A simple scheme was proposed for identifying the length and the depth of a semi-elliptical surface crack in a conductive body from D.C. potential readings measured at several points on the surfaces of the body. This scheme is based on the comparison of measured potential readings with theoretical ones calculated by three-dimensional boundary element analyses. For each potential reading a characteristic curve was constructed, which represented the possible combinations of the crack length and the depth, by referring to the calculated potential distributions. The intersection of the characteristic curves, which correspond to the potential values observed at several points, gives the estimation of the crack length and the depth. A sensitivity matrix was introduced to predict errors involved in the crack identification from errors in the potential measurement, and further to determine the optimum combination of locations of potential measuring probes for the identification. This scheme was applied to monitor the length and the depth of a surface crack propagating in a steel plate subjected to fatigue loadings. It was found that the proposed scheme was useful for the estimation of the length and the depth of the surface crack. The sensitivity matrix was also found to be useful to determine good combinations of probe positions.
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References
1.
JohnsonH.H., Calibrating the electric potential method for studying slow crack growth, Mater. Research Standards5 (1965) 442–445.
2.
ClarkG. and KnottJ.F., Measurement of fatigue cracks in notched specimens by means of theoretical electrical potential calibrations, J. Mech. Phys. Solids23 (1975) 265–276.
3.
RitchieR.O. and BatheK.J., On the calibration of the electric potential technique for monitoring crack growth using finite element methods, Int. J. Fract.15 (1979) 47–55.
4.
WilkowskiG.M. and MaxeyW.A., Review and applications of the electric potential method for measuring crack growth in specimens, flawed pipes, and pressure vessels, ASTM STP791 (1983) pp. II266–II294.
5.
SaxenaA., Electrical potential technique for monitoring subcritical crack growth at elevated temperatures, Eng. Fract. Mech.13 (1980) 741–750.
6.
OrazemM.E. and RughW., An improved analysis of the potential drop method for measuring crack lengths in compact tension specimens, Int. J. Fract.31 (1986) 245–258.
7.
PulleD.W.J., Crack length measurement: Analysis of the electro-potential method using a finite element method, J. Strain Analysis21 (1986) 127–134.
8.
HicksM.A. and PickardA.C., A comparison of theoretical and experimental methods of calibrating the electric potential drop technique for crack length determination, Int. J. Fract.20 (1982) 91–101.
9.
YagawaG. and FukudaT., Applications of the electric potential drop method in fracture mechanics, Science of Machines36 (1984) 27–32.
10.
HayashiM., OhtakaM., EnomotoK., SasakiT. and KikuchiT., Detection of configuration of surface fatigue crack in inside of stainless steel pipe by DC potential drop method, J. Soc. Mater. Sci., Jpn.35 (1986) 936–941.
11.
CoffinL.F., Damage evaluation and life extension of structural components, Trans. ASME, Vibration J., Acoustics, Reliability in Design108 (1986) 241–248.
12.
MiyoshiT. and NakanoS., A study of the determination of surface crack shape by the electric potential method, Trans. Jpn. Soc. Mech. Eng., Ser. A52 (1986) 1097–1102.
13.
SmithR.A. and CameronA.D., A three dimensional wax analogue for the calibration of the electrical potential technique of crack growth monitoring, Advances in Fracture Research (Fracture 84), ed. ValleriS.R.. (Pergamon, 1986) Vol. 5, 3371–3376.
14.
AbeH., SakaM., WachiT. and KanohY., An inverse problem in non-destructive inspection of a crack in a hollow cylinder by means of electrical potential method, Computational Mechanics ‘88, ed. AtluriS.N. and YagawaG. (Springer, 1988) 1, 12.ii.1-12.ii.4.
15.
MichaelD.H., WaechterR.T. and CollinsR., The measurement of surface cracks in metals by using a.c. electric fields, Proc. Royal Soc. London A, 381 (1982) 139–157.
16.
KagawaY., MuraiT. and NakasaiT., Boundary element simulation of nondestructive inspection by electric impedance approach, Proc. 2nd Japan National Symp. on Boundary Element Method, 1985, 269–274
17.
LeeK.H., LaiM.O. and TanT.H., An application of the boundary element method to the A-C field measurement crack detection technique, Boundary Elements VIII Conf.1986 (Springer, 1986) Vol. I, 179–192.
18.
MclverM., Characterization of surface-breaking cracks in metal sheets by using AC electric fields, Proc. Royal Soc. London A, 421 (1989) 179–194.
19.
OhjiK., KuboS. and SakagamiT., Electric potential CT method for measuring location and size of two- and three-dimensional cracks (Development of boundary element inverse analysis method for electric potential problems and its application to non-destructive crack measurement), Trans. Jpn. Soc. Mech. Eng., Ser. A, 51 (1985) 1818–1827.
20.
KuboS., SakagamiT., and OhjiK., Electric potential CT method based on BEM inverse analyses for measurement of three-dimensional cracks, Computational Mechanics ‘86 (Springer-Verlag) Vol. 1, V-339-V-344.
21.
KuboS., SakagamiT. and OhjiK., Reconstruction of a surface crack by electric-potential CT method, Computational Mechanics ‘88, ed. AtluriS.N. and YagawaG. (Springer, 1988) Vol. 1, 12.i.l-12.i.5.
22.
SakagamiT., KuboS., HashimotoT., YamawakiH. and OhjiK., Quantitative measurement of two-dimensional inclined cracks by the electric-potential CT method with multiple current applications, JSME Int. J., Ser. I, 31 (1988) 76–86.
23.
KuboS., SakagamiT., OhjiK., HashimotoT. and MatsumuroY., Quantitative measurement of three-dimensional surface cracks by the electric-potential CT method, Trans. Jpn. Soc. Mech. Eng., Ser. A, 54 (1988) 218–225.
24.
SakagamiT., KuboS. and OhjiK., A hierarchical inversion analysis scheme for reconstructing 3-D internal crack from electric potential distribution, Proc. ASME1989Pressure Vessels and Piping Conf-JSME Cospon-sorship, Nondestructive Evaluation: NDE Planning and Application ASME, 1989, NDE Vol. 5, 157-162.
25.
SakagamiT., KuboS., OhjiK., YamamotoK. and NakatsukaK., Identification of three-dimensional internal crack by the electric potential CT method, Trans. Jpn. Soc. Mech. Eng., Ser. A, 56 (1990) 27–32.
26.
KuboS. and OhjiK., Applications of the boundary element method to inverse problems, in: Applications of the Boundary Element Method (Corona Publ., 1987) pp. 181–198.
27.
KuboS., Inverse problems related to the mechanics and fracture of solids and structures, JSME Int. J., Ser. I, 31 (1988) 157–166.
28.
KuboS., TsujiM. and OhjiK., Inverse computation of initial residual stress distributions for prediction of fatique crack propagation lives, Trans. Jpn. Soc. Mech. Eng., Ser. A, 54 (1988) 892–899.
29.
MurakamiY. and IsidaM., Analysis of an arbitrarily shaped surface crack and stress field at crack front near surface, Trans. Jpn. Soc. Mech. Eng., Ser A, 51 (1985) 1050–1056.
