Abstract
Background
Residual stresses often cause distortion to occur when machining slender workpieces like those used in aeronautics. This distortion is undesirable and may even cause the workpiece to be scrapped. Identifying these residual stresses during machining is therefore crucial to limit their effect on the final geometry of the part.
Objective
The aim of this work is to identify the through-thickness residual stress distribution by processing displacement/strain fields measured on the workpiece during machining.
Methods
Digital Image Correlation is employed to measure, between successive milling passes, the displacement and strain fields on the lateral surface of the workpiece. These fields are then processed with the Virtual Fields Method to identify the through-thickness residual stress distribution. Compared to previous studies on this topic, no assumption is made concerning the real through-thickness displacement field.
Results
Simulations performed with synthetic data provided by a finite element model show the feasibility of this approach and quantifies its robustness when displacements are affected by measurement noise. Results obtained with this approach in a real case are then compared with their counterparts obtained with another identification technique, which assumes that the workpiece behaves as a beam.
Conclusion
This study shows that it is possible to measure the through-thickness distribution of residual stress in slender workpieces during machining by using a classic subset-based DIC software and the Virtual Fields Method to process the displacement/strain maps. This opens the way for future developments aimed for instance at updating in live machining sequences in order to obtain machined parts immune from distortions caused by residual stresses.
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References
Grédiac M, Hild F (eds) (2012) Full-field measurements and identification in solid mechanics. Wiley, iSBN: 9781848212947, 496 pages
Sutton M, Orteu J, Schreier H (2009) Image Correlation for Shape, Motion and Deformation Measurements. Basic Concepts, Theory and Applications. Springer
Pierron F, Grédiac M (2021) Towards Material Testing 2.0. A review of test design for identification of constitutive parameters from full-field measurements. Strain 57(1):e12,370
Billur E (2020) Digital image correlation: How it changed the bulge test. Metal Forming Magazine pp 978–985
Mishra A, Thuillier S (2014) Investigation of the rupture in tension and bending of DP980 steel sheet. Int J Mech Sci 84:171–181
Pottier T, Vacher P, Toussaint F et al (2012) Out-of-plane testing procedure for inverse identification purpose: Application in sheet metal plasticity. Exp Mech 52(7):951–963
Schwindt CD, Stout M, Iurman L et al (2015) Forming limit curve determination of a dp-780 steel sheet. Procedia Mater Sci 8:978–985
Corigliano P, Crupi V, Pei X et al (2021) DIC-based structural strain approach for low-cycle fatigue assessment of aa 5083 welded joints. Theor Appl Fract Mech 116(103):090
Louëdec GL, Pierron F, Sutton M et al (2013) Identification of the local elasto-plastic behavior of FSW welds using the Virtual Fields Method. Exp Mech 53(5):849–859
Milosevic N, Younise B, Sedmak A et al (2021) Evaluation of true stress-strain diagrams for welded joints by application of digital image correlation. Eng Fail Anal 128(105):609
Texier D, Zedan Y, Amoros T et al (2016) Near-surface mechanical heterogeneities in a dissimilar aluminum alloys friction stir welded joint. Mater Des 108:217–229
Harzallah M, Pottier T, Gilblas R et al (2018) A coupled in-situ measurement of temperature and kinematic fields in ti-6al-4v serrated chip formation at micro-scale. Int J Mach Tools Manuf 130–131:20–35
Rebergue G, Blaysat B, Chanal H et al (2018) Advanced DIC for accurate part deflection measurement in a machining environment. J Manuf Process 33:10–23
Rebergue G, Blaysat B, Chanal H et al (2022) In-situ measurement of machining part deflection with digital image correlation. Measurement 187(110):301
Cheng W, Finnie I (2007) Residual stress measurement and the slitting method. Springer Science & Business Media. https://doi.org/10.1007/978-0-387-39030-7
Dreier S, Denkena B (2014) Determination of residual stresses in plate material by layer removal with machine-integrated measurement. Procedia CIRP 24:103–107
Hospers F, Vogelesang L (1975) Determination of residual stresses in aluminum-alloy sheet material. Exp Mech 15(3):107–110
Jiang LM, Peng J, Liao YG et al (2011) A modified layer-removal method for residual stress measurement in electrodeposited nickel films. Thin Solid Films 519(10):3249–3253
Treuting RG, Read WT (1951) A mechanical determination of biaxial residual stress in sheet materials. J Appl Phys 22:130–134
Salehi SD, Rastak MA, Shokrieh MM et al (2020) Full-field measurement of residual stresses in composite materials using the incremental slitting and digital image correlation techniques. Exp Mech 60(9):1239–1250
Olson MD, Watanabe BT, Wong TA et al (2022) Near surface residual stress measurement using slotting. Experimental Mechanics Accepted, online
Prime MB, Hill MR (2002) Residual stress, stress relief, and inhomogeneity in aluminum plate. Scr Mater 46(1):77–82
Baldi A (2014) Residual stress measurement using hole drilling and integrated digital image correlation techniques. Exp Mech 54(3):379–391
Baldi A (2019) On the implementation of the integral method for residual stress measurement by integrated digital image correlation. Exp Mech 59(7):1007–1020
Gao J, Shang H (2009) Deformation pattern based digital image correlation method and its application to residual stress measurement. Appl Opt 48(7):1371–1381
Razumovskii IA, Usov SM (2021) Development of the hole-drilling method as applied to the study of inhomogeneous residual stress fields. J Mach Manuf Reliab 50(8):727–734
ASTM (2021) ASTM E 837: Standard test method for determining residual stress by the hole drilling strain-gauge method. https://www.astm.org/standards/e837, ASTM Standard, American Society for Testing and Materials
Jovani T, Chanal H, Blaysat B et al (2022) Direct residual stress identification during machining. J Manuf Process. https://doi.org/10.1016/j.jmapro.2022.08.015, accepted, online
Pierron F, Sutton MA et al (2011) Ultra high speed DIC and Virtual Fields Method analysis of a three-point bending impact test on an aluminium bar. Exp Mech 51(4):537–563
Berry A, Olivier R (2016) Identification of spatially correlated excitations on a bending plate using the Virtual Fields Method. J Sound Vib 375:76–91
Berry A, Robin O, Pierron F (2014) Identification of dynamic loading on a bending plate using the Virtual Fields Method. J Sound Vib 333(26):7151–7164
Kaufmann R, Ganapathisubramani B, Pierron F (2019) Full-field surface pressure reconstruction using the Virtual Fields Method. Exp Mech 59(8):1203–1221
O’Donoughue P, Robin O, Berry A (2019) Time-space identification of mechanical impacts and distributed random excitations on plates and membranes. Proc Inst Mech Eng C J Mech Eng Sci 233(18):6436–6447
Olufsen SN, Kaufmann R, Fagerholt E et al (2022) RECOLO: A Python package for the reconstruction of surface pressure loads from kinematic fields using the Virtual Fields Method. J Open Source Softw 7(71):3980
Kaufmann R, Olufsen S, Fagerholt E et al (2022) Reconstruction of surface pressures on flat plates impacted by blast waves using the virtual fields method. Int J Impact Eng p 104369
Grédiac M, Sur F, Blaysat B (2016) The grid method for in-plane displacement and strain measurement: a review and analysis. Strain 52(3):205–243
Cao Q, Li Y, Xie H (2020) Orientation-identified Virtual Fields Method combined with moiré interferometry for mechanical characterization of single crystal Ni-based superalloys. Opt Lasers Eng 125:105,854
Pierron F, Grédiac M (2012) The Virtual Fields Method. Springer, 517 pages, ISBN: 978-1-4614-1823-8
Martins J, Andrade-Campos A, Thuillier S (2018) Comparison of inverse identification strategies for constitutive mechanical models using full-field measurements. Int J Mech Sci 145:330–345
Zhang L, Thakku S, Beotra M et al (2017) Verification of a Virtual Fields Method to extract the mechanical properties of human optic nerve head tissues in vivo. Biomech Model Mechanobiol 16(3):871–887
Dym J, Shames H (1973) Solid Mechanics: A Variational Approach. McGraw-Hill Book Company, New York, 685 pages, ISBN: 978-0070185562
Grédiac M (1989) Principe des travaux virtuels et identification. Comptes Rendus de l’Académie des Sciences 309-II:1–5. Gauthier-Villars. In French with abridged English version
Cherif I, Cotton D, Poulachon G et al (2019) Instrumented clamping device and numerical simulations to study machining distortion. Int J Adv Manuf Technol 105(7):3093–3103
Avril S, Grédiac M, Pierron F (2004) Sensitivity of the virtual fields method to noisy data. Comput Mech 34:439–452
International Digital Image Correlation Society, Jones EMC, Iadicola MA (Eds) (2018) A good practices guide for Digital Image Correlation. https://doi.org/10.32720/idics/gpg.ed1, online
Acknowledgements
This work has been sponsored by the French government research program “Investissements d’Avenir” through the IDEX-ISITE initiative 16-IDEX-0001 (CAP 20-25). The authors also gratefully acknowledge the financial supports from the French National Research Agency (ANR) through the ICAReS and IMaDe projects (ANR-18-CE08-0028-01 and ANR-19-CE10-0002 grants, respectively), and from the AURA regional council.
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Jovani, T., Blaysat, B., Chanal, H. et al. Applying the Virtual Fields Method to Measure During Milling the Through-Thickness Residual Stress Distribution in Aluminum-Alloy Sheet Material. Exp Mech 63, 221–235 (2023). https://doi.org/10.1007/s11340-022-00909-8
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DOI: https://doi.org/10.1007/s11340-022-00909-8