Durability Insights from the ISA for Tire Tread Compound Development

My last blog post (Getting a Quick Read on Durability with the Intrinsic Strength Analyser) highlighted a one-hour test on the Intrinsic Strength Analyser (ISA) to screen elastomer materials for long-term fatigue performance, with applications in materials R&D and plant mixing quality control. To illustrate the use of this approach for rubber compound development, we recently had the opportunity to collaborate with Dr. Nihat Isitman from Goodyear Tire & Rubber Company in Akron, Ohio and Dr. Radek Stoček from Polymer Research Laboratory in Zlín, Czech Republic.1 Dr. Isitman led this project and was scheduled to present our research at the Spring 2020 Technical Meeting of the ACS Rubber Division, but the meeting was cancelled due to COVID-19 precautions. Instead, the Rubber Division is offering the content online, and the meeting presentations are available here for a modest fee.

Our study considered model tread compounds based on the well-known green tire formulation, which is a compatible blend of solution styrene-butadiene rubber (SBR) and high-cis butadiene rubber (BR) that is reinforced with a silica-silane system for low rolling resistance (improved fuel economy) passenger tires. Additional production compounds used in actual tire treads were also tested, but the proprietary results for these materials were not included in the public presentation. The SBR/BR ratio, silica loading, and crosslink density were all varied in this investigation. For each rubber formulation, the ISA was used to measure the fatigue threshold (T0) and critical tearing energy (tear strength; Tc), which bracket the two ends of the fatigue crack growth curve as shown below.

The established cutting method of Lake and Yeoh2,3 is used for assessing T0 on the ISA, and the one-hour test on this benchtop instrument is concluded with a tearing procedure to measure Tc. The ISA is manufactured by Coesfeld GmbH & Co. in Dortmund, Germany, and distributed in the Americas by Endurica LLC (see photo).

The slide image below summarizes the key findings of this research collaboration. Optimization of T0 and Tc is possible thanks to different sensitivities to the various compounding variables. It is important to measure both fatigue threshold and tear strength to quantify durability potential of rubber materials, and the ISA is an efficient and effective instrument for these measurements. To learn more about this testing equipment for the rubber lab, please contact me at cgrobertson@endurica.com.

References

  1. N. Isitman, R. Stoček, and C. G. Robertson, “Influences of compounding attributes on intrinsic strength and tearing behavior of model tread rubber compounds”, paper scheduled to be presented at the 197th Technical Meeting of the Rubber Division, ACS, Independence, OH, April 28-30, 2020 (online presentation due to meeting cancellation).
  2. G. J. Lake and O. H. Yeoh, “Measurement of Rubber Cutting Resistance in the Absence of Friction”, International Journal of Fracture 14, 509 (1978).
  3. C. G. Robertson, R. Stoček, C. Kipscholl, and W. V. Mars, “Characterizing the Intrinsic Strength (Fatigue Threshold) of Natural Rubber/Butadiene Rubber Blends”, Tire Sci. Technol. 47, 292 (2019).
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Getting a Quick Read on Durability with the Intrinsic Strength Analyser

There is now a one-hour test on a benchtop instrument for the rubber lab to screen materials for long-term fatigue performance. Please continue reading to learn more about this commercialization of a classical elastomer characterization methodology.

Rubber products manufacturers and raw materials suppliers seeking improved materials for next-generation applications depend on lab tests to predict end-use performance. These predictive tests should balance accuracy, relevance, and testing time. The testing time component is particularly challenging when the performance characteristic of interest is fatigue lifetime. The image of traditional fatigue testers chattering along for days or weeks comes to mind for those of us with experience in industrial rubber labs. The time consideration is the reason why tensile stress-strain testing (stretching a material to high strains until failure) is the most common physical test for the fracture behavior of rubber, in clear contrast to the most prevalent application condition for rubber products which is cyclic loading (fatigue) at much lower strains.

Fatigue crack growth is a key element of elastomer behavior that must be determined in order to predict durability, as illustrated below. For example, fatigue crack growth (FCG) testing provides the FCG rate law that is essential for predicting when and where cracks will show up in rubber products using Endurica’s elastomer fatigue software for finite element analysis [https://endurica.com/integrated-durability-solutions-for-elastomers/]. Endurica has developed a finitely scoped, reduced variability measurement approach1 which is used in our Fatigue Property Mapping testing services and is available on the Coesfeld Tear and Fatigue Analyser (TFA). Our standard FCG measurement protocol takes 20 hours of continuous testing. This testing time is very efficient for characterizing best candidate materials in the development process, but a faster test is needed for narrowing down, for example, 20 initial materials to 5 best candidates or for use in a plant lab to monitor quality of rubber compounding processes.

The Intrinsic Strength Analyser (ISA) is a recent addition to the durability testing solutions for elastomers. The ISA was developed through a partnership between Coesfeld GmbH & Co. (Dortmund, Germany) and Endurica LLC (Findlay, OH, USA), and this benchtop instrument employs a testing protocol based on the long-established cutting method of Lake and Yeoh.3,4 Endurica’s president, Dr. Will Mars, discusses the importance of measuring intrinsic strength (fatigue threshold) in this video on our YouTube channel which also shows some footage of the ISA in operation:

https://www.youtube.com/watch?v=BL92ppsJZfE

The fatigue crack growth curve of rubbery materials is bounded by the fatigue threshold, T0, on the low tearing energy (T) side and by the critical tearing energy (tear strength), Tc, at the high-T end. This is depicted in the generalized figure below. A streamlined one-hour procedure on the ISA can measure both T0 and Tc which can then be used to estimate the slope (F) of the intermediate FCG power law response that correlates well with the actual F from rigorous FCG testing using the TFA (see figure). More information about this quick ISA approach to characterizing rubber crack growth behavior for materials development and quality control can be found in the Annual Review 2019 issue of Tire Technology International (open access).2

The fatigue crack growth slope, F, from the ISA should be considered an approximate value that is useful for comparing the relative FCG behavior of materials. However, the determination of T0 on the ISA is highly quantitative and the only realistic option for assessing this parameter, since the near-threshold crack growth testing on the TFA needed to define T0 would take about a month. The implementation areas for the ISA and TFA are compared in the following table. A very conservative approach to product development for elastomer durability is to create a combination of material behavior and component design that places the final operation of the rubber product below the fatigue threshold. If this is your company’s approach to engineering for durability, then the ISA is the testing instrument you need.

Crack precursor size is another key characteristic of elastomers that needs to be quantified in order to predict durability. In combination with a standard tensile stress-strain test, the critical tearing energy (Tc) from the ISA can also be used to assess crack precursor size, as we showed recently in an open access publication.5

Endurica is the exclusive Americas distributor of the Coesfeld ISA and TFA instruments. Endurica’s efficient and effective testing protocols are provided on these high-quality instruments for the rubber laboratory. To learn more about how to add these testing capabilities to your lab, please contact me at cgrobertson@endurica.com.

References

  1. J. R. Goossens and W. V. Mars, “Finitely Scoped, High Reliability Fatigue Crack Growth Measurements”, Rubber Chem. Technol. 91, 644 (2018).
  2. C. G. Robertson, R. Stoček, R. Kipscholl, and W. V. Mars, “Characterizing Durability of Rubber for Tires”, Tire Technology International, Annual Review 2019, pp. 78-82.
  3. G. J. Lake and O. H. Yeoh, “Measurement of Rubber Cutting Resistance in the Absence of Friction”, International Journal of Fracture 14, 509 (1978).
  4. C. G. Robertson, R. Stoček, C. Kipscholl, and W. V. Mars, “Characterizing the Intrinsic Strength (Fatigue Threshold) of Natural Rubber/Butadiene Rubber Blends”, Tire Sci. Technol. 47, 292 (2019).
  5. C. G. Robertson, L. B. Tunnicliffe, L. Maciag, M. A. Bauman, K. Miller, C. R. Herd, and W. V. Mars, “Characterizing Distributions of Tensile Strength and Crack Precursor Size to Evaluate Filler Dispersion Effects and Reliability of Rubber”, Polymers 12, 203 (2020).
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Durability of 3D Printed Elastomer Structures

If you are involved in 3D printing with elastomers, can you predict the fatigue behavior?

How is product lifetime affected by complex lattice designs with multiaxial stresses, and what is the impact of printing defects?

Scientific literature and social media are abound with amazing examples of the potential for 3D printed articles made from metals, plastics and elastomers for use in many fields including the biomedical area. Researchers at ETH Zürich recently 3D printed a functioning artificial heart made from a silicone material. A picture of the device is shown below, and the story can be viewed elsewhere.1,2 This pioneering work represents a very noteworthy achievement. This research also highlights the importance of understanding elastomer durability in these cutting edge applications, as the silicone heart only survived 3,000 beats or about 30 minutes.

One of the key differences between 3D printing (additive manufacturing) and conventional manufacturing is the ability of 3D printing processes to create complex structures containing open spaces, often lattice-like in nature. Perhaps the most innovative and high profile example of a 3D printed product with lattice construction is the midsole for the Adidas Futurecraft 4D shoe that is created using the Carbon 3D technology.3

Overall stresses that are relatively modest and unidirectional translate into much higher stress, multiaxial conditions within the struts of a lattice structure like the shoe sole example above. The finite element simulation below illustrates this for a lattice structure undergoing simple compression (thanks to Mark Bauman, engineering analyst at Endurica).

Multiaxial load cases, crack closure considerations, and other complexities that arise in lattice designs and make it impossible to predict fatigue behavior using simplistic approaches such as Wohler / stress(S)-lifetime(N) curves, can be readily handled using the Endurica CL elastomer fatigue solver for Abaqus, MSC Marc, and ANSYS finite element analysis to predict when and where cracks will show up in the structure.

Cracks in an elastomer start out as microscopic precursors that grow due to applied cyclic loading according to a characteristic crack growth rate law for the material.4 In combination with critical plane analysis, this rubber fracture mechanics approach is the cornerstone of our Endurica CL software. The crack precursors – also called intrinsic defects or flaws – are especially important to pay attention to in the additive manufacturing of products in which voids or defects can be introduced by the printing process. The Core Module of our Fatigue Property Mapping testing services includes quantification of crack precursor size, and our new Reliability Module characterizes its distribution. The figure below illustrates the clear influence of crack precursor size on tensile strength in a study wherein we intentionally introduced glass microspheres as flaws in the rubber compound.5 Fatigue lifetime shows the same strong dependence on flaw size.

Endurica has the software, testing solutions, and expertise to help you understand and improve the durability of your 3D printed elastomer applications, so contact us to see how we can help you #GetDurabilityRight in the additive manufacturing world.

References

  1. https://www.sciencealert.com/this-3d-printed-soft-artificial-heart-beats-just-like-a-real-one
  2. https://www.youtube.com/watch?v=YUYNXeHfTdQ
  3. https://www.youtube.com/watch?v=qlomslovAnI
  4. W. V. Mars, “Fatigue life prediction for elastomeric structures”, Rubber Chemistry and Technology 80, 481 (2007), https://doi.org/10.5254/1.3548175.
  5. C. G. Robertson, L. B. Tunnicliffe, L. Maciag, M. A. Bauman, K. Miller, C. R. Herd, and W. V. Mars, “Characterizing Tensile Strength Distribution to Evaluate Filler Dispersion Effects and Reliability of Rubber”, paper presented at the Fall 196th Technical Meeting of the Rubber Division, American Chemical Society (International Elastomer Conference), Cleveland, OH, October 8-10, 2019.

 

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Top 10 Reasons to Celebrate Endurica’s 10-Year Anniversary

In considering ways to capture the contributions and essence of Endurica LLC to celebrate its tenth year of existence – and educating myself some more about the company I joined a little more than a year ago – I decided to put together the following top 10 list.  Enjoy this informative snapshot of Endurica.

10 years of providing software and testing solutions for elastomer applications to #GetDurabilityRight in automotive, tire, aerospace, sealing, defense, consumer products, energy, and medical industries.

9 countries are using Endurica’s elastomer fatigue analysis software products (Endurica CL™, fe-safe/Rubber™, Endurica DT™, and Endurica EIE™) for finite element analysis (FEA).

8 specialized elastomer characterization modules are available in our Fatigue Property Mapping testing services.

7 years ago, the first training course was offered by Endurica. Today there are three courses that are each taught multiple times around the world every year.

6 is the number of full-time teammates working at Endurica LLC.

5 types of integrated durability solutions are offered by Endurica: FEA software, material characterization services, testing instruments, training, and consulting.

4 patents for Endurica’s innovative technology (3 granted plus 1 pending application). 

3 testing instruments are available in the Americas region through our partnership with Coesfeld GmbH & Co. KG (Germany).

2 members of the Endurica team received the Sparks-Thomas Award from the Rubber Division of the American Chemical Society for outstanding contributions and innovations in the field of elastomers.

1st (and only) commercial FEA software to predict when and where cracks will show up in an elastomer product with complex loading and geometry for users of Abaqus™, ANSYS™, and MSC Marc™.

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Just Because You Can Doesn’t Mean You Should

When you have an unmet simulation or testing need, should you build or buy the capability?

There are testing instruments and software packages available in the market – which have been improved through years of R&D and quality management – that can meet the needs of a technical team in their product development efforts. Despite these turn-key resources, we sometimes see a company tasking some of its engineers to build their own.

Why does this happen?

Companies hire smart and creative engineers and scientists with advanced degrees to populate their R&D centers. It is common, and even expected in many situations, for a graduate student to create customized equipment or software as a part of a Ph.D. or M.S. research project. Pushing the boundaries of science and technology often requires such development of devices or code. Also, limited research funding in academia can force students to build their own equipment. When young engineers start their industrial careers after graduate school, they carry with them the mindset of building and programming things themselves. These individuals excitedly offer to create when a new analysis or measurement need arises within a company, and managers like to encourage the enthusiasm of their technical staff.

But, even if your sharp engineer can build a DIY testing device or computer program that recreates the state-of-the-art commercial products created by teams of engineers across many years, is this an efficient and strategic use of the engineer’s abilities? If your company makes tires, for example, then shouldn’t you have your smart people focused on making better tires rather than making testing instruments or software?  What are the labor costs, and the opportunity costs, of your highly-skilled engineer building a piece of testing equipment compared to the price of the commercial instrument or relative to the return you could make on an actual improvement to your product? Unless you are in a position to surpass the commercial solution, there is no competitive advantage in the DIY solution. Once you have created your own solution, who will maintain and support it? Will you be able to keep it up to date with advances in technology? Do you have the capabilities and resources to validate your solution more strongly than the market has already validated the commercial solution?

Through my 15 years of experience in materials research and development in the tire and rubber industry, I have seen several pieces of home-built testing equipment collecting dust within companies. Either they were half finished and abandoned or could only be reliably operated by the creator who moved to another department or company.

There can be circumstances where the needed instrument or simulation product is not commercially available. Sometimes the capability exists in the marketplace, but it is not discovered because the maker mindset leads to a halfhearted search. For customized solutions, you may consider working with a vendor to leverage their expertise in creating the required device or program.

If your analysis and testing needs are in the rubber fatigue and lifetime area, please talk to us before you decide to invest in creating your own solutions. Our solutions embody decades of experience. They are the most competitive and strongly validated solutions you can buy. Endurica has specialized finite element analysis software that predicts elastomer durability for complex geometries and loads, and we offer testing instruments for accurately characterizing the fracture mechanics of elastomers through our partnership with Coesfeld GmbH & Co. KG. We can take you quickly to the forefront of fatigue management capabilities.

 

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Integrated Durability Solutions for Elastomers

Will the durability of your new rubber product meet the expectations of your customers? 

Do you have a comprehensive capability that fully integrates all of the disciplines required to efficiently achieve a targeted durability spec?

Your engineers use finite element analysis (FEA) to model the elastomer component in the complex geometry and loading cycle for the desired product application.  One traditional approach to predicting durability is to develop a rough estimate of lifetime by looking at maximum principal strain or stress in relation to strain-life or stress-life fatigue curves obtained for the material using lab specimens in simple tension.  The difficulties and uncertainties with this method were discussed in a recent blog post.

 

A modern approach to elastomer durability is to use the Endurica CL™ durability solver for FEA.  This software uses rubber fracture mechanics principles and critical plane analysis to calculate the fatigue lifetime – which is the number of times the complex deformation cycle can be repeated before failure – for every element of the model.  This provides engineers with the ability to view lifetime throughout the FEA mesh, allowing them to modify design features or make material changes as needed to resolve short-lifetime areas.

A sound finite element model of the elastomer product in the specified loading situation and fundamental fatigue material parameters from our Fatigue Property Mapping™ testing methods are the two essential inputs to the Endurica CL software.  This is illustrated in the figure below.

The requisite elastomer characterization methods can be conducted by us through our testing services or by you in your laboratory with our testing instruments.  For some companies, consulting projects are a route to taking advantage of the software before deciding to license the unique predictive capabilities.  The following diagram shows how our products and services are integrated.

For companies that are just getting started with implementing our durability solutions, the following is a typical testing services and consulting project:

  1. We use our Fatigue Property Mapping™ testing methods, through our collaboration with Axel Products Physical Testing Services, to characterize the properties of cured sheets of rubber compounds sent to us by the client. The minimum requirements for fatigue modeling are crack precursor size and crack growth rate law, and these are quantified within our Core Fatigue Module.  Special effects like strain-induced crystallization and aging/degradation are accounted for using other testing modules when applicable.
  2. The client sends us the output files from their finite element analysis (FEA) of their elastomer part design for the deformation of their complex loading cycle. It is common for the goal to be a comparison of either two designs, two distinct loading profiles, two different rubber compounds, or combinations of these variations.  Our software is fully compatible with Abaqus™, ANSYS™, and MSC Marc™, so the simulations can be conducted on any of these FEA platforms.  In some situations where a client does not have their own FEA capabilities, one of Endurica’s engineers will set up the models and perform the analyses instead.
  3. The fatigue parameters and FEA model are inputted to Endurica CL fatigue solver to calculate values of the fatigue lifetime for every element of the model. The lifetime results are then mapped back onto the finite element mesh in Abaqus, ANSYS, or MSC Marc so that the problem areas (short lifetime regions) within the geometry can be highlighted.
  4. We review the results with the client and discuss any opportunities for improving the fatigue performance through design and material changes.

Advanced implementors of our durability solutions have licensed the Endurica CL software and are using our rubber characterization methods in their laboratories on a routine basis, with instruments provided through our partnership with Coesfeld GmbH & Co. (Germany).  One recently publicized example of a company using the Endurica approach to a very high degree is Tenneco Inc., which you can read about here.

We want to help you #GetDurabilityRight, so please contact me at cgrobertson@endurica.com if you would like to know more about how Endurica’s modern integrated durability solutions for elastomers can help enable a product development path that is faster, less expensive, and more confident.

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Strain-Induced Crystallization in High Cis Butadiene Rubber: Fact or Fiction?

There is an ongoing drive to create synthetic rubber that can give mechanical performance matching the properties of natural rubber (NR) – excellent strength, tear resistance, and fatigue crack growth resistance – which are attributed to the ability of NR to strain crystallize.  I have attended several technical conferences in the tire and rubber field where I have witnessed presentations about new grades of polybutadiene (butadiene rubber (BR)) with high cis-1,4 structure, wherein a claim is made about the improved ability of the BR to undergo strain-induced crystallization (SIC) for better mechanical properties in tires and other rubber applications.  Similar statements can be found in technical marketing materials and in patents.1,2  To what extent is this true?  This post takes a closer look at this topic.

It is first useful to show why strain-induced crystallization is key to the unique mechanical properties of natural rubber.  One of the most conclusive studies on the function of strain-induced crystals to slow the growth of cracks in cyclic fatigue is the work by Brüning et al.3  The movie below from this research shows an edge crack region in NR reinforced with 40 phr of N234 carbon black that is experiencing cyclic deformation from 0% to 70% planar tension at a frequency of 1 Hz.  Each pixel at each time in the video represents a wide-angle X-ray diffraction pattern collected in real time while stretching in a synchrotron X-ray beam, with red color used to indicate crystallinity and black for purely amorphous regions.  You can see the crystals form during stretching which self-reinforces the rubber at the crack tip region to resist further growth of the crack.  These experiments are very revealing, but they are extremely difficult and expensive to perform, as they require scattering analysis expertise, specially designed stretching devices with precise spatial control, and access to one of the few national laboratory sites where synchrotron X-ray studies can be performed.

Stereoregular polymers can crystallize in a window bounded by the glass transition temperature (Tg) and the melting temperature (Tm). When stretched, a polymer can crystallize at temperatures above its normal melting temperature due to melting temperature elevation caused by the well-known chain orientation/entropy effect.4  Chain orientation results in an increase in melting temperature from Tm to Tm,SIC.  This is shown schematically in the figure below for NR and BR.  The Tg and Tm for BR are significantly lower than the values for NR.  Therefore, even after perfecting the structure of polybutadiene to achieve >98% cis-1,4 structure though catalyst and process innovations, BR still has an intrinsic disadvantage compared to NR when it comes to SIC in the common temperature range where durable rubber components are employed.

 

Gent and Zhang5 recognized the lower Tm,SIC for BR compared to NR for samples crystallized in uniaxially strained conditions.  Ultra high cis BR with 98% cis content did not show any evidence of strain-induced crystallization at 23 °C whereas NR clearly exhibited SIC in a study by Kang and coworkers.6  In an investigation by Toki et al.,7 it was necessary to reduce the temperature to 0°C before high cis BR showed a crystalline X-ray scattering pattern at a strain of 5 (500% elongation).

As an aside, I will caution the use of the entropy-driven melting temperature increase as the only explanation for strain-induced crystallization above the normal Tm.  Natural rubber is quite a slow crystallizing polymer in the unstretched state, even when annealed in the prime crystallization regime midway between Tg and Tm.  In stark contrast, strain-induced crystallization occurs very fast in NR which highlights the complexity of behavior beyond the over-simplification given in the figure above.

So, why is there not more focus on synthetic high cis-1,4-polyisoprene which has the same polymer microstructure and strain crystallization window as NR?  The short answer is that the butadiene monomer is much more commercially available than isoprene at many synthetic rubber plants around the world.  I remember the early years in my industrial R&D career when I was working with some very talented polymer chemists at Bridgestone / Firestone.   I was developing new molecular architectures for improved synthetic rubber to use in various tire compounds.  The chemists told me that they could make almost any polymer design I wanted, as long as it could be made from styrene and/or butadiene.  This restriction reflected the fact that these two monomers were the commonly available feedstocks at the commercial plants where the polymers would eventually be produced.

In closing, it is a fact that high cis polybutadiene can strain crystallize at sub-ambient temperatures, but it is fiction that it will strain crystallize in the same manner as natural rubber at room temperature and above.

Do you want to see if your rubber will really exhibit strain-induced crystallization in a practical way that is relevant to end-use applications?  Contact me (via email: cgrobertson@endurica.com) to learn more about the Non-Relaxing Module in Endurica’s portfolio of testing services that was specifically developed to efficiently highlight SIC effects.8-10

References

1 http://arlanxeo.de/uploads/tx_lxsmatrix/sustainable_mobility_01.pdf

2  S. Luo, K. McKauley, and J. T. Poulton, “Bulk polymerization process for producing polydienes”, U.S. Patent 8,188,201, granted May 29, 2012 to Bridgestone Corporation.

3 K. Brüning, K. Schneider, S. V. Roth, and G. Heinrich, “Strain-induced crystallization around a crack tip in natural rubber under dynamic load”, Polymer 54, 6200 (2013).; movie provided to Endurica LLC by the authors (movie to be used only with permission from Karsten Brüning).

4 P. J. Flory, “Thermodynamics of crystallization in high polymers. I. Crystallization induced by stretching”, Journal of Chemical Physics 15, 397 (1947).

5 A. N. Gent and L.-Q. Zhang, “Strain-induced crystallization and strength of elastomers. I. cis-1,4-polybutadiene”, Journal of Polymer Science Part B: Polymer Physics 39, 811 (2001)

6 M. K. Kang, H.-J. Jeon, H. H. Song, and G. Kwag, Strain-induced crystallization of blends of natural rubber and ultra high cis polybutadiene as studied by synchrotron X-ray diffraction”, Macromolecular Research 24, 31 (2016).

7 S. Toki, I. Sics, B. S. Hsiao, S. Murakami, M. Tosaka, S. Poompradub, S. Kohjiya, and Y. Ikeda, “Structural developments in synthetic rubbers during uniaxial deformation by in situ synchrotron X-ray diffraction”, Journal of Polymer Science Part B: Polymer Physics 42, 956 (2004).

8 K. Barbash and W. V. Mars, “Critical Plane Analysis of Rubber Bushing Durability under Road Loads”, SAE Technical Paper 2016-01-0393, 2016, https://doi.org/10.4271/2016-01-0393.

9 W. V. Mars and A. Fatemi. “A phenomenological model for the effect of R ratio on fatigue of strain crystallizing rubbers”, Rubber Chemistry and Technology 76, 1241 (2003).

10 https://endurica.com/specifying-strain-crystallization-effects-for-fatigue-analysis/

 

 

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