d e n t a l m a t e r i a l s 2 5 ( 2 0 0 9 ) 956–959
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The relationship between Shore hardness of elastomeric dental materials and Young’s modulus Iranthi M. Meththananda, Sandra Parker ∗ , Mangala P. Patel, Michael Braden IRC in Biomedical Materials, Dental Physical Sciences, Barts and the London School of Medicine and Dentistry, Queen Mary, University of London, London, UK
a r t i c l e
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a b s t r a c t
Article history:
Objectives. Hardness of elastomers can be directly related to Young’s modulus, a relationship
Received 15 September 2008
that was investigated in detail by Gent in a paper in 1958. The aim of this study was to test
Received in revised form
this relationship for 13 dental elastomers (12 silicone and 1 polyether) using the equation
22 December 2008
derived by Gent and one from BS 903 (1950) that accounts for departures at low values.
Accepted 10 February 2009
Methods. The dental elastomers were subjected to tensile testing and Shore A scale hardness measurements. Young’s moduli were calculated from the hardness values using the Gent equation and the BS 903 equation. These calculated values were then compared with values
Keywords:
derived experimentally from the tensile tests.
Elastomer
Results. Hardness values were in the range 30.2 (±0.5)–62.9 (±0.8) with the corresponding
Silicone
calculated modulus values in the range 1.1–4.1 MPa and 0.9–4.3 MPa for the Gent and mod-
Mechanical testing
ified equations, respectively. Young’s modulus values derived from the tensile data were
Elasticity
in the range 0.8 (±0.3)–4.1 (±0.3) MPa, showing good agreement with those calculated from
Shore A scale hardness
the hardness values. Providing viscoelastic creep is minimal during the duration of the
Young’s modulus
test, there is a reasonably well-defined relationship between Shore hardness and Young’s modulus in the hardness range studied. Significance. Simple, non-destructive hardness measurements can be used to determine Young’s modulus values. Such values are needed in any calculations of stress distributions in soft lining materials, e.g. by FEA. © 2009 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Hardness measurements offer a rapid and easily performed method of testing solids, and have their origins in the testing of metals. Such tests are convenient for quality control and specification purposes, as for example in the various grades of gold alloys [1]. Hardness measurements abound in the literature on composite filling materials [2–4]. A variety of tests are available [5] (Knoop, Brinell, Rockwell, Barcol), defined by the geometry and dimensions of the
indenter, and the load applied. In the case of metals, and other solids such as glassy polymers, composites, and calcified tissues, the indenter on application of a load produces a permanent indentation, and the hardness number is usually the load per unit surface area of the indentation. The underlying physics of such indentation measurements was described in detail by Tabor [6], where it was shown that hardness is related to yield stress in compression. This relationship has also been shown to apply to dental amalgam, and dentine [7,8].
∗ Corresponding author at: Dental Physical Sciences, Frances Bancroft Building, Barts and the London School of Medicine and Dentistry, Queen Mary, University of London, Mile End Road, London E1 4NS, UK. Tel.: +44 207 882 7976; fax: +44 207 882 7979. E-mail address:
[email protected] (S. Parker). 0109-5641/$ – see front matter © 2009 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.dental.2009.02.001
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Hardness testing is also carried out on elastomeric materials, for example the Shore hardness and ISO tests. Again, it is a convenient quality control, easily and rapidly carried out. Some manufacturers of impression materials use it to characterize the stiffness of set impression materials. However, the character of what is being measured is completely different to the tests described above. The indentation in the case of elastomers is predominantly elastic in nature, i.e. is recoverable. Depending on the type of test, the indenter is either flat-ended (Shore), or spherical (ISO). For a flat-ended indenter, the appropriate equation is [9]: F=
2aEw 1 − 2
(1)
where F = force, a = the radius of the indenter, E = Young’s modulus, w = the depth of indentation, and = Poisson’s ratio. This, and the succeeding equations derived from it are for a semi-infinite solid. In practice this means the dimensions of an actual test piece need to be sufficient that the stress field caused by the indentation has sensibly decayed to zero at the bounding surfaces. Since elastomers are sensibly incompressible [10], = 0.5, and Eq. (1) becomes: F=
4Ea1/2 w3/2 3(1 − 2 )
9 16Eaw3/2
0.0981(56 + 7.66s) 0.137505(254 − 2.54s)
(5)
where s = the Shore hardness. Ideally, the hardness scale should convert a modulus range of 0–∞ to a hardness scale of 0–100. Clearly Eq. (5) fulfills this for s = 100 but not for s = 0, and there are small departures from the master curve at s values below 40 given in Gent’s paper, based on BS 903(1950). Eq. (6), [14] however, does meet the above criterion: H = 100 erf(kE1/2 )
(6)
where k = 3.186 × 10−4 Pa−1/2 . In this study, both of these two equations have been tested for a range of dental silicone elastomers and one polyether impression material.
Materials and methods
(2)
(3)
The dental elastomers included in the study are listed in Table 1 all of which cure at room temperature and all the silicones included are addition cure. The polyether used was Impregum PS (3M ESPE).
2.1.
and with = 0.5 for rubber-like material [11], becomes: F=
E(MPa) =
2.
8 3aEw
In the case of a sphere the corresponding equation is [7]: F=
The relationship between Shore and ISO hardness and Young’s modulus was investigated in detail by Gent [13], who derived the following semi-empirical equation:
(4)
Eqs. (1) and (3) were originally derived by Hertz [12]. In both cases, the degree of indentation (w) against a constant force (F) is a direct function of E. Hence a priori, there should be a direct relationship between Shore or ISO hardness and Young’s modulus (E), and indeed Shear (rigidity) modulus (G), as for elastomers at small strains E = 3G.
Sample preparation
All specimens were prepared using the following procedure. Sheets of materials (2 mm thick for tensile testing and 6.5 mm thick for hardness testing) were prepared in metal moulds lined with acetate sheets. The materials were all mixed/dispensed according to the manufacturers’ instructions. Material was packed into the appropriate metal mould which was placed in a hand-operated hydraulic press (Quayle Dental, Sussex, UK) under 100 bar pressure. The sample was then left for at least 2 h to ensure complete cure.
Table 1 – Materials. Material Tokuyama soft Tokuyama medium soft GC soft GC extra soft Odontosil Episil-E Epiform flex Zerosil soft Zerosil super soft Zerosil light Zerosil mono Extrude Impregum PS
Manufacturer
Application
Tokuyama Corp., Tokyo, Japan Tokuyama Corp., Tokyo, Japan GC Corp., Tokyo, Japan GC Corp., Tokyo, Japan Dreve-Dentamid Gmbh, Germany Dreve-Dentamid Gmbh, Germany Dreve-Dentamid Gmbh, Germany Dreve-Dentamid Gmbh, Germany Dreve-Dentamid Gmbh, Germany Dreve-Dentamid Gmbh, Germany Dreve-Dentamid Gmbh, Germany Kerr Corp., Michigan, USA 3M ESPE, Loughborough, UK
Soft lining material Soft lining material Soft lining material Soft lining material Orthodontics Maxillo facial Maxillo facial Impression material Impression material Impression material Impression material Impression material Impression material
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Table 2 – Results of actual/real hardness and calculated values. Materials
Hardness (S.D.)
Young’s modulus (MPa) Direct (S.D.)
Odontosil Episil-E Epiform flex Tokuyama soft Tokuyama medium soft GC soft GC extra soft Zerosil soft Zerosil super soft Zerosil light Zerosil mono Extrude Impregum PS
2.2.
60.8 (0.3) 38.3 (0.3) 30.2 (0.5) 33.1 (0.4) 42.1 (0.4) 56.3 (0.5) 42.9 (0.5) 54.5 (0.7) 53.1 (0.5) 56.7 (0.2) 62.9 (0.8) 53.2 53.7
4.0 (0.7) 1.2 (0.4) 0.8 (0.3) 1.0 (0.3) 1.7 (0.2) 3.1 (0.3) 1.8 (0.1) 3.5 (0.3) 3.0 (0.4) 3.5 (0.3) 4.1 (0.3) 2.6 2.9
Hardness testing
Shore A hardness testing was carried out in accordance with ASTM D 2240-86 and ISO 868 using a H17A Shore A Hardness Tester with Congenix data control software (Wallace, Kingston, UK). The minimum dwell time of 1 s was used in order to minimise creep effects and tests were carried out at 23 ± 1 ◦ C. Measurements were taken at regular intervals at least 12 mm from the edge of the specimen and 10 mm apart. These requirements are to ensure the stress fields arising from the indentation are zero at the edges and bottom surface of the sample, as noted in Section 1 following Eq. (1). A minimum of six readings was taken for each specimen and the mean calculated.
3.
4.0 1.5 0.9 1.1 1.8 3.4 1.9 3.2 3.0 3.4 4.3 2.6 2.6
Calc. Gent equation 3.7 1.6 1.1 1.1 1.8 2.9 1.9 2.9 2.8 3.2 4.1 2.8 2.8
Tensile testing
Tensile specimens were then cut from the prepared 2 mm thick sheets with a dumb-bell shaped die (type A2) specified by the standard test method for rubber properties in tension (ASTM D412-87). A minimum of seven specimens was cut for each material. Thickness and width of the central section of each specimen were measured using a digital micrometer (±0.001 mm) (572-046, RS, England) and the cross-sectional area calculated. A 20 mm length of the central section was marked with strips of fluorescent, white tape to enable extension to be measured continuously using a video extensometer. Specimens were tested on an Instron MK30 using a crosshead speed of 500 mm/min at ambient temperature (23 ± 2 ◦ C) according to ISO 37: 1994.
2.3.
Calc. error function
Fig. 1 – Relationship between Young’s modulus and hardness.
Young’s modulus for both equations. Linear regression was carried out on both sets of data as shown on the figure.
4.
Discussion
From the results shown in figure in Table 2 and Figs. 1 and 2, it is evident that the correspondence between the theoretically predicted and experimental values is satisfactory, particularly
Results
The stress–strain plots showed a distinctive initial linear region the slope of which was used to calculate the Young’s modulus (E) values. Table 2 contains, respectively, the Shore hardness and Young’s modulus values obtained experimentally and the theoretical Young’s modulus values derived from Eqs. (5) and (6). Fig. 1 shows plots of log E calculated from both equations and determined experimentally as a function of hardness. Fig. 2 shows a plot of calculated versus measured
Fig. 2 – Plot of calculated Young’s modulus against measured Young’s modulus for Eqs. (5) and (6).
d e n t a l m a t e r i a l s 2 5 ( 2 0 0 9 ) 956–959
with Eq. (6) at the lower values. It should be noted that the Shore hardness scale compresses the differences in Young’s moduli, a fundamental elastic constant. The range of hardness studied in this work covers a scale of ∼2:1, whereas the corresponding scale of moduli is ∼4:1. This follows the trend of Gent’s paper [13], which studied various natural rubber vulcanisates. Some circumspection is needed when using these theories for dental elastomers as a whole. The theory is based on classical elasticity theory, with the tacit assumption that viscoelastic creep is negligible over the dwell time of the instrument. In this study the minimum dwell time of 1 s was used. Hence it is unlikely to be satisfactory for the so-called soft acrylic denture lining materials, which have extremely high mechanical loss tangents. Typically, soft acrylics have tan ı values in the range 0.685–1.23, whereas silicones are in the range 0.02–0.1 [15]. These values are in good agreement with earlier studies [16]. Creep can be related to visco-elastic data from sinusoidal oscillations by use of the Fourier integral. The constant load used over a given time interval for the study of creep, is represented as a rectangular pulse, expressed as a Fourier integral. The creep function is obtained by applying the complex modulus to this integral. The resulting analysis predicts creep to be directly proportional to tan ı [17]. Young’s modulus values are needed in any calculations of stress distributions in soft lining materials, e.g. by FEA [18–20]. This study has shown that values can be obtained from hardness measurements using simple, non-destructive techniques.
5.
Conclusions
Providing viscoelastic creep is minimal during the duration of the test, there is a reasonably well-defined relationship between Shore hardness and Young’s modulus in the hardness range studied (30.2–62.9).
Acknowledgements The authors are indebted to the Engineering and Physical Sciences Research Council for the core grant to the IRC in Biomedical Materials, of which this work is a part. The Wallace Shore A hardness tester was purchased with funds awarded by the University of London Central Research Fund.
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