Can You Estimate Modulus from Durometer Hardness for Silicones? Yes, but Only Roughly … and You Must Choose Your Modulus Carefully!

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Can You Estimate Modulus From Durometer Hardness for Silicones? Yes, but only roughly … and you must choose your modulus carefully!

By Kent Larson

such crosslinker and adhesion promoter 10,00010,000 movement can create a 3-5A hardness Adhesives, Coatings difference between the bottom and the 1,0001,000 and Hard Encapsulants top of a sample cured in an open container. 100100 Young’s Modulus Testing Silicone Molding Tough Gels and 10 Compounds Soft Encapsulants Testing of Young’s modulus (= “Tensile” modulus = Modulus of Elasticity) is most 1 s Modulus, MPa commonly done by generating a stress/ Soft Gels Optical and Die strain curve in tension. Young’s modulus

oung’ 0.10.1 Attach Adhesives Y is defined as the initial slope of the stress/ Moldable 0.010.01 strain response. However, measuring Rubbers slope is not as easy, while taking a tensile 0.0010.001 strength at a given elongation is. Tensile strength divided by elongation is a Gel Hardness OO Scale A Scale D Scale “Secant” modulus. Such a Secant modulus = Young’s modulus only when the stress/ Introduction • Non-planarity of the material’s surface strain response is linear. For products that have such a very linear response Durometer Testing • Surface defects over a long range of strain, the simplest • Voids or other defects near the surface Durometer hardness testing is a very reasonable estimate of Young’s modulus is (may not be visible) simple, inexpensive and fast way to the tensile strength at 100% elongation. characterize elastomers. When used • Macro non-homogeneities near the However, most products do not have such within the boundaries of 10-90 points (or surface, such as from poor mixing of a linear stress/strain relationship. It is even 20-80) it is quite reproducible and two component formulations common to see an initial steeper slope, is often used as roughly correlating to The extent of cure/crosslinking of an followed by a much lower slope that Young’s modulus. Young’s modulus, on elastomer has a large impact on the eventually steepens again as the material the other hand, is not so simply measured, durometer hardness. Products cured approaches failure/breakage. and what many tend to refer to as Young’s at low temperatures can often see a modulus is in fact only an estimate – and For these products, a Secant modulus 5A hardness increase when heat cured sometimes a poor one at that. Data is also at 100% elongation (often referred or after a hot post-cure. Less well sometimes referred to as a “modulus” to as a “100% modulus”) may grossly known is that concentration gradients when instead it is a tensile strength at underestimate Young’s modulus. In an can begin to form in many products a given elongation. attempt to refine the estimate, sometimes immediately upon dispensing as some values will be reported at some smaller Durometer hardness is measured with a mobile ingredients move toward the strain, such as “10% Modulus” or “25% spring loaded indenter. Readings can be container or air interface. For room Modulus”. In some cases this will be a impacted by: temperature condensation cure products, Secant modulus, where, for instance, the tensile strength at 10% strain is divided Two other means of estimating Young’s Young’s modulus (E) is approximated as: by that strain (0.1). In other cases what is modulus are commonly used: E = 2G*(1+ v), where v = Poisson’s Ratio. reported may just be the tensile strength • Dynamic Mechanical Analysis (DMA) For silicones, Poisson’s ratio is commonly at that strain. Generally, a Secant modulus taken as 0.48-0.495. With 1 + v therefore can be a reasonably good estimate of • Rheometric Dynamic Analysis (RDA) essentially = 1.5, the equation can be Young’s modulus at sufficiently low or Moving Die Rheometer (MDR) simplified to: E = 3G’. strains – for many products such as LSRs Common data outputs from both are in the Correlations Between Durometer it seems 25% or less is reasonable, though form of storage (G’) and loss (G”) moduli. for other products much lower strains of and Young’s Modulus The complex storage modulus (G*) is <5% may be required. Perhaps the most widely known defined as: G*2 = G’2 + G”2. The common practice of reporting correlation of durometer values to For most curable silicones with a “modulus” as the 100% Secant modulus can Young’s modulus was put forth in 1958 durometer hardness at least into 1 be misinterpreted as being essentially the by A. N. Gent : the 00 scale, G’ >> G”, with G’ often same as Young’s modulus, but in some 0.0981(56 + 7.62336S) >10G”. In this case G* can be reasonably E = applications such a Secant modulus may 0.137505(254 – 2.54S) approximated by G’. Note that this may better describe a material’s properties not be the case with very soft materials Where E = Young’s modulus in MPa and in a given application where typical such as gels, or more “lossy” materials S = ASTM D2240 Type A durometer movement may fall within that range like psa’s, hot melts and TPSiVs. hardness. This equation is considered a of strain. Likewise, for applications with considerable strain cycling and especially with products having a pronounced Mullins effect, a modulus taken at an Comparison of Young’s Modulus to Shore A Durometer application-dependent strain and after a 1000 DMA prescribed movement history may be most 100 y = 0.2354e0.0657x appropriate to understand performance. 10

1 6 1-25% Secant 10 Modulus, MPa Mix and Giacomin RRC y = 0.1614e0.0541x report 184; Journal of 0.1 RDA 105 Testing and Evaluation, oung ’s 0.058x kPa)

in press 2011. Y y = 0.1611e ( D 0.01 E 104 C B DO 0.001 M 1000 A 0 10 20 30 40 50 60 70 80 90 100

Modulus, CF Nominal Shore A Durometer Hardness O 100 E OO 1-25% Secant DMA RDA oung ’s OOO Y OOO-S 10 0 20 40 60 80 100 Scale Reading, s Comparison of Young’s Modulus to Shore A Durometer 1000

1000 100

100 10

1 10 Modulus, MPa

E, MPa 0.1 oung ’s 1 Y 0.01 0 10 20 30 40 50 60 70 80 90 100 0.1 0 10 20 30 40 50 60 70 80 90 100 Nominal Shore A Durometer Hardness Durometer Hardness, s 1-25% Secant RDA Gent Equation Ruess Equation Expon. (1-25% Secant)

pg 2 good first-order approximation of Young’s Comparison of Young’s Modulus to Shore A Durometer for LSRs modulus from A hardness of 80 down to 100 20, though some have considered it of a less value below a hardness of 40A. Other 10 equations have also been postulated by Ruess such as²:

Modulus, MP 1-25% Secant 1 Shore-A to Young’s Modulus (in MPa): y = 0.4865e0.0345x

log10 E = 0.0235S - 0.6403 oung ’s Y Shore-D to Young’s Modulus (in MPa): 0.1 0 10 20 30 40 50 6 0 70 80 90 log10 E = 0.0235(S + 50) - 0.6403 Nominal Shore A Durometer Hardness An estimate of the relation between ASTM 1-25% Secant DMA Gent Equation Ruess Equation D2240 type D hardness and the elastic modulus for a conical indenter with a 15° Young’s Modulus Compared to Durometer for TPSiV Products cone is given by Qi³: 100 y = 0.6851e0.0578x 20(-78.188 + √6113.36 + 781.88E) SD = 100 –

E a 10 where SD is the ASTM D2240 type D hardness, and E is in MPa.

Mix and Giacomin4 derive comparable Modulus, MP 1 equations for all 12 scales that are 0.0472x

oung ’s y = 0.5587e standardized by ASTM D2240. Y All of these proposed correlations have 0.1 been created empirically and suffer from 0 10 20 30 40 50 60 70 80 90 100 a common issue – significant scatter in Nominal Shore A Durometer Hardness whatever data sets they have worked with. 1-25% Secant DMA Gent Equation Ruess Equation

Comparison of Young’s Modulus to Shore D Durometer Results 10000 Durometer Scale A – All Products y = 11.31e0.0645x 1000 Even with the scatter, there are clear 100 trends. The RDA and Secant derived data have exceptionally similar curve fits, 10 s Modulus, MPa while that of the DMA data is shifted to 1 oung’

higher modulus in comparison. Y 0.1 Comparing the Secant and RDA data to 0 10 20 30 40 50 60 70 80 90 100 the Gent and Ruess equations shows Nominal Shore D Durometer Hardness reasonably good correlation, with the Ruess 1-25% Secant DMA RDA Ruess Equation Qi Equation Expon. (DMA) equation perhaps fitting somewhat better. Young’s Modulus Comparison to Shore OO Durometer Durometer Scale A – LSRs 10 While a great deal of scatter was found within the data when looking across all 1 products within the A hardness scale, y = 0.0037e0.0718x much less so was found when narrowing Modulus, MPa the focus to a given family of products, 0.1 1-25% Secant such as to LSRs. oung ’s Y Here Gent’s equation appears to model 0.01 the data quite well, at least down to 0 10 20 30 40 50 60 70 80 90 30-40A durometer. The Excel derived Nominal Shore OO Durometer Hardness

pg 3 exponential curve fit also appears to fit compressive pressure can often significant impact on cured properties. very well to the data. Again, the DMA lead to further crosslinking which Going beyond that tolerance can shift derived modulus is significantly higher can increase modulus and hardness modulus, durometer and other properties than that from stress/strain curves (there values. This is commonly observed outside of the product specifications was not enough RDA data available to plot). in compression set testing. Such and warranties. In general, using less changes can be thought of as further crosslinker will make cured products Durometer Scale D curing at milder temperatures, or they softer and lower modulus, while adding The D durometer hardness scale typically can be a result of oxidative or other more has minimal impact (note, for aligns with silicone products with 80A = 20D. degradation mechanisms at higher the extremely soft gels, adding more This data also had a lot of scatter, and far temperatures. crosslinker can significantly increase hardness and modulus). fewer products that used this hardness • Exposure to soluble liquids and oils scale. The data points above 80D are from can cause plasticization, which lowers As mentioned in the Limitations, exposure Silicone Molding Compounds, assuming modulus and hardness. Such changes to soluble liquids and oils will essentially their measured Flexural modulus should can be temporary or permanent, plasticize silicones, lowering hardness and 5 be a good estimate for Young’s modulus . depending on the volatility of the modulus. Some formulators will purposely The Ruess and Qi equations do not seem contaminant. add silicone or organic oils to achieve the same purpose. However, such practices to fit the data very well above 20-30D, • Stress/strain characteristics can be can lead to unintentional consequences, although the Qi equation does again fit profoundly affected by temperature. such as oil migration out of the cured at about 90D. However, this does follow Most silicones undergo a slight silicone (called bleed) which can cause relatively closely with a comparison of crystallization around -48°C. Below visual blemishes and negatively impact Young’s modulus and Shore D durometer that transition temperature, these 6 adhesion of adhesives, sealants, paints and found by Pampush . elastomers will be significantly inks on nearby surfaces. Over time, such harder and higher modulus. Some Durometer Scale 00 modified silicones may appear to harden silicones contain semi-crystalline and stiffen as the plasticizing oil migrates There was considerable scatter in the silicone resins which can exhibit a away. It is generally not recommended to data when the durometer values moved melting or softening point. Durometer use this approach to modify properties into the 00 scale, where a 65 00 usually = and modulus characteristics can unless there is a very clear understanding about 8A. Looking at just the stress/ strain significantly change when the of the long term durability effects on the data, a reasonable fit can be made with an temperature crosses such transitions. exponential curve. silicone itself and on surrounding surfaces. • Modulus can be impacted by cyclic Note that some silicones are originally Limitations When Converting strain frequency. DMA and RDA formulated with small amounts of such Durometer to Modulus are commonly used to characterize oils – these are commonly called out as property responses over temperature “self-lubricating” or other terminology to Besides the obviously large scatter in and frequency ranges. indicate their presence. Two-part room the data, especially at low hardness temperature curing condensation cure values, other factors also influence how a Modifying Modulus silicones also commonly include a small material performs in application induced Properties of commercial products are amount of non-curing silicone polymer extensions (and compressions). designed to meet standards usually called used as a diluent for the cure catalyst. • Cyclic stress give way to the Mullins out in technical data sheets and sales Modulus and hardness modifications can effect, where stress/strain responses specifications. Modulus and hardness can be achieved as above, but these can be are impacted by prior maximum be unwittingly or purposely modified in prone to poor durability of the desired loading stress. Such changes are often several ways. properties as well as other unintended recoverable at low strains, but can For two-part products, the specified mix consequences. Other methods to reduce become permanent at higher strains. ratio will create a mixture that meets crosslink density in a more stable manner • Material fatigue over time and/or cycling the intended property profile. Products or change reinforcing filler levels can count can induce defects such as tears are formulated to allow for expected mix create products with desired hardness and or cracks that dramatically reduce the tolerances from dispense equipment, modulus characteristics. stress required to cause failure. which typically should be ± 3% from • Exposures to high temperatures, reputable vendors. Many products can and especially when coupled with tolerate ± 5% in the mix ratio without

pg 4 Conclusions References Durometer hardness and Young’s modulus 1. A. N. Gent (1958), On the relation should be related since one relates applied between indentation hardness and stress to extension and the other to an Young’s modulus, Institution of Rubber indenter compression. From data collected Industry -- Transactions, 34, pp. 46–57. over a wide range of silicone products the following conclusions could be drawn: 2. Https://www.3dvision.com/blog/ • Curve fits for RDA and stress/strain entry/2011/07/14/convert-durometer-to- data matched closely for hardness youngs-modulus.html scales of A and 00. 3. Qi, H. J., Joyce, K., Boyce, M. C. • DMA showed a higher Young’s (2003), Durometer hardness and the modulus estimate vs RDA and stress-strain behavior of elastomeric stress/strain data. materials, Rubber Chemistry and • There was far less scatter in the data Technology, 76(2), pp. 419–435. when comparing products within at 4. A. W. Mix and A. J. Giacomin (2011), least some formulation series or type, Standardized Polymer Durometry, such as for LSRs. Journal of Testing and Evaluation, 39(4), • The RDA and stress/strain data fit pp. 1–10. reasonable well to equations by Gent 5. Keith Pedersen, CAPinc CAPUniversity, and Ruess within the Shore A scale. Frequently Asked Questions on • The data also fit reasonably well to a Material Properties for Simulation simple exponential curve fit. Answered on September 25, 2013. • Fitting gel hardness and 00, A and D 6. J. D. Pampush, et. al., Technical Note: hardness scales to overlay on known Converting Durometer Data into crossover points from the data, Elastic Modulus in Biological Materials, Young’s modulus could be tracked Am. J. OF Physical Anthropology 146:650–653 (2011). over seven orders of magnitude within silicone formulations. The curve fits should allow for calculations of an estimated Young’s modulus from durometer readings to a “first order” accuracy that is likely sufficient for many uses.

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