Towards better rubber compound selection: Introducing Endurica’s new Companion(TM) App

Rubber can be formulated in a very wide range of properties.  For materials developers, this cuts two ways. On one hand, it means that there are almost always excellent options for a given application.  On the other, it means that those options are usually hidden among lots of bad options.  This is job security for rubber compounders, but it unfortunately also underlies the fact that there are so many instances of sub-optimal materials selection decisions when it comes to rubber.  One study found that more than 40% of rubber product failures could have been avoided with better materials selection.

One cause of this statistic is poor visibility into how material properties map into application performance.  Too often, the material options are judged based on an over-simplified lab test, or an incomplete specification of application conditions. We made the CompanionTM app to address this gap.  Companion makes it easier to find the rubber properties that ensure durability in your application.  Companion can compare materials for strain-, stress- and energy control.  It can compare applications with different modes of deformation (tension, compression, shear).  It can account for fully relaxing and nonrelaxing loading. It can account for temperature effects.

Another cause of too-high rates of poor materials selection is that sometimes different parts of an organization use incompatible approaches to specify, characterize and analyze the material and the application.  Gaps between the materials, product and testing silos sometimes create unnecessary confusion, conflict and wasted effort, leading to poor durability.  Companion was built with the aim of getting materials engineers and product engineers using a common, validated framework.  The material properties and analysis principles in the Companion App are the same as those used in our product simulation software, but the user experience in the app is centered around the materials selection decision.  No special knowledge of fatigue theory or simulation technology is needed to start using the app.

You can use the basic version of Companion for free.  Go to companion.endurica.com to set up your account and try it out.  The free version lets you define one material and one loading condition.  A subscription-based professional version is also available for about $1 USD / day.  The subscription version lets you compare 2 materials and 2 load cases side-by-side, it lets you save your material definitions to a local database for future use, and it includes several outputs that give deeper insight into the fatigue behavior of your materials.  The workflow is simple: 1) define your material(s), 2) define your load case(s), 3) run the calculation, and 4) review the results and compare performance of the materials for the given load cases.

Give it a try and let us know what you think.

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Tire Society Takeaways 2021

The Tire Society held its 40th annual meeting last month with the theme The Virtual Tire.  It has always been the place to see up and coming ideas, to see who is pushing into the frontiers of the field, and to renew professional connections across the industry.  Endurica was very proud to sponsor this year.

Here’s a brief recap of our favorite talks…

GM’s Mike Anderson, Executive Director of Global Virtual Design, Development and Validation, kicked off the meeting with his keynote lecture, titled “The Move To Virtual”.  He spoke of GM’s target to achieve 100% virtual design by 2025.  Anderson explained that this doesn’t mean that physical testing will go away, but rather that GM is dead serious about getting to a “right the first time” scenario rather than a “discover and recover” mode.  “It’s a measure twice, cut once” culture, he said.  He noted that upstart competitors are sprinting ahead in areas like EVs through the use of simulation and that the speed of discovery has increased significantly in the current competitive environment.  Simulation drives learning speed, not only because of the opportunity to get engineering answers at the pre-build phase but also because it enables exploration of more of the design space and more of the performance outcomes.  He told the conference that “we need to go beyond just replicating physical tests with simulation, we need to leverage the strength of simulation to go beyond test”.  In the Q&A, Anderson was asked whether suppliers will also be expected to be virtual.  “That’s gonna be tough to play together” for rubber part suppliers that can’t engage via simulation.

There were three talks given by Endurica users at this year’s Tire Society meeting.

Pooya Behroozinia of Maxxis Tires spoke on “Tire Durability Prediction Using Three-Element Layered Mesh for Cord-Rubber Composites”.  Behroozinia shared a tire meshing technique for improving representation of interlaminar shearing in their tire model.  They used Endurica DT to simulate the damage accruing across all of the 6 steps in a stepped-up load durability test, and they were able to predict correctly the lower sidewall failure mode, the life (45 hours observed, 38 hours predicted), and the crack orientation.  They also had a 2nd validation case in which the loads were increased by 10% in all steps of the test.  The simulation again predicted correct failure, and the comparison of experimental life (41000 km) to simulated life (36330 km) was in good agreement.

Vidit Bansal of CEAT spoke on “Incremental, Critical Plane Analysis and Experimental Verification for TBR Tyre Bead Endurance Applications”.  Similar to the Maxxis paper, CEAT used Endurica DT to simulate a multi-step durability test with loads ranging from 80% to 250%.  In this paper, two different truck tire sizes were modeled and tested, a 10.00R20 and an 11.00R20.  The analysis correctly predicted the ply turnup as the critical location.  The predicted lives of the two tire sizes were predicted at 90-93% of the actual tested life in both cases.

Tom Ebbott and Gobi Gobinath of Goodyear spoke on “A Model for Predicting Residual Casing Life of a Tire Following an Impact Event”.  This work demonstrated the consequences on tire damage development of a range of impact event scenarios (3 speeds, 4 impact angles, 3 different wear states) early in the life of the tire.  It used Endurica DT to accrue damage from both the impact event (computed with explicit FEA) and subsequent tire runout under steady state rolling conditions (computed with implicit FEA).  The crack growth rate curve during the impact was based upon experimental measurements of the critical tearing energy at impact rates.  When asked about experimental validation of the simulation results during the Q&A, Ebbott noted that “the modeling work stands on its own – it is based on sound physics”.

We at Endurica were delighted with the significance and innovation on display in all of these talks.  We have often been challenged to show validation for tire durability predictions, but such measurements are difficult to obtain without significant tire testing resources. So, the fact that the Maxxis and CEAT papers showed multiple direct comparisons of tire durability tests with simulations, and the fact that excellent predictions of both failure mode and tire life were achieved was a very significant moment for us and for the industry.

The Goodyear paper was significant for a different reason.  Their paper showed an application that would have been difficult or impossible to evaluate with physical testing.  They showed how getting the right physics into the model builds the trust necessary to leverage simulation to increase the speed and scope of discovery and to go beyond the limits of physical testing.  It was the perfect illustration of keynoter Mike Anderson’s point that simulation opens significant opportunities for competitive advantage and ‘right the first time’ engineering.

 

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Virtual vs. Physical in 2021 and Beyond

These days everybody’s talking about whether to meet in person or online.  There are great tools available for online meetings, and these have helped us navigate Covid-19. Like everyone else, Endurica teammates regularly use online meeting technology.  But if there is one thing we learned over the last year, it is that sometimes physical presence really matters. Living and working in isolation is just not healthy in the long run.

The new normal during the pandemic had some benefits that were enabled by the virtual world. Time and energy that used to be consumed by travel were rechanneled into improving our software, testing services, and marketing materials. In our personal lives, we had more opportunities to spend quality time with our immediate families and found more time for fitness activities. We previously talked about our pandemic pivots to bring our training courses online and offer webinars to stay in touch with our existing and potential customers.

But virtual meetings can’t replace the full experience of being together in person.  The face-to-face engagement at a trade show, the serendipitous bumping into a client, the spontaneous discussion of ideas with fellow conference-goers with a shared interest, the rapport building that comes from shared experiences.  We fundamentally need physical connection. A hug, delivered via Zoom, will never feel the same.

The world of 2021 and beyond is hybrid: part virtual, part in-person.  The benefits of the virtual are too great to set aside, and the necessity of the physical is too compelling to neglect.  Both are critical to our future, at home and at work.

So, too, with Endurica’s simulation workflows. It was NEVER Simulation OR Build-and-Break. Even the best simulations are not enough to completely skip physical testing. The virtual approach saves significant time and money in product development and design refinement. It allows you to explore a huge space of compound options and of design features before investment in building and testing prototypes. Our simulations enable you to balance difficult trade-offs. Still, before you head into production, you must complete actual physical testing on your rubber part – the physical world is what counts in the end. It is simulation AND build-and-break that are both needed in concert to #GetDurabilityRight.

Just as a Zoom hug will never replace the real thing, software will never replace the role of physical testing.  But just as online meetings are creating new opportunities and efficiencies, Endurica’s tools position you for unprecedented success when it’s time to test.

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Use This One Simple Trick to Ensure Rubber Part Durability

We’ve just added a new output to the Endurica fatigue solver: Safety Factor.  This feature makes it simple to focus your analysis on whether cracks have the minimum energy required to grow. Safety Factor is a quick and inexpensive way to identity potential failure locations.  It minimizes the number of assumptions you need to defend, and it is backed by hard science.  You don’t need to measure or explain the many influences that together determine how fast cracks grow.  You don’t need lengthy materials characterization experiments that take days or weeks.  You do need to know your material’s Intrinsic Strength T0 (ie Fatigue Threshold) and its crack precursor size c0. The test takes about an hour using the Coesfeld Intrinsic Strength Analyser.

The Safety Factor S is computed as the ratio of T0 to the driving force T on a potential crack precursor.  If the value of the Safety Factor S = T0/T is greater than 1, it indicates the margin by which crack growth is avoided.  If S is less than 1, it indicates that crack growth is inevitable. The calculation of the Safety Factor includes a search for the most critical plane, as we do for our full fatigue life computations.

Although the Safety Factor can’t tell you how long a part will endure, it nevertheless does offer great utility.  You can make a contour plot showing the locations in your part where the Safety Factor is the lowest.  This is a quick and inexpensive way to identity potential failure locations.  You can make statements about the reserve capacity of your design that are easy to communicate and understand with a wide audience.

The images above show a vibration isolation grommet operating under small (Safety Factor 2.6) and large displacements (Safety Factor 0.83).  Color contours indicate the Endurica-computed Safety Factor, and use the same scale for both images.  Large Safety Factors are shown in blue.  Safety Factors approaching 1 are shown in red.  Safety Factors smaller than 1 are indicated in black.  These results show that the grommet can be expected to operate indefinitely under the small displacements, but that large displacements will produce cracks at some point, in the regions colored black.

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Durability by Design on Any Budget

Durability by Design

So, you’ve got a tricky durability problem to solve, a budget, and a deadline.  Let’s look at a helpful framework for sorting which Endurica workflows you need.  In the grid below, each row represents a potential approach you can take.  The approaches are, in order of increasing complexity and cost, the Infinite Life approach, the Safe Life approach, the Damage Tolerant approach, and the Fail Safe approach.

Endurica Durability Workflows

The Infinite Life approach is by far the simplest approach.  Here, we say that damage will not be allowed at all.  All locations in the part must operate, at all times, below the fatigue limit (ie intrinsic strength) of the rubber.  The required material testing is minimal: we need only know the fatigue limit T0 and the crack precursor size c0.  We avoid the question of how long the part may last, and we focus on whether or not we can expect indefinite life.  We report a safety factor S indicating the relative margin (ie S = T0 / T) by which each potential failure location avoids crack development.  When S>1, we predict infinite life.  For S<=1, failure occurs in finite time and we must then go on to the next approach…

In the Safe Life approach, the chief concern is whether or not the part’s estimated finite life is adequate relative to the target life.  The material characterization now becomes more sophisticated.  We must quantify the various “special effects” that govern the crack growth rate law (strain crystallization, temperature, frequency, etc.).  We consider the specific load case(s), then compute and report the number of repeats that the part can endure.  If the estimated worst-case life is greater than the target life then we may say that the design is safe under the assumptions considered.  If not, then we may need to increase the part’s load capacity, or alternatively to decrease the applied loading to a safe level.  In critical situations, we may also consider implementing the next level…

The Damage Tolerant approach acknowledges that, whatever the reasons for damage, the risk of failure always exists and therefore should be actively monitored.  This approach monitors damage development via inspection and via tracking of accrued damage under actual loading history.  A standard nominal load case may be assumed for the purpose of computing a remaining residual life, given the actual loading history to date.  Changes in material properties due to cyclic softening or ageing may also be tracked and considered in computing forecasts of remaining life.

The Fail Safe approach takes for granted that failure is going to occur, and obliges the designer to implement measures that allow for this to happen safely.  This can take the form of a secondary / redundant load path that carries the load once the primary load path has failed.  It can take the form of a sacrificial weak link / “mechanical fuse” that prevents operation beyond safe limits.  It can take the form of a Digital Twin that monitors structural health, senses damage, and requests maintenance when critical damage occurs.

The last three columns of the grid show which Endurica fatigue solver workflows align with each design approach.  The Endurica solvers give you complete coverage of all approaches.  Whether you need a quick Infinite Life analysis of safety factors for a simple part, or deep analysis of Damage Tolerance or Fail Safety, or anything in-between, our solvers have just what you need to get durability right.

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Things that went right in 2020 at Endurica

2020 is burned in all our minds as a chaotic and tough year.  Just like the rest of the world, Endurica staff experienced times of isolation and loss due to the pandemic.  On a positive note, we invested heavily in making our tools and workflows better than ever so that we’re ready to come back strong in 2021.  Here is a list of our top new developments in 2020:

Endurica Software Enhancements

  • Endurica DT’s new Ageing Feature now enables you to simulate how ageing affects your rubber product. Your compound’s stiffness, strength, and fatigue properties can all evolve with time.
  • Our new Linux distribution takes our solutions beyond the Windows world.
  • We’ve added an encryption feature to safeguard your trade secrets.
  • Viewer Improvements make it easier than ever to visualize your fatigue simulation results.
  • EIE Enhancements give you blazing-fast compute speed for full road-load signals.
  • We’ve also planned an aggressive development agenda for 2021. Stay tuned for a new Endurica-based smartphone app for materials engineers, for a new feature that computes fatigue threshold safety margins, for a new block cycle schedule extraction algorithm, and more!

Training

  • The new Fatigue Ninja Friday webinar series provides step-by-step application training for key the workflows that you need to get durability right. All of the recorded episodes are now available in the online Endurica academy.
  • The new Winning on Durability webinar series provides high-level overviews of both technical and business topics so you can connect Endurica tools to your strategic imperatives. All of these recorded webinars are available gratis on our website.
  • We’ve recast our in-person training events as LIVE, ONLINE workshops accessible safely around the world.

Testing Instruments

Fatigue Property Mapping Testing Service

  • We added the Reliability Module to our Fatigue Property Mapping testing service. Use it to quantify crack precursor size statistics when you need to estimate probability of failure.
  • We also reorganized the Thermal Module and the Ageing Module into Basic and Advanced levels, to offer a lower price-point when a basic option will suffice.

Want to leverage any of these new capabilities in your next durability project?  Give us a call and let’s talk!

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Does hydrostatic loading cause fatigue damage in rubber?

A question was recently put to us regarding the effects of cyclic hydrostatic loading on rubber.  In hydrostatic loading, no shearing stresses are present, and the 3 principal stresses all have the same value p.  For this case, all 3 Mohr’s circles degenerate to a single point on the normal stress axis.

Figure 1. Mohr’s circles degenerate to single point for the case of compressive hydrostatic pressure.

Under dynamic hydrostatic loading, the point may move along the normal stress axis in either of the tensile (p>0) or compressive directions (p<0).  When we have pure hydrostatic compression, cracks in all orientations are closed with a tearing energy of zero.  We expect infinite fatigue life in this case.  On the other hand, when we have hydrostatic tension, growth of a crack will release energy, and so the tearing energy is positive. We then expect crack growth to occur at a rate determined by the tearing energy.  Endurica estimates tearing energy T via the following rule:

in which a is the size of the crack, and Wc is the cracking energy density. For a slightly compressible material under hydrostatic loading, the cracking energy density calculation becomes

and, remembering that for volumetric deformation, the linear strain is 1/3 of the volumetric dilatation, we finally obtain

where W is the dilatational strain energy density.

 

So let’s compute an example using the following material definition:

Let’s compute 8 different fully relaxing hydrostatic loading cases: 4 in hydrostatic compression, 4 in hydrostatic tension.  We’ll take these loaded extreme strain levels: -10%, -5%, -2%, -1%, 1%, 2%, 5%, 10%, which correspond to extreme dilatations of -27%, -14%, -6%, -3%, 3%, 6%, 16%, 33%.

As a first check, we plot the hydrostatic pressures computed for each case.  The slope of the line is 3000 MPa, which agrees with the assigned bulk modulus.

Figure 2. Computed volume strain – hydrostatic pressure relationship.

Next, we compute the strain energy density and the cracking energy density for each case.  As expected, we verify that for p<0, crack closure results in CED=0, and for p>0, CED=SED/3.

Figure 3. Comparison of strain energy density and cracking energy density for hydrostatic compression and tension.

Finally, we compute the fatigue life for each case.  In all cases, we see that the damage sphere is uniform over its entire surface, indicating that all possible crack orientations receive equal damage.  We also see that for cases involving hydrostatic compression, life is essentially infinite.  For cases involving hydrostatic tension, we verify that finite life is predicted, with shorter life at higher hydrostatic tension, as expected.

Figure 4.  Predicted life and damage sphere for compressive and tensile hydrostatic loading.

In summary, we have verified that the Endurica fatigue solver behaves as follows with respect to hydrostatic loading:

  • In hydrostatic compression, no damage accrues, and life is indefinite.
  • In hydrostatic tension, crack growth is predicted, with shorter fatigue life for higher values of tension. The cracking energy density is 1/3 of the strain energy density for hydrostatic tension.
  • For all hydrostatic cases, there is no single preferred critical plane. Rather, all planes show equal potential for crack development.
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Is It Validated?

“Is it validated?” – that’s often the first question we hear after introducing our durability simulation capabilities. And for good reason, given the weight that hangs on the hinge of product durability. Endurica takes verification and validation (V&V) very seriously. Let’s look at what that means.

First, it means that our tools are built on well-known, well-established foundations.  These foundations include 1) definition of material / crack behavior via fracture mechanics (Rivlin and Thomas, 1953), 2) integration of the crack growth rate law to predict fatigue life (Gent, Lindley and Thomas, 1964), 3) the fact that crack precursors occur naturally in all locations and all orientations in a rubber sample (Choi and Roland 1996, Huneau et al 2016), 4) hyperelastic stress-strain laws compatible with commercial FEA codes (see Muhr 2005 for an excellent review), and 5) rubber’s fatigue threshold (Lake and Thomas 1967).  The validation case thus begins with the cumulative authority of thousands of reports that have confirmed these classical results over nearly 70 years.

Critical plane analysis for rubber has now been around for 20+ years, and it has been validated in multiple ways (material level, component level, system level), across multiple experimental programs (industrial and academic), by multiple independent research groups working on multiple applications (see Google/scholar, for example).  It has been validated that: 1) it correctly predicts crack plane orientation under uniaxial, proportional and nonproportional loadings (Harbour et al 2008), 2) it correctly predicts fatigue life across different modes of deformation (Mars 2002), 3) it correctly accounts for the effects of crack closure (Mars 2002), 4) it correctly predicts the development of off-axis cracks for nonrelaxing cycles in strain-crystallizing materials (Ramachandran 2017), 5) it correctly predicts the effects of finite straining on crack orientation (Mars and Fatemi 2006).

The literature is full of old experiments that we have used as validation targets.  We have validated Endurica’s strain crystallization models by simulating experimental results published by Cadwell et al (1940) and by Fielding et al (1943).  We have validated the ability to predict deformation mode effects by simulating experimental results for simple and biaxial tension published by Roberts and Benzies (1977).  We have validated Endurica’s temperature dependence against measurements reported by Lake and Lindley (1964).  We have validated against multiaxial fatigue experiments reported by Saintier, Cailletaud and Piques (2006).

We’ve done our own validation experiments.  My PhD dissertation (University of Toledo, 2001) contains an extensive database of tension/torsion/compression fatigue tests against which our critical plane algorithms were validated.  Two additional PhD dissertations that I co-advised generated additional validations.  Dr. Malik Ait Bachir’s thesis (2010) validated mathematically that the scaling law we use for small cracks is valid across all multiaxial loading states.  Dr. Ryan Harbour’s thesis (2006) contains a database of multiaxial, variable amplitude fatigue experiments against which our rainflow and damage accumulation procedures were extensively validated.

Validation from partners.  We partner with several testing labs.  We have invested in testing protocols that produce clean, accurate data and we have run validation programs with our partners to verify the effectiveness of our testing protocols.  We’ve demonstrated significant improvements to test efficiency and reproducibility (Goosens and Mars 2018) and (Mars and Isasi 2019).  We’ve validated techniques for estimating precursor size and size distribution (Robertson et al 2020, Li et al 2015).

Validation from users.  Three (3) of the top 12 tire companies and six (6) of the top 10 global non-tire rubber companies now use our solutions.  Most of our users have run internal validation programs to show the effectiveness of our solutions for their applications.  Most of these studies are unpublished, but the fact that our user base has continued growing at ~20%/year for 12 years (as of this year) says something important both about the technical validation case and the business validation case.  Validation studies have been published with the US Army (Mars, Castanier, Ostberg 2017), GM (Barbash and Mars 2016), Tenneco (Goossens et al 2017) and Caterpillar (Ramachandran et al 2017).

Validation from external groups.  There are several academic groups that have independently applied and validated components of our approach.  There are too many to list completely, but a few recent examples include Zarrin-Ghalami et al (2020), Belkhira et al (2020) and Tobajas et al (2020).

Software verification, benchmarking and unit testing.  In addition to the experimental validations mentioned above, each time we build a new version of our software, we execute a series of automated tests.  These tests verify every line of code against expected function, and they ensure that as we add new features, we do not introduce unintended changes.  The benchmarks include tests that verify things like coordinate frame objectivity (rigid rotations under static load should do no damage and the same strain history written in two different coordinate systems should have the same life), and check known results pertaining to material models and cycle counting rules.  You can read more about our software quality processes here.

It is safe to say that no other solution for fatigue life prediction of rubber has been tested and validated against a larger number of applications than Endurica’s.

References

Aıt-Bachir, M. “Prediction of crack initiation in elastomers in the framework of Configurational Mechanics.” PhD diss., Ph. D. thesis, Ecole Centrale de Nantes, Nantes (France), 2010.

Barbash, Kevin P., and William V. Mars. Critical plane analysis of rubber bushing durability under road loads. No. 2016-01-0393. SAE Technical Paper, 2016.

Belkhiria, Salma, Adel Hamdi, and Raouf Fathallah. “Cracking energy density for rubber materials: Computation and implementation in multiaxial fatigue design.” Polymer Engineering & Science (2020).

Cadwell, S. M., R. A. Merrill, C. M. Sloman, and F. L. Yost. “Dynamic fatigue life of rubber.” Rubber Chemistry and Technology 13, no. 2 (1940): 304-315.

Choi, I. S., and C. M. Roland. “Intrinsic defects and the failure properties of cis-1, 4-polyisoprenes.” Rubber chemistry and technology 69, no. 4 (1996): 591-599.

Fielding, J. H. “Flex life and crystallization of synthetic rubber.” Industrial & Engineering Chemistry 35, no. 12 (1943): 1259-1261.

Goossens, J.R., Mars, W., Smith, G., Heil, P., Braddock, S. and Pilarski, J., 2017. Durability Analysis of 3-Axis Input to Elastomeric Front Lower Control Arm Vertical Ride Bushing (No. 2017-01-1857). SAE Technical Paper. https://doi.org/10.4271/2017-01-1857

Goossens, Joshua R., and William V. Mars. “Finitely Scoped, High Reliability Fatigue Crack Growth Measurements.” Rubber Chemistry and Technology 91, no. 4 (2018): 644-650. https://doi.org/10.5254/rct.18.81532

Harbour, Ryan Joseph. Multiaxial deformation and fatigue of rubber under variable amplitude loading. Vol. 67, no. 12. 2006.

Harbour, Ryan J., Ali Fatemi, and Will V. Mars. “Fatigue crack orientation in NR and SBR under variable amplitude and multiaxial loading conditions.” Journal of materials science 43, no. 6 (2008): 1783-1794.

Huneau, Bertrand, Isaure Masquelier, Yann Marco, Vincent Le Saux, Simon Noizet, Clémentine Schiel, and Pierre Charrier. “Fatigue crack initiation in a carbon black–filled natural rubber.” Rubber Chemistry and Technology 89, no. 1 (2016): 126-141.

Lake, G. J., and P. B. Lindley. “Cut growth and fatigue of rubbers. II. Experiments on a noncrystallizing rubber.” Journal of Applied Polymer Science 8, no. 2 (1964): 707-721.

Li, Fanzhu, Jinpeng Liu, W. V. Mars, Tung W. Chan, Yonglai Lu, Haibo Yang, and Liqun Zhang. “Crack precursor size for natural rubber inferred from relaxing and non-relaxing fatigue experiments.” International Journal of Fatigue 80 (2015): 50-57.

Mars, William Vernon. Multiaxial fatigue of rubber. 2001.

Mars, Will V. “Cracking energy density as a predictor of fatigue life under multiaxial conditions.” Rubber chemistry and technology 75, no. 1 (2002): 1-17.

Mars, W. V., and A. Fatemi. “Analysis of fatigue life under complex loading: Revisiting Cadwell, Merrill, Sloman, and Yost.” Rubber chemistry and technology 79, no. 4 (2006): 589-601.

Mars, W. V., and A. Fatemi. “Nucleation and growth of small fatigue cracks in filled natural rubber under multiaxial loading.” Journal of materials science 41, no. 22 (2006): 7324-7332.

Mars, W. V. “Computed dependence of rubber’s fatigue behavior on strain crystallization.” Rubber Chemistry and Technology 82, no. 1 (2009): 51-61. https://doi.org/10.5254/1.3557006

Mars, William V., Matthew Castanier, David Ostberg, and William Bradford. “Digital Twin for Tank Track Elastomers: Predicting Self-Heating and Durability.” In Proceedings of the 2017 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS). 2017.pdf here

Mars, W. V., and M. Isasi. “Finitely scoped procedure for generating fully relaxing strain-life curves.” In Constitutive Models for Rubber XI: Proceedings of the 11th European Conference on Constitutive Models for Rubber (ECCMR 2019), June 25-27, 2019, Nantes, France, p. 435. CRC Press, 2019.

Muhr, A. H. “Modeling the stress-strain behavior of rubber.” Rubber chemistry and technology 78, no. 3 (2005): 391-425.Lake and Thomas 1967

Ramachandran, Anantharaman, Ross P. Wietharn, Sunil I. Mathew, W. V. Mars, and M. A. Bauman. “Critical Plane Selection Under Nonrelaxing Simple Tension with Strain Crystallization.” In Fall 192nd Technical Meeting of the Rubber Division, pp. 10-12. 2017.

Rivlin, R. S., and A. G. Thomas. “Rupture of rubber. I. Characteristic energy for tearing.” Journal of polymer science 10, no. 3 (1953): 291-318.Gent, Lindley and Thomas, 1964

Roberts, B. J., and J. B. Benzies. “The relationship between uniaxial and equibiaxial fatigue in gum and carbon black filled vulcanizates.” Proceedings of rubbercon 77, no. 2 (1977): 1-13.

Robertson, Christopher G., Lewis B. Tunnicliffe, Lawrence Maciag, Mark A. Bauman, Kurt Miller, Charles R. Herd, and William V. Mars. “Characterizing Distributions of Tensile Strength and Crack Precursor Size to Evaluate Filler Dispersion Effects and Reliability of Rubber.” Polymers 12, no. 1 (2020): 203. Pdf here

Saintier, Nicolas, Georges Cailletaud, and Roland Piques. “Multiaxial fatigue life prediction for a natural rubber.” International Journal of Fatigue 28, no. 5-6 (2006): 530-539.

Tobajas, Rafael, Daniel Elduque, Elena Ibarz, Carlos Javierre, and Luis Gracia. “A New Multiparameter Model for Multiaxial Fatigue Life Prediction of Rubber Materials.” Polymers 12, no. 5 (2020): 1194.

Zarrin-Ghalami, Touhid, Sandip Datta, Robert Bodombo Keinti, and Ravish Chandrashekar. Elastomeric Component Fatigue Analysis: Rubber Fatigue Prediction and Correlation Comparing Crack Initiation and Crack Growth Methodologies. No. 2020-01-0193. SAE Technical Paper, 2020.

 

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Keeping Your Secrets

The old saying “loose lips sink ships” is as true in product development as it is in war.  Maybe more so – while warships are heavily armored, intellectual property is never more secure than the least ethical person’s willingness and ability to misappropriate.  And the stakes have never been higher. Simulation software makes it easier than ever to document material properties, geometry, physics and functions of your next product.  So, collaborators can communicate design intentions more easily and more fully than ever before.  The downside?  It’s easier than ever for an adversary (or the next disgruntled employee) to walk out with your crown jewels!

This is why we’ve just implemented an encryption feature in the Endurica fatigue solvers.  Now you can password-protect sensitive information.  You control which information gets encrypted, and which stays as plain text.  You can share material property or load case definitions for use by collaborators without revealing private details in which you are heavily invested.

Here is a quick demo of how the new feature works.  Check it out.

One more way we are helping you to win on durability.

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Two Decades of Critical Plane Analysis

It has been 20 years since Critical Plane Analysis for rubber was first conceived and validated.  There were early signs of its significance.  It won awards wherever I presented it. At the 1999 SAE Fatigue Design and Evaluation meeting, it won the Henry Fuchs award.  At the 2000 Tire Society meeting, it won the Superior Paper award. At the Fall 2000 ACS Rubber Division meeting, it won the Best Paper award.  Upon completing my 2001 doctoral thesis, we applied for and received a US patent (2003) on it.

The strongest early sign was that I soon found myself in company with others pursuing similar thinking.  The earliest was Dr. Nicolas Saintier.  As far as I know, neither of us was aware of the other’s work until 2006.  That was when he published an account similar enough to my own that when it came across my desk and I first started to read it, I felt certain he would cite my 2001 work as a source.  I have to admit to initially feeling let down when I reached the end of his paper and found no mention of my work.  I immediately looked for his other papers and found his 2001 doctoral thesis titled “Fatigue multiaxiale dans un élastomère de type NR chargé: mécanismes d’endommagement et critère local d’amorçage de fissure.” (Multiaxial fatigue life of a natural rubber: crack initiation mechanisms and local fatigue life criterion).  There it was – the same founding principle of Critical Plane Analysis that I had worked so hard to articulate and validate – the idea that cracks develop on a material plane, specifically the most critical material plane, and that their localized experience drives their evolution.  That we both articulated this beautifully simple and powerful principle in the same year with complete independence from each other, when no one else working on elastomers had yet spoken of this approach (there were precedents in the field of metal fatigue analysis), just shows that it was an idea whose time had come.

Although the foundational principle of Critical Plane Analysis was the same, there were also important differences between our accounts.  We differed on 1) how the critical plane is selected, 2) what criterion is used to quantify the severity of loading experience by the critical plane, 3) how damage on the critical plane evolves under solicitation.  The following table summarizes the key differences:

 

Table 1. Comparison of the Mars and Saintier Frameworks for Critical Plane Analysis.

Mars 2001 Saintier 2001
Critical Plane Selection Method Minimize the computed life after evaluation of damage on all planes Maximize the principal stress prior to evaluation of damage
Multiaxial Criterion Energy release rate estimated via cracking energy density on every plane Stress traction on the assumed critical plane
Damage Evolution Law Integration of crack growth rate law Power law Wohler curve
Strain Crystallization Law Treated as R ratio dependence of the crack growth rate law Treated as a modifier of the stress experienced on the critical plane

It may be said that Saintier’s approach followed more closely the precedents for Critical Plane Analysis in metal fatigue, particularly with respect to the method used to select the critical plane.  Selecting the plane is the first step in his method (identify the plane in order to compute the damage), but it is the last step in our method (compute the damage on each plane first and lastly pick the plane with the most damage).  Saintier’s approach also depends on a Wohler curve style characterization of fatigue behavior, where ours is defined via a crack growth rate law.  We have previously discussed the pros and cons of Wohler curves vs. fracture mechanics.  In our approach, we placed a high priority on taking advantage of the very large pre-existing body of knowledge on the fracture mechanical behavior of elastomers, and on the economic and operational advantages that crack growth experiments enjoy.

Since my and Saintier’s first steps, there have now been many others who have contributed in various forms to the overall method, its validation and/or its application.  It is safe to say that Critical Plane Analysis is here to stay, and set to continue expanding for many years (there are now several hundred research papers!).

For our part, Endurica is now in year 12 of delivering commercial grade fatigue analysis solutions built on this method.  Today, Critical Plane Analysis is a production analysis workflow used by many engineering organizations to solve critical durability issues.  It is the heart of the Endurica fatigue solver, and there are hundreds of trained users (look up the #fatigueninjas on twitter!).  It is unrivaled for its reliability, speed and accuracy in computing the impacts of multiaxial loading on durability.

What do the next 20 years hold?  We are going to see a transition in how fatigue analysis is used.  OEM organizations that manage durability and risk across rubber component supply chains will transition away from receiving fatigue simulation results on an optional basis towards requiring fatigue simulations by default on every part at the inception of new programs.  Expectations and achievement of cost-reduction, light weighting and sustainability initiatives will increase as product optimization begins to fully account for actual product use cases.  Critical Plane Analysis has already laid the foundation for these things to happen.  Older fatigue analysis methods that do not compete well against critical plane methods will become obsolete.  On the research side, there will be further development of material models for use in the critical plane framework.  Ageing, inelasticity, rate and anisotropy effects still need further development, for example.  In 20 years, durability will be just one more thing that engineers do well every day, whether or not they know that Critical Plane Analysis was how they did it.

Mars, W. V,  Multiaxial fatigue of rubber. Ph.D. Dissertation, University of Toledo, 2001.

Mars, W. V. “Multiaxial fatigue crack initiation in rubber.” Tire Science and Technology 29, no. 3: 171-185, 2001.

Mars, W. V. “Cracking energy density as a predictor of fatigue life under multiaxial conditions.” Rubber chemistry and technology 75, no. 1: 1-17, 2002.

Mars, W. V., “Method and article of manufacture for estimating material failure due to crack formation and growth.” U.S. Patent No. 6,634,236. 21 Oct. 2003.

Saintier, N, “Fatigue multiaxiale dans un élastomère de type NR chargé: mécanismes d’endommagement et critère local d’amorçage de fissure.” Ph. D Dissertation., Ecole des Mines de Paris, 2001.

Saintier, N, G. Cailletaud, R. Piques. “Crack initiation and propagation under multiaxial fatigue in a natural rubber.” International Journal of Fatigue 28, no. 1: 61-72, (2006).

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