Shore durometer

{{Short description|Hardness-testing device}} thumb|Digital Shore hardness tester [[File:Bont High Roller G4 110mm 85A and 83A.jpg|thumb|Two inline skate wheels with different durometer – 85A and 83A]]

The '''Shore durometer''' is a device for measuring the hardness of a material, typically of polymers.<ref name="matweb">{{cite web |url=http://www.matweb.com/reference/shore-hardness.asp |title=Shore (Durometer) Hardness Testing of Plastics |access-date=2006-07-22 }}</ref>

Higher numbers on the scale indicate a greater resistance to indentation and thus harder materials. Lower numbers indicate less resistance and softer materials. Note that 'hardness' here is used in the colloquial sense, since a Shore durometer measures resistance to any localized deformation; in contrast with the technical definition (used in the article on hardness), which only concerns resistance to localized ''plastic'' deformation.

The term is also used to describe a material's rating on the scale, as in an object having a "'Shore durometer' of 90."

The scale was defined by Albert Ferdinand Shore, who developed a suitable device to measure hardness in the 1920s. It was neither the first hardness tester nor the first to be called a ''durometer'' (ISV ''duro-'' and ''-meter''; attested since the 19th century), but today that name usually refers to '''Shore hardness'''; other devices use other measures, which return corresponding results, such as for Rockwell hardness.

== 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 ones, while the D scale is for harder ones. The image of Bareiss digital durometer is shown in the photo.

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.<ref name="uofm">{{cite web |url = http://www.calce.umd.edu/general/Facilities/Hardness_ad_.htm#3.5 |title = Material Hardness |publisher = CALCE and the University of Maryland |year = 2001 |access-date = 2006-07-22 |url-status = dead |archive-url = https://web.archive.org/web/20070707141201/http://www.calce.umd.edu/general/Facilities/Hardness_ad_.htm#3.5 |archive-date = 2007-07-07 }}</ref>

== Method of measurement == thumb|300px|lang=en|Diagram of a durometer ''indenter'' or ''presser foot'' used for Shores A and D

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 allow 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 {{cvt|6|mm}} thick.<ref name="npl"> {{cite web |url=http://www.npl.co.uk/server.php?show=ConWebDoc.379 |title=Rubber Hardness |publisher=National Physical Laboratory, UK |year=2006 |access-date=2006-07-22 }}</ref> Theoretical background of the test is considered in Stoßprobleme in Physik, Technik und Medizin by Grundlagen und Anwendungen.<ref>{{Cite book|last=Willert|first=Emanuel|url=https://www.springer.com/de/book/9783662602959|title=Stoßprobleme in Physik, Technik und Medizin: Grundlagen und Anwendungen|date=2020|publisher=Springer Vieweg|doi=10.1007/978-3-662-60296-6 |isbn=978-3-662-60295-9 |s2cid=212954456 |language=de}}</ref>

{| class="wikitable" style="text-align:center" |+ Test setup for type A & D<ref name="npl"/> ! Durometer !! Indenting foot !! Kilogram-force (kgf) !! Newton (N) |- ! scope=row| Type A | Hardened steel rod {{cvt|1.1-1.4|mm}} diameter, with a truncated 35° cone, {{cvt|0.79|mm}} diameter || {{cvt|0.822|kgf|N|disp=tablecen|sigfig=4}} |- ! scope=row| Type D | Hardened steel rod {{cvt|1.1-1.4|mm}} diameter, with a 30° conical point, {{cvt|0.1|mm}} radius tip || {{cvt|0.822|kgf|N|disp=tablecen|sigfig=4}} |}

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.<ref name="CCSi, Inc.">{{cite web|title=DuroMatters! Basic Durometer Testing Information|url=http://www.ccsi-inc.com/t-durometer-testing.pdf|publisher=CCSi, Inc.|access-date=29 May 2011|archive-date=24 March 2012|archive-url=https://web.archive.org/web/20120324173555/http://www.ccsi-inc.com/t-durometer-testing.pdf|url-status=dead}}</ref>

{| class="wikitable sortable" style="text-align:center"

! Durometer type !! Configuration !! Diameter !! Extension !! Spring force<ref>{{cite journal|url=https://www.astm.org/Standards/D2240.htm |title=Standard Test Method for Rubber Property—Durometer Hardness1 |number=D2240 − 15´1 |website=ASTM International|date=November 2017|page=5 |doi=10.1520/D2240-15E01|url-access=subscription }}</ref> |- | A || 35° truncated cone (frustum) || {{cvt|1.40|mm|in}} || {{cvt|2.54|mm|in}} || {{cvt|8.05|N|gf}} |- | B || 30° cone || {{cvt|1.40|mm|in}} || {{cvt|2.54|mm|in}} || {{cvt|8.05|N|gf}} |- | C || 35° truncated cone (frustum) || {{cvt|1.40|mm|in}} || {{cvt|2.54|mm|in}} || {{cvt|44.45|N|gf}} |- | D || 30° cone || {{cvt|1.40|mm|in}} || {{cvt|2.54|mm|in}} || {{cvt|44.45|N|gf}} |- | E || {{cvt|2.5|mm|in}} spherical radius || {{cvt|4.50|mm|in}} || {{cvt|2.54|mm|in}} || {{cvt|8.05|N|gf}} |- | M || 30° cone || {{cvt|0.79|mm|in}} || {{cvt|1.25|mm|in}} || {{cvt|0.765|N|gf}} |- | O || {{cvt|1.20|mm|in}} spherical radius || {{cvt|2.40|mm|in}} || {{cvt|2.54|mm|in}} || {{cvt|8.05|N|gf}} |- | OO || {{cvt|1.20|mm|in}} spherical radius || {{cvt|2.40|mm|in}} || {{cvt|2.54|mm|in}} || {{cvt|1.111|N|gf}} |- | DO || {{cvt|1.20|mm|in}} spherical radius || {{cvt|2.40|mm|in}} || {{cvt|2.54|mm|in}} || {{cvt|44.45|N|gf}} |- | OOO || {{cvt|6.35|mm|in}} spherical radius || {{cvt|10.7|-|11.6|mm|in}} || {{cvt|2.54|mm|in}} || {{cvt|1.111|N|gf}} |- | OOO-S || {{cvt|10.7|mm|in}} radius disk || {{cvt|11.9|mm|in}} || {{cvt|5.0|mm|in}} || {{cvt|1.932|N|gf}} |}

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 {{cvt|18|+/-|0.5|mm|in|sigfig=2}} 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.<ref name="CCSi, Inc."/>

Some conditions and procedures that have to be met, according to DIN ISO 7619-1 standard are: * For measuring Shore A the foot indents the material while for Shore D the foot penetrates the surface of the material. * Material for testing needs to be in laboratory climate storage at least one hour before testing. * Measuring time is 15s. * Force is {{cvt|1|+|0.1|kg|lb}} for Shore A, and {{cvt|5|+|0.5|kg|lb}} for Shore D. * Five measurements need to be taken. * Calibration of the Durometer is one per week with elastomer blocks of different hardness.

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 {{cvt|2.54|mm}} 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. But if the hardness is <10 °Sh or >90 °Sh the results are not to be trusted. The measurement must be redone with adjacent scale type. thumb|Pig sticker used to measure the hardness of pugged clay 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.<ref name="matweb" />

{| class="wikitable" style="text-align:center" |+ Shore Durometers of Common Materials |- ! Material !! Durometer !! Scale |- | Bicycle gel seat || 15–30 || OO |- | Chewing gum || 20 || 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 |- | Pneumatic O-ring || 65–75 || 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 |- | Nylon|| 80 || D |}

== 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. Gent's relation has the form:<ref name="Gent">{{cite journal |last1=Gent |first1=A. N. |title=On the Relation between Indentation Hardness and Young's Modulus |journal=Rubber Chemistry and Technology |date=September 1958 |volume=31 |issue=4 |pages=896–906 |doi=10.5254/1.3542351}}</ref>

:{{math|''E'' {{=}} {{sfrac|0.0981(56 + 7.62336''S'')|0.137505(254 - 2.54''S'')}} }}

where {{mvar|E}} is the Young's modulus in MPa and {{mvar|S}} is the ASTM D2240 type A hardness.

This relation gives a value of {{math|''E'' {{=}} ∞ }} at {{math|''S'' {{=}} 100}} but departs from experimental data for {{math|''S'' < 40}}.

Mix and Giacomin derive comparable equations for all 12 scales that are standardized by ASTM D2240.<ref name="Mix">{{cite journal |last1=Mix |first1=A. W. |last2=Giacomin |first2=A. J. |title=Standardized Polymer Durometry |journal=Journal of Testing and Evaluation |date=1 July 2011 |volume=39 |issue=4 |pages=696–705 |doi=10.1520/JTE103205}}</ref>

Another relation, that fits the experimental data slightly better, is<ref name=BS903>British Standard 903 (1950, 1957), Methods of testing vulcanised rubber Part 19 (1950) and Part A7 (1957).</ref>

:{{math|''S'' {{=}} 100 erf({{val|3.186|e=-4}} ''E''{{sup|0.5}}) }}

where {{math|erf}} is the error function, and {{mvar|E}} is in units of Pa.

To make that a little more insightful, here is a list of Shore A values with their corresponding Young's modulus (in MPa), where "MPa" is computed from "ShoreA" using first formula, and then "AltShoreA" is computed from "MPa" using second formula : {| class="wikitable" |+ ShoreA -> MPa -> Alt ShoreA |- ! Shore A !! MPa !! Alt Shore A |- | 10.0 || 0.413 || 22.776 |- | 20.0 || 0.732 || 30.011 |- | 30.0 || 1.142 || 36.989 |- | 40.0 || 1.690 || 44.191 |- | 50.0 || 2.456 || 51.986 |- | 60.0 || 3.605 || 60.772 |- | 70.0 || 5.520 || 71.024 |- | 80.0 || 9.351 || 83.175 |- | 90.0 || 20.844 || 96.032 |}

A first-order estimate of the relation between ASTM D2240 type D hardness (for a conical indenter with a 15° half-cone angle) and the elastic modulus of the material being tested is<ref name="Qi">{{cite journal |last1=Qi |first1=H. J. |last2=Joyce |first2=K. |last3=Boyce |first3=M. C. |title=Durometer Hardness and the Stress-Strain Behavior of Elastomeric Materials |journal=Rubber Chemistry and Technology |date=May 2003 |volume=76 |issue=2 |pages=419–435 |doi=10.5254/1.3547752}}</ref> :{{math|''S''{{sub|D}} {{=}} 100 - {{sfrac|20(-78.188 + {{sqrt|6113.36 + 781.88''E''}})|''E''}} }}

where {{math|''S''{{sub|D}}}} is the ASTM D2240 type D hardness, and {{mvar|E}} is in MPa.

Another Neo-Hookean linear relation between the ASTM D2240 hardness value and material elastic modulus has the form<ref name=Qi/>

:{{math|log{{sub|10}} ''E'' {{=}} 0.0235''S'' - 0.6403}}, <math>\quad S = \begin{cases} S_\text{A} & \text{for}~20 < S_A < 80, \\ S_\text{D} + 50 & \text{for}~30 < S_D < 85, \end{cases} </math>

where {{math|''S''{{sub|A}}}} is the ASTM D2240 type A hardness, {{math|''S''{{sub|D}}}} is the ASTM D2240 type D hardness, and {{mvar|E}} is the Young's modulus in MPa.

== Patents ==

* {{US patent reference | number = 1770045 | title = Apparatus for Measuring the Hardness of Materials | inventor = A. F. Shore | y = 1930 | m = 07 | d = 08 }} * {{US patent reference | number = 2421449 | title = Hardness Measuring Instrument | inventor = J. G. Zuber | y = 1947 | m = 06 | d = 03 }}

== See also ==

* {{annotated link|Brinell hardness test}} * {{annotated link|Bloom (test)}} * {{annotated link|Knoop hardness test}} * {{annotated link|Leeb Rebound Hardness Test}} * {{annotated link|Rockwell hardness test}} * {{annotated link|Vickers hardness test}}

== References ==

== External links == * [https://www.durometer.com/technical-information/ Comparison Chart] * [https://www.durometer.com/technical-information/ Reference Guide] * [http://geotm.dp.ua/index.php/ru/year-2010-ru/86 Растеряев Ю.К., Агальцов Г.Н. Связь между твёрдостью и модулем упругости резин (Connection between hardness and a modulus of gums)] * [https://www.endustri.io/shore-hardness-convertor/ Shore Hardness Converter] *[https://www.caltechindia.com/product/coating-inspection/hardness-testers/digital-shore-hardness-meter/ Digital Shore Hardness Tester - Caltech India] *[https://www.caltechindia.com/product/coating-inspection/hardness-testers/ces-202-shore-hardness-tester/ Shore Hardness Tester - Caltech India]

Category:Dimensionless numbers of physics Category:Hardness tests Category:Rubber properties