스틸코드잔류응력의새로운측정방법과잔류응력이내피로성에미치는영향 JUNE 010 1
목차 1. 고탄소강선의인장강도별적용분야. 고탄소강선의기계적특성영향인자 3. 소선피로특성의종류및해석 4. 소선피로특성및표면결함측정방법 5. 기존잔류응력분석방법 6. 신규 FIB-DIC법의소개 7. 잔류응력및피로특성 8. 결론
고탄소강선의인장강도별적용분야 고탄소강선의인장강도변천 SAW WIRE (> 3300 MPa) STEEL CORD (> 750 MPa) High strength PC WIRE (> 1700 MPa) ROPE WIRE (> 000 MPa) CABLE WIRE (> 150 MPa) <ref. J. of Mater. Sci. 39 (004) p.3889> 고탄소강선의기계적특성요구 고강도 우수한내피로성 3
고탄소강선의기계적특성영향인자 인장강도와내피로성과같은기계적특성은, 다음두요소에크게영향을받는다. 내적인자 ( 미세조직 ) - Lamellar spacing 1) -ferrite/cementite 간계면면적 ) 외적인자 - 표면잔류응력 3) - 표면결함 4) 1) G. T. Gray et al., Met. Trans. A, 16A, (1985).753 ) M. A. Daeubler et al., Metallurgical Transactions A, 1A April (1990) 95 3) Renz P et al., Wire I Int 1996, 64. 4) I. Verpoest et al., Int. J. Fatigue, October (1985) 199 4
기계적특성영향인자의개선방향 기계적특성 제조조건의변화 such as 신선열처리 목표 내피로성 인장강도 will be improved by 합금원소첨가 such as shot peening C, Cr, V.. However, 문제 formation of nd cementite phase segregation of carbide (Cr-,V-) 제조프로세스 Rod Descaling Coating 1 st drawing Patenting Decaling Coating nd drawing Patenting Decaling Coating 3 rd drawing Stranding Tire cords Zn Coating Stranding Bridge cable 5
고탄소강선의기계적특성영향인자분석방법 영향인자분석방법문제점 내적인자 ( 미세조직 ) lamellar spacing ferrite/cementite 간계면면적 SEM SEM 국부영역만관찰 관찰위치별산포가큼 국부영역만관찰 수치화곤란, 시간이많이걸림 관찰위치별산포가큼 국부영역만관찰 XRD 분석결과의산포가큼 외적인자 표면잔류응력 Stress relaation 시간이많이걸림 측정자에따른산포가큼. 반복측정시산포가큼 FIB-DIC * 국부영역만관찰 3D-profiler 국부영역만관찰 표면결함 Roughness tester 세선에서측정이어려움. 6
소선피로특성의종류및해석 구분 저주기피로특성 ( 소성영역에서의피로, strain-life) 인장방향균열 고주기피로특성 ( 탄성영역에서의피로, stress-life) 연성찢어짐파단 파면형태 연성찢어짐파단 압축방향균열 균열진행방향 균열의발생균열의전파파단 파괴기구 주요인자 균열의전파가피로수명의대부분을차지함. 표면특성은피로수명에영향을주지않음. 재료인성이높을수록저주기피로특성은증가함. 슬립변형모형도 균열의발생이피로수명의대부분을차지함. 표면특성이피로수명에많은영향을미침. 재료강도가높을수록고주기피로특성은증가함. 평가방법한계피로수명 * 한계피로응력 ** * 신뢰수준 95% 에서파괴확률이 10% 미만이되는한계피로수명 ** 신뢰수준 95% 에서파괴확률이 10% 미만이되는한계피로응력피로특성결과의해석은하기국제표준에따라평가함. ISO 1107 Metallic materials-fatigue testing-statistical planning and analysis of data 7
소선피로특성의측정방법 Low cycle fatigue test (C-type fatigue tester) High cycle fatigue test (RBT fatigue tester) Fiing Clamps Driven Disc Filament Pin Pretension W(N)=400MPa π r Fatigue stress(mpa) =1.198 young s modulus d L(mm) 8
표면결함의평가방법 3D profiler 9
XRD 에의한잔류응력의측정 X-ray (XRD) Equipment & Parameters Diffractometer D8 DISCOVER with GADDS Tube. kw Co Long Fine Focus (mounted for Point Focus) Primary Optics parallel Graphite Monochromator Mono-cap 0.1 mmx-ray Radiation Co Tilt Angles ψ 0, 9, 18, 7, 36, 45 Stepsize Δθ 0.0 (used for line integration) Stress Calculation sin ψ -Method Elastic Constant 1/s 13.40 10-6 mm/n 공시재및시험결과 와이어로드화학성분 : 0.8wt%C 습식신선감면율 96.9% (Φ1.68mm Φ0.98mm) Sample A : 평균감면율 14%, 사상감면율 9%. Sample B : 평균감면율 16%, 사상감면율 9%. Sample C : 평균감면율 14%, 사상감면율 5%. Results of the residual stress measurement by XRD Eulerian cradle Laser/video microscope laser spot Hi-star detector wire ais Residual stress (MPa) 1,600 1,400 1,00 1,000 800 600 400 5% of the mean value 1% of the mean value 74% of the mean value 00 - Sample A Sample B Sample C <ref. J. G. Bae, Master thesis, 006> 10
XRD 에의한잔류응력의측정 X-ray (XRD) Sample-A (Φ=0.98) ε ϕψ -sin ψ - Function, ϕ = 0 (-360 ) Normal Stress s11 = (+1065 ± 74) Mpa Error range(%) = (1339-791)/1065*100 = 5% Sample-B (Φ=0.98) ε ϕψ -sin ψ - Function, ϕ = 0 (-360 ) Normal Stress s11 = (+1105 ± 118) Mpa Error range(%) = (13-987)/1105*100 = 1% Sample-C (Φ=0.98) ε ϕψ -sin ψ - Function, ϕ = 0 (-360 ) Normal Stress s11 = (+679 ± 5) Mpa Error range(%) = (1339-791)/1065*100 = 74% 잔류응력측정결과의산포가큼 ( 중심값의 1~74%) <ref. J. G. Bae, Master thesis, 006> 11
Stress relaation 에의한잔류응력의측정 Stress relaation method Equipment & parameters wire Removed area with nital (0%) 공시재및시험결과 와이어로드화학조성 : 0.8wt%C 소선경 : Φ0.1mm d 0 / d 1 / ρ 1 ρ after etching σ (d d ) (d d ) (d d )(d 3 d 3 0 + 1 g 0 1 0 1 0 1 ) 1 1 M a = + 8 3(d d M b = E I g 0 + 1 ) ρ 1 ρ 0 1 π 8 d d ( d d ) d d 4 4 1 0 1+ 0 0 1 ( d1+ d 0 ) I= ( d1 d 0 ) 16 8 9 g + + 18 d d + 18 d d π π 1 + 0 π 1 + 0 Where, Ma :moment at removed area, Mb :moment of curvature with/ without etching, σ: residual stress, d0 : Wire diameter without etching, d 1 : Wire diameter with etching, E: Young s modulus, I : nd moment with etching, ρ 0 : curvature without etching, ρ 1 : curvature with etching d 0 (mm) d 1 (mm) ρ 0 (mm) ρ 1 (mm) σ R (MPa) N 10 10 10 10 10 Min. 0.10 0.087 199 4 345 Ma. 0.11 0.10 460 40 705 Ave. 0.11 0.097 35 31 497 S.D. 0.000 0.003 79 5 13 잔류응력측정결과에서표준편차가매우높음. 와이어에서잔류응력을측정하기위한적절한방법개발이필요함. 1
FIB-DIC 에의한잔류응력측정방법이란? Advanced Stress relaation method Materials F U F a - σ R a θ h h Analytic approimation K IF K IIF K IIIF U = U Fnocrack + [ K IR K IIR K IIIR ] da E` + + F F F K IF U = K IR da E` F A (1 v ) a K IF U = K IR da 0 U Where K IR E A F 1.115(1 v ) a σ R 0 = E f f da 1 = 1.1σ πa f 1 (a/h), f 1 (a/h) = (1-a/h) (1/-s) (1+λa/h) K IF = (F/ πa) f (θ) f 1 (a/h), f (θ) = cosθ(1+[(1-ν)] -1 sin θ) θ = tan -1 (/a) Before etching, U fnocrack =0 Only Mode is occurred. II=III=0 Where E` = E for plane stress E`=E/(1-v ) for plane strain E`=E/(1-v ) at Plane strain (1.1+0.18sech (tanθ)) Materials properties DLC Si Ref. - J.W.Hutchinson et al., Adv. Appl. Mech. 9 (199) p.63 E (GPa) 199 04 ν 0. 0.3 13
FIB-DIC 법의최적화 왜최적화가필요한가? a b c d Current Length Width Depth Shape of contour (I, pa) (L,μm) (w, μm) (a, μm) ( = displacement) a 100 38.0 1.0 3.4 Best b 100 38.0 1.0. Good c 300 38.0 1.0 3.4 Worst d 100 38.0 0. 3.4 Worst 실험조건이최적화되지않으면, 금속선재에서잔류응력을측정할수없음. 14
FIB-DIC 법에의한잔류응력측정단계 1. Selection of interested area. DIC pattern generation 3. Reference line 4. 1 st SEM image capture 5. Ion milling (slot making) 6. nd SEM image capture 7. Ion milling & 3 rd SEM image capture 8. Digital image correlation by VIC-D 9. Calculation of analytic displacement 10. Residual stress 15
FIB-DIC 법에의한잔류응력측정단계 1. Selection of interested area FIB SEM. DIC pattern generation 3. Making reference line y z Wire FIB interesting plane Interest region 4. 1 st SEM image capture FIB equipment cond. 5. Ion milling (slot making) Acc. voltage SEM Resolution 5 to 30 kv 4 nm at 30 kv 6. nd SEM image capture Current Characteristics 10 pa @ 5 kv 1 pa @ 30 KV 7. Ion milling & 3 rd SEM image capture 8. Digital image correlation by VIC-D 9. Calculation of analytic displacement 10. Residual stress 16
FIB-DIC 법에의한잔류응력측정단계 1. Selection of interested area FIB. DIC pattern generation 3. Making reference line y z Wire FIB interesting plane Interest region 4. 1 st SEM image capture 5. Ion milling (slot making) 6. nd SEM image capture Milling condition : 40 pa @ 5 kv 7. Ion milling & 3 rd SEM image capture 8. Digital image correlation by VIC-D 9. Calculation of analytic displacement 10. Residual stress 17
FIB-DIC 법에의한잔류응력측정단계 1. Selection of interested area SEM. DIC pattern generation 3. Making reference line y z Wire FIB interesting plane Interest region 4. 1 st SEM image capture 5. Ion milling (slot making) 6. nd SEM image capture 7. Ion milling & 3 rd SEM image capture 8. Digital image correlation by VIC-D reference mark 9. Calculation of analytic displacement 10. Residual stress 18
FIB-DIC 법에의한잔류응력측정단계 1. Selection of interested area FIB SEM. DIC pattern generation 3. Making reference line y z Wire FIB interesting plane Interest region 4. 1 st SEM image capture 5. Ion milling (slot making) 6. nd SEM image capture 7. Ion milling & 3 rd SEM image capture 8. Digital image correlation by VIC-D Milling condition : 100 pa @ 30 kv Slot condition : depth = 3.4, width =1, length 38 μm L y Slot a w u 9. Calculation of analytic displacement slot 10. Residual stress 19
FIB-DIC 법에의한잔류응력측정단계 1. Selection of interested area FIB SEM. DIC pattern generation 3. Making reference line y z Wire FIB interesting plane Interest region 4. 1 st SEM image capture 5. Ion milling (slot making) 6. nd SEM image capture 7. Ion milling & 3 rd SEM image capture 8. Digital image correlation by VIC-D Milling condition : 100 pa @ 30 kv Slot condition : depth = 3.4, width =1, length 38 μm Slot L y C protecting layer a w u 9. Calculation of analytic displacement depth 10. Residual stress 0
FIB-DIC 법에의한잔류응력측정단계 1. Selection of interested area. DIC pattern generation 3. Making reference line 4. 1 st SEM image capture 5. Ion milling (slot making) 6. nd SEM image capture 7. Ion milling & 3 rd SEM image capture 8. Digital image correlation by VIC-D Software with a resolution of 1/100 th in a piel 1 st SEM image nd SEM image contour image 9. Calculation of analytic displacement 10. Residual stress 1
FIB-DIC 법에의한잔류응력측정단계 1. Selection of interested area. DIC pattern generation a - σ R a θ F U F 3. Making reference line 4. 1 st SEM image capture 5. Ion milling (slot making) 6. nd SEM image capture 7. Ion milling & 3 rd SEM image capture 8. Digital image correlation by VIC-D U Pearlite = U Fnocrack K [ IF KIIF KIIIF + KIR + KIIR + KIIIR ] da o E F F F A K R K IF o IR F A U = K da E where U F nocrack : Displacement with no crack E o : Young s modulus @ plain strain K I~III : stress intensity factor @ mode I~III : // generated by residual stress where K IR = 1.115σR πa K IF = F πa -1/ f(θ) cosθ(1+[(1-ν)]-1sinθ)(1.1 +0.18sech(tanθ)), θ = tan-1(/a) E o =E/(1-ν ) -1 h 9. Calculation of analytic displacement U 1.115(1 v ) a σ R 0 = E fda 10. Residual stress σ R (-1 GPa), E (10 GPa), ),ν (0.3) for carbon steel
FIB-DIC 법에의한잔류응력측정단계 1. Selection of interested area. DIC pattern generation Contour map showing displacement 3. Making reference line 4. 1 st SEM image capture Wire center 5. Ion milling (slot making) 6. nd SEM image capture 7. Ion milling & 3 rd SEM image capture 8. Digital image correlation by VIC-D 9. Calculation of analytic displacement 10. Residual stress 8 10 1 14 16 18 0 u : Measured displacement U : Analytic displacement under σ VR (virtual stress) Ψ : Residual stress Φ : Translation in SEM Measured u (nm) 110 108 106 104 10 100 98 96 94 Residual stress (σ R = Ψ) in interested area Error range u = Ψ U + Φ Calculated U (nm) 3
잔류응력분석방법비교 : FIB-DIC 법 & stress relaation 법 공시재 습식신선감면율 96.8% (Φ1.68mm Φ0.30mm) 10m 길이시편을 1m 간격으로등분하여각평가방법으로분석함 (n=10) 1) NT : Tensile strength,910mpa, 0.7wt% Carbon steel. ) HT : Tensile strength 3,60MPa, 0.8wt% Carbon steel. 3) ST : Tensile strength 3,50MPa, 0.9wt% Carbon + 0.wt% Chromium steel 잔류응력의측정 FIB-DIC method Slot dimension : 3.4μm in depth, 1μm in width, 38μm in length. Current stress relaation method Etching Condition : 30% HNO3 (1l, 0 ), 60sec. 피로특성평가 (ISO 1107에따름 ) C형피로 strain life RBT 피로 stress life 표면결함측정 3D profiler 측정 4
잔류응력분석방법비교 : FIB-DIC 분석결과 (NT) Mea. u (nm) 30 9 8 7 6 5 4 D Linear Fit of Data1_D Y=0.610+35.07 Mea. u (nm) 30 8 6 4 C Data1C Y=-0.545+3.88 3 1 8 10 1 14 16 18 0 4 6 Cal. U (nm) 0 8 10 1 14 16 18 0 4 6 Cal. U (nm) Mea. u (nm) 30 8 6 4 B Linear Fit of Data1_B Y=-0.60+34.75 Mea. u (nm) 68 66 64 6 60 58 Y=0.736+48.66 56 Mea. u (nm) 5 0 15 10 5 0 8 10 1 14 16 18 0 4 6 Cal. U (nm) Y=0.60+4.15 B Linear Fit of Data1_B 0 5 10 15 0 5 30 Cal. U (nm) 54 5 8 10 1 14 16 18 0 4 6 Cal. U (nm) B Linear Fit of Data1_B Eq. σ R (MPa) Error range(%) Y=0.610+35.07 610 3.0 Y=-0.545+3.8 545 Y=-0.60+34.7 60 Y=0.736+48.66 736 Y=0.60+4.15 60 Mean σ R (MPa) 619 -.8 1.6 1.8 1.5 5
잔류응력분석방법비교 : FIB-DIC 분석결과 (HT) Mea. u (nm) 6 4 0 18 16 14 1 Y=0.884+8.91 5 10 15 0 5 30 Cal. U (nm) B Linear Fit of Data1_B Mea. u (nm) 35 34 33 3 31 30 9 8 6 8 10 1 14 16 18 0 4 6 Cal. u (nm) D Linear Fit of Data1_D Y=0.678+37. Mea. u (nm) 35 34 33 3 31 30 C Linear Fit of Data1_C Y=0.751+37.76 Mea. u (nm) 36 34 3 30 B Linear Fit of Data1_B Y=0.83+37. 9 8 8 7 6 8 10 1 14 16 18 0 4 6 Cal. u (nm) 6 6 8 10 1 14 16 18 0 4 6 Cal. u (nm) Mea. u (nm) 64 6 60 58 56 54 5 50 48 Y=0.930+39.4 D Linear Fit of Data1_D 10 15 0 5 30 35 40 Cal. U (nm) Eq. σ R (MPa) Error range(%) Y=0.884+8.91 884 1.5 Y=0.678+37. 678 1. Y=0.751+37.76 751 1.3 Y=0.83+37. 83 1.0 Y=0.930+39.4 930 1.1 Mean σ R (MPa) 813. - 6
잔류응력분석방법비교 : FIB-DIC 분석결과 (ST) 55 Y=-1.017 +35.3 B Linear Fit of Data1_B 34 3 Y= 0.961+6.44 50 30 8 Mea. u (nm) 45 40 35 30 5 10 15 0 5 30 Cal. U (nm) 35 30 Y=1.001 +5.83 Mea. u (nm) 6 4 0 18 16 D 14 Linear Fit of Data1_D 1 5 10 15 0 5 30 35 30 Cal. U (nm) Y= 1.017+4.93 Mea. u (nm) 5 0 Mea. u (nm) 5 0 15 C Linear Fit of Data1_C 10 5 10 15 0 5 30 Cal. U (nm) 15 10 5 10 15 0 5 30 Cal. U (nm) B Linear Fit of Data1_B Mea. u (nm) 4 40 38 36 34 3 30 8 6 Y=-0.8806+47.85 D Eq. σ R (MPa) Error range(%) Linear Fit of Data1_D Y=1.017 +35.3 1017. 8 10 1 14 16 18 0 4 6 8 Cal. U (nm) Y= 0.961+6.44 961 Y=1.001 +5.83 1001 Y= 1.017+4.93 1017 Y=-0.8806+47 880 Mean σ R (MPa) 975. - 1.4 1.0 1. 1. 7
잔류응력분석방법비교 : FIB-DIC 법 & stress relaation 법 잔류응력비교 (FIB-DIC & stress relaation) 및피로특성 Residual stress (MPa),000 1,500 1,000 500 - FIB-DIC (S.D=70) Current (S.D=408) FIB-DIC (S.D=101) Current (S.D=180) FIB-DIC (S.D=58) Current (S.D=160) 4000 3500 3000 500 000 한계피로응력 (MPa)/ 한계피로수명 ( 회 ) 1500-500 -1,000 1000-1,500 -,0000 960 103 1004 95 300 316 NT HT ST 한계피로응력 (Mpa) 한계피로수명 ( 회 ) 1500 1000 500 0 * 표면결함은전체 0.03~0.04 μm로동일함 ( 신선조건동일 ) 8
결론 FIB-DIC 잔류응력측정시 1 회측정시 Error range( 그래프에서기울기편차 ) 는 3.0% 이하로양호하였다. 반복실험에서 FIB-DIC 측정시표준편차가 70~101 로기존방법의 160~408 대비 5~50% 수준으로우수하였다. FIB-DIC 법으로기존대비보다정밀하게소선의잔류응력측정이가능함. 고주기피로특성 (stress life) 은알려진바와같이소선 TS 가높을수록증가하였다. 그러나, 그증가폭은표면인장잔류응력이증가할수록감소하였다. * 인장잔류응력 : NT 960MPa, HT 1004MPa, ST 103MPa * 피로한계응력 : NT - TS 의 33%, HT TS 의 31%, ST 는 TS 의 9% 저주기피로수명 (strain life) 은표면품질보다소선의가공량등인성에더많은영향을받는다. 동일한가공량에서는소선 TS 가증가할수록향상되었다. 소선의표면인장잔류응력을낮추면고주기피로특성을향상시킬수있음. 9