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An Inverse Identification Method for the Characterization of Elastic Conforming Contact Behavior During Flat Punch Indentation

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Abstract

Background

The flat punch indentation problem is a typical prototype of conforming contact which can be frequently encountered in many applications. Its characterization is of great difficulty as the interface is embedded and the stress is highly concentrated at the contact boundary.

Objective

In this work, an inverse identification method is developed for reconstructing the interfacial stress during flat punch indentation from the measured displacement field.

Methods

This method consists of a modeling procedure and a characterization procedure. In the modeling, the basic tendencies of interfacial stress distributions are established and the relationship between the stress and displacement are formulated. In the characterization, the parameters in the model, including the profiles of contact interface and the stress distributions are optimized by matching the calculated displacement to the experiment data. Segmentation-aided digital image correlation is implemented for the displacement acquisition near the contact interface. An optimization framework is developed so the different kinds of parameters can be accurately obtained.

Results

Both of simulated experiment and real-world experiment are carried out, and results show that the proposed method can accurately characterize the elastic contact behavior.

Conclusions

The modeling merely constrains the tendencies rather than gives a close-form solution of interfacial stress and the identification only requires the measurement of local displacement, which can greatly increase its applicability in applications.

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References

  1. Patil SS, Karuppanan S, Atanasovska I (2016) Experimental measurement of strain and stress state at the contacting helical gear pairs. Measurement 82:313–322. https://doi.org/10.1016/j.measurement.2015.12.046

    Article  Google Scholar 

  2. Wang Y, Zou B, Huang C, Qi H, Song J (2019) Feasibility study of the ti(c7n3)-based cermet micro-mill based on dynamic fatigue behavior and modeling of the contact stress distribution on the round cutting edge. Int J Mech Sci 155:143–158. https://doi.org/10.1016/j.ijmecsci.2019.02.038

    Article  Google Scholar 

  3. Yongsheng L, Yuanzhong H, Linqing Z (1999) Adhesive Contact of Flat-Ended Wedges: Theory and Computer Experiments. J Tribol 121(1):128–132. https://doi.org/10.1115/1.2833793

    Article  Google Scholar 

  4. Johnson KL (1987) Contact mechanics, Cambridge University Press

  5. Sun C, Li Y, Chen J (2020) Strain concentration characterization for the multi-tooth contact based on multi-resolution digital image correlation and orthogonal analysis. Int J Mech Sci 167. https://doi.org/10.1016/j.ijmecsci.2019.105238

  6. Witek L (2006) Failure analysis of turbine disc of an aero engine. Eng Fail Anal 13(1):9–17. https://doi.org/10.1016/j.engfailanal.2004.12.028

    Article  Google Scholar 

  7. Sinclair GB (2017) Friction Effects on the Edge-of-Contact Stresses for Sliding Contact Between a Flat Punch With Rounded Corners and a Half Space. J Appl Mech. 84(12):121002. https://doi.org/10.1115/1.4037968

  8. Delaine-Smith R, Burney S, Balkwill F, Knight M (2016) Experimental validation of a flat punch indentation methodology calibrated against unconfined compression tests for determination of soft tissue biomechanics. J Mech Behav Biomed Mater 60:401–415. https://doi.org/10.1016/j.jmbbm.2016.02.019

    Article  Google Scholar 

  9. Cao Y, Ma D, Raabe D (2009) The use of flat punch indentation to determine the viscoelastic properties in the time and frequency domains of a soft layer bonded to a rigid substrate. Acta Biomater 5(1):240–248. https://doi.org/10.1016/j.actbio.2008.07.020

    Article  Google Scholar 

  10. Nowell D, Dini D, Hills D (2006) Recent developments in the understanding of fretting fatigue. Engineering Fracture Mechanics. Advanced Fracture Mechanincs for Life Safety Assessments 73(2):207–222. https://doi.org/10.1016/j.engfracmech.2005.01.013

  11. Barber J (2018) Contact Mechanics. Springer International Publishing, Solid Mechanics and Its Applications

    Book  Google Scholar 

  12. Fabrikant VI (1986) Inclined Flat Punch of Arbitrary Shape on an Elastic Half-Space. J Appl Mech 53(4):798–806. https://doi.org/10.1115/1.3171861

    Article  MATH  Google Scholar 

  13. Sackfield A, Mugadu A, Barber J, Hills D (2003) The application of asymptotic solutions to characterising the process zone in almost complete frictionless contacts. J Mech Phys Solids 51(7):1333–1346. https://doi.org/10.1016/S0022-5096(03)00020-6

    Article  MATH  Google Scholar 

  14. Jaffar M (2002) Frictionless contact between an elastic layer on a rigid base and a circular flat-ended punch with rounded edge or a conical punch with rounded tip. Int J Mech Sci 44(3):545–560. https://doi.org/10.1016/S0020-7403(01)00104-7

    Article  MATH  Google Scholar 

  15. Zhang Z, Kristiansen H, Liu J (2007) A method for determining elastic properties of micron-sized polymer particles by using flat punch test. Comput Mater Sci 39(2):305–314. https://doi.org/10.1016/j.commatsci.2006.06.009

    Article  Google Scholar 

  16. Nguyen VT, Hwu C (2020) Indentation by multiple rigid punches on two-dimensional anisotropic elastic or viscoelastic solids. Int J Mech Sci 178. https://doi.org/10.1016/j.ijmecsci.2020.105595

  17. Scheibert J, Prevost A, Debrégeas G, Katzav E, Adda-Bedia M (2009) Stress field at a sliding frictional contact: Experiments and calculations. J Mech Phys Solids 57(12):1921–1933. https://doi.org/10.1016/j.jmps.2009.08.008

    Article  MathSciNet  MATH  Google Scholar 

  18. Kane BJ, Cutkosky MR, Kovacs GT (2000) A traction stress sensor array for use in high-resolution robotic tactile imaging. J Microelectromech Syst 9(4):425–434. https://doi.org/10.1109/84.896763

    Article  Google Scholar 

  19. Spitas VA, Costopoulos TN, Spitas CA (2006) Optimum gear tooth geometry for minimum fillet stress using bem and experimental verification with photoelasticity. J Mech Des 128(5):1159–1164. https://doi.org/10.1115/1.2216731

    Article  MATH  Google Scholar 

  20. Burguete R, Patterson E (1997) A photoelastic study of contact between a cylinder and a half-space. Exp Mech 37(3):314–323. https://doi.org/10.1007/BF02317424

    Article  Google Scholar 

  21. Papadopoulos G (2004) Experimental estimation of the load distribution in bearings by the method of caustics. Exp Mech 44(4):440–443. https://doi.org/10.1007/BF02428098

    Article  Google Scholar 

  22. Li M, Zhang J, Fang J, Shu D, Stronge W (2006) Dynamic analysis of contact forces in disc assemblies by the shadow method of caustics. J Strain Anal Eng Design 41(8):609–622. https://doi.org/10.1243/03093247JSA107

    Article  Google Scholar 

  23. Yoon SH, Siviour CR (2018) Application of the virtual fields method to a relaxation behaviour of rubbers. J Mech Phys Solids 116:416–431. https://doi.org/10.1016/j.jmps.2016.09.001

  24. Zhang Z, Pan B, Grédiac M, Song W (2018) Accuracy-enhanced constitutive parameter identification using virtual fields method and special stereo-digital image correlation. Opt Lasers Eng 103:55–64. https://doi.org/10.1016/j.optlaseng.2017.11.016

    Article  Google Scholar 

  25. Wang W, Mottershead JE, Sebastian CM, Patterson EA (2011) Shape features and finite element model updating from full-field strain data. Int J Solids Struct 48(11):1644–1657. https://doi.org/10.1016/j.ijsolstr.2011.02.010

    Article  MATH  Google Scholar 

  26. He T, Liu L, Makeev A (2018) Uncertainty analysis in composite material properties characterization using digital image correlation and finite element model updating. Compos Struct 184:337–351. https://doi.org/10.1016/j.compstruct.2017.10.009

    Article  Google Scholar 

  27. Sutton M, Wolters W, Peters W, Ranson W, McNeill S (1983) Determination of displacements using an improved digital correlation method. Image Vis Comput 1(3):133–139. https://doi.org/10.1016/0262-8856(83)90064-1

    Article  Google Scholar 

  28. Chen B, Zhao J, Pan B (2020) Mirror-assisted multi-view digital image correlation with improved spatial resolution. Exp Mech 60:283–293. https://doi.org/10.1007/s11340-019-00563-7

    Article  Google Scholar 

  29. Xie HM, Yang W, Kang YL, Zhang Q, Han B, Qiu W (2021) In-situ strain field measurement and mechano-electro-chemical analysis of graphite electrodes via fluorescence digital image correlation. Exp Mech. https://doi.org/10.1007/s11340-021-00749-y

  30. 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. https://doi.org/10.1111/str.12182

    Article  Google Scholar 

  31. Jin H, Haldar S, Bruck HA, Lu W-Y (2011) Grid method for microscale discontinuous deformation measurement. Exp Mech 51:565–574. https://doi.org/10.1007/s11340-010-9459-7

    Article  Google Scholar 

  32. Viala R, Placet V, Cogan S (2018) Identification of the anisotropic elastic and damping properties of complex shape composite parts using an inverse method based on finite element model updating and 3d velocity fields measurements (femu-3dvf): Application to bio-based composite violin soundboards. Compos A Appl Sci Manuf 106:91–103. https://doi.org/10.1016/j.compositesa.2017.12.018

    Article  Google Scholar 

  33. Chemisky Y, Meraghni F, Bourgeois N, Cornell S, Echchorfi R, Patoor E (2015) Analysis of the deformation paths and thermomechanical parameter identification of a shape memory alloy using digital image correlation over heterogeneous tests. Int J Mech Sci 96:13–24. https://doi.org/10.1016/j.ijmecsci.2015.03.007

    Article  Google Scholar 

  34. Mathieu F, Hild F, Roux S (2012) Identification of a crack propagation law by digital image correlation. Int J Fatigue 36(1):146–154. https://doi.org/10.1016/j.ijfatigue.2011.08.004

    Article  Google Scholar 

  35. Sun C, Zhou Y, Chen J, Miao H (2017) Modeling and experimental identification of contact pressure and friction for the analysis of non-conforming elastic contact. Int J Mech Sci 133:449–456. https://doi.org/10.1016/j.ijmecsci.2017.09.007

    Article  Google Scholar 

  36. Sun C, Zhou Y, Chen J, Miao H (2015) Measurement of deformation close to contact interface using digital image correlation and image segmentation. Exp Mech 55(8):1525–1536. https://doi.org/10.1007/s11340-015-0055-8

    Article  Google Scholar 

  37. Zhang ZF, Kang YL, Wang HW, Qin QH, Qiu Y, Li XQ (2006) A novel coarse-fine search scheme for digital image correlation method. Measurement 39(8):710–718. https://doi.org/10.1016/j.measurement.2006.03.008

    Article  Google Scholar 

  38. Nocedal J, Wright S (2006) Numerical Optimization. Springer, New York

    MATH  Google Scholar 

Download references

Acknowledgements

This research work was supported by the National Natural Science Foundation of China, Grant Nos. 11902196 and 11732009, the supports are gratefully acknowledged.

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Correspondence to J. B. Chen.

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Sun, C., Lin, Q.L. & Chen, J.B. An Inverse Identification Method for the Characterization of Elastic Conforming Contact Behavior During Flat Punch Indentation. Exp Mech 62, 745–759 (2022). https://doi.org/10.1007/s11340-021-00811-9

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