Research Papers

Polymer Modulus of Elasticity and Hardness From Impact Data

[+] Author and Article Information
Hany A. Sherif

Department of Mechanical Engineering,
College of Engineering-Qassim University,
P.O. Box 6677,
Buraidah 51452, Saudi Arabia
e-mail: hasherif@qec.edu.sa

Fahad A. Almufadi

Department of Mechanical Engineering,
College of Engineering-Qassim University,
P.O. Box 6677,
Buraidah 51452, Saudi Arabia
e-mail: almufadi@qec.edu.sa

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received March 22, 2018; final manuscript received July 4, 2018; published online August 20, 2018. Assoc. Editor: Tetsuya Ohashi.

J. Eng. Mater. Technol 141(1), 011010 (Aug 20, 2018) (8 pages) Paper No: MATS-18-1082; doi: 10.1115/1.4040830 History: Received March 22, 2018; Revised July 04, 2018

The present paper introduces a simple method to predict the modulus of elasticity and the hardness of polymeric materials that range from soft elastomers to hard plastics. Hertzian elastic impact model is used to define the relationship between the contact time duration and the maximum force of normal contact due to the impact of a hard sphere indenter with the tested polymer sample. It is shown that the adopted model and experimental method can be used as a tool for extracting the magnitude of the complex modulus of elasticity. Moreover, a new impact index is shown to be proportional to the polymer shore hardness. Theoretical and experimental results based on the force–time signals are consistent and show good correlation.

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Forney, J. L. , 1974, “On the Duration of Contact for the Hertzian Impact of a Spherical Indenter on a Maxwell Solid,” Int. J. Solids Struct., 10(6), pp. 621–624. [CrossRef]
Fischer-Cripps, A. C. , 1999, “The Hertzian Contact Surface,” J. Mater. Sci., 34(1), pp. 129–137. [CrossRef]
Yang, J. , and Komvopoulos, K. , 2004, “Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space,” ASME/STLE International Joint Tribology Conference, Long Beach, CA, Oct. 24–27, pp. 1--8.
Jayadeep, U. B. , Bobji, M. S. , and Jog, C. S. , 2013, “Energy Loss in the Impact of Elastic Spheres on a Rigid Half-Space in Presence of Adhesion,” Tribol. Lett., 53(1), pp. 79–89. [CrossRef]
Ahmad, M. , Ismail, K. A. , and Mat, F. , 2016, “Impact Models and Coefficient of Restitution: A Review,” J. Eng. Appl. Sci., 11(10), pp. 6549–6555. https://pdfs.semanticscholar.org/d542/6e2ee5da56d87ca2004f77e0521c26580b71.pdf
Li, L. Y. , Wu, C. Y. , and Thornton, C. , 2002, “A Theoretical Model for the Contact of Elastoplastic Bodies,” Proc. IMechE, Part C, 216(4), pp. 421–431. [CrossRef]
Sherif, H. A. , and Almufadi, F. A. , 2016, “Identification of Contact Parameters From Elastic-Plastic Impact of Hard Sphere and Elastic Half Space,” Wear, 368–369, pp. 358–367. [CrossRef]
Van Landingham, M. R. , Villarrubia, J. S. , Guthrie, W. F. , and Meyers, G. F. , 2001, “Nanoindentation of Polymers: An Overview,” Macromol. Symp., 167(1), pp. 15–19. [CrossRef]
Zamfirova, G. , Lorenzo, V. , Benavente, R. , and Peren, J. M. , 2003, “On the Relationship Between Modulus of Elasticity and Microhardness,” J. Appl. Polym. Sci., 88(7), pp. 1794–1798. [CrossRef]
Constantinides, G. , Tweedie, C. A. , Savva, N. , Smith, J. F. , and Van Vliet, K. J. , 2009, “Quantitative Impact Testing of Energy Dissipation at Surfaces Experimental,” Exp. Mech., 49(4), pp. 511–522. [CrossRef]
Tirupataiah, Y. , and Sundararajan, G. , 1991, “A Dynamic Indentation Technique for the Characterization of the High-Strain Rate Plastic-Flow Behavior of Ductile Metals and Alloys,” J. Mech. Phys. Solids, 39(2), pp. 243–271. [CrossRef]
Sughash, G. , and Zhang, H. , 2007, “Dynamic Indentation Response of ZrHf-Based Bulk Metallic Glasses,” J. Mater. Res., 22(2), pp. 478–485. [CrossRef]
Vriend, N. M. , and Kren, A. P. , 2004, “Determination of the Viscoelastic Properties of Elastomeric Materials by the Dynamic Indentation Method,” Polym. Test., 23(4), pp. 369–375. [CrossRef]
Rudnitsky, V. A. , Kren, A. P. , and Tsarik, S. V. , 2000, “Method of Identification of Viscoelastic Materials With a Stress Relaxation Function,” 15th World Conference on Nondestructive Testing, Rome, Italy, Oct. 15–21, pp. 15–21.
Kevin, P. M. , 1999, Dynamic Mechanical Analysis: A Practical Introduction, CRC Press, Boca Raton, FL.
Màs, J. , Vidaurre, A., Meseguer, J. M., Romero, F., Monleón Pradas, M., Gómez Rebelles, J. L., Maspoch, M. L. L., Santana, O. O., Pagés, P., and Pérez-Folch, J., 2002, “Dynamic Mechanical Properties of Polycarbonate and Acrylonitrile-Butadiene-Styrene Copolymer Blends,” J. Appl. Polym. Sci., 83(7), pp. 1507–1516. [CrossRef]
Nair, T. M. , Kumaran, M. G. , Unnikrishnan, G. , and Pillai, V. B. , 2009, “Dynamic Mechanical Analysis of Ethylene-Propylene-Diene Monomer Rubber and Styrene-Butadiene Rubber Blends,” J. Appl. Polym. Sci., 112(1), pp. 72–81. [CrossRef]
Chakravartula, A. , and Komvopoulos, K. , 2006, “Viscoelastic Properties of Polymer Surfaces Investigated by Nanoscale Dynamic Mechanical Analysis,” Appl. Phys. Lett., 88(13), p. 131901. [CrossRef]
ASTM, 1999, “Standard Test Method for Rubber Property-International Hardness,” ASTM International, West Conshohocken, PA, Standard No. ASTM D1415-88.
Siddiqui, A. , Bradenb, M. , Patel, M. , and Parkerb, S. , 2010, “An Experimental and Theoretical Study of the Effect of Sample Thickness on the Shore Hardness of Elastomers,” Dent. Mater, 26(6), pp. 560–564. [CrossRef] [PubMed]
Mohamed, M. I. , and Aggag, G. A. , 2003, “Uncertainty Evaluation of Shore Hardness Testers,” Measurement, 33(3), pp. 251–257. [CrossRef]
Qi, H. J. , Joyce, K. , and Boyce, M. C. , 2003, “Durometer Hardness and the Stress-Strain Behavior of Elastomeric Materials,” Rubber Chem. Technol., 76(2), pp. 419–435. [CrossRef]
Gent, A. N. , 1958, “On the Relation Between Indentation Hardness and Young's Modulus,” Rubber Chem. Technol., 31(4), pp. 896–906.
Neideck, K. , Franzel, W. , and Grau, P. , 1999, “Dynamic Ball Hardness Tests on Polymers,” J. Macromol. Sci., Part B, 38(5–6), pp. 669–680. [CrossRef]
Yamamoto, M. , Yamamoto, T. , Urata, M. , Miyahara, K. , Maki, S. , and Nakamura, M. , 2011, “Proof Experiments on Small and Hard Ball Rebound Hardness Test Using Free Fall,” J. Mater. Test. Res. Assoc. Jpn., 56(4), pp. 185–190 (in Japanese).
Yamamoto, T. , Miyahara, K. , Yamamoto, M. , and Maki, S. , 2013, “Discussion on Mass Effect of Rebound Hardness Through Development of Small Ball Rebound Hardness Testing Machine,” J. Mater. Test. Res. Assoc. Jpn., 58(2), pp. 75–80 (in Japanese).
Maki, S. , and Yamamoto, T. , 2014, “Computer Simulation of Micro Rebound Hardness Test,” Procedia Eng., 81, pp. 1396–1401. [CrossRef]
Hunter, S. C. , 1960, “The Hertz Problem for a Rigid Spherical Indenter and Viscoelastic Half-Space,” J. Mech. Phys. Solids, 8(4), pp. 196–369. [CrossRef]
Johnson, K. , 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
Greszczuk, L. B. , 1982, Impact Dynamics, Wiley, New York.
Deresiewicz, H. , 1968, “A Note on Hertz's Theory of Impact,” Acta Mech., 6(1), pp. 110–112. [CrossRef]
Professional plastic, Inc.,1984, “Mechanical Properties of Plastic Materials,” Fullerton, CA, accessed July 27, 2018, https://www.professionalplastics.com/professionalplastics/MechanicalPropertiesofcs.pdfPlastics.pdf
Smithers, R., 2012, “Physical Testing of Plastics,” Rapra Technology Ltd, Shewsbury Shropshire, accessed July 27, 2018, https://www.smithersrapra.com/SmithersRapra/media/Sample-Chapters/Physical-Testing-of-Plastics.pdf


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Fig. 1

Effect of contact coefficient k on the contact time–force relationship (m = 0.1 g)

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Fig. 2

Time variation of the normal force of contact (γ = 3.26, k = 1.0 kN/m1.5)

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Fig. 3

Pendulum impact test rig

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Fig. 4

Scheme of pendulum test setup

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Fig. 5

Image of test setup

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Fig. 6

Measured normal force–time histories (d = 2.5 mm). (a) High shore A hardness and (b) low shore A hardness.

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Fig. 7

Standard calibration rubber blocks

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Fig. 8

Variation of the contact time duration with the normal force of contact: (a) shore A samples and (b) shore D samples

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Fig. 9

Variation of the impact index of standard samples with the velocity of impact

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Fig. 10

Relationship between average impact index and average shore hardness of standard calibration rubber samples with the standard error of the mean

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Fig. 11

Variation of the magnitude of complex modulus of elasticity of standard samples with the velocity of impact

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Fig. 12

Dependence of shore A hardness on the impact index

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Fig. 13

Polymer tested samples

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Fig. 14

Variation of the impact index of selected samples with the velocity of impact

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Fig. 15

Hardness test of the selected polymer samples using durometer

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Fig. 16

Variation of the magnitude of complex modulus of elasticity of selected samples with the velocity of impact



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