Indentation of a Sensitive Clay by a Flat-Ended Axisymmetrical Punch

  • Mireille Sandrine Ewane
  • Vincenzo Silvestri
  • Michael James
Original Paper
  • 2 Downloads

Abstract

This paper presents a description and the results of instrumented macro-scale laboratory indentation testing of Champlain Sea Clay with a stainless steel, flat-tipped, cylindrical indenter. The results of the tests were analyzed using published analytical solutions for the indentation testing of elastic–plastic materials. The relationship between the depth of indentation, h, and the load on the indenter, P, the hardness, the undrained shear strength and the Young’s modulus of the clay were determined from these methods. The undrained shear strength and Young’s modulus were compared to values from conventional geotechnical testing. Indentation testing was simulated numerically using the finite element method. The clay was modelled using the conventional Mohr–Coulomb elastic–plastic model. The distribution of total vertical stress below the indenter from the simulations compared well with an analytical solution based on elastic theory. The simulations using material properties derived from the conventional geotechnical tests (Set 1) and derived from the indentation testing (Set 2) with a Poisson’s ratio of 0.49 (undrained loading) did not produce load-penetration (Ph) curves in good agreement with the curves from indentation testing. However, simulations with the material properties derived from indentation testing and a Poisson’s ratio of 0.2 (drained loading), produced load-penetration curves in good agreement with the indentation testing results.

Keywords

Indentation tests Cylindrical flat-ended indenter Champlain Sea clay Elastic–plastic Numerical simulation 

Notes

Acknowledgements

The authors express their gratitude to the National Sciences and Engineering Research Council of Canada for the financial support received during this study.

References

  1. Attaf MT (2004) Connection between the loading curve models in elastoplastic indentation. Mater Lett 58(27–28):3491–3498.  https://doi.org/10.1016/j.matlet.2004.06.049 CrossRefGoogle Scholar
  2. Barquins M, Maugis D (1982) Adhesive contact of axisymmetric punches on an elastic half-space-the modified Hertz-Hubers stress tensor for contacting spheres. J Mec Theor Appl 1(2):331–357Google Scholar
  3. Bhattacharya A, Nix W (1988) Finite element simulation of indentation experiments. Int J Solids Struct 24(9):881–891CrossRefGoogle Scholar
  4. Bishop R, Hill R, Mott N (1945) The theory of indentation and hardness tests. Proc Phys Soc 57(3):147CrossRefGoogle Scholar
  5. Boussinesq J (1885) Application des potentiels à l’étude de l’équilibre et du mouvement des solides élastiques. Gauthier-Villars, Paris, LilleGoogle Scholar
  6. Bowles JE (1996) Foundation analysis and design. McGraw Hill Companies, New YorkGoogle Scholar
  7. Box GEP, Cox DR (1964) An analysis of transformations. J R Stat Soc Ser B (Methodol) 26(2):211–252Google Scholar
  8. Brinell JA (1900) Way of determining the hardness of bodies and some applications of the same. Teknisk Tidskrift 5:69Google Scholar
  9. Briscoe BJ, Sebastian KS, Adams MJ (1994) The effect of indenter geometry on the elastic response to indentation. J Phys D Appl Phys 27(6):1156–1162.  https://doi.org/10.1088/0022-3727/27/6/013 CrossRefGoogle Scholar
  10. Briscoe BJ, Fiori L, Pelillo E (1998) Nano-indentation of polymeric surfaces. J Phys D Appl Phys 31(19):2395–2405.  https://doi.org/10.1088/0022-3727/31/19/006 CrossRefGoogle Scholar
  11. Chen W-Q (1999) Inclined circular flat punch on a transversely isotropic piezoelectric half-space. Arch Appl Mech 69(7):455–464CrossRefGoogle Scholar
  12. Chen K, Meng W, Mei F, Hiller J, Miller D (2011) From micro-to nano-scale molding of metals: size effect during molding of single crystal Al with rectangular strip punches. Acta Mater 59(3):1112–1120CrossRefGoogle Scholar
  13. Cheng YT, Cheng CM (2004) Scaling, dimensional analysis, and indentation measurements. Mater Sci Eng R Rep 44(4):91–149CrossRefGoogle Scholar
  14. Chitkara NR, Butt MA (1992) Numerical construction of axisymmetric slip-line fields for indentation of thick blocks by rigid conical indenters and friction at the tool-metal interface. Int J Mech Sci 34(11):849–862.  https://doi.org/10.1016/0020-7403(92)90016-a CrossRefGoogle Scholar
  15. Datsko J (1966) Material properties and manufacturing processes. Wiley, New YorkGoogle Scholar
  16. Datsko J (1977) Materials in design and manufacturing. Malloy, Ann Harbor, MichiganGoogle Scholar
  17. Desai C, Zaman M, Lightner J, Siriwardane H (1984) Thin-layer element for interfaces and joints. Int J Numer Anal Methods Geomech 8(1):19–43CrossRefGoogle Scholar
  18. Desai C, Muqtadir A, Scheele F (1986) Interaction analysis of anchor-soil systems. J Geotech Eng 112(5):537–553CrossRefGoogle Scholar
  19. Doerner M, Nix W (1986) A method for interpreting the data from depth-sensing indentation instruments. J Mater Res 1(4):601–609CrossRefGoogle Scholar
  20. Fischer-Cripps AC (2007) Mechanical properties of materials. In: Introduction to contact mechanics, pp 1–30Google Scholar
  21. Fischer-Cripps A (2009) The IBIS handbook of nanoindentation. Fisher-Cripps Laboratories, SydneyGoogle Scholar
  22. Fischer-Cripps AC (2011) Contact mechanics. In: Nanoindentation. Springer, New York, pp 1–19Google Scholar
  23. Guha S, Sangal S, Basu S (2014) Numerical investigations of flat punch molding using a higher order strain gradient plasticity theory. Int J Mater Form 7(4):459–467CrossRefGoogle Scholar
  24. Häggblad B, Nordgren G (1987) Modelling nonlinear soil-structure interaction using interface elements, elastic–plastic soil elements and absorbing infinite elements. Comput Struct 26(1–2):307–324CrossRefGoogle Scholar
  25. Harding JW, Sneddon IN (1945) The elastic stresses produced by the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch. In: Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University Press, pp 16–26Google Scholar
  26. Houlsby GT, Wroth CP (1982) Direct solution of plasticity problems in soils by the method of characteristics. In: NASA STI/Recon Technical Report N. AA (Oxford University (England)), AB (Oxford University (England)), Presented at 4th international conference on numerical methods in geomechanics, Edmonton, p 21192Google Scholar
  27. Hu Z, Lynne KJ, Markondapatnaikuni SP, Delfanian F (2013) Material elastic–plastic property characterization by nanoindentation testing coupled with computer modelling. Mater Sci Eng A 587:268–282CrossRefGoogle Scholar
  28. Hu Z, Lynne K, Delfanian F (2015) Characterization of materials’ elasticity and yield strength through micro-/nano-indentation testing with a cylindrical flat-tip indenter. J Mater Res 30(04):578–591CrossRefGoogle Scholar
  29. Johnson K (1985) Contact Mechanics. Cambridge University Press, LondonCrossRefGoogle Scholar
  30. Johnson W, Mahtab F, Williams A (1965) Experiments concerning geometric similarity in indentation. Int J Mech Sci 7(6):389–398CrossRefGoogle Scholar
  31. Kou S-Q, Huang Y, Tan X-C, Lindqvist P-A (1998) Identification of the governing parameters related to rock indentation depth by using similarity analysis. Eng Geol 49(3–4):261–269CrossRefGoogle Scholar
  32. Lockett FJ (1963) Indentation of a rigid/plastic material by a conical indenter. J Mech Phys Solids 11(5):345–355.  https://doi.org/10.1016/0022-5096(63)90035-8 CrossRefGoogle Scholar
  33. Love AEH (1939) Boussinesq’s problem for a rigid cone. Q J Math 10(1):161–175.  https://doi.org/10.1093/qmath/os-10.1.161 CrossRefGoogle Scholar
  34. Marsh D (1964) Plastic flow in glass. In: Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences. The Royal Society, pp 420–435Google Scholar
  35. Mott BW (1956) Micro-indentation hardness testing. Butterworths Scientific Publications, OxfordGoogle Scholar
  36. Mulhearn T (1959) The deformation of metals by Vickers-type pyramidal indenters. J Mech Phys Solids 7(2):85–88CrossRefGoogle Scholar
  37. Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7(06):1564–1583CrossRefGoogle Scholar
  38. Pharr GM, Oliver WC, Brotzen FR (1992) On the generality of the relationship among contact stiffness, contact area, and elastic-modulus during indentation. J Mater Res 7(3):613–617.  https://doi.org/10.1557/Jmr.1992.0613 CrossRefGoogle Scholar
  39. Ramaekers J, Veenstra P (1970) The relation between effective deformation and micro-hardness in a state of large plastic deformation. Ann CIRP 18:541–545Google Scholar
  40. Samuels L, Mulhearn T (1957) An experimental investigation of the deformed zone associated with indentation hardness impressions. J Mech Phys Solids 5(2):125–134CrossRefGoogle Scholar
  41. Schubert G (1942) Zur Frage der Druckverteilung unter elastisch gelagerten Tragwerken. Ingenieur Arch 13(3):132–147.  https://doi.org/10.1007/BF02095912 CrossRefGoogle Scholar
  42. Shield RT (1955) On the plastic flow of metals under conditions of axial symmetry. In: Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences. The Royal Society, pp 267–287Google Scholar
  43. Sneddon IN (1946) Boussinesq’s problem for a flat-ended cylinder. In: Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University Press, pp 29–39Google Scholar
  44. Sneddon I (1951) Fourier Transforms, 542. McGraw-Hill, New YorkGoogle Scholar
  45. Stronge W (1990) Plane punch indentation of anisotropic elastic half space. J Appl Mech 57:85Google Scholar
  46. Tabor D (1951) The hardness of metals. Oxford University Press, LondonGoogle Scholar
  47. Timoshenko S (1934) Theory of elasticity, 1st edn. Mcgraw-Hill Book Company Inc., New YorkGoogle Scholar
  48. Timoshenko S, Goodier J (1951) Theory of elasticity. McGraw-Hill book Company, New YorkGoogle Scholar
  49. Wang S, Sloan S, Liu H, Tang C (2011) Numerical simulation of the rock fragmentation process induced by two drill bits subjected to static and dynamic (impact) loading. Rock Mech Rock Eng 44(3):317–332CrossRefGoogle Scholar
  50. Wright S, Huang Y, Fleck N (1992) Deep penetration of polycarbonate by a cylindrical punch. Mech Mater 13(4):277–284CrossRefGoogle Scholar
  51. Xu H, Pharr G (2006) An improved relation for the effective elastic compliance of a film/substrate system during indentation by a flat cylindrical punch. Scripta Mater 55(4):315–318CrossRefGoogle Scholar
  52. Yang J, Ke L-L (2008) Two-dimensional contact problem for a coating–graded layer–substrate structure under a rigid cylindrical punch. Int J Mech Sci 50(6):985–994CrossRefGoogle Scholar
  53. Zeng K, Chiu CH (2001) An analysis of load-penetration curves from instrumented indentation. Acta Mater 49(17):3539–3551.  https://doi.org/10.1016/S1359-6454(01)00245-2 CrossRefGoogle Scholar
  54. Zhang P, Li S, Zhang Z (2011) General relationship between strength and hardness. Mater Sci Eng A 529:62–73CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Mireille Sandrine Ewane
    • 1
  • Vincenzo Silvestri
    • 1
  • Michael James
    • 2
  1. 1.Department of Civil, Geological, and Mining EngineeringÉcole PolytechniqueMontréalCanada
  2. 2.Research Institute on Mines and Environment UQAT- PolytechniqueRouyn-NorandaCanada

Personalised recommendations