Shore durometer

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Two inline skates wheels with different durometer - 85A and 83A.

Durometer is one of several measures of the hardness of a material. Hardness may be defined as a material's resistance to permanent indentation. The durometer scale was defined by Albert F. Shore, who developed a measurement device called a durometer in the 1920s. The term durometer is often used to refer to the measurement, as well as the instrument itself. Durometer is typically used as a measure of hardness in polymers, elastomers, and rubbers.^[1]

Durometer scales

There are several scales of durometer, used for materials with different properties. The two most common scales, using slightly different measurement systems, are the ASTM D2240 type A and type D scales. The A scale is for softer plastics, while the D scale is for harder ones. However, the ASTM D2240-00 testing standard calls for a total of 12 scales, depending on the intended use; types A, B, C, D, DO, E, M, O, OO, OOO, OOO-S, and R. Each scale results in a value between 0 and 100, with higher values indicating a harder material.^[2]

Method of measurement

Durometer, like many other hardness tests, measures the depth of an indentation in the material created by a given force on a standardized presser foot. This depth is dependent on the hardness of the material, its viscoelastic properties, the shape of the presser foot, and the duration of the test. ASTM D2240 durometers allows for a measurement of the initial hardness, or the indentation hardness after a given period of time. The basic test requires applying the force in a consistent manner, without shock, and measuring the hardness (depth of the indentation). If a timed hardness is desired, force is applied for the required time and then read. The material under test should be a minimum of 6.4 mm (.25 inch) thick.^[3]

Test setup for type A & D^[3]
Durometer	Indenting foot	Applied mass [kg]	Resulting force [N]
Type A	Hardened steel rod 1.1 mm - 1.4 mm diameter, with a truncated 35° cone, 0.79 mm diameter	0.822	8.064
Type D	Hardened steel rod 1.1 mm - 1.4 mm diameter, with a 30° conical point, 0.1 mm radius tip	4.550	44.64

The ASTM D2240 standard recognizes twelve different durometer scales using combinations of specific spring forces and indentor configurations. These scales are properly referred to as durometer types; i.e., a durometer type is specifically designed to determine a specific scale, and the scale does not exist separately from the durometer. The table below provides details for each of these types, with the exception of Type R.^[4]

Durometer Type	Configuration	Diameter	Extension	Spring force
A	35° truncated cone (frustum)	1.40 mm (0.055 in)	2.54 mm (0.100 in)	822 gf (8.06 N)
C	35° truncated cone (frustum)	1.40 mm (0.055 in)	2.54 mm (0.100 in)	4,536 gf (44.48 N)
D	30° cone	1.40 mm (0.055 in)	2.54 mm (0.100 in)	4,536 gf (44.48 N)
B	30° cone	1.40 mm (0.055 in)	2.54 mm (0.100 in)	822 gf (8.06 N)
M	30° cone	0.79 mm (0.031 in)	1.25 mm (0.049 in)	78 gf (0.76 N)
E	2.5 mm (0.098 in) spherical radius	4.50 mm (0.177 in)	2.54 mm (0.100 in)	822 gf (8.06 N)
O	1.20 mm (0.047 in) spherical radius	2.40 mm (0.094 in)	2.54 mm (0.100 in)	822 gf (8.06 N)
OO	1.20 mm (0.047 in) spherical radius	2.40 mm (0.094 in)	2.54 mm (0.100 in)	113 gf (1.11 N)
DO	1.20 mm (0.047 in) spherical radius	2.40 mm (0.094 in)	2.54 mm (0.100 in)	4,536 gf (44.48 N)
OOO	6.35 mm (0.250 in) spherical radius	10.7 mm (0.42 in) - 11.6 mm (0.46 in)	2.54 mm (0.100 in)	113 gf (1.11 N)
OOO-S	10.7 mm (0.42 in) radius disk	11.9 mm (0.47 in)	5.0 mm (0.20 in)	197 gf (1.93 N)

Note: "Type R is a designation, rather than a true "type". The R designation specifies a presser foot diameter (hence the R, for radius; obviously D could not be used) of 18 ± 0.5 mm (0.71 ± 0.02 in) in diameter, while the spring forces and indenter configurations remain unchanged. The R designation is applicable to any D2240 Type, with the exception of Type M; the R designation is expressed as Type xR, where x is the D2240 type, e.g., aR, dR, etc.; the R designation also mandates the employment of an operating stand".^[4]

The final value of the hardness depends on the depth of the indenter after it has been applied for 15 seconds on the material. If the indenter penetrates 2.54 mm (0.100 inch) or more into the material, the durometer is 0 for that scale. If it does not penetrate at all, then the durometer is 100 for that scale. It is for this reason that multiple scales exist. Durometer is a dimensionless quantity, and there is no simple relationship between a material's durometer in one scale, and its durometer in any other scale, or by any other hardness test.^[1]

Durometers of various common materials
Material	Durometer	Scale
Bicycle gel seat	15-30	OO
Chewing gum	20	OO
Sorbothane	40	OO
Sorbothane	30-70	OO
Rubber band	25	A
Door seal	55	A
Automotive tire tread	70	A
Soft wheels of roller skates and skateboard	78	A
Hydraulic O-ring	70-90	A
Hard wheels of roller skates and skateboard	98	A
Ebonite rubber	100	A
Solid truck tires	50	D
Hard hat (typically HDPE)	75	D

Relation between ASTM D2240 hardness and elastic modulus

Using linear elastic indentation hardness, a relation between the ASTM D2240 hardness and the Young's modulus for elastomers has been derived by Gent^[5]and by Mix and Giacomin. ^[6] Gent's relation has the form

$E={\cfrac {0.0981(56+7.62336S)}{0.137505(254-2.54S)}}$

where $E$ is the Young's modulus in MPa and $S$ is the ASTM D2240 type A hardness. This relation gives a value of $E=\infty$ at $S=100$ but departs from experimental data for $S<40$ . Mix and Giacomin derive comparable equations for all 12 scales that are standardized by ASTM D2240.

Another relation that fits the experimental data slightly better is^[7]

$S=100~{\mathrm {erf}}(3.186\times 10^{{-4}}~E^{{1/2}})$

where ${\mathrm {erf}}$ is the error function and $E$ is in units of Pa.

A first order estimate of the relation between ASTM D2240 type D hardness and the elastic modulus for a conical indenter with a 15 degree cone is ^[8]

$S_{D}=100-{\cfrac {20(-78.188+{\sqrt {6113.36+781.88E}})}{E}}$

where $S_{D}$ is the ASTM D2240 type D hardness and $E$ is in MPa.

Another linear relation between the ASTM D2240 and elastic modulus has the form:

$\ln(E)=0.0235S-0.6403~;~~S={\begin{cases}S_{A}&{\mathrm {for}}~20<S_{A}<80\\S_{D}+50&{\mathrm {for}}~30<S_{D}<85\end{cases}}$

where $S_{A}$ is the ASTM D2240 type A hardness, $S_{D}$ is the ASTM D2240 type D hardness, and $E$ is the Young's modulus in MPa.

Patents

US patent 1770045, A.F. Shore, "Apparatus for Measuring the Hardness of Materials", issued 1930-07-08

US patent 2421449, J.G. Zuber, "Hardness Measuring Instrument", issued 1947-06-03

References

↑ 1.0 1.1 "Shore (Durometer) Hardness Testing of Plastics". Retrieved 2006-07-22.
↑ "Material Hardness". CALCE and the University of Maryland. 2001. Retrieved 2006-07-22.
↑ 3.0 3.1 "Rubber Hardness". National Physical Laboratory, UK. 2006. Retrieved 2006-07-22.
↑ 4.0 4.1 "DuroMatters! Basic Durometer Testing Information". CCSi, Inc. Retrieved 29 May 2011.
↑ A.N. Gent, (1958), On the relation between indentation hardness and Young's modulus, Institution of Rubber Industry -- Transactions, 34, pp. 46–57.
↑ A. W. Mix and A. J. Giacomin, (2011), Standardized Polymer Durometry, Journal of Testing and Evaluation, 39(4), pp. 1–10.
↑ British Standard 903, (1950,1957), Methods of testing vulcanised rubber Part 19 (1950) and Part A7 (1957).
↑ Qi, HJ and Joyce, K. and Boyce, MC, (2003), Durometer hardness and the stress-strain behavior of elastomeric materials, Rubber Chemistry and Technology, 76(2), pp. 419-435.

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