Dow White Paper 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 0.0541x Mix and Giacomin RRC ’s y = 0.1614e report 184; Journal of 0.1 RDA 105 Testing and Evaluation, oung 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 ’s O 100 E OO 1-25% Secant DMA RDA oung 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 ’s E, MPa 0.1 oung 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 ’s 1 Shore-A to Young’s Modulus (in MPa): y = 0.4865e0.0345x log10 E = 0.0235S - 0.6403 oung 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. 4 Modulus, MP Mix and Giacomin derive comparable ’s 1 equations for all 12 scales that are 0.0472x oung 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, ’s 0.1 1-25% Secant such as to LSRs. oung 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.