒw w ww p. msteel r 2mm w w š PVA w r 3~4 mm w w. PVA w r ³ ƒ r w», PVA w w x w w ww ƒ k q. 3.2.2 { { (Flexural toughness) gj p p ùkü t w - š ùkü. w» x ³ (JCI-SF4; ASTM C 1018) š ù, JCI-SF4 w { 1/150 w w ¾ { w š, ƒ { t 4. yw { { Fiber Type PVA04 PVA10 msteel S/C Flexural Strength (kn) Flexural Toughness(kN-mm) 1.33 mm (L/150) 2.67 mm (2L/150) Post-Peak 0.4 1.73 1.70 3.89 2.47 0.6 1.99 1.54 3.79 4.94 0.8 2.02 1.50 3.62 5.15 1.0 2.07 1.72 4.15 4.26 0.4 1.33 1.30 3.00 2.47 0.6 1.47 1.40 3.06 4.97 0.8 1.56 1.21 2.82 5.01 1.0 1.37 1.30 2.96 3.77 0.4 2.88 2.49 6.04 3.76 0.6 3.01 2.88 6.69 2.88 0.8 3.46 3.38 7.77 5.25 1.0 3.59 3.65 8.23 4.71 10. yw { 27ƒ 5A 2007 9œ 741
11. s³ ³ d t 5. yw { s³ ³ S/C Fiber Type 2/150 w w {»³ z Post- Peak { w w, t 4 10 ùkü. PVA w PVA04 r PVA10 r 8 w - š y w 2L/150 ¾ w, 2L/150 j w z w. L/150 2L/150 { x ƒƒ w ùkü y w., msteel r w { yƒ yw ùkù, ƒ ƒw L/150 2L/150 { ƒw y w. 3.2.3 ³ p j y w p w w w ³ w p» w, w š HPFRCC w. p w ³ z w» w, w wƒ óù r w ³ d w. ³ ³ w sw, 11 d» wš,» m w ³ s³ w. PVA04 r 5 ³ w, PVA10 r S/Cƒ 0.4 w s³ 5 { ³ ùkû. msteel r S/ Cƒ 0.4 ³ w, S/Cƒ ƒw ³ ƒ ƒw ùkû. 4. PVA04 PVA10 msteel 0.4 5.7 3.7 1.0 0.6 8.3 5.3 2.0 0.8 7.7 5.7 2.0 1.0 9.3 5.3 4.7 š p w { ³ p š w w x ww, w. 1. HPFRCC w» p w x ww. ³ w w x mw p w p w. x k q j w, ³ w k w q û. p q û w š HPFRCC w ³ w w ù kû. 2. w š HPFRCC { x ww. PVA w ³ ƒ w ³ - p ƒ 0.8~1.0 ùk û. PVA w { r r w ³ z ƒz ³ - y x w ƒ ƒw w ww ùkû. 3. w r { x ³ y w { { ƒw š, PVA w r 2.7 {. k ƒ ³ ƒ (Crack Bridging Stress) w». 4. k ³ z p w. PVA x- yx (sliphardening) p w (Pull-out) q p, ƒ { ƒ w ù, p ƒ ƒ w w» { ƒ j. š x ½ w, ½ y, ½, ½ (2005) j j w š p w w p w x, w gj pwz, w gj pwz, 17«, 2y, pp. 263-271. ½, ½, ½, w», ½ (2005) j w w ECC(Enginerred Comentitious Composite) w p, w gj pwz, w gj pwz, 17«, 5y, pp. 705-716., š k, k, ½ (2005) š p w ƒ e w, w gj pwz, w gj pwz, 17«, 1y, pp. 35-41., x, z(2005) š w g j p { p, w gj pwz, w g j pwz, 17«, 4y, pp. 543-550. ASTM C 1018 (1998) Standard Test Method for Flexural Toughness and First Crack Strength of Fiber Reinforced Concrete, American Society of Testing and Materials, Philadelphia. Balaguru, P. and Surendra, P. (1992) Fiber-reinforced cement composites, Elsevier. Bazant, Z.P. and Planas J.S. (1998) Fracture and Size Effect in Concrete and Other Quasibrittle Materials, CRC Press. Bentur, A. and Mindess, S. (1990) Fiber reinforced cementitious composites, McGraw-Hill. 742
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