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.

References

References
1.
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
.
2.
Fischer-Cripps
,
A. C.
,
1999
, “
The Hertzian Contact Surface
,”
J. Mater. Sci.
,
34
(
1
), pp.
129
137
.
3.
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.
4.
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
.
5.
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
6.
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
.
7.
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
.
8.
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
.
9.
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
.
10.
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
.
11.
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
.
12.
Sughash
,
G.
, and
Zhang
,
H.
,
2007
, “
Dynamic Indentation Response of ZrHf-Based Bulk Metallic Glasses
,”
J. Mater. Res.
,
22
(
2
), pp.
478
485
.
13.
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
.
14.
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
.
15.
Kevin
,
P. M.
,
1999
,
Dynamic Mechanical Analysis: A Practical Introduction
,
CRC Press
, Boca Raton, FL.
16.
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
.
17.
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
.
18.
Chakravartula
,
A.
, and
Komvopoulos
,
K.
,
2006
, “
Viscoelastic Properties of Polymer Surfaces Investigated by Nanoscale Dynamic Mechanical Analysis
,”
Appl. Phys. Lett.
,
88
(
13
), p.
131901
.
19.
ASTM,
1999
, “
Standard Test Method for Rubber Property-International Hardness
,” ASTM International, West Conshohocken, PA, Standard No. ASTM D1415-88.
20.
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
.
21.
Mohamed
,
M. I.
, and
Aggag
,
G. A.
,
2003
, “
Uncertainty Evaluation of Shore Hardness Testers
,”
Measurement
,
33
(
3
), pp.
251
257
.
22.
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
.
23.
Gent
,
A. N.
,
1958
, “
On the Relation Between Indentation Hardness and Young's Modulus
,” Rubber Chem. Technol.,
31
(4), pp. 896–906.
24.
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
.
25.
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).
26.
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).
27.
Maki
,
S.
, and
Yamamoto
,
T.
,
2014
, “
Computer Simulation of Micro Rebound Hardness Test
,”
Procedia Eng.
,
81
, pp.
1396
1401
.
28.
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
.
29.
Johnson
,
K.
,
1985
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
30.
Greszczuk
,
L. B.
,
1982
,
Impact Dynamics
,
Wiley
,
New York
.
31.
Deresiewicz
,
H.
,
1968
, “
A Note on Hertz's Theory of Impact
,”
Acta Mech.
,
6
(
1
), pp.
110
112
.
32.
Professional plastic, Inc.,1984, “Mechanical Properties of Plastic Materials,” Fullerton, CA, accessed July 27, 2018, https://www.professionalplastics.com/professionalplastics/MechanicalPropertiesofcs.pdfPlastics.pdf
33.
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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