Abstract
This paper deals with the accurate calculation of strain using the grid method. The strain field is first directly deduced from the fringe pattern without calculating the displacement field. This procedure is validated with two numerical examples. Two types of experiment are then carried out: a translation and a tensile test. It is observed that some additional fictitious strains appear in both cases. They are due to two main reasons which interact with each other: the grid defects and the displacement of the grid lines during testing. A suitable procedure is proposed to cancel out these fictitious strains. This procedure is successfully applied in two cases of fringe patterns.
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Patterson E, Brailly P, Burgete R, Hack E, Siebert T, Whelan M (2007) A challenge for high performance full-strain measurement system. Strain 43(3):167–180
Kim JH, Pierron F, Wisnom MR, Syed-Muhamad K (2007) Identification of the local stiffness reduction of a damaged composite plate using the virtual fields method. Composites Part A 38(9):2065–2075
Hamam R, Hild F, Roux S (2007) Stress intensity factor gauging by digital image correlation: application in cyclic loading. Strain 43(3):181–192
Tabourot L, Vacher P, Coudert T, Toussaint T, Arrieux R (2005) Numerical determination of strain localization during finite element simulation of deep-drawing operations. J Mater Process Technol 159(2):152–158
Kobayashi A (1993) Handbook on experimental mechanics. Wiley, New York
Surrel Y (1994) Moiré and grid methods in optics: a signal-processing approach. Proceedings of the SPIE 2342:213–220
Cordero RR, Molimard J, Labbé F, Matinez A (2008) Strain maps obtained by phase-shifting interferometry: an uncerntainty analysis. Optics Commun 281:2195–2206
Avril S, Feissel P, Pierron F, Villon P (2008) Estimation of the strain field from full-field displacement noisy data. Eur J Comput Mech 17(5–7):857–868
Sciammarella CA, Narayanan R (1984) The determination of the componentss of the strain tensor in holographic interferometry. Exp Mech 24(5):257–264
Dupré JC, Brémand F, Lagarde A (1993) Numerical spectral analysis of a grid: application to strain measurements. Opt Lasers Eng 18(3):159–172
Sciammarella CA, Kim T (2005) Frequency modulation interpretation of fringes and computation of strains. Exp Mech 45(5):393–403
Schroeter BM, McDowell DL (2003) Measurement of deformation fields in polycrystalline ofhc copper. Int J Plast 19:1355–1376
Moulart R, Rotinat R, Pierron F, Lerondel G (2007) On the realization of microscopic grids for local strain measurement by direct interferometric photolithography. Opt Lasers Eng 45(12):1131–1147
Piro JL, Grédiac M (2004) Producing and transferring low-spatial-frequency grids for measuring displacement fields with moiré and grid methods. Exp Tech 28(4):23–26
Sciammarella CA, Kim T (2003) Determination of strains from fringe patterns using space-frequency representation. Optic Eng 42(11):3182–3193
Surrel Y (2000) Fringe analysis, chapter photomechanics, Topics Appl Phys 77:55–102
Papoulis A (1962) The Fourier integral and its applications. McGraw-Hill. New York
Mallat S (1999) A wavelet tour of signal processing. Academic, London
Cherbuliez M, Jacquot P, Colonna de Lega X (1999) Wavelet processing of interferometric signals and fringe patterns. In SPIE, editor, SPIE conference on wavelet applications in signal and image processing VII, vol. 3813, pp. 692–702
Kadooka K, Kunoo K, Uda N, Ono K, Nagayasu T (2003) Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform. Exp Mech 43:45–51
Zhong J, Weng J (2005) Phase retrieval of optical fringe pattern from the ridge of a wavelet transform. Optic Lett 19:2560–2562
Quan C, Fu Y, Tay CJ, Tan JM (2005) Profiling of objects with height steps by wavelet analysis of shadow moiré fringes. Appl Optic 44(15):3284–3290
Lui H, Cartwright AN, Basaran C (2004) Moiré interferogram phase extraction: a ridge detection algorithm for continuous wavelet transform. Appl Optic 43(4):850–856
Fu Y, Tay CJ, Quan C, Chen LJ (2004) Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry. Optic Eng 43(11):2780–2787
Huntley JM (1989) Noise-immune phase unwrapping algorithm. Appl Optic 28(16):2780–2787
Bornert M, Brémand F, Doumalin P, Dupré JC, Fazzini M, Grédiac M, Hild F, Mistou S, Molimard J, Orteu JJ, Robert L, Surrel Y, Vacher P, Wattrisse B (2008) Assessment of digital image correlation measurement errors: methodology and results. Exp Mech (in press)
Haddadi H, Belhabib S (2008) Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique. Opt Lasers Eng 46(2):185–196
Kaiser G, Schneider W (2008) Estimation of sensor point spread function by spatial subpixel analysis. Int J Remote Sensing 29(7–8):2137–2155
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Ms. M. Georgescu is gratefully acknowledged for her help in the characterization of the grid with a microscope.
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Badulescu, C., Grédiac, M., Mathias, J.D. et al. A Procedure for Accurate One-Dimensional Strain Measurement Using the Grid Method. Exp Mech 49, 841–854 (2009). https://doi.org/10.1007/s11340-008-9203-8
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DOI: https://doi.org/10.1007/s11340-008-9203-8