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1 26ƒ 2A Á œ pp. 363 ~ 370 ª š w»» d ƒ w ¼ Electromechanical Relation of Conductive Materials with High Electrical Resistance and Its Application to the Estimation of In_situ Stress of Structural Tendons Ÿ Á» Zi, GoangseupÁJun, Kiwoo Abstract It is proposed that the electromechanical relation of the conductive materials with high electrical resistance may be used to estimate the current stress of prestressing tendons. To choose the best conductive material to this end, we studied the electromechanical relations of carbon fibers and metalic heat wires experimentally. The strain of those materials was controlled instead of the stress during the experiment. It is found that the relation of carbon fibers can be modelled by a parabolic(or hyperbolic) function in the early stage of deformation. However because the relation is not consistent when it is unloaded and reload, carbon fibers are not suitable for this purpose. Metallic heat wires show a consistent linear relation during loading and unloading in the elastic deformation and are suitable for this purpose. To estimate the electromechanics relation of metallic wires, we developed a simple formula based on the rigid plasticity. We propose a new kind of prestressing tendons whose stress can be monitored. As a side result of this study, we found that the electromechanical relation of carbon fibers without epoxy matrix becomes almost linear after a certain strain. Keywords : Electromechanical Relation, prestressing tendons, Estimation of In_situ Stress, Metallic heat wires, carbon fibers v p ¼ x wš dw š w»» w w. š w kw» w k p x mw x w. k x» s xk ù w- w»»ƒ w ww y. k w, w w w x ww y.»» dw» w» w w w. w w ¼ d ƒ w ¼ w. we k, p x z ƒ x w x»» w w. w :»», ¼, d,, k 1. œ gj p m k. 1 1 gj p w 8 10 ü k w» w» w v p» w. ³ w v p ƒ 1(a) s d j w. v p v p z ƒ,, j v gj p x w. v p k y g t ³» j, w ƒw w k ( 1(b)). v p gj p sƒwš w ƒ w x ¼ d y w. * z Áš w zy lœw ( g-zi@korea.ac.kr) **š w zy lœw ( junkiwoo@korea.ac.kr) 26ƒ 2A œ 363

2 1. v p y x ƒ w ¼ d w d w (Saiidi, 1994), q w (Chen, 2001; Chen, 2002; di Scalea, 2003), x w d (Civjan, 1995), ³ w (Azizinamini, 1996). w ³ w w ƒ ë w. ù œ x mw z y ¼ d w» w ƒ w w» w ƒ w, w w w œ w» q š. q w ¼ wš k ƒ w q y dw» w šƒ ƒ v w, e q š w w q v w ƒ (Chen 2002). w, x w v p š gj p w z, d w ¼ d w d w w. ³ w v p t k y w x w» w x w w v w. ƒ ¾ ywš rw d w ( y, 1999). x ƒw» w yƒ»»» w ¼ dw w.,»» w xk ¼ j» w». w»» w ƒ l š. m Ÿ w š k w (Carbon fiber reinforced plastics; w CFRP) š w q w ƒw»», w CFRP w ƒ w š (Abry, 1998; Kupke, 2000; Abry, 2001; Prasse, 2001; Park, 2002; i, 2004). w ƒ. w, s w (Ionic polymer-metal composites, IPMCs) s»» w,», œ w (Nemat-Nasser, 2000; Kim, 2005)ƒ w ù, x w w y š w w w w. ¼ d ƒ w š w k»» x w, š w»» w wš x w. š w ¼ w. 2.»» d w š x ¼ š» w ë»» š w.»» xk x tx. ρ = kε» ρ=δr/r 0 w y, ΔR w y, R 0 x» w, k»», ε x. 3 x ƒ 8 l xk tx w (Sevostianov, 2000). x ù k x w k (1) x w (2) x (deformation history) w. (1) t 1. k x r r r v p k [GPa] s we w (mm/sec) CF_A HTA3K 3, CF_B TC35-12K 12, CF_C SK f e 3, CF_ D HTA3K 3, (b) š 364

3 ρ = f( Δε, ε)»» w» w xk ƒœ ww w dw k dw ( 2). 3.k (Carbon fiber)»» 3.1. x (2) 2. k dw» w x ; (a), (b) d k (Carbon Fiber)»» p q w» w x w x w y d w. Ì 10 mm j q s k, x» j q š jš r p w z wd» (multimeter) w x w d w. x k s ƒ we Toho Tenex HTA3K yg High Gain Industrial imited Tairyfil TC35-12K, š HTA3K s we k SK f e w v v w. 3. k»» ; (a) s we k w ; CF_A, CF_B, (b) s we k w ; CF_C, (c) s we k x w; CF_D 26ƒ 2A œ 365

4 r 4 ƒƒ r k t 1. ¼ 510 mm š 470 mm w w mm/sec mw ww x š 3(a) 3(b) x ƒ k. r CF_A CF_B x ƒ ³e xk»» ù kü ù, CF_C s w x (CF_C1, CF_C2, CF_C3)ƒ w š ³ ew. k x 0.01 w» x s xk x» ƒw q w š (Xu, 1996; Cho, 2000; Park, 2001). ρ = n f ( n n f ) +( 1+ 2ν)ε», n k v p, n f q k v p, ν k s. q w, z w w» w(unloading)» w (Xu, 1996; Abry, 1998; Abry, 2001; Prasse, 2001). k»»» p w. s xk ƒw k p x ( 0.01) z w š. 3(a) x. x w w» w 3(b) w kw x w. w w (relaxation) z. 4 w w w x w. w» 2.23 l 26.16¾ s xk ƒw ù, w w k x ƒw w 4. k (CF_B) x»» (3). w w k kƒ w š x ƒw k q w k z» w w k q y w 4 w w ³e. k s p we CFRP w (Xu, 1996) p k w w w kƒ 2.5 j. ù x ƒ v xk ùkù w w ƒ. x w w x 0.01 w w ƒ ƒw.»» w k q w ƒ w q. w wš w w» w w, w, w w y w, x yw w w yƒ w. w 4 k, w(unloading) z, k=1.91~0.83 ƒ w š ƒ w» w k w» z. w, q y j š, w q w y j»ƒ. 4. (Metallic heat wires)»» 4.1. x (Fe) k x x ƒ w p ùkü. š x z w» k»» w p. x f (dislocation) e w q e. š ¼ ¼ ƒ x w q x y w». ¼» w d w ƒw ù,» w 9.68Ü10 8 Ωm d ƒ w x ƒ û. w j (Cr) 22%, (Al) 4%~5%ƒ ƒ 1mm x x 1.85 Ω/m w ƒ. w ƒ œ» l(heater). w k» w 137 Ω/m w w p l w y w dw», DC 10 ma ƒwš, w dw z w dw. w w» w w dw s³e w. 366

5 5. w- w- w mw x ƒ R = ( ΔV + + ΔV ) I», ΔV +, ΔV ƒƒ w ƒ w, I. x 510 mm x» ew z x» 450 mm w x dw. s w w. s ƒ e z 100 C o 1 w z x ww.»» x w» w ƒ x š w. (a) w- w- w mw x 2%¾ ƒ, (b) w z k ü x. x kƒ x w q w» w š š, x œ q w» w š x š x x 0~0.015 ƒ w x ƒw 5 ùkü. w k 2.02 d š w w k 2.52~ w ƒ. (4) 6. k x»» w- w k ew, x m s³ 2.56, t r 0.02 e p š y. k w w kƒ w 91% ù, w 26.7% j. w d 7. w z k ü x 26ƒ 2A œ 367

6 w y l x w. 6 t x ε t, max z w ww k x ε e, max ƒ z š,»» k. k x ε e, max ƒ z z ù x ε t, max -ε e, max x z wš, ƒ 0 ( 6 ). 5 x k x 0.28%~0.32%. 6 l k x w y ρ w x ε w w. ε ρ ρ max = ε k tmax,», ρ max w y, ε t, max =ε e, max x, ε p x. x ε p w d w x ε t, max w z. x k ü x m w w w ƒ y w ( 7). x z k x 0.30%¾ z wwš s 0.20% 5z w w. 7 d ƒ. 5. w k w»» w w» w š w ƒ w (1) w f d w w, (2) xw z k z k kƒ w w, (3) ƒ x y z kƒ w w, (4) x w š w ƒ q š, (5) x k z wš kƒ f w. k x mw r x w ƒ w z. w w d»» ƒ x w, x k w. w x 0~0.015 k z wš kƒ 2.56 f w w š q. x v p ¼ ¼ 0.7% x ƒw. k 4 x q ù w- w w.. 6. ü ¼ d ƒ w v p ¼ 6.1. ¼ w»»» (5) 8. ¼ d ƒ w ¼ 9. ¼ d ƒ w ¼ w d w. š w w d w. ¼ ƒ š w» ¼ w ù s gq ¼ w. š w s w ¼ w w w. 8 ü ¼ d ƒ w ¼ ùkü. x ¼ 9(a) w, x ¼ 9(b) ù x w. ù x ¼ ù x e»ww p š w w d ¼ d ƒ w ¼ d (1) ¼ š w»», (2) š w ¼ w š (3) ¼ w d» w y l w. x w w, w kƒ (5) w x w. ¼ ¼ w z e ew» x ε t,max ùkü e w w d w.» ¼ ü ¼. ü ¼ gj p k kƒ ë w x d 368

7 x w ù wd mw w y ρ max d w. ρ ε max = tmax, k i», k i» w. 5 k i z x ¼ w d w (5) (6) mw ¼ š w x x w. x ¼, š w» ¼ x ε š w x ε l (5) w x w. ù x ¼ ù x š w w ¼ x ε š w x ε l š ƒ ( ). 8l 2 4νD 2 θ 2 + ε =», D ¼, l ƒƒ ¼ š w ¼, θ ¼ ƒ, ν ¼ s. (7) w ¼ x ¼ w ¼ wš w ¼ d w ε 4l 2 D 2 θ 2 1 l d ƒ w š w w š k»» x w. k»» ƒ j x w w ƒ j ù d ww. 2. we k p x z»» ƒ s xkƒ x w x, w ƒ ƒ v w. d v w. 3. w w w kƒ w k ü x w ùkþ. w p š w w w y l x w w w. 4.»» w ¼ d ƒ w ¼ d w w. ¼ ¼ y š w, y ƒ ƒ w w x ƒ ƒ w w (6) (7) (KRF D00387) m ƒ wš w msƒ k ww 2005 w» 05 w D11. : x ¼ š w w w ¼ š w ¼ w. D D r = --- coste sinte + e dr D D d ---- = --- sinte te 1 cos e l = θ dr t dr t = ---- dr ---- θ dr dr = l 2 D = ---θ 2 dr ---- dr (8) (9) (10) (11)» r š w»ww xkw, D ¼, l ƒƒ ¼ š w ¼, θ w ¼ ƒ ( 10). (11) l ¼ x ε š w x ε l tx. l = l( 1 + ε l ) l 2 = ( 1+ 2ε l ) Δ 10. x ¼ w ε = = = D 2 ( 1 2νε 1 ) θ 2 4 D 2 ( 1 2νε 1 ) l 2 ( 1+ 2ε l ) θ 2 4 = = l 2 D θ 2 4», ', l' x z ¼ š w ¼. (12) 8l 2 2νD 2 θ ε 4l 2 D 2 θ l (13) 26ƒ 2A œ 369

8 š x y (1999) v p d w.», w», m«191y pp Abry, J. C., Bochard, S., Chateauminois, A., Salvia, M., and Giraud, G. (1999) In situ detection of damage in CFRP laminates by electrical resistance measurements. Comput Sci. Technol., Vol. 59, No. 6, pp Abry, J. C., Choi, Y. K., Chateauminois, A., Dalloz, B., Giraud, G., and Salvia, M. (2000) In-situ monitoring of damage in CFRP laminates by means of AC and DC measurements. Comput Sci. Technol. Vol. 61, No. 6, pp Angelidis, N., Wei, C. Y., and Irving, P. E. (2004) The electrical resistance response of continuous carbon fibre composites laminate to mechanical strain. Composites A, Vol. 35, No, 10, pp Azizinamini, A., Keeler, B. J., Rohde J., and Mehrabi, A. B. (1996) Application of a New Nondestructive Evaluation Technique to a 25-Year-Old Prestressed Concrete Girder. PCI Journal, Vol. 41, No. 3, pp Chen, H.-. and Wissawapaisal, K. (2001) Measurement of tensile forces in a seven-wire prestressing strand using stress waves. J Eng. Mech., Vol. 127, No. 6, pp Chen, H.-. and Wissawapaisal, K. (2002) Application of wignerville transform to evaluate tensile forces in seven-wire prestressing strands. J. Eng. Mech., Vol. 128, No. 11, pp Cho, J. W. and Choi, J. S. (2000) Relationship between electrical resistance and strain of carbon fibers upon loading. J. App. Polym. Sci., Vol. 77, No. 9, pp Civjan, S. A., Jirsa, O., Carrasquillo, R.. and Fowler, D. W. (1995) Method to Evaluation Remaining Prestress in Damaged Prestressed Bridge Girders, Texas Department of Transportation. di Scalea, F.., Rizzo, P. and Seible, F. (2003) Stress measurement and defect detection in steel strands by guided stress waves. J. Mater. Civil. Eng., Vol. 15, No. 3, pp Kim, S. J., Kim, M. S., Shin, S. R., Kim, I. Y., Kim, S. I., ee, S. H., ee, T. S. and Spinks, G. M. (2005) Enhancement of the electromechanical behavior of IPMCs based on chitosan/polyaniline ion exchange membranes fabricated by freeze-drying. Smart Mater Struct., Vol. 14, No. 5, pp Kupke, M., Schulte, K., and Schuler, R. (2001) Non-destructive testing of FRP by D.C. and A.C. electrical methods. Comput Sci. Technol. Vol. 61, No. 6, pp.g i, H., Zhou, W. S., and Ou, J. P. (2004) Study on electromechanical behavior of unidirectional carbon fibre sheet without epoxy resin matrix. Adv. Struct. Eng., Vol. 7, No. 5, pp Nemat-Nasser, S. and i, J. Y. (2000) Electromechanical response of ionic polymer-metal composites. J. Appl. Phys., Vol. 87, No. 7, pp Park, J. B., Okabe, T., and Takeda, N. (2003) New concept for modeling the electromechanical behavior of unidirectional carbon-fiber-reinforced plastic under tensile loading. Smart mater. struct., Vol. 12 No. 1, pp.g Park, J. B., Okabe, T., Takeda, N., and Curtin, W. A. (2002) Electromechanical modeling of unidirectional CFRP composites under tensile loading condition. Composites A, Vol. 33, No. 2, pp Prasse, T., Michel, F., Mook, G., Schulte, K., and Bauhofer, W.A (2001) A comparative investigation of electrical resistance and acoustic emission during cyclic loading of CFRP laminates. Comput. Sci. Technol., Vol. 61, No. 6, pp Saiidi, M., Douglas, B., and Feng, S. (1994) Prestress Force Effect on Vibration Frequency of Concrete Bridges. J. Struct. Eng., ASCE, Vol. 120, No. 7, pp Sevostianov, I. and Kachanov, M. (2000) Microcracking in Piezoelectrics Weakens the Electromechanical Coupling and Changes Its Directionality. Int. J. fracture., Vol. 101, No. 3, pp. 1-8 Xu, M. X., iu, W. G., Gao, Z. X., Fang,. P., and Yao, K. D. (1996) Correlation of change in electrical resistance with strain of carbon fiber-reinforced plastic in tension. J. App. Polym. Sci., Vol. 60, No. 10, pp ( : / : / : ) 370