Research Papers

Prediction of Asymmetric Yield Strengths of Polymeric Materials at Tension and Compression Using Spherical Indentation

[+] Author and Article Information
Noriyuki Inoue, Yousuke Watanabe

Department of Precision Mechanics,
Chuo University,
1-13-27 Kasuga, Bunkyo,
Tokyo 112-8551, Japan

Akio Yonezu

Department of Precision Mechanics,
Chuo University,
1-13-27 Kasuga, Bunkyo,
Tokyo 112-8551, Japan
e-mail: yonezu@mech.chuo-u.ac.jp

Hiroshi Yamamura

Department of Integrated Science
and Engineering for Sustainable Society,
Chuo University,
1-13-27 Kasuga, Bunkyo,
Tokyo 112-8551, Japan

Baoxing Xu

Department of Mechanical and
Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: bx4c@virginia.edu

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received May 5, 2016; final manuscript received September 7, 2016; published online February 1, 2017. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 139(2), 021002 (Feb 01, 2017) (11 pages) Paper No: MATS-16-1133; doi: 10.1115/1.4035268 History: Received May 05, 2016; Revised September 07, 2016

Engineering polymers generally exhibit asymmetric yield strength in tension and compression due to different arrangements of molecular structures in response to external loadings. For the polymeric materials whose plastic behavior follows the Drucker–Prager yield criterion, the present study proposes a new method to predict both tensile and compressive yield strength utilizing instrumented spherical indentation. Our method is decomposed into two parts based on the depth of indentation, shallow indentation, and deep indentation. The shallow indentation is targeted to study elastic deformation of materials, and is used to estimate Young's modulus and yield strength in compression; the deep indentation is used to achieve full plastic deformation of materials and extract the parameters in Drucker–Prager yield criterion associated with both tensile and compressive yield strength. Extensive numerical computations via finite element method (FEM) are performed to build a dimensionless function that can be employed to describe the quantitative relationship between indentation force-depth curves and material parameters of relevance to yield criterion. A reverse algorithm is developed to determine the material properties and its robustness is verified by performing both numerical and experimental analysis.

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Fig. 1

True stress-true strain curves in uniaxial tension and compression test for polycarbonate (PC) at strain rate of 10−3 s−1

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Fig. 2

Relationship between yield strength and strain rate obtained from tension and compression tests

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Fig. 3

Indentation curves of shallow indentation using spherical indenter R = 500 μm for PC (a) and PMMA (b)

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Fig. 4

Calculated Young's modulus with respected to indentation depth during loading process for PC (a) and PMMA (b)

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Fig. 5

Relationships between indentation force and depth h3/2 for PC (a) and PMMA (b)

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Fig. 6

Two-dimensional model of FEM computation for spherical indentation

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Fig. 7

Examples of indentation curve, in which it investigates the effect of the yield strength σY (a) and the parameter α (b)

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Fig. 8

Relationship between (F(h/R=0.5)/σY⋅h2) and (E∗/σr) at each parameter α

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Fig. 9

Contour map of error distribution for σY (a) and differences (input value—estimation value) of parameter α (b)

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Fig. 10

Comparison between the input value and the estimation from reverse analysis for representative materials for sensitivity analysis

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Fig. 11

Indentation curves of deep indentation test using spherical indenter R = 20 μm for PC (a) and PMMA (b)

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Fig. 12

Relationships between the yield strength σY and parameter α, which are from theory (Eq. (6)) and experimental estimation from Eq. (12) for PC (a) and PMMA (b).

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Fig. 13

Changes in coefficients (A1, A2, and A3) in Table 2 with respect to parameter α




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