William V. Mars, Ph.D., P.E.

Dr. Will Mars is an international leader in the failure mechanics of rubber. He is the founder and president of Endurica LLC, and the firm’s products and services are used by leading firms around the world to manage durability. He is the author of the Endurica fatigue life solver, the world’s best-validated fatigue life simulation system for elastomers. Dr. Mars’ career focuses on applying experimental and computational mechanics in pursuit of better-performing rubber products and he has three decades of experience developing testing and simulation methods in the rubber industry. Dr. Mars earned his Honors BSME with Polymer Specialization at the University of Akron, and his MS and Ph.D. degrees at the University of Toledo. He has received several awards for his scientific contributions and innovations including the 2022 Herzlich Medal for outstanding impact and innovation in the tire industry, the 2020 Tibbett’s Award from the Small Business Administration of the United States for excellence in creating cutting-edge technologies, the 2017 Rubber Division ACS Arnold Smith Special Service Award, the 2007 Sparks Thomas award of ACS Rubber Division, and the 1999 Henry Fuchs award of the SAE Fatigue Design & Evaluation committee. Dr. Mars served as the chief editor of Rubber Chemistry and Technology for 10 years and is a former editor of Tire Science and Technology as well. He has over 60 peer-reviewed scientific publications and four patents in the area of elastomer durability.

Get Durability AND Sustainability Right with Endurica

June 1, 2022February 22, 2022 by William V. Mars, Ph.D., P.E.

Sustainability is all about Precycling with Endurica

How do you respond to the call for sustainable solutions in the rubber industry? Is it via bio-sourced polymers or fillers? elimination of carcinogenic additives from the compound? Inclusion of recycled content in the material? light-weighting aimed at reducing material use or at fuel economy improvements? supply of critical components to EVs?

There are many paths to sustainability, but they are all constrained by these three filters:

Most alternatives risk a reduction in durability (despite the optimistic claims of suppliers).
Your product still must pass its durability qualification requirements.
The number of development iterations is severely limited by the time and cost of durability testing.

Endurica workflows have been driving a “right the first time” engineering culture for the last 14 years. Putting durability characterization and simulation upfront in your development programs means that you find and resolve issues earlier and cheaper than if you depended only on your qualification to discover issues.

With Endurica, you can rapidly evaluate the durability of a series of alternative materials under realistic conditions before you build the first physical prototype. The impacts of polymer alternatives, filler alternatives, additives, recycled content alternatives, etc. can be characterized with a minimal sample of the material and represented accurately with Endurica’s material modeling capabilities. You can see how material property changes play out in your actual part geometry, under actual part loading histories. All without building a single prototype part. The modeling process is simple to automate, enabling much richer explorations of the available design space. Where a purely prototype-based development program may be able to compare two or three alternatives over a six-month period, a simulation-based program can compare several hundred alternatives in the space of a week!

Just because it can be hard to find a sustainable alternative doesn’t mean that they aren’t out there. It is their relative rarity that makes them so valuable. The next crop of winning products will come from those who can quickly and reliably navigate durability.

User Requests and New Features: You Asked For It, You Got It

June 9, 2022December 23, 2021 by William V. Mars, Ph.D., P.E.

You asked for it, Endurica gives you new features! Once a year, we ask our users to weigh in on what we can do to further improve your experiences with the Endurica fatigue solvers. The feedback helps us aim our development at bringing you winning capabilities. It is also a marker we can use to gauge progress.

Here are the survey results from 2020:

Results from consumer survey stating which products they are most likely to use.

How did we do this year? Check it out:

Support for additional channels in Endurica’s Efficient Interpolation Engine (EIE). EIE makes it possible to compute strain histories and fatigue life from lengthy road load signals. To date, EIE has supported up to 3 independent load channels. But we’ve had several of our best users tell us they need 6 channels. The expanded capability was a big focus for development this year, and now it is complete and nearly ready for launch. Stay tuned for more details to come out in early 2022.

Safety Factor. The Safety Factor calculation is a feature of Endurica’s new Katana CL that launched this year. It avoids the need for full characterization of the crack growth rate law but gives you the benefits of critical plane analysis. Given only the intrinsic strength (fatigue threshold) and precursor size, it calculates the margin by which the most critical loads remain below your material’s fatigue limit. It tells you whether you may expect indefinite life (or not). Use it with the Intrinsic Strength Analyser experiment. Perfect for analysis projects where you need to demonstrate capacity for long life with limited timeline or budget.

UHYPER. Abaqus users can now define their own hyperelastic law in Endurica. The Endurica UHYPER interface matches the UHYPER Abaqus interface so that you can use the same subroutine with both codes.

Linux Support. Did you know that the Endurica solvers are available on both Windows and Linux? Our Linux users can now run the entire Endurica suite of software (CL, DT, and EIE) on their systems.

Execution Speed. The recently launched Katana solver (for CL and DT licenses) offers unprecedented speed. Our benchmarks show that on a single thread, users will cut run times by more than ½. And the Katana solver also offers multithreading. Our benchmarks showed excellent scaling behavior up to >40 parallel threads. These capabilities means that users will be able to run much larger jobs, and to complete their existing jobs with much shorter run times.

Improved hfi syntax / error checking. Another feature of the Katana solver is its adoption of the json format for the input file. The switch to the widely adopted json standard means that our solutions are now much easier to script via python or matlab and that there are file editors which automatically do the syntax / error checking.

Cosimulation Interface for Ansys. The cosimulation capability of Endurica DT updates the finite element solution so that material property evolution can be simulated. It has previously only been available to Abaqus users, but has now been developed for Ansys. It is currently being beta tested. We expect to launch this addition in Q1 2022. This means that Ansys users will very soon be able to make full use of Endurica DT’s Cyclic Softening modules and Ageing Workflow.

Materials database expansion. The next Endurica release will have an addition to the materials database: a series of six HNBRs. We are also preparing to release the database in several common unit systems, rather than the prior single unit system.

With 2021 behind us now, its time to look forward to 2022 (and beyond!). Look for the client survey and let us know how to best serve your upcoming needs.

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

June 9, 2022October 18, 2021 by William V. Mars, Ph.D., P.E.

Endurica Companion App | Fatigue Property Comparator

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 Companion^TM 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.

With the Companion App you can choose different variables to see how they affect the performance of the rubber

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.

Tire Society Takeaways 2021

June 15, 2022October 15, 2021 by William V. Mars, Ph.D., P.E.

Image of a Tire The Tire Society held its 40^th 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 2^nd 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.

Click here to download a .pdf summary of this blog post: Endurica Spotlight on The Tire Society 2021 Annual Meeting The Virtual Tire

Virtual vs. Physical in 2021 and Beyond

June 9, 2022August 16, 2021 by William V. Mars, Ph.D., P.E.

An insight to how Endurica stayed connected during Covid-19, by using Microsoft teams to meet virtually. 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.

It's a Hybrid World from Here | Endurica's tools position you for unprecedented success when it’s time to test.

Use This One Simple Trick to Ensure Rubber Part Durability

June 9, 2022August 11, 2021 by William V. Mars, Ph.D., P.E.

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.

A vibration isolation grommet operating under small displacement

A vibration isolation grommet operating under large displacement

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.

Durability by Design on Any Budget

June 9, 2022June 7, 2021 by William V. Mars, Ph.D., P.E.

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.

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.

Things that went right in 2020 at Endurica

June 9, 2022January 8, 2021 by William V. Mars, Ph.D., P.E.

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

Coesfeld Tear and Fatigue Analyser – we hosted Coesfeld President Christian Kipscholl for one of the Winning On Durability episodes (#7). We walked through a demo of the T&FA’s fully automated, high-reliability testing workflow.
Intrinsic Strength Analyser – we hosted another Winning On Durability episode (#3) focused on understanding how a rapid cutting experiment tells us about long term fatigue behavior. We also completed a successful validation this year comparing direct measurement of the fatigue threshold with a measurement from the cutting method.

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!

Does hydrostatic loading cause fatigue damage in rubber?

June 9, 2022January 7, 2021 by William V. Mars, Ph.D., P.E.

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 W_c 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.

Is It Validated?

June 9, 2022January 5, 2021 by William V. Mars, Ph.D., P.E.

“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.

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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

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