The plastic properties that characterize the uniaxial stress–strain response of a plastically isotropic material are not uniquely related to the indentation force versus indentation depth response. We consider results for three sets of plastic material properties that give rise to essentially identical curves of indentation force versus indentation depth in conical indentation. The corresponding surface profiles after unloading are also calculated. These computed results are regarded as the “experimental” data. A simplified Bayesian-type statistical approach is used to identify the values of flow strength and strain hardening exponent for each of the three sets of material parameters. The effect of fluctuations (“noise”) superposed on the “experimental” data is also considered. We build the database for the Bayesian-type analysis using finite element calculations for a relatively coarse set of parameter values and use interpolation to refine the database. A good estimate of the uniaxial stress–strain response is obtained for each material both in the absence of fluctuations and in the presence of sufficiently small fluctuations. Since the indentation force versus indentation depth response for the three materials is nearly identical, the predicted uniaxial stress–strain response obtained using only surface profile data differs little from what is obtained using both indentation force versus indentation depth and surface profile data. The sensitivity of the representation of the predicted uniaxial stress–strain response to fluctuations increases with increasing strain hardening. We also explore the sensitivity of the predictions to the degree of database refinement.
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January 2019
Research-Article
Identification of Plastic Properties From Conical Indentation Using a Bayesian-Type Statistical Approach
Yupeng Zhang,
Yupeng Zhang
Department of Materials Science and
Engineering,
Texas A&M University,
College Station, TX 77843
Engineering,
Texas A&M University,
College Station, TX 77843
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Jeffrey D. Hart,
Jeffrey D. Hart
Professor
Department of Statistics,
Texas A&M University,
College Station, TX 77843
Department of Statistics,
Texas A&M University,
College Station, TX 77843
Search for other works by this author on:
Alan Needleman
Alan Needleman
Professor
Fellow ASME
Department of Materials Science
and Engineering,
Texas A&M University,
College Station, TX 77843
Fellow ASME
Department of Materials Science
and Engineering,
Texas A&M University,
College Station, TX 77843
Search for other works by this author on:
Yupeng Zhang
Department of Materials Science and
Engineering,
Texas A&M University,
College Station, TX 77843
Engineering,
Texas A&M University,
College Station, TX 77843
Jeffrey D. Hart
Professor
Department of Statistics,
Texas A&M University,
College Station, TX 77843
Department of Statistics,
Texas A&M University,
College Station, TX 77843
Alan Needleman
Professor
Fellow ASME
Department of Materials Science
and Engineering,
Texas A&M University,
College Station, TX 77843
Fellow ASME
Department of Materials Science
and Engineering,
Texas A&M University,
College Station, TX 77843
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 23, 2018; final manuscript received August 28, 2018; published online October 1, 2018. Editor: Yonggang Huang.
J. Appl. Mech. Jan 2019, 86(1): 011002 (9 pages)
Published Online: October 1, 2018
Article history
Received:
August 23, 2018
Revised:
August 28, 2018
Citation
Zhang, Y., Hart, J. D., and Needleman, A. (October 1, 2018). "Identification of Plastic Properties From Conical Indentation Using a Bayesian-Type Statistical Approach." ASME. J. Appl. Mech. January 2019; 86(1): 011002. https://doi.org/10.1115/1.4041352
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